In this correspondence, we correct the following points in the above paper.

We investigate privacy-preserving spectral clustering for community detection within stochastic block models (SBMs). Specifically, we focus on edge differential privacy (DP) and propose private algorithms for community recovery. Our work explores the fundamental trade-offs between the privacy budget and the accurate recovery of community labels. Furthermore, we establish information-theoretic conditions that guarantee the accuracy of our methods, providing theoretical assurances for successful community recovery under edge DP.

Collaborative inference among multiple wireless edge devices has the potential to significantly enhance Artificial Intelligence (AI) applications, particularly for sensing and computer vision. This approach typically involves a three-stage process: a) data acquisition through sensing, b) feature extraction, and c) feature encoding for transmission. However, transmitting the extracted features poses a significant privacy risk, as sensitive personal data can be exposed during the process. To address this challenge, we propose a novel privacy-preserving collaborative inference mechanism, wherein each edge device in the network secures the privacy of extracted features before transmitting them to a central server for inference. Our approach is designed to achieve two primary objectives: 1) reducing communication overhead and 2) ensuring strict privacy guarantees during feature transmission, while maintaining effective inference performance. Additionally, we introduce an over-the-air pooling scheme specifically designed for classification tasks, which provides formal guarantees on the privacy of transmitted features and establishes a lower bound on classification accuracy.

Cyber–physical multiagent systems are driving rapid technological advancements that automate a wide range of critical functions, thereby enabling safer, more accessible, and more efficient autonomous operations across diverse sectors. We refer to the capability of such systems to self-organize and coordinate toward accomplishing shared objectives as autonomy. The unique characteristics of these systems prompt a reevaluation of their security concepts, including their vulnerabilities, and mechanisms to mitigate these vulnerabilities. This survey article examines how advancements in wireless networking, coupled with sensing and computing capabilities, can foster novel security concepts for autonomous cyber–physical systems (CPSs). It delves into three main themes related to securing multiagent CPSs. First, we discuss the threats that are particularly relevant to multiagent CPSs, given the potential lack of trustworthiness between agents. Second, we present prospects for sensing, contextual awareness, and authentication, enabling the inference and measurement of a form of interagent “quantitative trust” or “cy-trust” for these systems. Third, we elaborate on the application of quantifiable trust notions to enable “resilient coordination,” where “resilient” signifies sustained functionality amid attacks on multiagent CPSs. This survey unveils the cyber–physical character of future interconnected systems as a pivotal catalyst for realizing robust autonomy.

We study the private online change detection problem for dynamic communities, using a censored block model (CBM). We consider edge differential privacy (DP) in both local and central settings, and propose joint change detection and community estimation procedures for both scenarios. We seek to understand the fundamental tradeoffs between the privacy budget, detection delay, and exact community recovery of community labels. Further, we provide theoretical guarantees for the effectiveness of our proposed method by showing necessary and sufficient conditions for change detection and exact recovery under edge DP. Simulation and real data examples are provided to validate the proposed methods.

The prohibitive sizes of Large Language Models (LLMs) today make it difficult to deploy them on memory-constrained edge devices. This work introduces $\rm CALDERA$ -- a new post-training LLM compression algorithm that harnesses the inherent low-rank structure of a weight matrix $\mathbf{W}$ by approximating it via a low-rank, low-precision decomposition as $\mathbf{W} \approx \mathbf{Q} + \mathbf{L}\mathbf{R}$. Here, $\mathbf{L}$ and $\mathbf{R}$ are low rank factors, and the entries of $\mathbf{Q}$, $\mathbf{L}$ and $\mathbf{R}$ are quantized. The model is compressed by substituting each layer with its $\mathbf{Q} + \mathbf{L}\mathbf{R}$ decomposition, and the zero-shot performance of the compressed model is evaluated. Additionally, $\mathbf{L}$ and $\mathbf{R}$ are readily amenable to low-rank adaptation, consequently enhancing the zero-shot performance. $\rm CALDERA$ obtains this decomposition by formulating it as an optimization problem $\min_{\mathbf{Q},\mathbf{L},\mathbf{R}}\lVert(\mathbf{Q} + \mathbf{L}\mathbf{R} - \mathbf{W})\mathbf{X}^\top\rVert_{\rm F}^2$, where $\mathbf{X}$ is the calibration data, and $\mathbf{Q}, \mathbf{L}, \mathbf{R}$ are constrained to be representable using low-precision formats. Theoretical upper bounds on the approximation error of $\rm CALDERA$ are established using a rank-constrained regression framework, and the tradeoff between compression ratio and model performance is studied by analyzing the impact of target rank and quantization bit budget. Results illustrate that compressing LlaMa-$2$ $7$B/$13$B/$70$B and LlaMa-$3$ $8$B models obtained using $\rm CALDERA$ outperforms existing post-training LLM compression techniques in the regime of less than $2.5$ bits per parameter.

We study the problem of minimizing energy costs for content delivery in wireless heterogeneous networks by jointly optimizing caching and power control strategies. This can be equivalently cast as a problem of maximizing the joint caching and power gain subject to meeting minimum signal-to-interference-plus-noise ratio constraints. The offline version of this problem is NP-hard, but we show that there exist polynomial-time approximation algorithms producing solutions within a constant factor 1 - 1/$e$from the optimal. We further provide an adaptive algorithm based on projected subgradient ascent over a concave relaxation of the expected joint caching and power gain, which yields the same approximation guarantee. We show that our proposed algorithm outperforms the alternating optimization method and other baseline algorithms in a number of network scenarios, in total power consumption and run time.

In this article, we develop a resilient binary hypothesis testing framework for decision making in adversarial multirobot crowdsensing tasks. This framework exploits stochastic trust observations between robots to arrive at tractable, resilient decision making at a centralized fusion center (FC) even when, first, there exist malicious robots in the network and their number may be larger than the number of legitimate robots, and second, the FC uses one-shot noisy measurements from all robots. We derive two algorithms to achieve this. The first is the two-stage approach (2SA) that estimates the legitimacy of robots based on received trust observations, and provably minimizes the probability of detection error in the worst-case malicious attack. For the 2SA, we assume that the proportion of malicious robots is known but arbitrary. For the case of an unknown proportion of malicious robots, we develop the adversarial generalized likelihood ratio test (A-GLRT) that uses both the reported robot measurements and trust observations to simultaneously estimate the trustworthiness of robots, their reporting strategy, and the correct hypothesis. We exploit particular structures in the problem to show that this approach remains computationally tractable even with unknown problem parameters. We deploy both algorithms in a hardware experiment where a group of robots conducts crowdsensing of traffic conditions subject to a Sybil attack on a mock-up road network. We extract the trust observations for each robot from communication signals, which provide statistical information on the uniqueness of the sender. We show that even when the malicious robots are in the majority, the FC can reduce the probability of detection error to 30.5% and 29% for the 2SA and the A-GLRT algorithms, respectively.

Intermittent connectivity of clients to the parameter server (PS) is a major bottleneck in federated edge learning frameworks. The lack of constant connectivity induces a large generalization gap, especially when the local data distribution amongst clients exhibits heterogeneity. To overcome intermittent communication outages between clients and the central PS, we introduce the concept of collaborative relaying wherein the participating clients relay their neighbors’ local updates to the PS in order to boost the participation of clients with poor connectivity to the PS. We propose a semi-decentralized federated learning framework in which at every communication round, each client initially computes a local averaging of a subset of its neighboring clients’ updates, and eventually transmits to the PS a weighted average of its own update and those of its neighbors’. We appropriately optimize these local averaging weights to ensure that the global update at the PS is unbiased with minimal variance – consequently improving the convergence rate. Numerical evaluations on the CIFAR-10 dataset demonstrate that our collaborative relaying approach outperforms federated averaging-based benchmarks for learning over intermittently-connected networks such as when the clients communicate over millimeter wave channels with intermittent blockages.

In this paper, we study distributed training by majority vote with the sign stochastic gradient descent (signSGD) along with over-the-air computation (OAC) under local differential privacy constraints. In our approach, the users first clip the local stochastic gradients and inject a certain amount of noise as a privacy enhancement strategy. Subsequently, they activate the indices of OFDM subcarriers based on the signs of the perturbed local stochastic gradients to realize a frequency-shift-keying-based majority vote computation at the parameter server. We evaluate the privacy benefits of the proposed approach and characterize the per-user privacy leakage theoretically. Our results show that the proposed technique improves the privacy guarantees and limits the leakage to a scaling factor of$\mathcal{O}(1/\sqrt{K})$, where$K$is the number of users, thanks to the superposition property of the wireless channel. With numerical experiments, we show that the proposed non-coherent aggregation is superior to quadrature-phase-shift-keying-based coherent aggregation, namely, one-bit digital aggregation (OBDA), in learning accuracy under time synchronization errors when the same privacy enhancement strategy is introduced to both methods.

The large memory footprint of high dimensional models require quantization to a lower precision for deployment on resource constrained edge devices. With this motivation, we consider the problems of learning a (i) linear regressor, and a (ii) linear classifier from a given training dataset, and quantizing the learned model parameters subject to a pre-specified bit-budget. The error metric is the prediction risk of the quantized model, and our proposed randomized embedding-based quantization methods attain near-optimal error while being computationally efficient. We provide fundamental bounds on the bit-budget constrained minimax risk that, together with our proposed algorithms, characterize the minimum threshold budget required to achieve a risk comparable to the unquantized setting. We also show the efficacy of our strategy by quantizing a two-layer ReLU neural network for non-linear regression. Numerical simulations show the improved performance of our proposed scheme as well as its closeness to the lower bound.

We develop a resilient binary hypothesis testing frame-work for decision making in adversarial multi-robot crowdsensing tasks. This framework exploits stochastic trust observations between robots to arrive at tractable, resilient decision making at a centralized Fusion Center (FC) even when i) there exist malicious robots in the network and their number may be larger than the number of legitimate robots, and ii) the FC uses one-shot noisy measurements from all robots. We derive two algorithms to achieve this. The first is the Two Stage Approach (2SA) that estimates the legitimacy of robots based on received trust observations, and provably minimizes the probability of detection error in the worst-case malicious attack. Here, the proportion of malicious robots is known but arbitrary. For the case of an unknown proportion of malicious robots, we develop the Adversarial Generalized Likelihood Ratio Test (A-GLRT) that uses both the reported robot measurements and trust observations to estimate the trustworthiness of robots, their reporting strategy, and the correct hypothesis simultaneously. We exploit special problem structure to show that this approach remains computationally tractable despite several unknown problem parameters. We deploy both algorithms in a hardware experiment where a group of robots conducts crowdsensing of traffic conditions on a mock-up road network similar in spirit to Google Maps, subject to a Sybil attack. We extract the trust observations for each robot from actual communication signals which provide statistical information on the uniqueness of the sender. We show that even when the malicious robots are in the majority, the FC can reduce the probability of detection error to 30.5% and 29% for the 2SA and the A-GLRT respectively.

This work considers the problem of Distributed Mean Estimation (DME) over networks with intermittent connectivity, where the goal is to learn a global statistic over the data samples localized across distributed nodes with the help of a central server. To mitigate the impact of intermittent links, nodes can collaborate with their neighbors to compute local consensus which they forward to the central server. In such a setup, the communications between any pair of nodes must satisfy local differential privacy constraints. We study the tradeoff between collaborative relaying and privacy leakage due to the additional data sharing among nodes and, subsequently, propose a novel differentially private collaborative algorithm for DME to achieve the optimal tradeoff. Finally, we present numerical simulations to substantiate our theoretical findings.

We consider a centralized detection problem where sensors experience noisy measurements and intermittent connectivity to a centralized fusion center. The sensors collaborate locally within predefined sensor clusters and fuse their noisy sensor data to reach a common local estimate of the detected event in each cluster. The connectivity of each sensor cluster is intermittent and depends on the available communication opportunities of the sensors to the fusion center. Upon receiving the estimates from all the connected sensor clusters the fusion center fuses the received estimates to make a final determination regarding the occurrence of the event across the deployment area. We refer to this hybrid communication scheme as a cloud-cluster architecture. We propose a method for optimizing the decision rule for each cluster and analyzing the expected detection performance resulting from our hybrid scheme. Our method is tractable and addresses the high computational complexity caused by heterogeneous sensors’ and clusters’ detection quality, heterogeneity in their communication opportunities, and non-convexity of the loss function. Our analysis shows that clustering the sensors provides resilience to noise in the case of low sensor communication probability with the cloud. For larger clusters, a steep improvement in detection performance is possible even for a low communication probability by using our cloud-cluster architecture.

When humans collaborate with each other, they often make decisions by observing others and considering the consequences that their actions may have on the entire team, instead of greedily doing what is best for just themselves. We would like our AI agents to effectively collaborate in a similar way by capturing a model of their partners. In this work, we propose and analyze a decentralized Multi-Armed Bandit (MAB) problem with coupled rewards as an abstraction of more general multi-agent collaboration. We demonstrate that naive extensions of single-agent optimal MAB algorithms fail when applied for decentralized bandit teams. Instead, we propose a Partner-Aware strategy for joint sequential decision-making that extends the well-known single-agent Upper Confidence Bound algorithm. We analytically show that our proposed strategy achieves logarithmic regret, and provide extensive experiments involving human-AI and human-robot collaboration to validate our theoretical findings. Our results show that the proposed partner-aware strategy outperforms other known methods, and our human subject studies suggest humans prefer to collaborate with AI agents implementing our partner-aware strategy.

We present a semi-decentralized federated learning algorithm wherein clients collaborate by relaying their neighbors’ local updates to a central parameter server (PS). At every communication round to the PS, each client computes a local consensus of the updates from its neighboring clients and eventually transmits a weighted average of its own update and those of its neighbors to the PS. We appropriately optimize these averaging weights to ensure that the global update at the PS is unbiased and to reduce the variance of the global update at the PS, consequently improving the rate of convergence. Numerical simulations substantiate our theoretical claims and demonstrate settings with intermittent connectivity between the clients and the PS, where our proposed algorithm shows an improved convergence rate and accuracy in comparison with the federated averaging algorithm.

We present a composite wireless fading model encompassing multipath fading and shadowing based on fluctuating two-ray (FTR) fading and inverse gamma (IG) shadowing. We first determine an alternative framework for the statistical characterization and performance evaluation of the FTR fading model, which is based on the fact that the FTR fading distribution can be described as an underlying Rician Shadowed (RS) distribution with continuously varying parameter$K_{T}$(ratio of specular to diffuse components). We demonstrate that this new formulation permits to obtain a closed-form expression of the generalized moment generating function (GMGF) of the FTR model, from which the PDF and CDF of the composite IG/FTR model can be obtained in closed-form. The exact and asymptotic outage probability of the IG/FTR model are analyzed and verified by Monte Carlo simulations.

In decentralized optimization, multiple nodes in a network collaborate to minimize the sum of their local loss functions. The information exchange between nodes required for this task, is often limited by network connectivity. We consider a setting in which communication between nodes is hindered by both (i) a finite rate-constraint on the signal transmitted by any node, and (ii) additive noise corrupting the signal received by any node. We propose a novel algorithm for this scenario: Decentralized Lazy Mirror Descent with Differential Exchanges (DLMD-DiffEx), which guarantees convergence of the local estimates to the optimal solution under the given communication constraints. A salient feature of DLMD-DiffEx is the introduction of additional proxy variables that are maintained by the nodes to account for the disagreement in their estimates due to channel noise and rate-constraints. Convergence to the optimal solution is attained by having nodes iteratively exchange these disagreement terms until consensus is achieved. In order to prevent noise accumulation during this exchange, DLMD-DiffEx relies on two sequences: one controlling the power of the transmitted signal, and the other determining the consensus rate. We provide insights on the design of these two sequences which highlights the interplay between consensus rate and noise amplification. We investigate the performance of DLMD-DiffEx both from a theoretical perspective as well as through numerical evaluations on synthetic data and MNIST. MATLAB and Python implementations can be found athttps://github.com/rajarshisaha95/DLMD-DiffEx.

This paper formulates the polar-code construction problem for the successive-cancellation list (SCL) decoder as a maze-traversing game, which can be solved by reinforcement-learning techniques. The proposed method provides a novel technique for polar-code construction that no longer depends on sorting and selecting bit-channels by reliability, as in most current algorithms. Instead, this technique decides whether the input bits should be frozen in a purely sequential manner. The equivalence of optimizing the polar-code construction for the SCL decoder under this technique and maximizing the expected reward of traversing a maze is drawn. Simulation results show that the standard polar-code constructions that are designed for the successive-cancellation decoder are no longer optimal for the SCL decoder with respect to the frame error rate (FER). In contrast, the proposed game-based construction method finds code constructions that have similar or lower FER for various code lengths and various list sizes of the SCL decoder, compared to the state-of-the-art construction methods. The advantage of the game-based constructions over the standard constructions increases with the channel signal-to-noise ratio and the list size of SCL decoding. Moreover, the learning is highly efficient in terms of the number of required training samples and computational operations.

This work considers the problem of resilient consensus, where stochastic values of trust between agents are available. Specifically, we derive a unified mathematical framework to characterize convergence, deviation of the consensus from the true consensus value, and expected convergence rate, when there exists additional information of trust between agents. We show that under certain conditions on the stochastic trust values and consensus protocol: First, almost sure convergence to a common limit value is possible even when malicious agents constitute more than half of the network connectivity; second, the deviation of the converged limit, from the case where there is no attack, i.e., the true consensus value, can be bounded with probability that approaches 1 exponentially; and third correct classification of malicious and legitimate agents can be attained in finite time almost surely. Furthermore, the expected convergence rate decays exponentially as a function of the quality of the trust observations between agents.

We present two alternative frameworks for the statistical characterization and performance evaluation of the fluctuating two-ray (FTR) fading model which simplify previous approaches. The new formulations are based on the fact that the FTR fading distribution can be described, for arbitrary$m$, as an underlying Rician Shadowed (RS) distribution with continuously varying parameter$K_{r}$(ratio of specular to diffuse power components), while for the special case of$m$being an integer, it is demonstrated that the FTR fading model can be described in terms of a finite number of underlying squared Nakagami-$m$distributions. It is shown that any performance metric that is computed by averaging over the probability density function (PDF) of the FTR fading model can be expressed in terms of a finite-range integral over the corresponding performance metric for the simpler RS (for arbitrary$m$) or Nakagami-$m$(for integer$m$) fading models, for which many results are available in closed-form. New expressions for some Laplace-domain statistics of interest are also obtained; these are used to analyze the outage probability of FTR fading under co-channel interference, as well as to obtain closed-form expressions for the main statistics of a composite wireless channel model encompassing FTR fading and shadowing.

In decentralized optimization, multiple nodes in a network collaborate to minimize the sum of their local loss functions. The information exchange between nodes required for this task is often limited by network connectivity. We consider a generalization of this setting, in which communication is further hindered by (i) a finite data-rate constraint on the signal transmitted by any node, and (ii) an additive noise corrupting the signal received by any node. We develop a novel algorithm for this scenario: Decentralized Lazy Mirror Descent with Differential Exchanges (DLMD-DiffEx), which guarantees convergence of the local estimates to the optimal solution. A salient feature of DLMD-DiffEx is the introduction of additional proxy variables that are maintained by the nodes to account for the disagreement in their estimates due to channel noise and data-rate constraints. We investigate the performance of DLMD-DiffEx both from a theoretical perspective as well as through numerical evaluations.

This paper characterizes the latency of the simplified successive-cancellation (SSC) decoding scheme for polar codes under hardware resource constraints. In particular, when the number of processing elements$P$that can perform SSC decoding operations in parallel is limited, as is the case in practice, the latency of SSC decoding is$O\left(N^{1-1/\mu}+ \frac{N}{P}\log_{2}\log_{2}\frac{N}{P}\right)$, where$N$is the block length of the code and$\mu$is the scaling exponent of polar codes for the channel. Three direct consequences of this bound are presented. First, in a fully-parallel implementation where$P=\frac{N}{2}$, the latency of SSC decoding is$O\left(N^{1-1/\mu}\right)$, which is sublinear in the block length. This recovers a result from an earlier work. Second, in a fully-serial implementation where$P=1$, the latency of SSC decoding scales as$O(N\, \log_{2}\log_{2}N)$. The multiplicative constant is also calculated: we show that the latency of SSC decoding when$P=1$is given by$(2+o(1))N\, \log_{2}\log_{2}N$. Third, in a semi-parallel implementation, the smallest$P$that gives the same latency as that of the fully-parallel implementation is$P=N^{1/\mu}$. The tightness of our bound on SSC decoding latency and the applicability of the foregoing results is validated through extensive simulations.

Fast SC decoding overcomes the latency caused by the serial nature of the SC decoding by identifying new nodes in the upper levels of the SC decoding tree and implementing their fast parallel decoders. In this work, we first present a novel sequence repetition node corresponding to a particular class of bit sequences. Most existing special node types are special cases of the proposed sequence repetition node. Then, a fast parallel decoder is proposed for this class of node. To further speed up the decoding process of general nodes outside this class, a threshold-based hard-decision-aided scheme is introduced. The threshold value that guarantees a given error-correction performance in the proposed scheme is derived theoretically. Analysis and hardware implementation results on a polar code of length 1024 with code rates 1/4, 1/2, and 3/4 show that our proposed algorithm reduces the required clock cycles by up to 8%, and leads to a 10% improvement in the maximum operating frequency compared to state-of-the-art decoders without tangibly altering the error-correction performance. In addition, using the proposed threshold-based hard-decision-aided scheme, the decoding latency can be further reduced by 57% at Eb/N0= 5.0 dB.

Consider the problem of estimating a latent signal from a lossy compressed version of the data when the compressor is agnostic to the relation between the signal and the data. This situation arises in a host of modern applications when data is transmitted or stored prior to determining the downstream inference task. Given a bitrate constraint and a distortion measure between the data and its compressed version, let us consider the joint distribution achieving Shannon's rate-distortion (RD) function. Given an estimator and a loss function associated with the downstream inference task, define the RD risk as the expected loss under the RD-achieving distribution. We provide general conditions under which the operational risk in estimating from the compressed data is asymptotically equivalent to the RD risk. The main theoretical tools to prove this equivalence are transportation-cost inequalities in conjunction with properties of compression codes achieving Shannon's RD function. Whenever such equivalence holds, a recipe for designing estimators from datasets undergoing lossy compression without specifying the actual compression technique emerges: design the estimator to minimize the RD risk. Our conditions are simplified in the special cases of discrete memoryless or multivariate normal data. For these scenarios, we derive explicit expressions for the RD risk of several estimators and compare them to the optimal source coding performance associated with full knowledge of the relation between the latent signal and the data.

This work analyzes the latency of the simplified successive cancellation (SSC) decoding scheme for polar codes proposed by Alamdar-Yazdi and Kschischang. It is shown that, unlike conventional successive cancellation decoding, where latency is linear in the block length, the latency of SSC decoding is sublinear. More specifically, the latency of SSC decoding is O(N1-1/μ), where N is the block length and μ is the scaling exponent of the channel, which captures the speed of convergence of the rate to capacity. Numerical results demonstrate the tightness of the bound and show that most of the latency reduction arises from the parallel decoding of subcodes of rate 0 or 1.

This paper formulates the polar-code construction problem for the successive-cancellation list (SCL) decoder as a maze-traversing game, which can be solved by reinforcement learning techniques. The proposed method provides a novel technique for polar-code construction that no longer depends on sorting and selecting bit-channels by reliability. Instead, this technique decides whether the input bits should be frozen in a purely sequential manner. The equivalence of optimizing the polar-code construction for the SCL decoder under this technique and maximizing the expected reward of traversing a maze is drawn. Simulation results show that the standard polar-code constructions that are designed for the successive-cancellation decoder are no longer optimal for the SCL decoder with respect to the frame error rate. In contrast, the simulations show that, with a reasonable amount of training, the game-based construction method finds code constructions that have lower frame-error rate for various code lengths and decoders compared to standard constructions.

We consider a detection problem where sensors experience noisy measurements and intermittent communication opportunities to a centralized fusion center (or cloud). The objective of the problem is to arrive at the correct estimate of event detection in the environment. The sensors may communicate locally with other sensors (local clusters) where they fuse their noisy sensor data to estimate the detection of an event locally. In addition, each sensor cluster can intermittently communicate to the cloud, where a centralized fusion center fuses estimates from all sensor clusters to make a final determination regarding the occurrence of the event across the deployment area. We refer to this hybrid communication scheme as a cloud-cluster architecture. Minimizing the expected loss function of networks where noisy sensors are intermittently connected to the cloud, as in our hybrid communication scheme, has not been investigated to our knowledge. We leverage recently improved concentration inequalities to arrive at an optimized decision rule for each cluster and we analyze the expected detection performance resulting from our hybrid scheme. Our analysis shows that clustering the sensors provides resilience to noise in the case of low communication probability with the cloud. For larger clusters, a steep improvement in detection performance is possible even for a low communication probability by using our cloud-cluster architecture.

An adaptive bandwidth allocation mechanism for the calendar associated with the Flexible Ethernet (FlexE) standard is proposed. The proposed method bases the FlexE calendar design on the clients' real transmit data rates. In particular, the proposed method treats clients with very low bandwidth utilization as minor clients and allows them to transmit in an opportunistic manner. Experiments on real Ethernet packet traces indicate that by using the proposed calendar scheme to allocate bandwidth to clients, the total required FlexE bandwidth can be reduced by up to 60% while meeting packet drop requirements.

This paper focuses on fast successive-cancellation (SC) decoding of polar codes. A threshold-based hard-decision-aided scheme is proposed to speed up the decoding process, especially when the communications channel has low noise. In addition, to eliminate the error-correction performance degradation caused by hard decisions, a backtracking strategy is introduced. Simulation results on a polar code of code length 1024 and rate 1/2 show that, with the help of the proposed scheme, the average decoding latency of existing fast SC decoding algorithms can be reduced by 53% at an Eb/N0 = 5.0 dB with negligible error-correction performance degradation.

This work analyzes the latency of the simplified successive cancellation (SSC) decoding scheme for polar codes proposed by Alamdar-Yazdi and Kschischang. It is shown that, unlike conventional successive cancellation decoding, where latency is linear in the block length, the latency of SSC decoding is sublinear. More specifically, the latency of SSC decoding is O(N1-1/μ), where N is the block length and μ is the scaling exponent of the channel, which captures the speed of convergence of the rate to capacity. Numerical results demonstrate the tightness of the bound and show that most of the latency reduction arises from the parallel decoding of subcodes of rate 0 and 1.

Many important schemes in signal processing and communications, ranging from the BCJR algorithm to the Kalman filter, are instances of factor graph methods. This family of algorithms is based on recursive message passing-based computations carried out over graphical models, representing a factorization of the underlying statistics. In order to implement these algorithms, one must have accurate knowledge of the statistical model of the underlying signals. In this work we implement factor graph methods in a data-driven manner when the statistics are unknown. In particular, we propose using machine learning (ML) tools to learn the factor graph, instead of the overall system task, which in turn is used for inference by message passing over the learned graph. We apply the proposed approach to learn the factor graph representing a finite-memory channel, demonstrating the resulting ability to implement BCJR detection in a data-driven fashion. We demonstrate that the proposed system, referred to as BCJRNet, learns to implement the BCJR algorithm from a small training set, and that the resulting receiver exhibits improved robustness to inaccurate training compared to the conventional channel-model-based receiver operating under the same level of uncertainty. Our results indicate that by utilizing ML tools to learn factor graphs from labeled data, one can implement a broad range of model-based algorithms, which traditionally require full knowledge of the underlying statistics, in a data-driven fashion.

For nano-scale communications, there must be cooperation and simultaneous communication between nano devices. To this end, in this paper, we investigate two-way (a.k.a. bi-directional) molecular communications between nano devices. If different types of molecules are used for the communication links, the two-way system eliminates the need to consider self-interference. However, in many systems, it is not feasible to use a different type of molecule for each communication link. Thus, we propose a two-way molecular communication system that uses a single type of molecule. We derive a channel model for this system and use it to analyze the proposed system's bit error rate, throughput, and self-interference. Moreover, we propose analog- and digital- self-interference cancellation techniques. The enhancement of link-level performance using these techniques is confirmed with both particle-based simulations and analytical results.

We present two modulation and detection techniques that are designed to allow for efficient equalization for channels that exhibit an arbitrary Doppler spread but no delay spread. These techniques are based on principles similar to techniques designed for time-invariant delay spread channels (e.g., Orthogonal Frequency Division Multiplexing or OFDM) and have the same computational complexity. Through numerical simulations, we show that effective equalization is possible for channels that exhibit a high Doppler spread and even a modest delay spread, whereas equalized OFDM exhibits a strictly worse performance in these environments. Our results indicate that, in rapidly time-varying channels, such as those found in high-mobility or mmWave deployments, new modulation coupled with appropriate channel estimation and equalization techniques may significantly outperform modulation and detection schemes that are designed for static or slowly time varying multipath channels.

This paper analyzes the impact of non-Gaussian multipath component (MPC) amplitude distributions on the performance of Compressed Sensing (CS) channel estimators for OFDM systems. The number of dominant MPCs that any CS algorithm needs to estimate in order to accurately represent the channel is characterized. This number relates to a Compressibility Index (CI) of the channel that depends on the fourth moment of the MPC amplitude distribution. A connection between the Mean Squared Error (MSE) of any CS estimation algorithm and the MPC amplitude distribution fourth moment is revealed that shows a smaller number of MPCs is needed to well-estimate channels when these components have large fourth moment amplitude gains. The analytical results are validated via simulations for channels with lognormal MPCs such as the NYU mmWave channel model. These simulations show that when the MPC amplitude distribution has a high fourth moment, the well known CS algorithm of Orthogonal Matching Pursuit performs almost identically to the Basis Pursuit De-Noising algorithm with a much lower computational cost.

Symbol detection plays an important role in the implementation of digital receivers. In this work, we propose ViterbiNet, which is a data-driven symbol detector that does not require channel state information (CSI). ViterbiNet is obtained by integrating deep neural networks (DNNs) into the Viterbi algorithm. We identify the specific parts of the Viterbi algorithm that depend on the channel model, and design a DNN to implement only those computations, leaving the rest of the algorithm structure intact. We then propose a meta-learning based approach to train ViterbiNet online based on recent decisions, allowing the receiver to track dynamic channel conditions without requiring new training samples for every coherence block. Our numerical evaluations demonstrate that the performance of ViterbiNet, which is ignorant of the CSI, approaches that of the CSI-based Viterbi algorithm, and is capable of tracking time-varying channels without needing instantaneous CSI or additional training data. Moreover, unlike conventional Viterbi detection, ViterbiNet is robust to CSI uncertainty, and it can be reliably implemented in complex channel models with constrained computational burden. More broadly, our results demonstrate the conceptual benefit of designing communication systems that integrate DNNs into established algorithms.

This paper proposes to use a deep neural network (DNN)- based symbol detector for mmWave systems such that channel state information (CSI) acquisition can be bypassed. In particular, we consider a sliding bidirectional recurrent neural network (BRNN) architecture that is suitable for the long memory length of typical mmWave channels. The performance of the DNN detector is evaluated in comparison to that of the Viterbi detector. The results show that the performance of the DNN detector is close to that of the optimal Viterbi detector with perfect CSI, and that it outperforms the Viterbi algorithm with CSI estimation error. Further experiments show that the DNN detector is robust to a wide range of noise levels and varying channel conditions, and that a pretrained detector can be reliably applied to different mmWave channel realizations with minimal overhead.

This work presents a new optimization framework for cellular networks using neighborhood-based optimization. Under this optimization framework, resources are allocated within virtual cells encompassing several base-stations and the users within their coverage areas. We form the virtual cells using hierarchical clustering with a minimax linkage criterion given a particular number of such cells. Once the virtual cells are formed, we consider a single-user detection interference coordination model in which base-stations in a virtual cell jointly allocate the channels and power to users within the virtual cell. We propose two new schemes for solving this mixed integer NP- hard resource allocation problem. The first scheme transforms the problem into a continuous variables problem; the second scheme proposes a new channel allocation method and then alternately solves the channel allocation problem using this new method, and the power allocation problem. We evaluate the average system sum rate of these schemes for a variable number of virtual cells. These results quantify the sum-rate along a continuum of fully- centralized versus fully-distributed optimization for different clustering and resource allocation strategies. These results indicate that the penalty of fully-distributed optimization versus fully-centralized (cloud RAN) can be as high as 50%. However, if designed properly, a few base stations within a virtual cell using neighborhood- based optimization have almost the same performance as fully-centralized optimization.

In this paper, a distributed convex optimization algorithm, termed distributed coordinate dual averaging (DCDA) algorithm, is proposed. The DCDA algorithm addresses the scenario of a large distributed optimization problem with limited communication among nodes in the network. Currently known distributed subgradient descent methods, such as the distributed dual averaging or the distributed alternating direction method of multipliers, assume that nodes can exchange messages of large cardinality. Such an assumption on the network communication capabilities is not valid in many scenarios of practical relevance. To address this setting, we propose the DCDA algorithm as a distributed convex optimization algorithm in which the communication between nodes in each round is restricted to a fixed number of dimensions. We bound the rate of convergence under different communication protocols and network architectures for this algorithm. We also consider the extensions to the cases of imperfect gradient knowledge and when transmitted messages are corrupted by additive noise or are quantized. Numerical simulations demonstrating the performance of DCDA in these different settings are also provided.

This paper proposes and analyzes a mmWave sparse channel estimation technique for OFDM systems that uses the Orthogonal Matching Pursuit (OMP) algorithm. This greedy algorithm retrieves one additional multipath component (MPC) per iteration until a stop condition is met. We obtain an analytical approximation for the OMP estimation error variance that grows with the number of retrieved MPCs (iterations). The OMP channel estimator error variance outperforms a classic maximum-likelihood (ML) non-sparse channel estimator by a factor of approximately 2L̂/M where L̂ is the number of retrieved MPCs (iterations) and M the number of taps of the Discrete Equivalent Channel. When the MPC amplitude distribution is heavy-tailed, the channel power is concentrated in a subset of dominant MPCs. In this case OMP performs fewer iterations as it retrieves only these dominant large MPCs. Hence for this MPC amplitude distribution the estimation error advantage of OMP over ML is improved. In particular, for channels with MPCs that have lognormally-distributed amplitudes, the OMP estimator recovers approximately 5-15 dominant MPCs in typical mmWave channels, with 15-45 weak MPCs that remain undetected.

This work presents a new resource allocation optimization framework for cellular networks using neighborhood-based optimization. Under this optimization framework resources are allocated within virtual cells encompassing several base-stations and the users within their coverage area. Incorporating the virtual cell concept enables the utilization of more sophisticated cooperative communication schemes such as coordinated multi-point decoding. We form the virtual cells using hierarchical clustering given a particular number of such cells. Once the virtual cells are formed, we consider a cooperative decoding scheme in which the base-stations in each virtual cell jointly decode the signals that they receive. We propose an iterative solution for the resource allocation problem resulting from the cooperative decoding within each virtual cell. Numerical results for the average system sum rate of our network design under hierarchical clustering are presented. These results indicate that virtual cells with neighborhood-based optimization leads to significant gains in sum rate over optimization within each cell, yet may also have a significant sum-rate penalty compared to fully-centralized optimization.

We consider the recovery of a continuous-time Wiener process from a quantized or a lossy compressed version of its uniform samples under limited bitrate and sampling rate. We derive a closed-form expression for the optimal tradeoff among sampling rate, bitrate, and quadratic distortion in this setting. This expression is given in terms of a reverse waterfilling formula over the asymptotic spectral distribution of a sequence of finite-rank operators associated with the optimal estimator of the Wiener process from its samples. We show that the ratio between this expression and the standard distortion rate function of the Wiener process, describing the optimal tradeoff between bitrate and distortion without a sampling constraint, is only a function of the number of bits per sample. We also consider a sub-optimal lossy compression scheme in which the continuous-time process is estimated from the output of an encoder that is optimal with respect to the discrete-time samples. We show that the latter is strictly greater than the distortion under optimal encoding but only by at most 3%. We, therefore, conclude that near optimal performance is attained even if the encoder is unaware of the continuous-time origin of the samples.

We present an algorithm that efficiently performs blind decoding of MIMO signals. That is, given no channel state information (CSI) at either the transmitter or the receiver, our algorithm takes a block of samples and returns an estimate of the underlying data symbols. In prior work, the problem of blind decoding was formulated as a non-convex optimization problem. In this paper, we present an algorithm that efficiently solves this non-convex problem in practical settings. This algorithm leverages the concepts of linear and mixed-integer linear programming. Empirically, we show that our technique has an error performance close to that of zero-forcing with perfect CSI at the receiver. Initial estimates of the run time of the algorithm presented in this paper suggest that the real-time blind decoding of MIMO signals is possible for even modest-sized MIMO systems.

The scaling of coherent and non-coherent channel capacity is studied in a single-input multiple-output (SIMO) block Rayleigh fading channel as both the bandwidth and the number of receiver antennas go to infinity jointly with the transmit power fixed. The transmitter has no channel state information (CSI), while the receiver may have genie-provided CSI (coherent receiver), or the channel statistics only (non-coherent receiver). Our results show that if the available bandwidth is smaller than a threshold bandwidth which is proportional (up to leading order terms) to the square root of the number of antennas, there is no gap between the coherent capacity and the non-coherent capacity in terms of capacity scaling behavior. On the other hand, when the bandwidth is larger than this threshold, there is a capacity scaling gap. Since achievable rates using pilot symbols for channel estimation are subject to the non-coherent capacity bound, this work reveals that pilot-assisted coherent receivers in systems with a large number of receive antennas are unable to exploit excess spectrum above a given threshold for capacity gain.

We consider the multiterminal remote source coding problem of estimating a Gaussian signal from a bit-restricted representation of distributed linear measurements corrupted by additive white Gaussian noise. For this problem, we study the performance of the multiterminal compress-and-estimate (CE) coding scheme in which multiple remote encoders compress their measurements so as to minimize a local distortion measure which depends solely on the distribution of these measurements. In reconstruction, the decoder estimates the signal from the lossy-compressed measurements having full knowledge of the statistics of the source signal and the noisy measurements. The CE coding scheme is motivated by the scenario in which source encoders, due to their limited capabilities, operate according to a pre-determined compression strategy and cannot adapt to the sensing environment while the fusion center has full knowledge and computational capabilities. We focus, in particular, on two scenarios: the centralized observation model in which measurements are collected at a single remote encoder and the distributed observation model where measurements are provided to multiple remote sensors. In both scenarios, we investigate the performance attainable through the CE coding scheme in which the measurements are compressed according to a quadratic distortion measure and compare it to the performance of the coding scheme having full system knowledge.

The design and analysis of communication systems typically rely on the development of mathematical models that describe the underlying communication channel. However, in some systems, such as molecular communication systems where chemical signals are used for transfer of information, the underlying channel models are unknown. In these scenarios, a completely new approach to design and analysis is required. In this work, we focus on one important aspect of communication systems, the detection algorithms, and demonstrate that by using tools from deep learning, it is possible to train detectors that perform well without any knowledge of the underlying channel models. We propose a technique we call sliding bidirectional recurrent neural network (SBRNN) for real-time sequence detection. We evaluate this algorithm using experimental data that is collected by a chemical communication platform, where the channel model is unknown and difficult to model analytically. We show that deep learning algorithms perform significantly better than a detector proposed in previous works, and the SBRNN outperforms other techniques considered in this work.

We consider the problem of joint source and channel coding of structured data such as natural language over a noisy channel. The typical approach to this problem in both theory and practice involves performing source coding to first compress the text and then channel coding to add robustness for the transmission across the channel. This approach is optimal in terms of minimizing end-to-end distortion with arbitrarily large block lengths of both the source and channel codes when transmission is over discrete memoryless channels. However, the optimality of this approach is no longer ensured for documents of finite length and limitations on the length of the encoding. We will show in this scenario that we can achieve lower word error rates by developing a deep learning based encoder and decoder. While the approach of separate source and channel coding would minimize bit error rates, our approach preserves semantic information of sentences by first embedding sentences in a semantic space where sentences closer in meaning are located closer together, and then performing joint source and channel coding on these embeddings.

The next generation of cellular networks are expected to support multiple user-oriented services that have various quality of service (QoS) requirements, yet must be serviced by a single infrastructure. To achieve this, network virtualization can play an important role by partitioning/slicing a single physical network resource into multiple virtual networks such that each of the slices can support various services independently. The main contribution of this work is an implementation of static and dynamic resource allocation schemes for different slices supporting different services. We use this implementation to study the effects of increasing the number of network slices on the number of optimization trigger events. Moreover, we propose a non-uniform resource sharing agreement (policy) between the participating network slices and investigate how these sharing agreements affect the frequency of optimization trigger events.

This paper focuses on molecular communication (MC) systems where the signaling molecules may participate in a reversible bimolecular reaction in the channel. The motivation for studying these MC systems is that they can realize the concept of constructive and destructive signal superposition, which leads to favorable properties such as inter-symbol interference (ISI) reduction and avoiding environmental contamination due to continuous release of molecules into the channel. This work first derives the maximum likelihood (ML) detector for a binary MC system with reactive signaling molecules under the assumption that the detector has perfect knowledge of the ISI. The performance of this genie-aided ML detector yields an upper bound on the performance of any practical detector. In addition, two suboptimal detectors of different complexity are proposed. The proposed ML detector as well as one of the suboptimal detectors require the channel response (CR) of the considered MC system. Moreover, the CR is needed for the performance evaluation of all proposed detectors. However, analyzing MC with reactive signaling is challenging since the underlying partial differential equations that describe the reaction-diffusion mechanism are coupled and non-linear. Therefore, an algorithm is developed in this paper for efficient computation of the CR to any arbitrary transmit symbol sequence. The accuracy of this algorithm is validated via particle-based simulation. Simulation results using the developed CR algorithm show that the performance of the proposed suboptimal detectors can approach that of the genie-aided ML detector. Moreover, these results show that MC systems with reactive signaling have superior performance relative to those with non-reactive signaling due to the reduction of ISI enabled by the chemical reactions.

Artificial Intelligence (AI) and Machine Learning (ML) approaches, well known from IT disciplines, are beginning to excite the networking and networked systems community. Of late, we are seeing a huge excitement about applying AI and ML to networked systems. Is this merely a hype? Are there use cases and genuine applications that could lead to real deployment and practical solutions? What are the key challenges in applying AI and ML to networked systems? Can researchers and practitioners in communication networks and networked systems tap into machine learning and AI techniques to optimize network architecture, control and management, leading to increased automation in network operations? Can researchers and practitioners in the AI community explore synergy with networking researchers to optimize network architecture and design? The above are some of the questions that would be addressed during the panel discussion. The objective of the panel discussion would be to tap the minds of the global experts in order to understand the merits and limitations and the future landscape in the intersection of networking/networked systems and AI/ML.

Wireless technology has enormous potential to change the way we live, work, and play over the next several decades. Future wireless networks will support 100 Gbps communication between people, devices, and the "Internet of Things," with high reliability and uniform coverage indoors and out. The shortage of spectrum to support such systems will be alleviated by advances in massive MIMO and mmW technology as well as cognitive radios. Wireless technology will also enable smart and energy-efficient homes and buildings, automated highways and skyways, and in-body networks for monitoring, analysis and treatment of medical conditions. Breakthrough energy-efficiency architectures, algorithms and hardware will allow wireless networks to be powered by tiny batteries, energy-harvesting, or over-the-air power transfer. Finally, new communication systems based on biology and chemistry to encode bits will enable a wide range of new micro and macroscale applications. There are many technical challenges that must be overcome in order to make this vision a reality. This talk will describe what the wireless future might look like along with some of the innovations and breakthroughs required to realize this vision.

Epilepsy is one of the most common neurological disorders affecting about 1% of the world population. For patients with focal seizures that cannot be treated with antiepileptic drugs, the common treatment is a surgical procedure for removal of the seizure onset zone (SOZ). In this work we introduce an algorithm for automatic localization of the seizure onset zone (SOZ) in epileptic patients based on electrocorticography (ECoG) recordings. The proposed algorithm builds upon the hypothesis that the abnormal excessive (or synchronous) neuronal activity in the brain leading to seizures starts in the SOZ and then spreads to other areas in the brain. Thus, when this abnormal activity starts, signals recorded at electrodes close to the SOZ should have a relatively large causal influence on the rest of the recorded signals. The SOZ localization is executed in two steps. First, the algorithm represents the set of electrodes using a directed graph in which nodes correspond to recording electrodes and the edges' weights quantify the pair-wise causal influence between the recorded signals. Then, the algorithm infers the SOZ from the estimated graph using a variant of the PageRank algorithm followed by a novel post-processing phase. Inference results for 19 patients show a close match between the SOZ inferred by the proposed approach and the SOZ estimated by expert neurologists (success rate of 17 out of 19).

We study non-coherent detection schemes for molecular communication (MC) systems with negligible inter-symbol interference that do not require knowledge of the channel state information (CSI). In particular, we first derive the optimal maximum likelihood (ML) multiple-symbol (MS) detector for MC systems. As a special case of the optimal MS detector, we show that the optimal ML symbol-by-symbol (SS) detector can be equivalently written in the form of a threshold-based detector, where the optimal decision threshold is constant and depends only on the statistics of the MC channel. The main challenge of the MS detector is the complexity associated with the calculation of the optimal detection metric. To overcome this issue, we propose an approximate MS detection metric that can be expressed in closed form. In addition, we develop a non-coherent decision-feedback detector, which introduces a lower detection delay compared with the optimal MS detector, and a suboptimal blind detector, which has a significantly lower complexity than the optimal MS detector. Finally, we derive analytical expressions for the bit error rate (BER) of the optimal SS detector, as well as upper and lower bounds for the BER of the optimal MS detector. Simulation results confirm the analysis and reveal the effectiveness of the proposed optimal and suboptimal detection schemes compared with the benchmark scheme that assumes perfect CSI knowledge, particularly, when the number of observations used for detection is sufficiently large. Simulation results are also presented that show the performance of the proposed detectors, when inter-symbol interference is non-negligible.

Representing a continuous-time signal by a set of samples is a classical problem in signal processing. We study this problem under the additional constraint that the samples are quantized or compressed in a lossy manner under a limited bitrate budget. To this end, we consider a combined sampling and source coding problem in which an analog stationary Gaussian signal is reconstructed from its encoded samples. These samples are obtained by a set of bounded linear functionals of the continuous-time path, with a limitation on the average number of samples per unit time given in this setting. We provide a full characterization of the minimal distortion in terms of the sampling frequency, the bitrate, and the signal's spectrum. Assuming that the signal's energy is not uniformly distributed over its spectral support, we show that for each compression bitrate there exists a critical sampling frequency smaller than the Nyquist rate, such that the distortion in signal reconstruction when sampling at this frequency is minimal. Our results can be seen as an extension of the classical sampling theorem for bandlimited random processes in the sense that they describe the minimal amount of excess distortion in the reconstruction due to lossy compression of the samples and provide the minimal sampling frequency required in order to achieve this distortion. Finally, we compare the fundamental limits in the combined source coding and sampling problem to the performance of pulse code modulation, where each sample is quantized by a scalar quantizer using a fixed number of bits.

A general expression for the quadratic distortion rate function (DRF) of cyclostationary Gaussian processes in terms of their spectral properties is derived. This expression can be seen as the result of orthogonalization over the different components in the polyphase decomposition of the process. We use this expression to derive, in a closed form, the DRF of several cyclostationary processes arising in practice. We first consider the DRF of a combined sampling and source coding problem. It is known that the optimal coding strategy for this problem involves source coding applied to a signal with the same structure as one resulting from pulse amplitude modulation (PAM). Since a PAM-modulated signal is cyclostationary, our DRF expression can be used to solve for the minimal distortion in the combined sampling and source coding problem. We also analyze in more detail the DRF of a source with the same structure as a PAM-modulated signal, and show that it is obtained by reverse waterfilling over an expression that depends on the energy of the pulse and the baseband process modulated to obtain the PAM signal. This result is then used to explore the effect of the symbol rate in PAM on the DRF of its output. In addition, we also study the DRF of sources with an amplitude-modulation structure, and show that the DRF of a narrow-band Gaussian stationary process modulated by either a deterministic or a random phase sine-wave equals the DRF of the baseband process.

In this demo paper we present a dynamic spectrum-level slicing (DSLS) implementation for heterogeneous networks based on an open source software/hardware platform known as OpenAirInterface. Assuming the network traffic load changes every time interval, we mathematically formulate the DSLS as an optimization problem with the corresponding sets of constraints.

The performance gains from dynamic allocation of radio resources across multiple heterogeneous networks is studied. Through virtualization, the physical radio resources of the heterogeneous networks are first abstracted into a centralized pool of virtual radio resources. A dynamic spectrum-level slicing algorithm to share these radio resources across the different networks is then presented. This algorithm is responsive to changing user load and channel conditions. Simulation results show that for representative user arrival statistics, dynamic allocation of radio resources significantly lowers the percentage of dropped packets. In addition, they reveal that the triggers for dynamic allocation of resources across coexisting virtual networks occur every other time interval under the worst case traffic variation in the system (i.e., traffic varies every time interval). Our results suggest that performance benefits can be had even if dynamic spectrum-level slicing does not happen on time scales similar to that of the local resource schedulers residing in each virtual network.

We propose a method for multiple-input multiple-output (MIMO) decoding when channel-state information (CSI) is unknown to both the transmitter and receiver. The proposed method requires some structure in the transmitted signal for the decoding to be effective, in particular that the underlying sources are drawn from a hypercubic space. Our proposed technique fits a minimum volume parallelepiped to the received samples. This problem can be expressed as a non-convex optimization problem that can be solved with high probability by gradient descent. Our blind decoding algorithm can be used when communicating over unknown MIMO wireless channels using either binary phase-shift keying or MPAM modulation. We apply our technique to jointly estimate MIMO-channel gain matrices and decode the underlying transmissions with only knowledge of the transmitted constellation and without the use of pilot symbols. Our results provide theoretical guarantees that the proposed algorithm is correct when applied to MIMO systems with four or fewer transmit antennas. Empirical results show small sample size requirements, making this algorithm suitable for block-fading channels with coherence times typically seen in practice. Our approach has a loss of less than 3 dB compared to zero forcing with perfect CSI, imposing a similar performance penalty as space-time coding techniques without the loss of rate incurred by those techniques.

This work presents a new multi-chemical experimental platform for molecular communication (MC) where the transmitter can release different chemicals. This platform is designed to be inexpensive and accessible, and it can be expanded to simulate different environments such as a portion of the body's cardiovascular system or a complex network of pipes in industrial complexes and city infrastructures. To demonstrate the capabilities of the platform, we implement a time-slotted binary communication system where information is carried via the pH of transmitted signals and, in particular, a 0-bit is represented by an acid pulse, and a 1-bit by a base pulse. The channel model for this system, which is nonlinear and has a long memory due to chemical reactions, is unknown. Therefore, we devise novel detection algorithms that use techniques from machine learning and deep learning to train a maximum-likelihood detector. Using these algorithms, the bit error rate (BER) improves by an order of magnitude relative to the approach used in previous works. Moreover, our system achieves a data rate that is an order of magnitude higher than any of the previous MC platforms.

We study diversity in one-shot communication over molecular timing channels. In the considered channel model the transmitter simultaneously releases a large number of information particles, where the information is encoded in the time of release. The receiver decodes the information based on the random time of arrival of the information particles. We characterize the asymptotic exponential decrease rate of the probability of error as a function of the number of released particles. We denote this quantity as the system diversity gain, as it depends both on the number of particles transmitted as well as the receiver detection method. Three types of detectors are considered: the maximum-likelihood (ML) detector, a linear detector, and a detector that is based on the first arrival (FA) among all the transmitted particles. We show that for random propagation characterized by right-sided unimodal densities with zero mode, the FA detector is equivalent to the ML detector, and significantly outperforms the linear detector. Moreover, even for densities with positive mode, the diversity gain achieved by the FA detector is very close to that achieved by the ML detector and much higher than the gain achieved by the linear detector.

We consider the problem of estimating the covariance matrix and the transition matrix of vector autoregressive (VAR) processes from partial measurements. This model encompasses settings where there are limitations in the data acquisition of the underlying measurement systems so that data is lost or corrupted by noise. An estimator for the covariance matrix of the observations is first presented. More refined estimators, factoring in structural constraints on the covariance matrix such as sparsity, bandedness, sparsity of the inverse and low-rankness are then introduced that are particularly useful in the high-dimensional regime. These estimates are then used to perform system identification by estimating the state transition matrix with or without further structural assumptions. Non-asymptotic guarantees are presented for all estimators.

This work introduces the particle-intensity channel (PIC) as a model for molecular communication systems and characterizes the properties of the optimal input distribution and the capacity limits for this system. In the PIC, the transmitter encodes information, in symbols of a given duration, based on the number of particles released, and the receiver detects and decodes the message based on the number of particles detected during the symbol interval. In this channel, the transmitter may be unable to control precisely the number of particles released, and the receiver may not detect all the particles that arrive. We demonstrate that the optimal input distribution for this channel always has mass points at zero and the maximum number of particles that can be released. We then consider diffusive particle transport, derive the capacity expression when the input distribution is binary, and show conditions under which the binary input is capacity-achieving. In particular, we demonstrate that when the transmitter cannot generate particles at a high rate, the optimal input distribution is binary.

We consider the problem of recovering a sparse vector from a quantized or a lossy compressed version of its noisy random linear projections. We characterize the minimal distortion in this recovery as a function of the sampling ratio, the sparsity rate, the noise intensity and the total number of bits in the quantized representation. We first derive a singe-letter expression that can be seen as the indirect distortion-rate function of the sparse source observed through a Gaussian channel whose signal-to-noise ratio is derived from these parameters. Under the replica symmetry postulation, we prove that there exists a quantization scheme that attains this expression in the asymptotic regime of large system dimensions. In addition, we prove a converse demonstrating that the MMSE in estimating any fixed sub-block of the source from the quantized measurements at a fixed number of bits does not exceed this expression as the system dimensions go to infinity. Thus, under these conditions, the expression we derive describes the excess distortion incurred in encoding the source vector from its noisy random linear projections in lieu of the full source information.

We consider the remote source coding setting in which a source realization is estimated from a lossy compressed sequence of noisy observations. Unlike in the optimal remote source coding problem, however, the encoder is bound to use good codes with respect to the observation sequence, i.e., codes that are optimal for the lossy reconstruction of the observation, rather than the remote source. This encoding strategy is denoted as the compress-and-estimate (CE) scheme. For the case of an i.i.d source observed through a memoryless channel, we show that the distortion in the CE scheme is characterized by a single-letter expression, referred to as the CE distortion-rate function (CE-DRF). In particular, we show that the CE-DRF can be attained by estimating the source from the output of a remote encoder employing any sequence of good codes with respect to the observation sequence. In addition, we show that the limiting distortion in estimating any finite sub-block of the source realization from the output of a remote encoder employing good codes, averaged over all sub-blocks, is also bounded by the CE-DRF.

We consider the problem of estimating the parameters of a vector autoregressive (VAR) process from low-dimensional random projections of the observations. This setting covers the cases where we take compressive measurements of the observations or have limits in the data acquisition process associated with the measurement system and are only able to subsample. We first present fundamental bounds on the convergence of any estimator for the covariance or state-transition matrices with and without considering structural constraints of sparsity and low-rankness. We then construct an estimator for these matrices or the parameters of the VAR process and show that it is order optimal.

We consider the remote vector source coding problem in which a vector Gaussian source is estimated from noisy linear measurements. For this problem, we derive the performance of the compress-and-estimate (CE) coding scheme and compare it to the optimal performance. In the CE coding scheme, the remote encoder compresses the noisy source observations so as to minimize a local distortion measure, independent from the joint distribution between the source and the observations. In reconstruction, the decoder, having full knowledge of the joint distribution of the source and observations, estimates the original source realization from the lossy-compressed noisy observations. For the CE scheme in the vector Gaussian case, we show that, if the code rate is less than a specific threshold, then the CE coding scheme attains the same performance as the optimal coding scheme. For code rates above this threshold, we introduce lower and upper bounds on the performance gap between the CE and the optimal scheme. The case of a two-dimensional Gaussian source observed through two noisy measurements is studied to illustrate the behavior of the performance gap.

A new modulation technique for the time-frequency dispersive channel is considered. The waveform construction, called Frequency-Domain Multiplexing with a Frequency-Domain Cyclic Prefix (FDM-FDCP) efficiently corrects for the Doppler spread introduced by the channel. The mathematical foundations behind this construction are described and efficient algorithms presented to modulate and demodulate information symbols. It is found that for channels with a high Doppler spread and a low delay spread, the construction can sustain good performance in terms of low SER and minimal overhead, whereas OFDM is strictly worse. This shows that, in rapidly time-varying time-frequency dispersive channels, general time-frequency signaling schemes (FDM-FDCP being an example) may outperform OFDM or other waveform constructions designed for multipath channels with low mobility.

In this work, energy coherence time, which is defined to be the coherence time of the channel quality information (CQI), is studied as a function of the number of antennas in a receiver with a large antenna array. It is found that, as a function of the number of receiver antennas, the energy coherence time can be much larger than the inverse of the Doppler frequency associated with the propagation environment. Numerical studies with representative values for cellular systems indicate that the net reduction in the frequency of adapting to changes in channel quality can be orders of magnitude higher with practical large antenna arrays.

A new two-dimensional modulation technique called Orthogonal Time Frequency Space (OTFS) modulation designed in the delay-Doppler domain is introduced. Through this design, which exploits full diversity over time and frequency, OTFS coupled with equalization converts the fading, time-varying wireless channel experienced by modulated signals such as OFDM into a time-independent channel with a complex channel gain that is roughly constant for all symbols. Thus, transmitter adaptation is not needed. This extraction of the full channel diversity allows OTFS to greatly simplify system operation and significantly improves performance, particular in systems with high Doppler, short packets, and large antenna arrays. Simulation results indicate at least several dB of block error rate performance improvement for OTFS over OFDM in all of these settings. In addition these results show that even at very high Dopplers (500 Km/h), OTFS approaches channel capacity through linear scaling of throughput with the MIMO order, whereas the performance of OFDM under typical design parameters breaks down completely.

Identifying properties and concentrations of components from an observed mixture, known as deconvolution, is a fundamental problem in signal processing. It has diverse applications in fields ranging from hyperspectral imaging to noise cancellation in audio recordings. This paper focuses on in-silico deconvolution of signals associated with complex tissues into their constitutive cell-type-specific components and a quantitative characterization of the cell types. Deconvolving mixed tissues/cell types is useful in the removal of contaminants (e.g., surrounding cells) from tumor biopsies, as well as in monitoring changes in the cell population in response to treatment or infection. In these contexts, the observed signal from the mixture of cell types is assumed to be a convolution, using a linear instantaneous (LI) mixing process, of the expression levels of genes in constitutive cell types. The goal is to use known signals corresponding to individual cell types and a model of the mixing process to cast the deconvolution problem as a suitable optimization problem. In this paper, we present a survey and in-depth analysis of models, methods, and assumptions underlying deconvolution techniques. We investigate the choice of the different loss functions for evaluating estimation error, constraints on solutions, preprocessing and data filtering, feature selection, and regularization to enhance the quality of solutions and the impact of these choices on the performance of commonly used regression-based methods for deconvolution. We assess different combinations of these factors and use detailed statistical measures to evaluate their effectiveness. Some of these combinations have been proposed in the literature, whereas others represent novel algorithmic choices for deconvolution. We identify shortcomings of current methods and avenues for further investigation. For many of the identified shortcomings, such as normalization issues and data filtering, we provide new solutions. We summarize our findings in a prescriptive step-by-step process, which can be applied to a wide range of deconvolution problems.

This paper investigates the information rate loss in analog channels, when the sampler is designed to operate independent of the instantaneous channel occupancy. Specifically, a multiband linear time-invariant Gaussian channel under universal sub-Nyquist sampling is considered. The entire channel bandwidth is divided into n subbands of equal bandwidth. At each time, only k constant-gain subbands are active, where the instantaneous subband occupancy is not known at the receiver and the sampler. We study the information loss through an information , that is, the gap of achievable rates caused by the lack of instantaneous subband occupancy information. We characterize the minimax information rate loss for the sub-Nyquist regime, provided that the number n of subbands and the SNR are both large. The minimax limits depend almost solely on the band sparsity factor and the undersampling factor, modulo some residual terms that vanish as n and SNR grow. Our results highlight the power of randomized sampling methods (i.e., the samplers that consist of random periodic modulation and low-pass filters), which are able to approach the minimax information rate loss with exponentially high probability.

We propose the new technique of physical-layer cryptography based on using a massive MIMO channel as a key between the sender and desired receiver, which need not be secret. The goal is for low-complexity encoding and decoding by the desired transmitter-receiver pair, whereas decoding by an eavesdropper is hard in terms of prohibitive complexity. The decoding complexity is analyzed by mapping the massive MIMO system to a lattice. We show that the eavesdropper's decoder for the MIMO system with M-PAM modulation is equivalent to solving standard lattice problems that are conjectured to be of exponential complexity for both classical and quantum computers. Hence, under the widely-held conjecture that standard lattice problems are hard to solve, the proposed encryption scheme has a more robust notion of security than that of the most common encryption methods used today such as RSA and Diffie-Hellman. In addition, we show that this scheme could be used to securely communicate without a pre-shared secret and little computational overhead. Thus, by exploiting the physical layer properties of the radio channel, the massive MIMO system provides for low-complexity encryption commensurate with the most sophisticated forms of application-layer encryption that are currently known.

The connectivity structure between neurons is useful for determining how groups of neurons perform tasks. Directed information is a measure that can be used to infer connectivity between neurons using their recorded time series. In this paper, we develop a method of calculating the directed information rate from one neuron to another neuron it is connected to, given a particular neuronal topology. We assume a leaky integrate-and-fire (LIF) neuron model with independent and identically distributed random spike train inputs, which governs how the membrane potential of the output neuron evolves. We use this neuron model to find the dynamics of the resulting output spike train from its membrane potential dynamics, both for when the past of the input neuron is observed and when it is not. We show that an action potential in the LIF model causes a conditional independence of the activity before and after it, and we capture this conditional independence via a Markov model. We use these spike train dynamics to then calculate the directed information between the spike train of the input neuron to the spike train generated by the LIF model. In addition, we show how changing the refractory period of the LIF model affects the directed information, and also how the spike train dynamics are affected by memory constraints, which are commonly imposed in estimators of directed information.

We consider a noncoherent uplink and downlink with a large antenna array at the base station. The modulation used is ON-OFF keying, with symbol-by-symbol single-user detection. A ray tracing propagation model is assumed with knowledge at the base station and transmitters of only the ray arrival angles and amplitudes. We identify the sources of performance degradation, quantify notions of diversity gain (related to the detection error performance) and multiplexing gain (related to the number of users simultaneously supported), and present numerical results to demonstrate these gains. Our results indicate that in this noncoherent system, increasing the number of antenna elements can support multiple users, with a vanishing probability of detection error, as long as the number of users is below a certain threshold which increases with the number of antennas. This contrasts with the fact that in a rich scattering propagation environment, uncoded noncoherent systems performing symbol-by-symbol detection cannot support more than one user with a vanishing probability of error.

We introduce the fluctuating two-ray (FTR) fading model, a new statistical channel model that consists of two fluctuating specular components with random phases plus a diffuse component. The FTR model arises as the natural generalization of the two-wave with diffuse power (TWDP) fading model; this generalization allows its two specular components to exhibit a random amplitude fluctuation. Unlike the TWDP model, all the chief probability functions of the FTR fading model (PDF, CDF, and MGF) are expressed in closed-form, having a functional form similar to other state-of-the-art fading models. We also provide approximate closed-form expressions for the PDF and CDF in terms of a finite number of elementary functions, which allow for a simple evaluation of these statistics to an arbitrary level of precision. We show that the FTR fading model provides a much better fit than Rician fading for recent small-scale fading measurements in 28 GHz outdoor mm-wave channels. Finally, the performance of wireless communication systems over FTR fading is evaluated in terms of the bit error rate and the outage capacity, and the interplay between the FTR fading model parameters and the system performance is discussed. Monte Carlo simulations have been carried out in order to validate the obtained theoretical expressions.

This work studies the impact of time-synchronization in molecular timing (MT) channels by analyzing three different modulation techniques. The first requires transmitter-receiver synchronization and is based on modulating information on the release timing of information particles. The other two are asynchronous and are based on modulating information on the relative time between two consecutive releases of information particles using indistinguishable or distinguishable particles. All modulation schemes result in a system that relate the transmitted and the received signals through an additive noise, which follows a stable distribution. As the common notion of the variance of a signal is not suitable for defining the power of stable distributed signals (due to infinite variance), we derive an expression for the geometric power of a large class of stable distributions, and then use this result to characterize the geometric signal-to-noise ratio (G-SNR) for each of the modulation techniques. In addition, for binary communication, we derive the optimal detection rules for each modulation technique. Numerical evaluations indicate that the bit error rate (BER) is constant for a given G-SNR, and the performance gain obtained by using synchronized communication is significant. Yet, it is also shown that by using two distinguishable particles per bit instead of one, the BER of the asynchronous technique can approach that of the synchronous one.

This work studies communication over diffusionbased molecular timing (DBMT) channels. The transmitter simultaneously releases multiple small information particles, where the information is encoded in the time of release. The receiver decodes the transmitted information based on the random time of arrival of the information particles, which is represented as an additive noise channel. For a DBMT channel, without flow, this noise follows the Levy distribution. Under this channel model, the maximum-likelihood (ML) detector is derived and shown to have high computational complexity. It is further shown that for any additive noise channel with -stable noise, α <; 1, such as the DBMT channel, a linear receiver is not able to take advantage of the release of multiple information particles. Thus, instead of the common low-complexity linear approach, a new detector, which is based on the first arrival (FA) among all the transmitted particles, is derived. Numerical simulations indicate that for a small to medium number of released particles, the performance of the FA detector is very close to the performance of the ML detector.

In active transport molecular communication (ATMC), information particles are actively transported from a transmitter to a receiver using special proteins. Prior work has demonstrated that ATMC can be an attractive and viable solution for on-chip applications. The energy consumption of an ATMC system plays a central role in its design and engineering. In this work, an energy model is presented for ATMC and this model is used to provide guidelines for designing energy efficient systems. The channel capacity per unit energy is analyzed and maximized. It is shown that based on the size of the symbol set and the symbol duration, there is a vesicle size that maximizes the rate per unit energy. It is also demonstrated that maximizing the rate per unit energy yields very different system parameters compared to maximizing the rate only.

A system with a single antenna at the transmitter and receiver and no channel state information at either is considered. The channel experiences block Rayleigh fading with a coherence time of T0symbol times and the fading statistics are assumed to be known perfectly. The system operates with a finite average transmit power. It is shown that the capacity optimal input distribution in the T0-dimensional space is the product of the distribution of an isotropically-distributed unit vector and a distribution on the 2-norm in the T0-dimensional space which is discrete and has a finite number of points in the support. Numerical evaluations of this distribution and the associated capacity for a channel with fading and Gaussian noise for a coherence time T0= 2 are presented for representative SNRs.It is also shown numerically that an implicit channel estimation is done by the capacity-achieving scheme.

This work introduces capacity limits for molecular timing (MT) channels, where information is modulated on the release timing of small information particles, and decoded from the time of arrival at the receiver. It is shown that the random time of arrival can be represented as an additive noise channel, and for the diffusion-based MT (DBMT) channel, this noise is distributed according to the Lévy distribution. Lower and upper bounds on the capacity of the DBMT channel are derived for the case where the delay associated with the propagation of information particles in the channel is finite. These bounds are also shown to be tight.

The minimal distortion attainable in recovering the waveform of a continuous-time Wiener process from an encoded version of its uniform samples is considered. We first introduce a combined sampling and source coding problem and prove an associated source coding theorem. We then derive an upper bound on the minimal distortion attainable under any sampling rate and a prescribed number of bits to encode the samples. We show that this bound is accurate to within a second order term in the sampling rate, and converges to the true distortion-rate function of the Wiener process as the sampling rate goes to infinity. For example, this bound implies that by providing a single bit per sample it is possible to achieve the optimal distortion-rate performance of the Wiener process, given by its distortion-rate function, to within a factor of 1.5. We conclude the distortion-rate function of the Wiener process is strictly smaller than the indirect distortion-rate function from its uniform samples obtained at any finite sampling rate. This is in contrast to stationary infinite bandwidth processes.

We consider a multiterminal source coding problem in which a random source signal is estimated from encoded versions of multiple noisy observations. Each encoded version, however, is compressed so as to minimize a local distortion measure, defined only with respect to the distribution of the corresponding noisy observation. The original source is then estimated from these compressed noisy observations. We denote the minimal distortion under this coding scheme as the compress-and-estimate distortion-rate function (CE-DRF). We derive a single-letter expression for the CE-DRF in the case of an i.i.d source. We evaluate this expression for the case of a Gaussian source observed through multiple parallel AWGN channels and quadratic distortion and in the case of a non-uniform binary i.i.d source observed through multiple binary symmetric channels under Hamming distortion. For the case of a Gaussian source, we compare the performance for centralized encoding versus that of distributed encoding. In the centralized encoding scenario, when the code rates are sufficiently small, there is no loss of performance compared to the indirect source coding distortion-rate function, whereas distributed encoding achieves distortion strictly larger then the optimal multiterminal source coding scheme. For the case of a binary source, we show that even with a single observation, the CE-DRF is strictly larger than that of indirect source coding.

We consider a multiterminal source coding problem in which a source is estimated at a central processing unit from lossy-compressed remote observations. Each lossy-encoded observation is produced by a remote sensor. The sensor first obtains a noisy version of the source, then compresses this observation based on minimizing a local distortion measure that depends only on the marginal distribution of its observation. The central node, on the other hand, has knowledge of the joint distribution of the source and all the observations and produces the source estimate that minimizes a different distortion measure between the source and its reconstruction. In this paper, we investigate the problem of optimally choosing the rate of each lossy-compressed remote estimate so as to minimize the distortion at the central processor, subject to bound on the sum of the communication rate between the sensors and the central unit. We focus, in particular, on two models of practical relevance: the case of a Gaussian source observed in additive Gaussian noise and reconstructed under quadratic distortion, and the case of a binary source observed in bit-flipping noise and reconstructed under Hamming distortion. In both scenarios we show that there exist regimes under which having more remote encoders does not reduce the source distortion. In other words, having fewer, high-quality remote estimates provides a smaller distortion than having more, lower-quality estimates.

In this paper, we present an approach to solve the nonconvex optimization problem that arises when designing the transmit covariance matrices in multiuser multiple-input multiple-output (MIMO) broadcast networks implementing simultaneous wireless information and power transfer (SWIPT). The MIMO SWIPT design is formulated as a nonconvex optimization problem in which system sum rate is optimized considering per-user harvesting constraints. Two different approaches are proposed. The first approach is based on a classical gradient-based method for constrained optimization. The second approach is based on difference of convex (DC) programming. The idea behind this approach is to obtain a convex function that approximates the nonconvex objective and, then, solve a series of convex subproblems that, eventually, will provide a (locally) optimum solution of the general nonconvex problem. The solution obtained from the proposed approach is compared to the classical block-diagonalization (BD) strategy, typically used to solve the nonconvex multiuser MIMO network by forcing no inter-user interference. Simulation results show that the proposed approach improves both the system sum rate and the power harvested by users simultaneously. In terms of computational time, the proposed DC programming outperforms the classical gradient methods.

Motivated by recently derived fundamental limits on total (transmit + decoding) power for coded communication with VLSI decoders, this paper investigates the scaling behavior of the minimum total power needed to communicate over AWGN channels as the target bit-error-probability tends to zero. We focus on regular-LDPC codes and iterative message-passing decoders. We analyze scaling behavior under two VLSI complexity models of decoding. One model abstracts power consumed in processing elements (node model), and another abstracts power consumed in wires which connect the processing elements (wire model). We prove that a coding strategy using regular-LDPC codes with Gallager-B decoding achieves order-optimal scaling of total power under the node model. However, we also prove that regular-LDPC codes and iterative message-passing decoders cannot meet existing fundamental limits on total power under the wire model. Furthermore, if the transmit energy-per-bit is bounded, total power grows at a rate that is worse than uncoded transmission. Complementing our theoretical results, we develop detailed physical models of decoding implementations using post-layout circuit simulations. Our theoretical and numerical results show that approaching fundamental limits on total power requires increasing the complexity of both the code design and the corresponding decoding algorithm as communication distance is increased or error-probability is lowered.

This paper is concerned with jointly recovering n node variables {xi}1≤i≤nfrom a collection of pairwise difference measurements. Imagine we acquire a few observations taking the form of xi- xj; the observation pattern is represented by a measurement graph G with an edge set ℰ, such that xi-xjis observed if and only if (i, j) ε ℰ. To account for noisy measurements in a general manner, we model the data acquisition process by a set of channels with given input/output transition measures. Employing information-theoretic tools applied to channel decoding problems, we develop a unified framework to characterize the fundamental recovery criterion, which accommodates general graph structures, alphabet sizes, and channel transition measures. In particular, our results isolate a family of minimum channel divergence measures to characterize the degree of measurement corruption, which together with the size of the minimum cut of G dictates the feasibility of exact information recovery. For various homogeneous graphs, the recovery condition depends almost only on the edge sparsity of the measurement graph irrespective of other graphical metrics; alternatively, the minimum sample complexity required for these graphs scales like (n log n)/(Hel1/2min) for certain information metric Hel1/2mindefined in the main text, as long as the alphabet size is not super-polynomial in n. We apply our general theory to three concrete applications, including the stochastic block model, the random corruption model, and the haplotype assembly problem. Our theory leads to orderwise tight recovery conditions for all these scenarios.

We consider communication over heterogeneous parallel channels, where a transmitter is connected to two users via two parallel channels: a multiple-input multiple-output (MIMO) broadcast channel (BC) and a noiseless rate-limited multicast channel. We characterize the optimal degrees of freedom (DoF) region of this setting when the transmitter has delayed channel state information (CSIT) regarding the MIMO BC. Our results show that jointly coding over the two channels strictly outperforms simple channel aggregation and can even achieve the instantaneous CSIT performance with completely outdated CSIT on the MIMO BC in the sum DoF sense; this happens when the multicast rate of the second channel is larger than a certain threshold. The main idea is to send information over the MIMO BC at a rate above its capacity and then use the second channel to send additional side information to allow for reliable decoding at both receivers. We call this scheme a two-phase overload-multicast strategy. We show that such a strategy is also sum DoF optimal for the K-user MIMO BC with a parallel multicast channel when the rate of the multicast channel is high enough and can again achieve the instantaneous CSIT performance (optimal sum DoF) with completely outdated CSIT. For the regime where the capacity of the multicast channel is small, we propose another joint coding strategy, which is sum DoF optimal.

We consider a one-shot communication setting in which several single antenna transmitters communicate with a receiver with a large number of antennas, i.e., the receiver decodes transmitted information at the end of every symbol time. Motivated by the optimal noncoherent detector in a Rayleigh fading channel, we consider a noncoherent energy-based communication scheme that does not require any knowledge of instantaneous channel state information at either the transmitter or the receiver; it uses only the statistics of the channel and noise. We show that, for general channel fading statistics, the performance of the considered one-shot multiuser noncoherent scheme is the same, in a scaling law sense, as that of the optimal coherent scheme exploiting perfect channel knowledge and coding across time. Furthermore, we present a numerical evaluation of the performance of this scheme in representative fading and noise statistics.

The amount of information lost in sub-Nyquist sampling of a continuous-time Gaussian stationary process is quantified. We consider a combined source coding and sub-Nyquist reconstruction problem in which the input to the encoder is a noisy sub-Nyquist sampled version of the analog source. We first derive an expression for the mean squared error in the reconstruction of the process from a noisy and information rate-limited version of its samples. This expression is a function of the sampling frequency and the average number of bits describing each sample. It is given as the sum of two terms: minimum mean square error in estimating the source from its noisy but otherwise fully observed sub-Nyquist samples, and a second term obtained by reverse waterfilling over an average of spectral densities associated with the polyphase components of the source. We extend this result to multi-branch uniform sampling, where the samples are available through a set of parallel channels with a uniform sampler and a pre-sampling filter in each branch. Further optimization to reduce distortion is then performed over the pre-sampling filters, and an optimal set of pre-sampling filters associated with the statistics of the input signal and the sampling frequency is found. This results in an expression for the minimal possible distortion achievable under any analog-to-digital conversion scheme involving uniform sampling and linear filtering. These results thus unify the Shannon-Whittaker-Kotelnikov sampling theorem and Shannon rate-distortion theory for Gaussian sources.

A unified graphical approach to random coding for any memoryless, single-hop, K -user channel with or without common information is defined through two steps. The first step is user virtualization. Each user is divided into multiple virtual sub-users according to a chosen rate-splitting strategy. This results in an enhanced channel with a possibly larger number of users for which more coding possibilities are available and for which common messages to any subset of users can be encoded. Following user virtualization, the message of each user in the enhanced model is coded using a chosen combination of coded time-sharing, superposition coding, and joint binning. A graph is used to represent the chosen coding strategies. Nodes in the graph represent codewords, while edges represent coding operations. This graph is used to construct a graphical Markov model, which illustrates the statistical dependence among codewords that can be introduced by the superposition coding or joint binning. Using this statistical representation of the overall codebook distribution, the error probability of the code is shown to vanish through a unified analysis. The rate bounds that define the achievable rate region are obtained by linking the error analysis to the properties of the graphical Markov model. This proposed framework makes it possible to numerically obtain an achievable rate region by specifying a user virtualization strategy and describing a set of coding operations. The union of these rate regions defines the maximum achievable rate region of our unified coding strategy. The achievable rates obtained based on this unified graphical approach to random coding encompass the best random coding achievable rates for all memoryless single-hop networks known to date, including broadcast, multiple access, interference, and cognitive radio channels, as well as new results for topologies not previously studied, as we illustrate with several examples.

An uplink system with a single antenna transmitter and a single receiver with a large number of antennas is considered. We propose a single-shot noncoherent scheme which does not use the instantaneous channel state information (CSI), but rather only the knowledge of the channel statistics, a transmitter that modulates information only in the amplitude of the symbols, and a receiver which measures only the average received energy across the antennas. This system model is motivated by the simplicity of the circuit design and the energy efficiency it entails for both the transmitter and the receiver. We propose constellation designs which are asymptotically optimal with respect to symbol error rate (SER) with an increasing number of antennas, for any finite signal-to-noise power ratio (SNR), under different assumptions on the availability of CSI statistics. We describe in detail the case when there is a bounded uncertainty on the moments of the fading distribution. We present the numerical results on the SER performance achieved by these designs and find that they outperform the existing amplitude-modulation-based noncoherent scheme of amplitude shift keying (ASK). They also achieve a smaller peak-to-average power ratio (PAPR) for scenarios with a low SNR or a large line-of-sight (LOS) component.

We consider one single-antenna transmitter communicating over a block-fading channel with a receiver that has a large number of antennas. We analyze coherent schemes with training overhead and noncoherent schemes with no training overhead. The latter systems only know the large scale fading statistics and the additive Gaussian noise power. In contrast to prior work on capacity characterizations of such systems, our approach is based on comparing error exponents with an increasing number of receive antennas. We provide an analytical lower bound on the error exponent for both coherent and noncoherent systems, and describe it explicitly for the case of a communication system with PSK constellations. Based on these analytic expressions, we show that noncoherent schemes can significantly outperform coherent schemes in channels with a strong line of sight component, low SNR or a short coherence time. We present numerical comparisons of our analytical BER performance bounds with Monte Carlo simulations for typical PSK constellations, system sizes and fading/noise statistics.

We consider one single antenna transmitter communicating with a receiver with a large number of antennas. Motivated by the optimal noncoherent detector in a Rayleigh fading channel, we propose a noncoherent energy-based communication scheme that does not require knowledge of instantaneous CSI (channel state information) at either the transmitter or the receiver; it uses only the statistics of the channel and noise. We explore the impact of coding to reduce the number of antennas needed for this system to achieve a given performance target. In particular, random coding error exponents for this system are used to determine tradeoff curves between the number of antennas and the blocklengths associated with a guaranteed performance target. However, since random codes have exponentially increasing decoding complexity with increasing blocklength, we also consider a simplified codebook design that has significantly lower encoding and decoding complexity. Simulations suggest that for small blocklengths, the performance of this simplified codebook is competitive with random coding constructions.

We propose a class of Generalized Two-Ray (GTR) fading channels that consists of two line of sight (LOS) components with random phase and a diffuse component. Observing that the GTR fading model can be expressed in terms of the underlying Rician distribution, we derive a closed-form expression for the moment generating function (MGF) of the signal-to-noise ratio (SNR) of this model. We then employ this approach to compute the ergodic capacity with receiver side information. The impact of the underlying phase difference between the LOS components on the average SNR of the signal received is also illustrated.

We investigate the degrees of freedom (DoF) for the two-user multiple-input multiple-output interference channel (MIMO IC) with parallel multicasting channels. Specifically, in addition to the MIMO IC, each transmitter is also connected to both receivers via an out-of-band multicast channel. Our main contribution lies in the characterization of the optimal sum DoF when the channel state information (CSI) on the MIMO IC is available to the transmitters with some delay (delayed CSIT). We show that jointly coding over the parallel multicast channels can achieve higher DoF than channel aggregation does. Furthermore, as long as the rate of the multicast channels is above a certain threshold, delayed CSIT is enough to achieve the same DoF performance as with instantaneous CSIT.

This paper is concerned with jointly recovering n node-variables {x1,..., xn} from a collection of pairwise difference measurements. Specifically, several noisy measurements of xi- xjare acquired. This is represented by a graph with an edge set ε such that xi- xjis observed only if (i, j) ∈ ε. To accommodate the noisy nature of data acquisition in a general way, we model the measurements by a set of channels with given input/output transition measures. Using information-theoretic tools applied to the channel decoding problem, we develop a unified framework to characterize a sufficient and a necessary condition for exact information recovery, which accommodates general graph structures, alphabet sizes, and channel transition measures. In particular, we isolate and highlight a family of minimum distance measures underlying the channel transition probabilities, which plays a central role in determining the recovery limits. For a broad class of homogeneous graphs, the recovery conditions we derive are tight up to some explicit constant, which depend only on the graph sparsity irrespective of other second-order graph metrics like the spectral gap.

A single-input multiple-output (SIMO) multiple access channel with a large number of uncoded non-cooperating single antenna transmitters and joint processing at a finite precision multi-antenna receiver is considered. We fix the number of receiver antennas per transmitter and investigate the effects of receiver quantization on the recovery of the transmitted signals in the asymptotic limit of a large number of transmitters. Our results suggest that a very fine quantization resolution at the receiver antennas is not necessary; even a modest increase in the number of bits of quantization (with the number of transmitting users) is sufficient to guarantee asymptotic reliability.

This paper studies noncoherent wideband systems with a single antenna transmitter and a multiple antenna receiver with many elements, under signaling with peak-to-average power ratio constraints. The analysis considers the scaling behavior of capacity and achievable rates by letting both the number of antennas and the bandwidth go to infinity jointly. In contrast to prior work on wideband single input single output (SISO) channels without a-priori channel state information, it is shown that a sufficiently large number of receive antennas can make up for the vanishingly small SNR at each antenna. In particular, it is shown that when bandwidth grows sufficiently slowly with the number of antennas, the capacity scaling with an increasing number of receive antennas is the same as the optimal coherent capacity scaling. If the bandwidth grows faster than a certain threshold, however, the additional bandwidth does not help because a finite transmit power is spread over an excessively large bandwidth.

The minimal sampling frequency required to achieve the rate-distortion function of a Gaussian stationary process is analyzed. Although the Nyquist rate is the minimal sampling frequency that allows perfect reconstruction of a bandlimited signal from its samples, relaxing perfect reconstruction to a prescribed distortion may allow a lower sampling frequency to achieve the optimal rate-distortion trade-off. We consider a combined sampling and source coding problem in which an analog Gaussian source is reconstructed from its rate-limited sub-Nyquist samples. We show that each point on the distortion-rate curve of the source corresponds to a sampling frequency fDRsmaller than the Nyquist rate, such that this point can be achieved by sampling at frequency fDRor above. This can be seen as an extension of the sampling theorem in the sense that it describes the minimal amount of excess distortion in the reconstruction due to lossy compression of the samples, and provides the minimal sampling frequency required in order to achieve that distortion.

Wireless technology has enormous potential to change the way we live, work, and play. Future wireless networks will support Gigabit per second multimedia communication between people and devices with high reliability and uniform coverage indoors and out. Software will create a virtual wireless network cloud, enabling resource management, seamless connectivity, and roaming across heterogeneous access networks, including WiFi and cellular systems. Wireless technology will also enable smart and energy-efficient homes and buildings, automated highways and skyways, and in-body networks for analysis and treatment of medical conditions. The shortage of spectrum will be alleviated by advances in cognitive radios, and breakthrough energy-efficiency algorithms and hardware will be employed to make wireless systems "green". There are many technical challenges that must be overcome in order to make this vision a reality. This talk will describe what the wireless future might look like and some of the innovations and breakthroughs that are required to realize this vision.

Statistical inference and information processing of high-dimensional data often require an efficient and accurate estimation of their second-order statistics. With rapidly changing data, limited processing power and storage at the acquisition devices, it is desirable to extract the covariance structure from a single pass over the data and a small number of stored measurements. In this paper, we explore a quadratic (or rank-one) measurement model which imposes minimal memory requirements and low computational complexity during the sampling process, and is shown to be optimal in preserving various low-dimensional covariance structures. Specifically, four popular structural assumptions of covariance matrices, namely, low rank, Toeplitz low rank, sparsity, jointly rank-one and sparse structure, are investigated, while recovery is achieved via convex relaxation paradigms for the respective structure. The proposed quadratic sampling framework has a variety of potential applications, including streaming data processing, high-frequency wireless communication, phase space tomography and phase retrieval in optics, and noncoherent subspace detection. Our method admits universally accurate covariance estimation in the absence of noise, as soon as the number of measurements exceeds the information theoretic limits. We also demonstrate the robustness of this approach against noise and imperfect structural assumptions. Our analysis is established upon a novel notion called the mixed-norm restricted isometry property (RIP-ℓ2/ℓ1), as well as the conventional RIP-ℓ2/ℓ2for near-isotropic and bounded measurements. In addition, our results improve upon the best-known phase retrieval (including both dense and sparse signals) guarantees using PhaseLift with a significantly simpler approach.

The performance analysis of random vector channels, particularly multiple-input-multiple-output (MIMO) channels, has largely been established in the asymptotic regime of large channel dimensions, due to the analytical intractability of characterizing the exact distribution of the objective performance metrics. This paper exposes a new nonasymptotic framework that allows the characterization of many canonical MIMO system performance metrics to within a narrow interval under finite channel dimensionality, provided that these metrics can be expressed as a separable function of the singular values of the matrix. The effectiveness of our framework is illustrated through two canonical examples. In particular, we characterize the mutual information and power offset of random MIMO channels, as well as the minimum mean squared estimation error of MIMO channel inputs from the channel outputs. Our results lead to simple, informative, and reasonably accurate control of various performance metrics in the finite-dimensional regime, as corroborated by the numerical simulations. Our analysis framework is established via the concentration of spectral measure phenomenon for random matrices uncovered by Guionnet and Zeitouni, which arises in a variety of random matrix ensembles irrespective of the precise distributions of the matrix entries.

A single-input multiple-output multiple access channel, with a large number of uncoded noncooperating single-antenna transmitters and joint processing at a multiantenna receiver is considered. The minimum number of receiver antennas per transmitter that is needed for perfect recovery of the transmitted signals with overwhelming probability is investigated. It is shown that in the limit of a large number of transmitters, and in a rich scattering environment, the per-transmitter number of receiver antennas can be arbitrarily small, not only with the optimal maximum likelihood decoding rule, but also with much lower complexity decoders. Comparison with the ergodic capacity of the channel in the limit of a large number of transmitters suggests that uncoded transmissions achieve the Shannon-theoretic scaling behavior of the minimum per-transmitter number of receiver antennas. Thus, the diversity of a large system not only makes the performance metrics for some coded systems similar to that of uncoded systems, but also allows efficient decoders to realize close to the optimal performance of maximum likelihood decoding.

We investigate the dynamic behavior of the stationary random process defined by a central complex Wishart matrix W(t) as it varies along a certain dimension t. We characterize the second-order joint cumulative distribution function (cdf) of the largest eigenvalue, and the second-order joint cdf of the smallest eigenvalue of this matrix. We show that both cdfs can be expressed in exact closed-form in terms of a finite number of well-known special functions in the context of communication theory. As a direct application, we investigate the dynamic behavior of the parallel channels associated with multiple-input multiple-output (MIMO) systems in the presence of Rayleigh fading. Studying the complex random matrix that defines the MIMO channel, we characterize the second-order joint cdf of the signal-to-noise ratio (SNR) for the best and worst channels. We use these results to study the rate of change of MIMO parallel channels, using different performance metrics. For a given value of the MIMO channel correlation coefficient, we observe how the SNR associated with the best parallel channel changes slower than the SNR of the worst channel. This different dynamic behavior is much more appreciable when the number of transmit (NT) and receive (NR) antennas is similar. However, as NT is increased while keeping NR fixed, we see how the best and worst channels tend to have a similar rate of change.

We study the diversity-multiplexing tradeoff (DMT) for the slow fading interference channel with a relay (ICR). We derive four inner bounds on the DMT region: the first is based on the compress-and-forward (CF) relaying scheme, the second is based on the decode-and-forward (DF) relaying scheme, and the last two bounds are based on the half-duplex (HD) and full-duplex (FD) amplify-and-forward (AF) schemes. For the CF and DF schemes, we find conditions on the channel parameters and the multiplexing gains, under which the corresponding inner bound achieves the optimal DMT region. We also identify the cases in which the DMT region of the ICR corresponds to that of two parallel slow fading relay channels, implying that interference does not decrease the DMT for each pair, and that a single relay can be DMT-optimal for two pairs simultaneously. For the HD-AF scheme, we derive conditions on the channel coefficients under which the proposed scheme achieves the optimal DMT for the AF-based relay channel. Finally, we identify the conditions under which adding a relay strictly enlarges the DMT region relative to the interference channel without a relay.

We analyze the level crossing rate and the average fade duration of amplify and forward multihop relay networks. We first calculate exact closed-form expressions for these statistics when the individual links are affected by log-normal fading with arbitrary autocorrelation. Based on these expressions, we formulate a log-normal approximation to the product of N Nakagami-m independent random processes. In particular, through a proper matching of the mean, variance and the autocorrelation function, we show that the product of N Nakagami-m stochastic processes can be closely approximated by a single log-normal process. This allows us to accurately approximate the crossing statistics for the cascaded Nakagami-m fading channel in closed-form. Using this analytical framework we characterize the dynamics of the equivalent multihop channel gain for different correlation models, and study the influence of the number of hops and the relay mobility in these second order statistics.

We present schemes for acquiring the null space of the interference channel between a User Equipment (UE) and an interfering Base Station Group (BSG) in Cooperative Multi-point cellular networks, whose only required network information is the interference levels at the UE. Specifically, the interfering BSG transmits a sequence of learning signals which inflicts interference on a UE served by a neighboring BSG. The UE treats interference as noise, measures its overall interference plus noise power, and feeds this value back to its serving BSG. Then, the latter distributes this information to the interfering BSG, from which it learns the null space of the interfering channel. We also present a null space tracking algorithm, whose performance includes an inherent tradeoff between the accuracy of the null space learning and the inflicted interference during learning, and characterize analytically and via simulations its performance under channel variations and noisy measurements. The proposed algorithms do not affect the transmission protocol between the UE and the serving BSG, do not add any signaling to the control channel between them, and do not require any protocol changes from the UE side.

We analyze a class of generalized two-ray (GTR) fading channels that consist of two line-of-sight (LOS) components with random phase plus a diffuse component. We derive a closed-form expression for the moment-generating function of the signal-to-noise ratio (SNR) for this model, which greatly simplifies its analysis. This expression arises from the observation that the GTR fading model can be expressed in terms of a conditional underlying Rician distribution. We illustrate the approach to derive simple expressions for statistics and performance metrics of interest, such as the amount of fading, the level crossing rate, the symbol error rate, and the ergodic capacity in GTR fading channels. We also show that the effect of considering a more general distribution for the phase difference between the LOS components has an impact on the average SNR.

This paper considers the rainfall effect on the capacities and achievable rates of millimeter-wave (mmW) multiple-input multiple-output (MIMO) systems. We first develop a new channel model for point-to-point mmW MIMO systems to characterize the rainfall effect. This rain propagation model is derived based on stochastic properties of signal propagation in a general random scattering medium. Under this model, we evaluate the channel capacity of the mmW MIMO system at various rain rates and show that rainfall does not always have a negative impact on the system performance, provided that accurate instantaneous channel state information (CSI) is available at both the transmitter and receiver. We also show that a transmit strategy of statistical water-filling (SWF) allows the mmW MIMO system to have near-optimal performance.

An uplink system with a single antenna transmitter and a single receiver with a large number of antennas is considered. For this system we propose an average energy-detection-based one-shot noncoherent communication scheme which does not use the instantaneous channel state information at either the transmitter or the receiver. We provide a constellation design that is asymptotically optimal in terms of achievable error exponent (in the number of receiver antennas) with an increasing constellation size. We also present numerical results on how this design performs in non-asymptotic regimes. Since the channel statistics may not be precisely known, we present a robust constellation design scheme which takes into account possible uncertainty in the large scale statistics and compare numerically its performance with the constellation design assuming perfect knowledge of channel and noise statistics. In terms of achievable symbol error rates, the robust constellation design is shown to perform almost as well as the scheme designed with perfectly known statistics despite mismatch in the channel statistics.

We propose and evaluate a new distributed algorithm for transmit power control (TPC) in wireless networks. We cast the TPC problem as a dynamic program which captures a fundamental tradeoff between transmit power and delay, and we use its solution to inform our design. The resulting algorithm is reminiscent of existing TPC approaches which seek to have each link maintain a constant signal-to-interference-plus-noise ratio (SINR), but with a key difference: a queue-dependent backoff threshold which allows links to temporarily stop transmitting when the interference grows too large. In high interference scenarios, this difference allows our algorithm to automatically induce a network behavior similar to time-division multiple access (TDMA), without any explicit cross-link coordination. As a result of this behavior, we demonstrate that our algorithm can provide substantial throughput improvements over previous schemes.

This paper explores covariance estimation from energy measurements that are collected via a quadratic form of measurement vectors. A popular structural model is considered where the covariance matrices possess low-rank and sparse structures simultaneously. We investigate a weighted convex relaxation algorithm tailored for this joint structure, which guarantees exact and universal recovery from a small number of measurements. The algorithm is also robust against noise and imperfect structural assumptions. In particular, when the non-zero entries of the covariance matrix exhibit power-law decay, our algorithm admits exact recovery as soon as the number of measurements exceeds the theoretic limit. Our method is related to sparse phase retrieval: the analysis framework herein recovers and strengthens the best-known performance guarantees by extending them to approximately sparse and noisy scenarios as well as a broader class of measurement vectors, and our results are derived using much simpler analysis methods.

We explore a fundamental problem of super-resolving a signal of interest from a few measurements of its low-pass magnitudes. We propose a 2-stage tractable algorithm that, in the absence of noise, admits perfect super-resolution of an r-sparse signal from 2r2-2r + 2 low-pass magnitude measurements. The spike locations of the signal can assume any value over a continuous disk, without increasing the required sample size. The proposed algorithm first employs a conventional super-resolution algorithm (e.g. the matrix pencil approach) to recover unlabeled sets of signal correlation coefficients, and then applies a simple sorting algorithm to disentangle and retrieve the true parameters in a deterministic manner. Our approach can be adapted to multi-dimensional spike models and random Fourier sampling by replacing its first step with other harmonic retrieval algorithms.

Cooperative Multi-Point (CoMP) has emerged as a new paradigm to improve both average cell and cell edge throughput in cellular networks. However, the performance is significantly degraded due to Out-of-Group Interference (OGI). One way to mitigate OGI is to restrict the interfering signal to lie inside the null space of the unintended receiver. Yet, accurately tracking this null space is a challenge in time-varying channels. In this work, we address the effect of null space variations on the OGI mitigation. A measure for accuracy of null space estimates is proposed and bounds are derived on the residual average worst-case interference. We define the Null Space Update Rate as the inverse of the Null Space Coherence Time; i.e., the time it takes a null space estimate to become outdated relative to an interference threshold on the unintended receiver. In the case of Rayleigh fading channels, we derive a bound on the Null Space Coherence Time in closed form, and compare the performance of a given null space tracking algorithm against this bound. Both Monte Carlo simulations and the analytical bounds show that the worst-case interference levels are sensitive to null space variations, independent of the null space learning algorithm employed.

This paper considers the problem of recovering the covariance matrix of a stream of high-dimensional data instances from a minimal number of stored measurements. We develop a quadratic random sampling method based on rank-one measurements of the covariance matrix, which serves as an efficient covariance sketching scheme for processing data streams. This also allows modeling of phaseless measurements that arise in high-frequency wireless communication and signal processing applications. We propose to recover the covariance matrix from the above quadratic measurements via convex relaxation with respect to the presumed parsimonious covariance structure. We show that in the absence of noise, exact and universal recovery of low-rank or Toeplitz low-rank covariance matrices can be achieved as soon as the number of stored measurements exceeds the fundamental sampling limit. The convex programs are also robust to noise and imperfect structural assumptions. Our analysis is established upon a novel notion called the mixed-norm restricted isometry property (RIP-ℓ2/ℓ1), as well as the conventional RIP-ℓ2/ℓ2for near-isotropic and bounded measurements. Our results improve upon best-known phase retrieval performance guarantees with a significantly simpler approach. Numerical results are provided to demonstrate the practical applicability of our technique.

A variety of information processing tasks in practice involve recovering n objects from single-shot graph-based measurements, particularly those taken over the edges of some measurement graph G. This paper concerns the situation where each object takes value over a group of M different values, and where one is interested to recover all these values based on observations of certain pairwise relations over G. The imperfection of measurements presents two major challenges for information recovery: 1) inaccuracy: a (dominant) portion 1 - p of measurements are corrupted; 2) incompleteness: a significant fraction of pairs are unobservable, i.e. G can be highly sparse. Under a natural random outlier model, we characterize the minimax recovery rate, that is, the critical threshold of non-corruption rate p below which exact information recovery is infeasible. This accommodates a very general class of pairwise relations. For various homogeneous random graph models (e.g. Erdös-Rényi random graphs, random geometric graphs, small world graphs), the minimax recovery rate depends almost exclusively on the edge sparsity of the measurement graph G irrespective of other graphical metrics. This fundamental limit decays with the group size M at a square root rate before entering a connectivity-limited regime. Under the Erdös-Rényi random graph, a tractable combinatorial algorithm is proposed to approach the limit for large M (M = nΩ(1)), while order-optimal recovery is enabled by semidefinite programs in the small M regime.

We consider communication over heterogeneous parallel channels, where a transmitter is connected to two users via two parallel channels: (1) a MISO broadcast channel (BC), and (2) a noiseless rate-limited multicast channel. We characterize the optimal degrees of freedom (DoF) region of this setting when the transmitter has delayed channel state information (CSIT) regarding the MISO BC. Our results show that jointly coding over the two channels can strictly outperform simple channel aggregation (or channel separation) and can even achieve the same performance as with instantaneous CSIT when the CSIT on the MISO BC is completely stale; this occurs when the multicast rate of the second channel is larger than a certain threshold, in the DoF sense. The main idea to achieve full DoF with completely stale CSIT is to send information over the MISO BC at a rate above its capacity and use the second channel to send additional side information to allow for reliable decoding at both receivers.

An expression for the distortion rate function of cyclostationary Gaussian processes is derived. This expression is given by water-filling over the eigenvalues of a spectral density matrix associated with the source. For processes in continuous time, the distortion rate function is given in terms of a limiting function of the eigenvalues of this matrix. A lower bound on the distortion-rate function, which does not involve eigenvalue computation, is also derived. This distortion rate function is evaluated for the processes obtained by modulating a Gaussian stationary narrowband pulse by a deterministic sine wave, and is shown to be equal to the distortion rate function of the stationary narrowband pulse.

An uplink system with a fixed number of single antenna transmitters and a single receiver with a large number of antennas is considered. For this system we propose an energy-based noncoherent communication scheme that does not use instantaneous channel state information at either the transmitter or the receiver: only the channel and noise statistics are used.We show that, in terms of the scaling law of achievable symmetric rates for two users, our scheme's performance is no different from that achievable with perfect CSI (channel state information) at the transmitters and the receiver. We also provide a simple constellation design using the design criterion of minimum distance and present numerical results on how these designs perform in non-asymptotic regimes with typical channel and noise statistics.

The optimal strategy for dynamic joint source-channel coding with feedback was recently shown to be a simple mapping between the source symbols and channel inputs, where the mapping only depends on the decoder's posterior belief about the source. In this work, we derive the optimal joint source-channel coding strategies for two specific channels - binary erasure channels and Z-channels. It is found that the mappings required for the optimal strategies and the way they are used vary significantly with the channel cost of transmission.

Directed information is a measure that can be used to infer connectivity between neurons using their recorded time series. In this paper we develop a method of finding the directed information of a particular neural topology analytically. We assume a leaky integrate-and-fire (LIF) neuron model, and calculate the directed information between the spike train of an input neuron to the LIF model and the corresponding spike train generated by the LIF model based on this input. We show that an action potential in the LIF model causes a conditional independence of the activity before and after it, and we capture this conditional independence via a Markov model. We then use this model to find the directed information analytically. Additionally, we show how the stationary distribution and transition probabilities of the Markov model can be found using parameters of the LIF neuron. This modeling technique can thus be used to obtain the value of the directed information in a particular neuronal topology.

The capacity of the multiantenna Gaussian cognitive interference channel is studied. The cognitive interference channel is a variation of the classical two-users interference channel in which one of the transmitters, the cognitive transmitter, is also provided with the message of the second transmitter, the primary transmitter. We study the capacity of the multiple-input multiple-output Gaussian model, that is the channel in which the inputs are vectors and the outputs are obtained as linear combinations of the channel inputs plus an additive complex Gaussian noise. This channel models a wireless scenario in which transmitters and receivers have multiple antennas. For this channel, we derive capacity to within an additive gap, that is we show that inner and outer bounds to capacity lie to within a constant distance of each other. The gap between the inner and outer bounds depends on the number of antennas at the cognitive receiver and both bounds can be easily evaluated by considering jointly Gaussian inputs. We also derive capacity to within a constant multiplicative factor of two, that is we show that the ratio between inner and outer bound is at most two. The additive gap well-characterizes the capacity at high SNR, while the multiplicative gap is useful at low SNR. We also derive the exact capacity for a subset of the "strong interference" regime: in this subset, the primary transmitter can decode the cognitive message without loss of optimality. This new capacity result extends and generalizes previously known capacity results, in particular, the capacity in the "very strong interference" and the "primary decodes cognitive" regimes.

The impact of cognitive radio techniques on the energy efficiency of a downlink cellular system in which multiple relays assist the transmission of the base station toward multiple receivers is studied. In particular, the fundamental tradeoff between the power consumption at the base station and the level of cooperation at the relay nodes is investigated. By increasing its transmit power, the base station can distribute the same message to multiple relays. In turn, the common knowledge at the relays enables cooperation, which results in a reduction in the power consumption due to interference management and coherent combining gains. This implies that the overall power efficiency can potentially be improved by an increase in the power consumption at the base station. We employ an information-theoretical analysis of the attainable power efficiency based on the chain graph representation of achievable schemes. This novel theoretical tool uses a graphical Markov model to represent coding operations and allows for the automatic derivation of achievable rate regions for general networks. This approach provides an effective tool to analyze the relationship between the energy consumption at the base station and power savings provided by relay cooperation through the use of transmission strategies such as superposition coding, interference decoding and rate-splitting. We present numerical evaluations for the scenario in which two relay nodes aid the communication between the base station and three receivers. These evaluations show that cooperative strategies at the relays provide clear advantages as compared to the non-cooperative scenario for varying channel conditions and target rates.

This paper investigates the effect of sub-Nyquist sampling upon the capacity of an analog channel. The channel is assumed to be a linear time-invariant Gaussian channel, where perfect channel knowledge is available at both the transmitter and the receiver. We consider a general class of right-invertible time-preserving sampling methods which includes irregular nonuniform sampling, and characterize in closed form the channel capacity achievable by this class of sampling methods, under a sampling rate and power constraint. Our results indicate that the optimal sampling structures extract out the set of frequencies that exhibits the highest signal-to-noise ratio among all spectral sets of measure equal to the sampling rate. This can be attained through filterbank sampling with uniform sampling grid employed at each branch with possibly different rates, or through a single branch of modulation and filtering followed by uniform sampling. These results reveal that for a large class of channels, employing irregular nonuniform sampling sets, while are typically complicated to realize in practice, does not provide capacity gain over uniform sampling sets with appropriate preprocessing. Our findings demonstrate that aliasing or scrambling of spectral components does not provide capacity gain in this scenario, which is in contrast to the benefits obtained from random mixing in spectrum-blind compressive sampling schemes.

The interference channel with a cognitive relay (IFC-CR) consists of the classical IFC with two independent source-destination pairs whose communication are aided by an additional node, referred to as the CR, that has a priori knowledge of both sources' messages. This a priori message knowledge is termed cognition and idealizes the relay learning the messages of the two sources from their transmissions over a wireless channel. This paper presents improved outer and inner bounds on the capacity region of the general memoryless IFC-CR that are shown to be tight for certain classes of channels. The new outer bound follows from arguments originally devised for broadcast channels, among which Sato's observation that the capacity region of channels with noncooperative receivers only depends on conditional marginal distributions of the channel output, not on their conditional joint distribution. A simplified expression for the inner bound is derived, which contains all previously proposed coding schemes. The new inner and outer bounds coincide for a class of channels satisfying some strong interference condition, i.e., for these channels there is no loss in optimality if both destinations decode both messages. This result parallels analogous results for the classical interference channel and for the cognitive interference channel and is the first known capacity result for the general IFC-CR. Numerical evaluations of the proposed inner and outer bounds are presented for the additive white Gaussian noise case.

We propose a learning technique for MIMO communication systems to perform spatial division multiple access with minimal cooperation between users. In the proposed technique, each user (in a two-user receiver-transmitter pair) learns the null space of the interference channel to the other user by transmitting a learning signal and observing an affine function of the other user's interference plus noise power. The only requirement is that each system broadcasts, through a low-rate control channel, a periodic beacon that is a function of its noise plus interference power, which in practice is typically known by each system's receiver and transmitter. Thus, the learning can be made by the two users' transmitters without affecting the communication protocol between each user's receiver and transmitter. The proposed learning scheme is particularly attractive for underlay cognitive radio, where only the secondary user (SU), which must not interfere with the primary user (PU), has to learn the null space. In this case, the PU can broadcast the scheme's beacon without being aware of the SU. Furthermore, if the PU uses a power control mechanism which maintains a constant signal to interference plus noise ratio, the SU can learn the null space even without a beacon, i.e., without any cooperation with the PU.

We study transmit power minimization in the two-user Z Interference Channel (ZIC). When the interference link gain is strong, the capacity of the ZIC has been fully characterized. For this strong interference regime, we derive the closed-form solution of the minimum required transmit power to achieve a given rate pair, and show that the resulting power allocation between the two users is not necessarily unique. When the interference link gain is weak, the capacity of the ZIC is still an open problem to date. For this weak interference regime, we develop an inner and outer bound for the required transmit power to achieve a given rate pair, and characterize the constant power ratio relation between the two bounds. In contrast to the strong interference case, rate splitting is necessary for power minimization in this regime. The optimal power-minimizing rate splitting solution is then derived, and performance in terms of total transmit power required for a given rate pair is analyzed.

We analyze the level crossing rate and the average fade duration of multihop amplify-and-forward relay networks. We obtain exact closed-form expressions for these statistics when the individual links are affected by log-normal fading with arbitrary autocorrelation. Using this analytical framework we characterize the dynamics of the equivalent multihop channel gain for different correlation models, and study the influence of sampling time, the number of hops and the relay mobility in the investigated scenarios.

Cooperative Multi-Point is a technology for improved spectrum utilization where a group of neighboring base stations coordinate their transmissions. However, the performance gain is severely degraded due to out-of-group interference. We propose simple schemes for null space learning and tracking of the interference channel between a terminal and an interfering base station group, whose only required network information is the interference levels at the terminal. In the proposed schemes, the interfering base station group transmits a sequence of learning signals which inflict low interference on a terminal of a neighboring group. The schemes utilize the fact that each terminal normally measures its interference levels and feeds them back to its serving base stations. Then, the serving group distributes this information to the interfering group, from which it learns the null space of the interfering channel. The proposed algorithms do not affect the transmission protocol between the terminal and the serving base stations, and do not add any signaling to the control channel between them. Each terminal communicates only with its serving group and treats the learning signals of the interfering group as noise.

We propose and evaluate a novel coordinated resource allocation scheme in Time Division Duplex (TDD) systems where the downlink/uplink (DL/UL) resources are allocated dynamically for asymmetric traffic adaptation. To eliminate the cross-subframe co-channel interference (CCI), we first formulate the dynamic reconfiguration problem as the cooperative control that operates on disjoint cell clusters. With this setup, the DL/UL configurations are no longer determined with respect to an individual cell, but are chosen in form of the cluster-specific configuration patterns (CPs) with optimized performance metrics. Additionally, a novel CCI cancelation (CCIC) method, termed cross-subframe coordinated scheduling/beamforming (CCS/CCB) is incorporated in the proposed reconfiguration approach. By jointly designing and optimizing the beamforming vectors and the traffic scheduling, the residual intra-cluster CCI can be mitigated.

A downlink cellular system in which multiple relays assist the transmission of the base station is considered. Cooperation strategies based on superposition coding are derived for this network. Superposition coding is attained by sending each message to one or more relays while satisfying the rate constraints of the base station-to-relay links. The chain graph representation of achievable schemes is used to maximize the network throughput over the set of feasible transmission strategies based on superposition coding. Rate advantages as compared to the non-cooperative scenario are obtained under varying relay positions and available power at the base station and relay nodes.

This paper considers the capacity of sub-sampled analog channels when the sampler is designed to operate independent of the instantaneous channel realization, and investigates sampling methods that minimize the worst-case (minimax) sampled capacity loss due to channel-independent (universal) sampling design. Specifically, a compound multiband channel with unknown subband occupancy is considered, when perfect channel side information is available to both the receiver and the transmitter. We restrict our attention to a general class of periodic sub-Nyquist samplers, which subsumes as special cases sampling with modulation and filter banks. Our results demonstrate that under both Landau-rate and super-Landau-rate sampling, the minimax sampled capacity loss due to universal design depends only on the band sparsity ratio and the undersampling factor, modulo a residual term that vanishes at high signal-to-noise ratio. We quantify the capacity loss under sampling with periodic modulation and low-pass filters, when the Fourier coefficients of the modulation waveforms are randomly generated (called random sampling). Our results highlight the power of random sampling methods, which achieve minimax sampled capacity loss uniformly across all channel realizations and are thus optimal in a universal design sense.

We consider a multiple access channel with a large number of transmitters sending symbols from a constellation to the receiver of a multi-antenna base station. We investigate the joint decoding of the signals from all the users using a low complexity convex relaxation of the maximum likelihood decoder (constellation search). We show that, in a rich scattering environment, and in the asymptotic limit of a large number of transmitters, reliable communication is possible even without employing coding at the transmitters.

This paper considers real time joint source-channel coding of a Markov source over a discrete memoryless channel with noiseless feedback. The encoder incurs a cost which is minimized along with a real-time end-to-end distortion. The problem is mapped to a partially observable Markov decision problem and the corresponding optimality equations, in the form of dynamic programming equations, are derived. As a consequence of the dynamic programming formulation, basic structural properties of the optimal encoding and decoding strategies are established. In addition, the problem formulation and solution obtained for dynamic joint source-channel coding with noiseless feedback is shown to encompass a much broader class of problems including that of information acquisition and real time tracking.

The cognitive interference channel is a variation of the classical interference channel in which one of the transmitters, the cognitive transmitter, has full and a priori knowledge of the message of the other user, the primary user. This additional knowledge is termed cognition and idealizes the cognitive transmitter learning the messages of the primary user by overhearing its transmissions over a wireless channel. This paper studies the multiple-input multiple-output cognitive interference channel and derives inner and outer bounds for the capacity of this channel model as well as approximate characterizations of the capacity region. In particular, it is shown that capacity can be achieved to within an additive gap which depends on the number of antennas at the cognitive decoder and to within a constant multiplicative factor of two.

Directed information between two neural signals has previously been used to successfully determine if there is a synapse connecting one neuron to the other. However, there are situations in which the directed information method leads to false positives for detecting connections due to the influence of a third neuron. We propose a method that accounts for these cases using the delay-profile of the causally-conditioned entropy rate to find a measured delay range and its intersection with a connection-based delay range. Through simulations in NEURON, we show how this method outperforms connectivity inference based on directed information alone.

We study the diversity-multiplexing tradeoff (DMT) for the slow fading interference channel with a relay (ICR). We first derive an outer bound on the DMT based on the cut-set bound. We then derive two inner bounds on the DMT: One is based on the compress-and-forward relaying scheme and the other is based on the decode-and-forward relaying scheme. We find conditions on the channel parameters and the multiplexing gains under which the proposed inner bounds achieve the optimal DMT. We also identify cases in which the DMT of the ICR is the same as two parallel fading relay channels, implying that interference does not decrease the DMT for each pair, and that a single relay can be DMT-optimal for two pairs simultaneously. Lastly, we identify conditions under which adding a relay strictly improves the DMT relative to the interference channel without a relay.

We propose the new technique of physical-layer cryptography based on using a massive MIMO channel as a key between the sender and desired receiver, which need not be secret. The goal is for low-complexity encoding and decoding by the desired transmitter-receiver pair, whereas decoding by an eavesdropper is hard in terms of prohibitive complexity. The massive MIMO system has a channel gain matrix that is drawn i.i.d. according to a Gaussian distribution, subject to additive white Gaussian noise. The decoding complexity is analyzed by mapping the massive MIMO system to a lattice. We show that the eavesdropper's decoder for the MIMO system with M-PAM modulation is equivalent to solving standard lattice problems that are conjectured to be of exponential complexity for both classical and quantum computers. Hence, under the widely-held conjecture that standard lattice problems are of worst-case complexity, the proposed encryption scheme has security that exceeds that of the most common encryption methods used today such as RSA and Diffie-Hellman. Additionally, we show that this scheme could be used to securely communicate without a pre-shared secret key and little computational overhead. In particular, a standard parallel channel decomposition allows the desired transmitter-receiver pair to encode and decode transmissions over the MIMO channel based on the singular value decomposition of the channel, while decoding remains computationally hard for an eavesdropper with an independent channel gain matrix, even if it knows the channel gain matrix between the desired transmitter and receiver. Thus, the massive MIMO system provides for low-complexity encryption commensurate with the most sophisticated forms of application-layer encryption by exploiting the physical layer properties of the radio channel.

In multiple-input multiple-output (MIMO) systems the communication channel can be split into s-parallel single-input single-output eigenchannels. The channel gains associated with these eigenchannels depend on the magnitude of the eigenvalues of the complex random matrix that characterizes the MIMO channel. We present a general framework for the characterization of the dynamics of MIMO channels. In addition, we provide new analytical results for the distribution of the largest eigenvalue of two correlated Wishart matrices, which enable a direct evaluation of different system performance metrics such as the probability of two consecutive outages separated by a given time window, the level crossing rate and the average fade duration.

The capacity region of the interference channel with common messages is studied. This channel model is a variation of the classical two user interference channel modified such that each encoder has both a private message as well as a common message to be decoded at both receivers. Achievable rates for this channel model can be characterized by the classical Han-Kobayashi achievable rate region for the interference channel in which, at each encoder, the codeword embedding the private message is superimposed over the codeword for the common message. We show that the achievable rates for this region can be improved upon by rate-sharing, which consist of transmitting part of the private message into the common codeword. This improved region is shown to approach the capacity for a class of injective semi-deterministic channels. Moreover, we show that the Fourier Motzkin elimination of the Han-Kobayashi with rate-sharing contains less rate bounds than the one without rate-sharing. This approach provides an alternative proof of the simplification of the Han-Kobayashi originally shown by Chong et al. This result is particularly interesting as it shows that simplifications in the spirit of Chong et al. for general channels can be performed through rate-sharing and Fourier-Motzkin elimination. This approach can be easily implemented algorithmically and is relevant in the context of the automatic derivation of achievable rate regions.

Gene expression analysis is generally performed on heterogeneous tissue samples consisting of multiple cell types. Current methods developed to separate heterogeneous gene expression rely on prior knowledge of the cell-type composition and/or signatures--these are not available in most public datasets. We present a novel method to identify the cell-type composition, signatures and proportions per sample without need for a-priori information. The method was successfully tested on controlled and semi-controlled datasets and performed as accurately as current methods that do require additional information. As such, this method enables the analysis of cell-type specific gene expression using existing large pools of publically available microarray datasets.

We explore two fundamental questions at the intersection of sampling theory and information theory: how channel capacity is affected by sampling below the channel's Nyquist rate, and what sub-Nyquist sampling strategy should be employed to maximize capacity. In particular, we derive the capacity of sampled analog channels for three prevalent sampling strategies: sampling with filtering, sampling with filter banks, and sampling with modulation and filter banks. These sampling mechanisms subsume most nonuniform sampling techniques applied in practice. Our analyses illuminate interesting connections between undersampled channels and multiple-input multiple-output channels. The optimal sampling structures are shown to extract out the frequencies with the highest SNR from each aliased frequency set, while suppressing aliasing and out-of-band noise. We also highlight connections between undersampled channel capacity and minimum mean-squared error (MSE) estimation from sampled data. In particular, we show that the filters maximizing capacity and the ones minimizing MSE are equivalent under both filtering and filter-bank sampling strategies. These results demonstrate the effect upon channel capacity of sub-Nyquist sampling techniques, and characterize the tradeoff between information rate and sampling rate.

We study the capacity of indecomposable finite-state channels (IFSCs) with feedback. It is first shown that the capacity-achieving input distribution for IFSCs with feedback is independent of the initial channel state, even though the capacity depends on the worst-case channel state. In addition, it is shown that for a large class of IFSCs for which the channel state is a deterministic function of a finite number of the most recent channel inputs and outputs, the feedback capacity depends only on the best-case channel state. This result is obtained by a novel transmission strategy whereby feedback is used to synchronize the beginning of the codeword transmission to be at the best-case channel state.

Reliable transmission of a discrete memoryless source to multiple destinations over a relay network is considered. Motivated by sensor network applications, it is assumed that the relays and the destinations all have access to side information correlated with the underlying source signal. Joint source-channel cooperative transmission is studied in which the terminals in the network help the transmission of the source signal to the destinations by using their overheard signals, as in the classical channel cooperation scenario, as well as the available correlated side information. Decode-and-forward-based cooperative transmission is studied in a network of multiple relay terminals and two different achievability schemes are proposed: 1) a regular encoding and sliding-window decoding scheme without explicit source binning at the encoder; and 2) a semiregular encoding and backward decoding scheme with binning based on the side information statistics. It is shown that both of these schemes lead to the same source-channel code rate, which is shown to be the source-channel capacity in the case of 1) a physically degraded relay network with a single destination in which the side information signals are degraded in the same order as the channel; and 2) a relay network with multiple destinations, in which all the terminals want to reconstruct the source reliably, while at most one of them can act as a relay.

The multiuser communication channel, in which multiple users exchange information with the help of a relay terminal, termed the multiway relay channel (mRC), is introduced. In this model, multiple interfering clusters of users communicate simultaneously, such that the users within the same cluster wish to exchange messages among themselves, i.e., each user multicasts its message to all the other users in its own cluster. It is assumed that the users cannot receive each other's signals directly. Hence, the relay terminal in this model is the enabler of communication. In particular, restricted encoders are considered, such that the encoding function of each user depends only on its own message and the received signal is used only for decoding the messages of the other users in the cluster. Achievable rate regions and an outer bound are characterized for the Gaussian mRC, and their comparison is presented in terms of the exchange rate, the symmetric rate point in the capacity region in a symmetric Gaussian mRC scenario. It is shown that the compress-and-forward (CF) protocol achieves exchange rates within a constant bit offset of the optimal exchange rate, independent of the power constraints of the terminals in the network. A finite bit gap between the exchange rates achieved by the CF and the amplify-and-forward protocols is also shown. The two special cases of the mRC, the full data exchange model, in which every user wants to receive messages of all other users, and the pairwise data exchange model which consists of multiple two-way relay channels, are investigated in detail. In particular for the pairwise data exchange model, in addition to the proposed random coding-based achievable schemes, a nested lattice coding-based scheme is also presented and is shown to achieve exchange rates within a constant bit gap of the exchange capacity.

We study the discrete memoryless Z-interference channel where the transmitter of the pair that suffers from interference is cognitive. We first provide an outer bound on the capacity region of this channel. We then show that, when the channel of the transmitter–receiver pair that does not experience interference is deterministic and invertible, our proposed outer bound matches the best known inner bound. The obtained results imply that in the considered channel, superposition encoding at the noncognitive transmitter as well as Gel'fand–Pinsker encoding at the cognitive transmitter is needed in order to minimize the impact of interference. As a byproduct of the obtained capacity region, we obtain the capacity under the generalized Gel'fand–Pinsker setting where a transmitter–receiver pair communicates in the presence of interference noncausally known at the encoder.

We investigate the achievable error probability in communication over an AWGN discrete time memoryless channel with noiseless delayless rate-limited feedback. For the case where the feedback rate$R_{\scriptscriptstyle FB}$is lower than the data rate$R$transmitted over the forward channel, we show that the decay of the probability of error is at most exponential in blocklength, and obtain an upper bound for increase in the error exponent due to feedback. Furthermore, we show that the use of feedback in this case results in an error exponent that is at least$R_{\scriptscriptstyle FB}$higher than the error exponent in the absence of feedback. For the case where the feedback rate exceeds the forward rate ($R_{\scriptscriptstyle FB}\geq R$), we propose a simple iterative scheme that achieves a probability of error that decays doubly exponentially with the codeword blocklength$n$. More generally, for some positive integer$L$, we show that a$L$-th order exponential error decay is achievable if$R_{\scriptscriptstyle FB}\geq (L-1)R$. While the above results are proved under an average feedback rate constraint, we show that all the achievability results for$R_{\scriptscriptstyle FB}\geq R$hold in a more restrictive case where the feedback constraint is expressed in terms of the per-channel-use feedback rate. Our results show that the error exponent as a function of$R_{\scriptscriptstyle FB}$has a strong discontinuity at$R$, where it jumps from a finite value to infinity.

We present a reduced-dimension multiuser detector (RD-MUD) structure for synchronous systems that significantly decreases the number of required correlation branches at the receiver front end, while still achieving performance similar to that of the conventional matched-filter (MF) bank. RD-MUD exploits the fact that, in some wireless systems, the number of active users may be small relative to the total number of users in the system. Hence, the ideas of analog compressed sensing may be used to reduce the number of correlators. The correlating signals used by each correlator are chosen as an appropriate linear combination of the users' spreading waveforms. We derive the probability of symbol error when using two methods for recovery of active users and their transmitted symbols: the reduced-dimension decorrelating (RDD) detector, which combines subspace projection and thresholding to determine active users and sign detection for data recovery, and the reduced-dimension decision-feedback (RDDF) detector, which combines decision-feedback matching pursuit for active user detection and sign detection for data recovery. We derive probability of error bounds for both detectors, and show that the number of correlators needed to achieve a small probability of symbol error is on the order of the logarithm of the number of users in the system. The theoretical performance results are validated via numerical simulations.

We propose a feedback optimization framework to minimize the total energy consumption in point-to-point wireless communication links. The energy cost of both the forward link and the feedback link are taken into account. Given the energy consumption profile of both links, we minimize error probability subject to the total energy budget and a delay constraint. The proposed framework is based on a multi-phase feedback scheme in which a transmission, if decoded incorrectly, is followed by a retransmission with boosted energy. We use this framework to show that the gain of utilizing feedback is highly dependent on the energy consumption profile of the links and the total available energy. In particular, we identify scenarios in which the use of feedback significantly increases the energy efficiency, as well as scenarios where, surprisingly, the use of feedback is strictly suboptimal as compared to communication without feedback.

This paper proposes a blind technique that enables a MIMO cognitive radio Secondary User (SU) to transmit in the same band simultaneously with a Primary User (PU) by utilizing separate spatial dimensions than the PU. Specifically, the SU transmits in the null space of the interference channel to the PU. The SU learns this null space without burdening the PU with any knowledge or explicit cooperation with the SU. The only condition required is that during the learning period, the SU is allowed to inflict “non-harmful” interference to the PU. The SU measures a monotonic function of this interference in order to learn the null space. Specifically, during the learning interval, the SU learns the null space by iteratively modifying the spatial orientation of its transmitted signal and measures the effect of this modification on the monotonic function that it observes. We provide simulation results demonstrating that the algorithm converges rapidly and is robust to quantization noise and other sources of interference.

We propose a robust near maximum-likelihood (ML) decoding metric that is robust to channel estimation errors and is near optimal with respect to symbol error rate (SER). The solution involves an exhaustive search through all possible transmitted signal vectors; this search has exponential complexity, which is undesirable in practical systems. Hence, we also propose a robust sphere decoder to implement the decoding with substantially lower computational complexity. For a real 4 x 4 MIMO system with 256-QAM modulation and at SER of 10^{-3}, our proposed robust sphere decoder has a coding loss of only 0.5 dB while searching through 2360 nodes (or less) compared to a 65536 node search using the exact ML metric. This translates to up to 228 times fewer real multiplications and additions in the implementation. We derive analytical upper bounds on the pairwise codeword error rate and symbol error rate of our robust sphere decoder and validate these bounds via simulation.

How do we design an error correcting code and a corresponding decoding implementation to minimize not just the transmit power, but the sum of transmit and decoding power? Recent interest in this question has led to new fundamental results that show the traditional approach of designing the code and the decoder implementation in isolation can be suboptimal. However, joint design of codes and their corresponding decoder implementations can be hard simply because of the sheer number of possibilities for both, and the human effort often required in optimizing the decoder implementation for a given code. In this paper, we suggest taking a middle-path between analyzing theoretical models of decoding and building decoder implementations. Based on circuit simulations of power consumption of decoders for simple regular LDPC codes, we develop circuit models for the decoding power for larger and more complex (but still regular) LDPC codes. These models are then used to search for the best code and corresponding decoder (within a limited set) for a given communication distance and error probability.

Blind Null Space Learning [1] has recently been proposed for fast and accurate learning of the null-space associated with the channel matrix between a secondary transmitter and a primary receiver. In this paper we propose a channel tracking enhancement of the algorithm, namely the Blind Null Space Tracking algorithm, that allows transmission of information to the Secondary Receiver while simultaneously learning the null-space of the time-varying target channel. Specifically, the enhanced algorithm initially performs a sweep in order to acquire the null space. Then, it performs modified Jacobi rotations such that the induced interference is kept lower than a given threshold PThwith probability p while information is transmitted to the secondary receiver simultaneously. The learning process is performed based on sensing whether the transmit power of the primary user has increased or decreased between adaptations. We present simulation results indicating that the proposed approach has strictly better performance over the Blind Null Space Learning algorithm for channels with independent Rayleigh fading at a low Doppler frequency.

The energy consumption of different cellular network architectures are analyzed. In particular, a comparison of the transmit energy consumption between a single large cell with multiple co-located antennas, multiple micro-cells with a single antenna at each cell, and a large cell with a distributed antenna system are presented. The influence of different system parameters such as cell size, spatial distribution of the users, and the availability of channel state information (CSI) toward the total required transmit energy are analyzed. It is shown that the current macro-cellular architecture with co-located antennas has poor energy efficiency in the absence of CSI, but has better energy efficiency than small cells when perfect CSI is available. Moreover, macro-cells with distributed antennas have the best energy efficiency of all three architectures under perfect CSI. These results shed light on design guidelines to improve the energy efficiency of cellular network architectures.

This paper proposes a blind technique for MIMO cognitive radio Secondary Users (SU) to transmit in the same band simultaneously with a Primary User (PU) under a maximum interference constraint. In the proposed technique, the SU is able to meet the interference constraint of the PU without explicitly estimating the interference channel matrix to the PU and without burdening the PU with any interaction with the SU. The only condition required of the PU is that for a short time interval it uses a power control scheme such that its transmitted power is a monotonic function of the interference inflicted by the SU. During this time interval, the SU iteratively modifies the spatial orientation of its transmitted signal and measures the effect of this modification on the PU's total transmit power. The entire process is based on energy measurements which is very desirable from an implementation point of view. The scheme can also be used as a multiple access technique in networks where users have equal priority, however, active users are protected from interference by new users.

We propose a learning technique for MIMO secondary users (SU) to spatially coexist with Primary Users (PU). By learning the null space of the interference channel to the PU, the SU can utilize idle degrees of freedom that otherwise would be unused by the PU. This learning process does not require any handshake or explicit information exchange between the PU and the SU. The only requirement is that the PU broadcasts a periodic beacon that is a function of its noise plus interference power, through a low rate control channel. The learning process is based on energy measurements, independent of the transmission schemes of both the PU and SU, i.e. independent of their modulation, coding etc. The proposed learning technique also provides a novel spatial division multiple access mechanism for equal-priority MIMO users sharing a common channel that highly increases the spectrum utilization compared to time-or frequency-base multiple access.

We explore several reduced-dimension multiuser detection (RD-MUD) structures that significantly decrease the number of required correlation branches at the receiver front-end, while still achieving performance similar to that of the conventional matched-filter (MF) bank. RD-MUD exploits the fact that the number of active users is typically small relative to the total number of users in the system and relies on ideas of analog compressed sensing to reduce the number of correlators. We first develop a general framework for both linear and nonlinear RD-MUD structures. We then present theoretical performance analysis for two specific detectors: the linear reduced-dimension decorrelating (RDD) detector, which combines subspace projection and thresholding to determine active users and sign detection for data recovery, and the nonlinear reduced-dimension decision-feedback (RDDF) detector, which combines decision-feedback orthogonal matching pursuit for active user detection and sign detection for data recovery. The theoretical performance results for both detectors are validated via numerical simulations.

This paper develops the fundamental capacity limits of a sampled analog channel under a sub-Nyquist sampling rate constraint. In particular, we derive the capacity of sampled analog channels over a general class of time-preserving sampling methods including irregular nonuniform sampling. Our results indicate that the optimal sampling structures extract out the set of frequencies that exhibits the highest SNR among all spectral sets of support size equal to the sampling rate. The capacity under sub-Nyquist sampling can be attained through filter-bank sampling, or through a single branch of modulation and filtering followed by uniform sampling. The capacity under sub-Nyquist sampling is a monotone function of the sampling rate. These results indicate that the optimal sampling schemes suppress aliasing, and that employing irregular nonuniform sampling does not provide capacity gain over uniform sampling sets with appropriate preprocessing for a large class of channels.

We provide fundamental information-theoretic bounds on the required circuit wiring complexity and power consumption for encoding and decoding of error-correcting codes. These bounds hold for all codes and all encoding and decoding algorithms implemented within the paradigm of our VLSI model. This model essentially views computation on a 2-D VLSI circuit as a computation on a network of connected nodes. The bounds are derived based on analyzing information flow in the circuit. They are then used to show that there is a fundamental tradeoff between the transmit and encoding/decoding power, and that the total (transmit + encoding + decoding) power must diverge to infinity at least as fast as cube-root of log 1/pe, where Peis the average block-error probability. On the other hand, for bounded transmit-power schemes, the total power must diverge to infinity at least as fast as square-root of log 1/Pedue to the burden of encoding/decoding.

The cognitive interference channel models cognitive overlay radio systems, in which cognitive radios overhear the transmission of neighboring nodes. For the Gaussian case capacity is known in three subsets of the parameter space: the “weak interference”, “very strong interference” and “primary decodes cognitive” regime. Capacity in the “very strong interference” regime is achieved by superposing the cognitive message over the primary message while in the “primary decodes cognitive” regime the cognitive message is binned against the primary message. This paper provides a new capacity result obtained by combining the capacity achieving schemes in these two regimes thus generalizing and extending these results. Interestingly, the capacity achieving strategy for a given channel also depends on the level of cooperation among the users: that is, either superposition coding or binning is employed depending on the amount of power allotted by the cognitive transmitter to aid the primary user.

The smallest network model that captures relaying in the presence of multiple communicating pairs causing interference to each other is the interference channel with a relay. In this paper, an achievable rate region for the interference channel with a relay is derived. Special cases of strong interference under which this region is the capacity region are presented. The results obtained demonstrate the benefits of interference forwarding at a relay. By forwarding interfering messages, the relay can improve their reception at unintended receivers and, thus, facilitate interference cancellation. We show that intentionally forwarding interfering messages can improve the achievable rates. The achievable rates and interference forwarding gains are also illustrated by numerical results in Gaussian channels. Finally, a sum-rate outer bound to the capacity region of the Gaussian interference channel with a relay is derived and compared with the achievable rate region. The cut-set bound for this channel is also derived and shown to be much looser than the new sum-rate outer bound.

In the simplest relaying strategy, a network node amplifies and forwards a received signal over a wireless channel. Multihop amplify-and-forward allows for a (noisy) linear combination of signals simultaneously sent from multiple sources to be propagated through the network over multiple layers of relays. The performance of multihop amplify-and-forward is limited by noise propagated to the destination over multiple hops, and we expect this strategy to perform well only in high SNR. In this paper, this intuition is formalized and high-SNR conditions under which multihop amplify-and-forward approaches capacity in a layered relay network are determined. By relating the received signal power and the received power of the propagated noise at the nodes, the rate achievable with multihop amplify-and-forward is determined. In particular, when all received powers are lower bounded by$1/\delta $, the noise power propagated to the destination over$L$layers is of the order$L\delta $. The result demonstrates that multihop amplify-and-forward approaches the cut-set bound as received powers at relays increase. As all powers in the network increase at the same rate, the multihop amplify-and-forward rate and the upper bound are within a gap that is independent of channel gains. This gap grows linearly with the number of nodes.

An encoder, subject to a rate constraint, wishes to describe a Gaussian source under squared-error distortion. The decoder, besides receiving the encoder's description, also observes side information consisting of uncompressed source symbol subject to slow fading and noise. The decoder knows the fading realization but the encoder knows only its distribution. The rate-distortion function that simultaneously satisfies the distortion constraints for all fading states was derived by Heegard and Berger. A layered encoding strategy is considered in which each codeword layer targets a given fading state. When the side-information channel has two discrete fading states, the expected distortion is minimized by optimally allocating the encoding rate between the two codeword layers. For multiple fading states, the minimum expected distortion is formulated as the solution of a convex optimization problem with linearly many variables and constraints. Through a limiting process on the primal and dual solutions, it is shown that single-layer rate allocation is optimal when the fading probability density function is continuous and quasiconcave (e.g., Rayleigh, Rician, Nakagami, and log-normal). In particular, under Rayleigh fading, the optimal single codeword layer targets the least favorable state as if the side information was absent.

An algorithm for the optimization of secondary user's transmission strategies in cognitive networks with imperfect network state observations is proposed. The secondary user minimizes the time average of a cost function while generating a bounded performance loss to the primary users' network. The state of the primary users' network, defined as a collection of variables describing features of the network (e.g., buffer state, ARQ state) evolves over time according to a homogeneous Markov process. The statistics of the Markov process is dependent on the strategy of the secondary user and, thus, the instantaneous idleness/transmission action of the secondary user has a long-term impact on the temporal evolution of the network. The Markov process generates a sequence of states in the state space of the network that projects onto a sequence of observations in the observation space, that is, the collection of all the observations of the secondary user. Based on the sequence of observations, the proposed algorithm iteratively optimizes the strategy of the secondary users with no a priori knowledge of the statistics of the Markov process and of the state-observation probability map.

An algorithm for the optimization of secondary user's transmission strategies in cognitive networks with imperfect network state observations is presented. The task of the secondary user is to maximize its performance while generating a bounded performance loss to the primary users' network. The state of the primary users' network, defined as a collection of variables describing features of the network (e.g., buffer state, ARQ state), evolves according to a Markov process whose statistics depend on the transmission strategy of the secondary user. The main contribution of this paper is an online learning algorithm that, without any a priori knowledge about the statistics of the network and state-observation map, iteratively optimizes the strategy of the secondary user based on a sample-path of noisy and partial state observations.

We consider the problem of allocating transmit power in the downlink of a distributed wireless communication system. We account for the power used in both channel estimation and data transmission, with the objective of minimizing the overall transmitted power while satisfying specified Quality of Service (QoS) constraints to the mobile users. We consider both single user and multi-user power control optimization; the problem formulation for both cases lead to a nonconvex program. We proposed solution strategies for both scenarios: For the single user case, a simple intuitive solution, where power is allocated to the antennas sequentially until the QoS constraint is satisfied, is presented. For the multi-user case, we use successive convex approximation (based on the single condensation method) to find a provably convergent solution. We also demonstrate, via numerical simulation, the convergence of the proposed multi-user power allocation strategy. Our numerical results indicate that the proposed single and multi-user power allocation lead to an overall savings of up to 45% when compared to the baseline method of equal power allocation.

We explore several fundamental questions at the intersection of sampling theory and information theory. In particular, we study how capacity is affected by a given sampling mechanism below the channel's Nyquist rate, and what sampling strategy should be employed to maximize capacity. Two classes of sampling mechanisms are investigated: uniform sampling with filtering and uniform sampling with a filter bank. Optimal filters that maximize capacity are identified for both cases. We also highlight connections between capacity and minimum mean squared error (MMSE) estimation from sampled data. Our results indicate that maximizing capacity of sampled analog channels is a joint optimization problem over both the trans mission strategy and the sampling technique.

We study a special class of the cognitive radio channel in which the receiver of the cognitive pair does not suffer interference from the primary user. Previously developed general encoding schemes for this channel are complex as they attempt to cope with arbitrary channel conditions, which leads to rate regions that are difficult to evaluate. The focus of our work is to derive simple rate regions that are easily computable, thereby providing more insights into achievable rates and good coding strategies under different channel conditions. We first present several explicit achievable regions for the general discrete memoryless case. We also present an improved outer bound on the capacity region for the case of high interference. We then extend these regions to Gaussian channels. With a simple outer bound we establish a new capacity region in the high-interference regime. Lastly, we provide numerical comparisons between the derived achievable rate regions and the outer bounds.

We study optimal transmission strategies in interfering wireless networks, under Quality of Service constraints. A buffered, dynamic network with multiple sources is considered, and sources use a retransmission strategy in order to improve packet delivery probability. The optimization problem is formulated as a Markov Decision Process, where constraints and objective functions are ratios of time-averaged cost functions. The optimal strategy is found as the solution of a Linear Fractional Program, where the optimization variables are the steady-state probability of state-action pairs. Numerical results illustrate the dependence of optimal transmission/interference strategies on the constraints imposed on the network.

We consider transceiver design in uncoded multiple input multiple-output (MIMO) systems with noisy channel state estimates. Specifically, we design a transceiver that takes into account the statistics of the CSI errors to minimize the average bit error rate (BER) of the system. Our design utilizes the noisy CSI estimates and the error statistics at the transmitter to partition the spatial channels into 'almost' independent streams. We also propose a joint bit and power loading (allocation) scheme to allocate information rate and power to each spatial stream. Exact maximum likelihood (ML) decoding incurs a high complexity at the receiver; to circumvent this, stream-by-stream ML decoding is used at the receiver. We verify, via numerical results, that for a 4 × 4 system, the BER performance of the proposed joint bit and power loading transmission scheme far surpasses that of the schemes where only bit loading or only power loading is used. At a BER of 10-3, the joint bit and power loading scheme has an approximately 4 dB gain over the bit loading scheme. In contrast, the scheme that ignores CSI errors has poor BER performance.

We consider the joint optimization of relay station (RS) placement and RS sleep/active probability to enhance the energy efficiency of a one-dimensional cellular network. When the RSs are always active, conditions for optimal RS placement that minimizes transmission power are derived, based on which closed-form solution is obtained with path-loss exponent being two, and a simple numerical method for general values of path-loss exponent is proposed. When the circuit power consumption of active RSs is considered, RSs should enter sleep mode appropriately to save power. An algorithm based on projected Newton method is proposed to jointly optimize the RS placement and sleep/active probability. It is shown via numerical examples that the benefit of implementing RSs and optimizing RS placement is substantial and increases with the path-loss exponent. We also justify the interaction between RS placement and RS sleep control, which is effectively tackled by the proposed algorithm to minimize the total power consumption.

We derive upper and lower bounds on the diversity-multiplexing tradeoff of the multiple-input multiple-output interference channel with a relay. The upper bound is derived from the cut-set bound and the lower bound is obtained by performing compress-and-forward at the relay. Based on the obtained bounds, we derive conditions under which the two bounds coincide, resulting in the optimal diversity-multiplexing tradeoff.

The interference channel with a cognitive relay consists of a classical interference channel with two source-destination pairs and with an additional cognitive relay that has a priori knowledge of the sources' messages and aids in the sources' transmission. We derive a new outer bound for this channel using an argument originally devised for the “more capable” broadcast channel, and show the achievability of the proposed outer bound for a class of channels where there is no loss in optimality if both destinations decode both messages. This result is analogous to the “very strong interference” capacity result for the classical interference channel and for the cognitive interference channel, and is the first capacity known capacity result for the general interference channel with a cognitive relay.

We explore the capacity of sub-Nyquist sampled analog channels based on modulation and filter bank sampling techniques. In particular, we derive the capacity of sampled analog channels under sampling via modulation banks and filter banks. A connection between these sampling mechanisms and MIMO Gaussian channels is illuminated. For sampling with a single branch of modulation and filtering, we identify the modulation sequence that optimizes capacity. These results illustrate the importance of the sampling technique on the capacity of sampled analog channels for a broad class of nonuniform sampling structures.

In this paper, we consider the full-duplex and half-duplex Gaussian relay channels where the noises at the relay and destination are arbitrarily correlated. We first derive the capacity upper bound and the achievable rates with three existing schemes: Decode-and-Forward (DF), Compress-and-Forward (CF), and Amplify-and-Forward (AF). We present two capacity results under specific noise correlation coefficients, one being achieved by DF and the other being achieved by direct link transmission (or a special case of CF). The channel for the former capacity result is equivalent to the traditional Gaussian degraded relay channel and the latter corresponds to the Gaussian reversely-degraded relay channel. For CF and AF schemes, we show that their achievable rates are strictly decreasing functions of the correlation coefficient when the correlation coefficient is negative. Moreover, when the noise correlation coefficient is positive, the CF achievable rate may also outperform the independent-noise case if the noise correlation coefficient is within a certain range. Through numerical comparisons under different channel settings, we observe that although DF completely disregards the noise correlation while the other two can potentially exploit such extra information, none of the three relay schemes always outperforms the others over different correlation coefficients. Moreover, the exploitation of noise correlation by CF and AF accrues more benefit when the source-relay link is weak. This paper also considers the optimal power allocation problem under the correlated-noise channel setting. With individual power constraints at the relay and the source, it is shown that the relay should use all its available power to maximize the achievable rates under any correlation coefficient. With a total power constraint across the source and the relay, the achievable rates are proved to be concave functions over the power allocation factor for AF and CF under full-duplex mode, where the closed-form power allocation strategy is derived.

We consider a flat fading multiantenna downlink system with a large number of users where the objective is to deliver equal rates to nonoutage users with a low complexity. We show that in the limit of a large number of users, a zero-forcing beamforming strategy combined with a low complexity user grouping algorithm based on a semi-orthogonal user selection achieves asymptotically optimal performance, with respect to an upper bound that can be achieved when no interference is present among users.

Cognitive radios, which enable the coexistence on the same bandwidth of licensed primary and unlicensed secondary users, have the potential for dramatically increasing the efficiency of wireless networks. In this paper, we propose an on line learning algorithm to optimize the transmission strategy of secondary users in interference mitigation scenarios, where the secondary users are allowed to superimpose their transmission onto those of the primary users. Due to practical imitations, the secondary users have access to only a fraction of the current state of the primary users'' network. Therefore, the strategy of the secondary users is defined on a reduced state space. Numerical results show that the proposed practical learning algorithm operates close to the performance of the system under full knowledge.

We consider robust receiver design in uncoded multiple-input multiple-output (MIMO) wireless communication systems. In practical systems, the channel state information (CSI) available at the receiver is often imperfect due to measurement errors, quantization errors and many other sources of errors. Consequently, using the erroneous CSI for decoding the transmitted symbols will significantly degrade the symbol error rate (SER) performance of any decoding schemes. In this paper, we formulate and implement a decoder for MIMO systems with imperfect CSI. The prozposed decoder is the maximum likelihood (ML) decoder under imperfect receiver CSI, which is the optimal decoder. This "robust" decoder has exponential complexity; with the goal of reducing its complexity, we propose a recursive search algorithm which is akin to a modified form of sphere decoding. We verify, via numerical simulation, that the recursive search algorithm (termed as robust sphere decoder) achieves performance almost the same as the ML solution, with significantly lower computational complexity. For a 2 × 2 256 QAM system, the robust sphere decoder compares approximately 4500 solutions in contrast to 65536 comparisons using a brute-force search method. In addition, the proposed decoder has a significant performance improvement over conventional ML decoding that ignores channel estimation error. For a 2 × 2 16 QAM system, where the variance of the CSI error ranges ranges from 0.1 to 10 times the variance of the additive noise, and at SER of 10-3, the proposed decoder has a 4.5 dB gain over the conventional ML decoder.

We present a cross layer technique to find and characterize optimal control policies for wireless networks operating at different time scales at the upper layer and physical layer. The technique can also be directly applied to networks carrying traffic with different time dependencies such as data or video. Our approach combines network utility maximization and adaptive modulation over an infinite discrete time horizon using a class of performance measures we call time smoothed utility functions. We describe the properties of optimal physical layer power and link rate policies and characterize optimal upper layer policies, which determine when packets should be injected into the network. We also characterize the behavior of optimal policies as different system parameters are used.

The tradeoff between diversity, multiplexing, and delay in multihop MIMO relay networks with ARQ is studied, where the random delay is caused by queueing and ARQ retransmission. This leads to an optimal ARQ allocation problem with a per-hop delay or end-to-end delay constraint. The optimal ARQ allocation has to trade off between the ARQ error that the receiver fails to decode in the allocated maximum ARQ rounds and the packet loss due to queueing delay. These two probability of errors are characterized using the diversity-multiplexing-delay tradeoff (DMDT) (without queueing) and the tail probability of random delay derived using large deviation techniques, respectively. Then the optimal ARQ allocation problem can be formulated as a convex optimization problem. We show that the optimal ARQ allocation should balance each link performance as well as avoid significant queue delay, which is also demonstrated by numerical examples.

We derive the outage capacity of a bursty version of the amplify-and-forward (BAF) protocol for small signal-to-noise ratios when incremental relaying is used. We show that the ratio between the outage capacities of BAF and the cut-set bound is independent of the relay position and that BAF is outage optimal for certain conditions on the target rate R. This is in contrast to decode-and-forward with incremental relaying, where the relay location strongly determines the performance of the cooperative protocol. We further derive the outage capacity for a network consisting of an arbitrary number of relay nodes. In this case the relays transmit in subsequent partitions of the overall transmission block and the destination accumulates signal-to-noise ratio until it is able to decode.

We introduce and study the discrete, finite-state broadcast channel (FSBC) with memory. For this class of channels we define physical degradedness and stochastic degradedness, and demonstrate these definitions with practical communication scenarios. We then show that a superposition codebook with memory achieves the capacity region of physically degraded FSBCs. This result is subsequently used to characterize the capacity region of stochastically degraded FSBCs. In both scenarios, we consider indecomposable as well as nonindecomposable channels.

In this paper, we consider the discrete, time-varying broadcast channel (BC) with memory under the assumption that the channel states belong to a set of finite cardinality. We study the achievable rates in several scenarios of feedback and full unidirectional receiver cooperation. In particular, we focus on two scenarios: the first scenario is the general finite-state broadcast channel (FSBC) where both receivers send feedback to the transmitter while one receiver also sends its channel output to the second receiver. The second scenario is the degraded FSBC where only the strong receiver sends feedback to the transmitter. Using a superposition codebook construction, we derive the capacity regions for both scenarios. Combining elements from these two basic results, we obtain the capacity regions for a number of additional broadcast scenarios with feedback and unidirectional receiver cooperation.

We consider three capacity definitions for composite channels with channel side information at the receiver. A composite channel consists of a collection of different channels with a distribution characterizing the probability that each channel is in operation. TheShannon capacityof a channel is the highest rate asymptotically achievable with arbitrarily small error probability. Under this definition, the transmission strategy used to achieve the capacity must achieve arbitrarily small error probability for all channels in the collection comprising the composite channel. The resulting capacity is dominated by the worst channel in its collection, no matter how unlikely that channel is. We, therefore, broaden the definition of capacity to allow for some outage. The capacity versus outage is the highest rate asymptotically achievable with a given probability of decoder-recognized outage. Theexpected capacityis the highest average rate asymptotically achievable with a single encoder and multiple decoders, where channel side information determines the channel in use. The expected capacity is a generalization of capacity versus outage since codes designed for capacity versus outage decode at one of two rates (rate zero when the channel is in outage and the target rate otherwise) while codes designed for expected capacity can decode at many rates. Expected capacity equals Shannon capacity for channels governed by a stationary ergodic random process but is typically greater for general channels. The capacity versus outage and expected capacity definitions relax the constraint that all transmitted information must be decoded at the receiver. We derive channel coding theorems for these capacity definitions through information density and provide numerical examples to highlight their connections and differences. We also discuss the implications of these alternative capacity definitions for end-to-end distortion, source-channel coding, and separation.

The problem of simultaneous multicasting of multiple messages with the help of a relay terminal is considered. In particular, a model is studied in which a relay station simultaneously assists two transmitters in multicasting their independent messages to two receivers. The relay may also have an independent message of its own to multicast. As a first step to address this general model, referred to as the compound multiple access channel with a relay (cMACr), the capacity region of the multiple access channel with a “cognitive” relay is characterized, including the cases of partial and rate-limited cognition. Then, achievable rate regions for the cMACr model are presented based on decode-and-forward (DF) and compress-and-forward (CF) relaying strategies. Moreover, an outer bound is derived for the special case, called the cMACr without cross-reception, in which each transmitter has a direct link to one of the receivers while the connection to the other receiver is enabled only through the relay terminal. The capacity region is characterized for a binary modulo additive cMACr without cross-reception, showing the optimality of binary linear block codes, and thus highlighting the benefits of physical layer network coding and structured codes. Results are extended to the Gaussian channel model as well, providing achievable rate regions for DF and CF, as well as for a structured code design based on lattice codes. It is shown that the performance with lattice codes approaches the upper bound for increasing power, surpassing the rates achieved by the considered random coding-based techniques.

The problem of joint source-channel coding in transmitting independent sources over interference channels with correlated receiver side information is studied. When each receiver has side information correlated with its own desired source, it is shown that source-channel separation is optimal. When each receiver has side information correlated with the interfering source, sufficient conditions for reliable transmission are provided based on a joint source-channel coding scheme using the superposition encoding and partial decoding idea of Han and Kobayashi. When the receiver side information is a deterministic function of the interfering source, source-channel separation is again shown to be optimal. In addition to these source-channel coding problems, a new channel model that generalizes the classical interference channel is introduced: the interference channel with message side information. Achievable rate regions are given and a single letter characterization of the capacity region for a special class of Z-interference channels is provided. Using this capacity result and the optimality of source-channel separation, we demonstrate that our sufficient conditions for reliable transmission when each receiver has side information correlated with the interfering source are also necessary for some special cases. As a by-product, the capacity region of a class of Z-channels with degraded message sets is also provided.

The performance of multiple-input multiple-output (MIMO) systems using spatial multiplexing is analyzed under channel prediction errors. We derive exact closed-form expressions for the conditional and average bit error rate (BER) for both fixed and adaptive modulation. We apply our analysis to design a rate adaptation policy that optimally adapts antenna use between beamforming and spatial multiplexing. Our results indicate that the prediction error degrades BER in MIMO systems with spatial multiplexing much more than in MIMO systems with beamforming due to the self-interference that arises from channel coupling. In particular, if interference between eigenchannels is high, spatial multiplexing should not utilize the weakest eigenchannels. In our policy, beamforming is used when prediction error is high to avoid interference, whereas multiplexing is used when it is low to achieve the maximum multiplexing gain. We show that this policy improves performance over prior adaptive policies that have been proposed in the literature.

A multi-hop relay network with multiple antenna terminals in a quasi-static slow fading environment is considered. The fundamental diversity-multiplexing gain tradeoff (DMT) is analyzed in the case of half-duplex relay terminals. While decode-and-forward (DF) relaying achieves the optimal DMT in the full-duplex relay scenario, it is shown that the dynamic decode-and-forward (DDF) protocol achieves the optimal DMT if the relay is constrained to half-duplex operation. For the latter case, static DF protocols are considered as well, and the corresponding DMT performance is shown to fall short of the optimal performance, which indicates that dynamic channel allocation is required for optimal DMT performance. The optimal DMT is expressed as the solution of a convex optimization problem and explicit DMT expressions are presented for some special cases. In the case of multiple relays, it is shown that the optimal diversity gain, which is achieved by exploiting the available "hop-diversity", is dominated by the neighboring two-hops with the minimum diversity gain.

Multiple input multiple output (MIMO) systems, in conjunction with orthogonal frequency division multiplexing (OFDM), are extensively used in modern communication systems in order to improve throughput and robustness in multipath fading environments. However, for an optimal operation of these techniques, channel state information (CSI) must be available in both the transmitter and receiver sides. In this paper, an exact closed-form expression for the bit error rate (BER) in MIMO-OFDM systems with transmit beamforming and maximal ratio combining (MRC) reception is obtained, under imperfect channel prediction and interpolation, in multipath Rayleigh fading. This expression is used to evaluate the BER performance of the system for different antenna configurations, prediction and interpolation filters, and channel conditions.

We consider the problem of maximum likelihood (ML) signal detection in multiple-input multiple-output (MIMO) wireless communication systems. We propose a new preprocessing algorithm in the form of channel ordering for sphere decoders. Numerical results show that this new channel ordering leads to significantly lower complexity (in the form of the number of nodes visited by the search algorithm); for MPSK modulation where M > 8 and a moderate SNR range of 15-24 dB, our channel ordering results in a two-fold to four-fold decrease in the number of nodes visited by the search algorithm. We also present a brief review of the SDR-ML detector, formulated using semidefinite programming and relaxation techniques. Finally, we propose a combined SDR-ML-sphere decoder and demonstrate that it further reduces the number of nodes visited by the search algorithm; for a 20 × 20 BPSK-modulated MIMO system and SNR of 8 dB, the SDR-ML-sphere decoder has an average complexity that is approximately 5 times less than the sphere decoder.

A multiple antenna multihop relay network consisting of a source, a relay, and a destination node, is considered. The diversity-multiplexing-delay tradeoffs (DMDT) for various multihop ARQ protocols are obtained. It is shown that the tradeoff region is limited by the performance of the weakest link, and hence the optimal ARQ protocol should balance the link performances by allocating the ARQ rounds among all links. Based on this argument, a variable block-length (VBL) ARQ protocol is proposed and its DMDT-optimality is shown.

We investigate the Gaussian relay channel where the additive noises at the relay and destination are correlated. We obtain achievable rates for the compress-and-forward and decode-and-forward relaying strategies, and compare them to each other and to the capacity upper bound.We show that neither scheme is uniformly best over all channel gains and correlation coefficients. We also derive specific relationships between the channel gains and noise correlations for which one of these schemes is capacity-achieving, thereby increasing the class of relay channels for which capacity is known.

Simultaneous multicasting of messages with the help of a relay is studied. A two-source two-destination network is considered, in which each destination can receive directly only the signal from one of the sources, so that the reception of the message from the other source (and multicasting) is enabled by the presence of the relay. An outer bound is derived, which is shown to be achievable in the case of finite-field modulo-additive channels by using linear codes, highlighting the benefits of structured codes in exploiting the underlying physical-layer structure of the network. Results are extended to the Gaussian channel model as well, providing achievable rate regions based on nested lattice codes. It is shown that for a wide range of power constraints, the performance with lattice codes approaches the upper bound and surpasses the rates achieved by the standard random coding schemes.

The multi-user communication channel, in which multiple users exchange information with the help of a single relay terminal, called the multi-way relay channel, is considered. In this model, multiple interfering clusters of users communicate simultaneously, where the users within the same cluster wish to exchange messages among themselves. It is assumed that the users cannot receive each other's signals directly, and hence the relay terminal is the enabler of communication. A relevant metric to study in this scenario is the symmetric rate achievable by all users, which we identify for amplify-and-forward (AF), decode-and-forward (DF) and compress-and-forward (CF) protocols. We also present an upper bound for comparison. The two extreme cases, namely full data exchange, in which every user wants to receive messages of all other users, and pairwise data exchange, consisting of multiple two-way relay channels, are investigated and presented in detail.

We study the discrete memoryless Z-interference channel (ZIC) where the transmitter of the pair that suffers from interference is cognitive. We first provide upper and lower bounds on the capacity of this channel. We then show that, when the channel of the transmitter-receiver pair that does not face interference is noiseless, the two bounds coincide and therefore define the capacity region. The obtained results imply that, unlike in the Gaussian cognitive ZIC, in the considered channel superposition encoding at the non-cognitive transmitter as well as Gel'fand-Pinsker encoding at the cognitive transmitter are needed in order to minimize the impact of interference. As a byproduct of the obtained capacity region, we obtain the capacity result for a generalized Gel'fand-Pinsker problem.

The tradeoff between storage and identification rates for multiple databases is investigated from an information theoretic perspective. In the assumed model, noisy observations of feature vectors of two distinct groups, called the ancestors, are compressed and stored in two separate databases. When queried with a noisy observation of a (possibly random) function of two randomly selected ancestors (one from each group), the system is required to correctly identify the ancestors with high probability. Single-letter inner and outer bounds are presented on the set of achievable rate points, which identify a tradeoff between the compression rates and the identification rate region: the lower the compression rates for storage, the larger the rate region achievable for identification.

We consider the two-receiver, discrete, time-varying broadcast channel with memory, under the assumption that the channel states belong to a set of finite cardinality. We study the achievable rates in several scenarios of feedback and receiver cooperation. In particular, using a superposition codetree we derive the capacity of three scenarios of the general finite-state broadcast channel with feedback and receiver cooperation.

The problem of multicasting multiple messages with the help of a relay, which may also have an independent message of its own to multicast, is considered. As a first step to address this general model, referred to as the compound multiple access channel with a relay (cMACr), the capacity region of the multiple access channel with a ldquocognitiverdquo relay is characterized, including the cases of partial and rate-limited cognition. Achievable rate regions for the cMACr model are then presented based on decode-and-forward (DF) and compress-and-forward (CF) relaying strategies. Moreover, an outer bound is derived for the special case in which each transmitter has a direct link to one of the receivers while the connection to the other receiver is enabled only through the relay terminal. Numerical results for the Gaussian channel are also provided.

We present the e-outage capacity of incremental relaying at low signal-to-noise ratios (SNR) in a wireless cooperative network with slow Rayleigh fading channels. The relay performs decode-and-forward and repetition coding is employed in the network, which is optimal in the low SNR regime. We derive an expression on the optimal relay location that maximizes the e-outage capacity. It is shown that this location is independent of the outage probability and SNR but only depends on the channel conditions represented by a path-loss factor. We compare our results to the e-outage capacity of the cut-set bound and demonstrate that the ratio between the e-outage capacity of incremental relaying and the cut-set bound lies within 1/¿2 and 1. Furthermore, we derive lower bounds on the e-outage capacity for the case of K relays.

This work explores the average bit error rate (BER) of uncoded MIMO systems in Rayleigh fading channels with co-channel interference (CCI) and background noise. We consider that maximal ratio transmission (MRT) is used at the transmit end. At the receiver we consider two different schemes: maximal ratio combining (MRC) and interference cancellation (IC) via null steering of the receive array radiation pattern. We provide analytical expressions of the BER for different modulation techniques and provide a comparison between the two proposed receiver schemes.

We describe Wireless Network Utility Maximization, WNUM, and compare its performance to NUM for wireless networks of interfering links under random time varying channel conditions. WNUM is shown to simultaneously offer greater rate and reliability performance in simulations operating under Rayleigh fading. A general method for finding adaptive network control policies is presented that is sample- based and converges to the optimal control policies for the network.

Cognitive radios hold tremendous promise for increasing spectral efficiency in wireless systems. This paper surveys the fundamental capacity limits and associated transmission techniques for different wireless network design paradigms based on this promising technology. These paradigms are unified by the definition of a cognitive radio as an intelligent wireless communication device that exploits side information about its environment to improve spectrum utilization. This side information typically comprises knowledge about the activity, channels, codebooks, and/or messages of other nodes with which the cognitive node shares the spectrum. Based on the nature of the available side information as well asa priorirules about spectrum usage, cognitive radio systems seek to underlay, overlay, or interweave the cognitive radios' signals with the transmissions of noncognitive nodes. We provide a comprehensive summary of the known capacity characterizations in terms of upper and lower bounds for each of these three approaches. The increase in system degrees of freedom obtained through cognitive radios is also illuminated. This information-theoretic survey provides guidelines for the spectral efficiency gains possible through cognitive radios, as well as practical design ideas to mitigate the coexistence challenges in today's crowded spectrum.

Source and channel coding over multiuser channels in which receivers have access to correlated source side information are considered. For several multiuser channel models necessary and sufficient conditions for optimal separation of the source and channel codes are obtained. In particular, the multiple-access channel, the compound multiple-access channel, the interference channel, and the two-way channel with correlated sources and correlated receiver side information are considered, and the optimality of separation is shown to hold for certain source and side information structures. Interestingly, the optimal separate source and channel codes identified for these models are not necessarily the optimal codes for the underlying source coding or the channel coding problems. In other words, while separation of the source and channel codes is optimal, the nature of these optimal codes is impacted by the joint design criterion.

We define a class of Z-interference channels for which we obtain a new upper bound on the capacity region. The bound exploits a technique first introduced by Korner and Marton. A channel in this class has the property that, for the transmitter-receiver pair that suffers from interference, the conditional output entropy at the receiver is invariant with respect to the transmitted codewords. We compare the new capacity region upper bound with the Han/Kobayashi achievable rate region for interference channels. This comparison shows that our bound is tight in some cases, thereby yielding specific points on the capacity region as well as sum capacity for certain Z-interference channels. In particular, this result can be used as an alternate method to obtain sum capacity of Gaussian Z-interference channels. We then apply an additional restriction on our channel class: the transmitter-receiver pair that suffers from interference achieves its maximum output entropy with a single input distribution irrespective of the interference distribution. For these channels, we show that our new capacity region upper bound coincides with the Han/Kobayashi achievable rate region, which is therefore capacity-achieving. In particular, for these channels superposition encoding with partial decoding is shown to be optimal and a single-letter characterization for the capacity region is obtained.

A transmitter without channel state information wishes to send a delay-limited Gaussian source over a slowly fading channel. The source is coded in superimposed layers, with each layer successively refining the description in the previous one. The receiver decodes the layers that are supported by the channel realization and reconstructs the source up to a distortion. The expected distortion is minimized by optimally allocating the transmit power among the source layers. For two source layers, the allocation is optimal when power is first assigned to the higher layer up to a power ceiling that depends only on the channel fading distribution; all remaining power, if any, is allocated to the lower layer. For convex distortion cost functions with convex constraints, the minimization is formulated as a convex optimization problem. In the limit of a continuum of infinite layers, the minimum expected distortion is given by the solution to a set of linear differential equations in terms of the density of the fading distribution. As the number of channel uses per source symbol tends to zero, the power distribution that minimizes expected distortion converges to the one that maximizes expected capacity.

We consider capacity of discrete-time channels with feedback for the general case where the feedback is a time-invariant deterministic function of the output samples. Under the assumption that the channel states take values in a finite alphabet, we find a sequence of achievable rates and a sequence of upper bounds on the capacity. The achievable rates and the upper bounds are computable for any N, and the limits of the sequences exist. We show that when the probability of the initial state is positive for all the channel states, then the capacity is the limit of the achievable-rate sequence. We further show that when the channel is stationary, indecomposable, and has no intersymbol interference (ISI), its capacity is given by the limit of the maximum of the (normalized) directed information between the input XNand the output YN, i.e., C=limNrarrinfin(1/n)max I(XNrarrYN) where the maximization is taken over the causal conditioning probability Q(xNparzN-1) defined in this paper. The main idea for obtaining the results is to add causality into Gallager's results on finite state channels. The capacity results are used to show that the source-channel separation theorem holds for time-invariant determinist feedback, and if the state of the channel is known both at the encoder and the decoder, then feedback does not increase capacity.

A two-user discrete memoryless compound multiple-access channel (MAC) with a common message and conferencing decoders is considered. The capacity region is characterized in the special cases of physically degraded channels and unidirectional cooperation, and achievable rate regions are provided for the general case. The results are then extended to the corresponding Gaussian model. In the Gaussian setup, the provided achievable rates are shown to lie within some constant number of bits from the boundary of the capacity region in several special cases. An alternative model, in which the encoders are connected by conferencing links rather than having a common message, is studied as well, and the capacity region for this model is also determined for the cases of physically degraded channels and unidirectional cooperation. Numerical results are also provided to obtain insights about the potential gains of conferencing at the decoders and encoders.

This work explores the performance of MIMO (multiple-input/multiple-output) systems in Rayleigh fading channels with co-channel interference (CCI) and thermal noise. We provide analytical expressions for the outage probability of maximal ratio transmission combined with one of two different receive antenna array schemes, maximal ratio combining (MRC) and interference cancellation (IC) via null steering of the array pattern. We derive the statistics of the signal to interference-plus- noise ratio (SINR) for each technique in a closed-form and obtain an integral expression to calculate the average bit error rate (BER) or symbol error rate (SER). Our results show the conditions under which IC yields significantly better performance than MRC and vice versa. We also determine the impact on performance of the number of antennas in the transmit array.

We present exact expressions for the average bit error rate (BER) and symbol error rate (SER) of different modulation techniques of a wireless system with multiple transmit and receive antennas. The receive antennas are assumed to use maximal ratio combining (MRC) or post-detection equal gain combining (EGC), whereas the transmit antenna that maximizes the output signal-to-noise ratio (SNR) is selected. Exact expressions of the moment generating function (MGF) of the output SNR and all its derivatives are also derived. We consider a Nakagami-m fading channel where the long-term SNR and fading parameters from the different transmit antennas are arbitrary and may be different from each other. For a given transmit antenna, the fading at the receive antennas is assumed to be independent and identically distributed (i.i.d). For the case when the Nakagami fading parameter m has an integer value in every channel, results are given in closed-form as a finite sum of simple terms. When fading parameters take any real value, our results are given in terms of the multivariate Lauricella hypergeometric function FA(n). Numerical results for the error rates of different modulation techniques are presented.. Our results are validated by Monte Carlo simulation.

We study communication in networks with multiple source-destination pairs and relays. In such networks, the channel output at any destination receiver consists of both the desired signal and interference. In this setting the relay can help forward the desired message of a user to the destination receiver, or help forward interference to a receiver to improve its ability to cancel the interference. Focusing on the impact of interference forwarding, we define a new relay-interferer channel (RIC) model, which serves as the basic building block for the study of interference in multiuser networks. Using the RIC we show that correlation between the codebooks of the relay and the interferer (e.g. superposition codebooks) is essential for obtaining performance benefits from interference forwarding. We conclude that in order to achieve rate gains from relaying interference using the decode-and-forward strategy, a superposition codebook is required. Otherwise, this relay strategy has the same rate as interference cancellation at the receiver. We also conclude that compress-and-forward is not useful for forwarding interference and has no better performance than just treating interference as noise at the decoder.

A multi-hop relay channel with multiple antenna terminals in a quasi-static slow fading environment is considered. For both full-duplex and half-duplex relays the fundamental diversity-multiplexing tradeoff (DMT) is analyzed. It is shown that, while decode-and-forward (DF) relaying achieves the optimal DMT in the full-duplex relay scenario, the dynamic decode- and-forward (DDF) protocol is needed to achieve the optimal DMT if the relay is constrained to half-duplex operation. For the latter case, static protocols are considered as well, and the corresponding achievable DMT performance is characterized.

We study the transmission of a stationary ergodic Gaussian source over a packet erasure channel, which is a composite channel with degraded states. A broadcast channel code can be applied to a composite channel to obtain different rates in the different channel states. However, we show that a non-broadcast direct transmission strategy achieves a higher expected rate than the broadcast code, although it does not meet Shannon's definition of reliable communication since it does not guarantee which bits will be received. Each channel code has a matching source code: the multiresolution source code allows the broadcast channel code to transmit prioritized information, and the symmetric multiple description source code enables direct transmission of unprioritized information. The end-to-end expected distortions of these schemes are also compared.

We present a cross-layer framework for optimizing the performance of wireless networks as measured by applications or upper layer protocols. The approach combines adaptive modulation with network utility maximization. We extend the approach to find optimal source rates and transmitter power and rate policies without explicit knowledge of the distribution of channel states. These optimal power and rate policies balance delay (backlog), transmission rate and energy to maximize network performance under constraints on average transmitter power and link buffer arrival and departure rates. Explicit policies are found for single links, and algorithmic methods presented to find optimal policies for complex interfering networks.

We present exact expressions for the average bit error rate (BER) and symbol error rate (SER) of different modulation techniques of a wireless system with multiple transmit and receive antennas. The receive antennas are assumed to use maximal ratio combining (MRC), whereas the transmit antenna that maximize the instantaneous post-processing signal-to-noise ratio (SNR) is selected. We consider an independent but non- identically distributed (i.n.d.) Nakagami-m fading channel where the long-term SNR and fading parameters from the different transmit antennas are arbitrary and may be different from each other. For the case when the Nakagami fading parameter m has an integer value in every channel, results are given in closed- form as a finite sum of simple terms For the case when fading parameters take any real value, our results are given in terms of the multivariate Lauricella hypergeometric function FA(n). Monte Carlo simulations are shown to validate our theoretical analysis.

In this paper we analyze the performance of multiple-input multiple-output (MIMO) multiplexing for BPSK and square M-QAM under Rayleigh fading. We derive exact closed-form expressions of the bit error rate (BER) assuming channel prediction error. Our analysis indicates that prediction error degrades MIMO multiplexing BER much more than MIMO beamforming BER. This is not surprising since prediction error in MIMO multiplexing leads to eigenchannel interference, which has a much greater impact on BER than the imperfect beamforming coefficients that result from such errors. Our numerical results also reveal that non-uniform rate allocation between ordered eigenchannels dramatically improves the BER.

It has been demonstrated that base station cooperation can reduce co-channel interference (CCI) and increase cellular system capacity. In this work we consider another approach by dividing the system into microcells through denser base station deployment. We adopt the criterion to maximize the minimum spectral efficiency of served users with a certain user outage constraint. In a two-dimensional hexagon array with homogeneous microcell structure, under the proposed propagation model denser base station deployment outperforms suboptimal cooperation schemes (zero-forcing) when the density increases beyond 3 - 12 base stations per km2, the exact value depending on the rules of outage user selection. However, close- to-optimal cooperation schemes (zero-forcing with dirty-paper- coding) are always superior to denser deployment. Performance of a hierarchial cellular structure mixed with both macrocells and microcells is also evaluated.

The cooperative dirty paper coding (DPC) rate region is investigated in a two-transmitter two-receiver network with full channel state information available at all terminals. The transmitters cooperate by first exchanging messages over an orthogonal cooperation channel, then they mimic a broadcast channel (BC) and jointly perform DPC to send to the two independent receivers. The allocation of network power and bandwidth between the data and the cooperation channel is studied to characterize the cooperative DPC rate region. First, the optimal sum power allocation for a multiple access channel (MAC) is presented. Then through an application of the MAC-BC capacity duality, the cooperative DPC rate region is evaluated under different bandwidth allocation assumptions. Cooperative DPC outperforms non-cooperative time-division (TD) only when the cooperation channel is strong, since the joint-encoding capacity gain is negated by the overhead of message exchanges in a weak cooperation channel. Moreover, the cooperative capacity advantage over TD is more pronounced at the maximum sum rate point than when the rate vector is skewed toward one of the users.

We investigate adaptive modulation using the network utility maximization framework. We derive new crosslayer optimal power and rate adaptation policies for several practical modulation schemes. The behavior of these crosslayer policies is found to differ from policies based on physical-layer optimization only. The multiple flow single link case is analyzed and optimal power and rate policies found. The multiple interfering link case is investigated and a numerical method presented to find optimal policies for this case.

We consider the discrete, time-varying broadcast channel with memory under the assumption that the channel states belong to a set of finite cardinality. We study the achievable rates in two scenarios where feedback (and cooperation) is available. One scenario is the general finite-state broadcast channel (FSBC) where both receivers send feedback to the transmitter, and in addition one receiver sends his channel outputs to the other receiver through a cooperation link. The second scenario is the degraded FSBC where only the strong receiver sends feedback to the transmitter. We find the capacity regions for both cases. In both scenarios we consider non-indecomposable as well as a class of indecomposable FSBCs.

Lossy transmission over a relay channel in which the relay has access to correlated side information is considered. First, a joint source-channel decode-and-forward scheme is proposed for general discrete memoryless sources and channels. Then the Gaussian relay channel where the source and the side information are jointly Gaussian is analyzed. For this Gaussian model, several new source-channel cooperation schemes are introduced and analyzed in terms of the squared-error distortion at the destination. A comparison of the proposed upper bounds with the cut-set lower bound is given, and it is seen that joint source-channel cooperation improves the reconstruction quality significantly. Moreover, the performance of the joint code is close to the lower bound on distortion for a wide range of source and channel parameters.

We apply a technique introduced by Korner and Marton to the converse of a class of Z-interference channels. This class has the properties that, for the transmitter-receiver pair that suffers from interference, 1) the conditional output entropy is invariant with respect to the input and, 2) the maximum output entropy is achieved by a single input distribution irrespective of the interference distribution. We show that for this class of channels, superposition encoding and partial decoding is optimal. We thus provide a single-letter characterization for the capacity region, which was previously unknown.

Capacity gains due to relaying in wireless networks with multiple source-destination pairs are analyzed. A two- source, two-receiver network with the relay is considered. The focus is on the scenario in which, due to channel conditions, the relay can observe the signal from only one source. The relay can thus help the intended receiver of this message, via message forwarding, to decode it. In addition, the relay can simultaneously help the unintended receiver subtract the interference associated with this message. We call the latter strategy interference forwarding. An achievable rate region employing decode-and-forward (that simultaneously does message and interference forwarding) at the relay is derived and analyzed. This strategy is shown to achieve the capacity region under certain conditions. Our results demonstrate that the relay can help both receivers, despite the fact that it forwards only the message intended for one of them. This applies in general to communications in the presence of an interferer transmitting at any arbitrary rate. Interference forwarding improves reception of interfering signals at the receivers. This facilitates decoding of the unwanted messages and eliminating the resulting interference. Therefore, in networks with multiple source-destination pairs, in addition to relaying messages, interference forwarding may also be employed to help in combating interference.

We consider the discrete, time-varying broadcast channel with memory under the assumption that the channel states belong to a set of finite cardinality. We first define the physically degraded finite-state broadcast channel for which we derive the capacity region. We then define the stochastically degraded finite-state broadcast channel and derive the capacity region for this scenario as well. In both scenarios we consider the non-indecomposable finite-state channel as well as the indecomposable one.

We consider relaying strategies in networks with multiple source-destination pairs and possibly additional outside sources of interference. We study these networks in the discrete, memoryless setup, and focus on relaying strategies based on forwarding the interference. In particular, the relay encodes the interference signal so as to make it easier for the receiver to remove it. The objective is to help receivers with weak interference by making the interference strong enough so that these receivers are able to cancel it completely. Our proposed approach is a combination of ideas from decode-and-forward (DF) and/or estimate-and-forward (EF) but applied to the interfering signal rather than the desired signal. When based only on DF, the relay first decodes (part of) the interfering signal it wants to enhance. It then encodes the interference in such a way as to increase the interference at the assisted receiver. The rate of the relayed interference is not limited by the rate from the relay to the original destination of the forwarded message, thus, interference cancellation is not a by-product of enhancing the desired information at its intended destination, but a goal in itself. We call this method interference-forwarding (IF). IF can also be based on EF where, instead of forwarding the exact interfering signal, the relay simply sends a compressed version of it to the assisted receiver. Rate increase can thus be obtained even if the signal received at the relay is independent of the desired message and consists only of interference and noise.

A framework is developed for optimizing the tradeoff between diversity, multiplexing, and delay in multiple-input multiple-output (MIMO) systems to minimize end-to-end distortion. The goal is to find the optimal balance between the increased data rate provided by antenna multiplexing, the reduction in transmission errors provided by antenna diversity and automatic repeat request (ARQ), and the delay introduced by ARQ. First, closed-form analytical results are developed to minimize end-to-end distortion of a vector quantizer concatenated with a space-time MIMO channel code in the high SNR regime. The minimization determines the optimal point on the diversity-multiplexing tradeoff curve. For large but finite SNR this optimal point is found via convex optimization, which is illustrated with an example of a practical joint source-channel code design. It is then shown that for MIMO systems with ARQ retransmission, sources without a delay constraint have distortion minimized by maximizing the ARQ window size. This results in a new multiplexing-diversity tradeoff region enhanced by ARQ. However, under a source delay constraint the problem formulation changes to account for delay distortion associated with random message arrival and random ARQ completion times. In this case, the simplifications associated with a high SNR assumption break down, and a dynamic programming formulation is required to capture the channel diversity-multiplexing tradeoff as well as the random arrival and retransmission dynamics. Results based on this formulation show that a delay-sensitive system obtains significant performance gains by adapting its operating point on the diversity-multiplexing-delay region to system dynamics.

Significant throughput improvements can be obtained in multiple-input multiple-output (MIMO) fading channels by merging beamforming at the transmitter and maximal ratio combining (MRC) at the receiver. In general, accurate channel state information (CSI) is required to achieve these performance gains. In this paper, we analyze the impact of channel prediction error on the bit error rate (BER) of combined beamforming and MRC in slow Rayleigh fading channels. Exact closed-form BER expressions are obtained in terms of elementary functions. Numerical results show that imperfect CSI causes little BER degradation using channel prediction of moderate complexity.

Capacity gains from transmitter and receiver cooperation are compared in a relay network where the cooperating nodes are close together. Under quasi-static phase fading, when all nodes have equal average transmit power along with full channel state information (CSI), it is shown that transmitter cooperation outperforms receiver cooperation, whereas the opposite is true when power is optimally allocated among the cooperating nodes but only CSI at the receiver (CSIR) is available. When the nodes have equal power with CSIR only, cooperative schemes are shown to offer no capacity improvement over non-cooperation under the same network power constraint. When the system is under optimal power allocation with full CSI, the decodeand- forward transmitter cooperation rate is close to its cut-set capacity upper bound, and outperforms compress-and-forward receiver cooperation. Under fast Rayleigh fading in the high SNR regime, similar conclusions follow. Cooperative systems provide resilience to fading in channel magnitudes; however, capacity becomes more sensitive to power allocation, and the cooperating nodes need to be closer together for the decode-and-forward scheme to be capacity-achieving. Moreover, to realize capacity improvement, full CSI is necessary in transmitter cooperation, while in receiver cooperation optimal power allocation is essential.

We explore tradeoffs between different reception strategies of multiple receive antennas in fading channels with co-channel interference (CCI). Our tradeoff analysis is based on outage probability. We assume the signal from the desired user at the receive antenna array to be affected by Rice, Nakagami or Rayleigh fading, while CCI signals are assumed to experience Rayleigh fading. We provide closed-form analytical expressions for the outage probability of different diversity schemes, such as maximal ratio combining (MRC) and optimum combining (OC), and also for interference cancellation (IC) based on antenna beamsteering, which steers nulls in the array radiation pattern in the direction of the strongest interferers. Our analysis provides a unified framework for studying outage probability of different multiple-antenna reception strategies, and our closed- form expressions are easily computed, facilitating a performance comparison under a range of operating conditions. Our numerical results show that IC yields significantly better performance than MRC if the system is interference-limited and the number of dominant interferers is lower than the number of receive antennas, or when the output SINR is low. In addition, when the background noise can be neglected, we provide numerical results for MRC and OC when the signals from the desired user at the different receive antennas are arbitrarily distributed.

Important throughput improvements in multiple- input multiple-output (MIMO) fading channels can be obtained by merging beamforming at the transmitter and maximal ratio combining (MRC) at the receiver. However, to attain these performance gains it is important to obtain accurate channel state information (CSI). For this purpose a channel estimation technique is used at the receiver: channel prediction to feed back to the transmitter for beamforming, and channel interpolation for MRC at the receiver. In this paper, the impact of imperfect channel prediction on bit error probability (BEP) is analyzed in Rayleigh fading, taking into account the channel response variations over the frame interval. An exact closed-form expression for BEP is obtained, and we evaluate this expression assuming both time-variant and time-invariant channel models. These results indicate that the BEP performance degrades on the order of 1.5 dB due to channel variations.

In this paper, we propose a new hybrid automatic repeat request (H-ARQ) scheme in MIMO. The proposed scheme performs bit-level exchanges and modifications every retransmission and covers all combinations of number of antennas and number of retransmissions in M-QAM. In order to obtain a better bitwise mapping scheme, we define two independent bitwise suboperations, which are called bit swapping and inversion (BSI) and bit shifting between antennas (BSA), and derive sets for BSI and BSA. The performance of the proposed scheme is evaluated through link simulations with a 3GPP long-term evolution (LTE) specification and is compared to previous H-ARQ schemes in MIMO. The results show that the proposed bitwise mapping scheme provides approximately 2 dB gain over the conventional scheme even at a high mobile speed.

Simultaneous support of multiple delay-critical application sessions such as multiuser video streaming require a paradigm shift in the design of ad-hoc wireless networks. Instead of the conventional layered approach, cross-layer optimization is needed for more efficient resource allocation, across the protocol stack and among multiple users. In this work, we extend our previous effort in joint capacity and flow assignment at the MAC and network layers, to include rate allocation at the application layer of each user. The proposed optimization aims to minimize the tradeoff between encoded video quality of all users versus overall network congestion. Compared to a scheme with oblivious layers, where capacity, flow and video rates are assigned individually, simulation results show significant performance gain of our proposed cross-layer approach, in terms of maximum sustainable rate and quality of the video streams.

In cellular systems a large reuse distance reduces co-channel interference while a small reuse distance increases bandwidth allocated to each cell. The optimal reuse distance is chosen to balance these two factors. Instead of applying a fixed reuse distance to the entire system, in this paper we study the effect of adaptive channel reuse based on channel strength. Assuming the traditional single base station transmission, adaptive channel reuse under different propagation models, with or without fading, is analyzed for the Wyner linear cellular model. A new approach where base stations collaborate in transmission is also considered. We observe that adjacent base cooperation does not show much advantage over traditional single base transmission under intra-cell orthogonal schemes and AWGN channel models. In order to fully exploit the benefit of base station cooperation, more sophisticated transmission schemes need to be investigated.

A transmitter without channel state information wishes to send a delay-limited Gaussian source over a slowly fading channel that has a finite number of discrete fading states. The source is coded in layers, with each layer successively refining the description in the previous one. These coded source layers are then superimposed and simultaneously transmitted to the receiver. The receiver decodes the layers that are supported by the realization of the channel, and combines the descriptions in the decoded layers to reconstruct the source up to a distortion. The expected distortion is minimized by optimally allocating the transmit power among the given number of source layers. For two layers, the allocation is optimal when power is first assigned to the higher layer up to a power ceiling that depends only on the channel fading distribution; all remaining power, if any, is allocated to the lower layer. For multiple layers, the overall expected distortion can be written as a set of recurrence relations, and the minimum expected distortion is found by recursively applying the two-layer optimization procedure at each recurrence step.

We provide a comparative performance of two different array processing techniques in a wireless system with multiple receive antennas in fading channels with co-channel interference (CCI). The signal from the desired user at the receive antenna array is assumed to be affected by Rice, Nakagami or Rayleigh fading, while CCI signals are assumed to experience Rayleigh fading. We provide analytical expressions for the outage probability and provide a comparative performance of MRC (to provide diversity) and IC (to cancel the strongest interferers). Our results show that IC yields significantly better performance than MRC if the system is interference-limited and the number of dominant interferers is lower than the number of receive antennas, or when the output SINR is low.

We consider three capacity definitions for general channels with channel side information at the receiver, where the channel is modeled as a sequence of finite dimensional conditional distributions not necessarily stationary, ergodic, or information stable. The Shannon capacity is the highest rate asymptotically achievable with arbitrarily small error probability. The outage capacity is the highest rate asymptotically achievable with a given probability of decoder-recognized outage. The expected capacity is the highest expected rate asymptotically achievable with a single encoder and multiple decoders, where the channel side information determines the decoder in use. Expected capacity equals Shannon capacity for channels governed by a stationary ergodic random process but is typically greater for general channels. These alternative definitions essentially relax the constraint that all transmitted information must be decoded at the receiver. We derive equations for these capacity definitions through information density. Examples are also provided to demonstrate their implications.

We consider transmission of a Gaussian source over a Gaussian relay channel, where the relay terminal has access to correlated side information. We propose several cooperative joint source-channel coding strategies that utilize both the broadcast nature of the wireless transmission and/or the availability of the correlated side information at the relay, and compare these to distortion lower bounds obtained by the cut-set arguments. In general, the best performing scheme depends on the correlation among the source and the relay signals, and the average link qualities. We illustrate that the strategies introduced in this paper perform very close to the lower bound in most cases.

Relaying is a fundamental building block of wireless networks. Sophisticated relaying strategies at the physical layer have been developed for a single flow, but multiple flows are typically handled by time sharing the channel between the flows at the network level. In this paper, time-sharing when forwarding two data streams at the relay is compared to joint relaying and network coding that allows the relay to combine data streams. Two commonly occurring blocks in wireless networks with both unicast and multicast traffic are considered. It is shown that joint relaying and network coding can achieve gains and even double the throughput for certain channel conditions.

An achievable region, outer bounds and a capacity result are established for two-sender two-receiver interference channels with one cognitive transmitter. Specifically, we assume that one transmitter knows either the full or, more realistically, the partial message of the other transmitter due to its cognitive capabilities. The achievable region is obtained by a rate-splitting strategy, which generalizes prior strategies under both weak and strong interference conditions. The outer bounds are based on an extension of the Nair-El Gamal outer bound for the broadcast channel capacity. When only the partial message is known to the cognitive user, the capacity region in strong interference is established. In this regime, the interference is such that both receivers can decode both messages with no rate penalty.

A transmitter without channel state information (CSI) wishes to send a delay-limited Gaussian source over a slowly fading channel. The source is coded in superimposed layers, with each layer successively refining the description in the previous one. The receiver decodes the layers that are supported by the channel realization and reconstructs the source up to a distortion. In the limit of a continuum of infinite layers, the optimal power distribution that minimizes the expected distortion is given by the solution to a set of linear differential equations in terms of the density of the fading distribution. In the optimal power distribution, as SNR increases, the allocation over the higher layers remains unchanged; rather the extra power is allocated towards the lower layers. On the other hand, as the bandwidth ratio b (channel uses per source symbol) tends to zero, the power distribution that minimizes expected distortion converges to the power distribution that maximizes expected capacity. While expected distortion can be improved by acquiring CSI at the transmitter (CSIT) or by increasing diversity from the realization of independent fading paths, at high SNR the performance benefit from diversity exceeds that from CSIT, especially when b is large.

A game-theoretic framework is used to study the effect of constellation size on the energy efficiency of wireless networks for M-QAM modulation. A non-cooperative game is proposed in which each user seeks to choose its transmit power (and possibly transmit symbol rate) as well as the constellation size in order to maximize its own utility while satisfying its delay quality-of-service (QoS) constraint. The utility function used here measures the number of reliable bits transmitted per joule of energy consumed, and is particularly suitable for energy-constrained networks. The best-response strategies and Nash equilibrium solution for the proposed game are derived. It is shown that in order to maximize its utility (in bits per joule), a user must choose the lowest constellation size that can accommodate the user's delay constraint. This strategy is different from one that would maximize spectral efficiency. Using this framework, the tradeoffs among energy efficiency, delay, throughput and constellation size are also studied and quantified. In addition, the effect of trellis-coded modulation on energy efficiency is discussed.

We analyze the sum-rate performance of a multi- antenna downlink system carrying more users than transmit antennas, with partial channel knowledge at the transmitter due to finite rate feedback. In order to exploit multiuser diversity, we show that the transmitter must have, in addition to directional information, information regarding the quality of each channel. Such information should reflect both the channel magnitude and the quantization error. Expressions for the SINR distribution and the sum-rate are derived, and tradeoffs between the number of feedback bits, the number of users, and the SNR are observed. In particular, for a target performance, having more users reduces feedback load.

We propose a new approach to outage probability analysis of predetection maximal ratio combining (MRC) diversity reception in Nakagami-$m$fading channels. We generalize prior work in that we consider L independent cochannel interferers with arbitrary powers and fading parameters as well as the effects of additive white Gaussian noise (AWGN). Our approach results in a general expression for outage probability under very broad assumptions. Moreover, our approach leads to a closed-form expression for outage probability in most cases of interest. We also provide numerical results that demonstrate the performance improvement obtained through MRC diversity combining in the presence of cochannel interferers.

We derive the capacity of time-varying channels with memory that have causal channel side information (CSI) at the sender and receiver. We obtain capacity of block-memoryless and asymptotically block-memoryless channels with block-memoryless or weakly decorrelating side information. Our coding theorems rely on causal generation of the codewords relative to the causal transmitter CSI. The CSI need not be perfect, and we consider the case where the transmitter and receiver have the same causal CSI as well as the case where the transmitter CSI is a deterministic function of the receiver CSI. For block-memoryless and asymptotically block-memoryless channels, our coding strategy averages mutual information density over multiple transmission blocks to achieve the maximum average mutual information. We apply the coding theorem associated with the block-memoryless channel to determine the capacity and optimal input distribution of intersymbol interference (ISI) time-varying channels with causal perfect CSI about the time-varying channel. The capacity of this channel cannot be found through traditional decomposition methods

Capacity improvement from transmitter and receiver cooperation is investigated in a two-transmitter, two-receiver network with phase fading and full channel state information (CSI) available at all terminals. The transmitters cooperate by first exchanging messages over an orthogonal transmitter cooperation channel, then encoding jointly with dirty-paper coding. The receivers cooperate by using Wyner-Ziv compress-and-forward over an analogous orthogonal receiver cooperation channel. To account for the cost of cooperation, the allocation of network power and bandwidth among the data and cooperation channels is studied. It is shown that transmitter cooperation outperforms receiver cooperation and improves capacity over noncooperative transmission under most operating conditions when the cooperation channel is strong. However, a weak cooperation channel limits the transmitter cooperation rate; in this case, receiver cooperation is more advantageous. Transmitter-and-receiver cooperation offers sizable additional capacity gain over transmitter-only cooperation at low signal-to-noise ratio (SNR), whereas at high SNR transmitter cooperation alone captures most of the cooperative capacity improvement.

The general joint design of the physical, MAC, and routing layers to minimize network energy consumption is complex and hard to solve. Heuristics to compute approximate solutions and high-complexity algorithms to compute exact solutions have been previously proposed. In this paper, we focus on synchronous small-scale networks with interference-free link scheduling and practical MQAM link transmission schemes. We show that the cross-layer optimization problems can be closely approximated by convex optimization problems that can be efficiently solved. There are two main contributions of this paper. First of all, we minimize the total network energy that includes both transmission and circuit energy consumptions, where we explore the tradeoff between the two energy elements. Specifically, we use interference-free TDMA as the medium access control scheme. We optimize the routing flow, TDMA slot assignment, and MQAM modulation rate and power on each link. The results demonstrate that the minimum energy transmission scheme is a combination of multihop and single-hop transmissions for general networks; including circuit energy favors transmission schemes with fewer hops. Secondly, based on the solved optimal transmission scheme, we quantify the best trade-off curve between delay and energy consumption, where we derive a scheduling algorithm to minimize the worst-case packet delay.

Cooperation among base stations has demonstrated substantial capacity gain in cellular systems. The optimal transmission scheme under full base station cooperation requires all users to transmit simultaneously and a central joint receiver for multi-user detection. We consider some sub-optimal but more practical schemes of orthogonal channel access either within a cell (intra-cell TDMA) or among cells (inter-cell time sharing), which correspond to a partitioning of overall channel resources. The effects of various schemes on the uplink capacity of a cellular system are then compared for a modified Wyner model.

Coverage spectral efficiency (CSE) characterizes the tradeoff between efficient channel reuse and the achievable rates per cell, under the assumption of detection by a single base station and intra-cell FDMA. It is well known that intra-cell FDMA is not in general optimal. In this paper we study an alternative intra- cell wide-band scheme as well as the base station cooperation in detection, which has demonstrated potential capacity gain. The effect on CSE of different schemes are then compared and the optimal reuse distance is determined for each scheme.

We consider the distributed estimation of an unknown vector signal in a bandwidth constrained sensor network with a fusion center (FC). Due to power and bandwidth limitations, each sensor compresses its data in order to minimize the amount of information that needs to be communicated to the FC. In this context, we design a linear decentralized estimation scheme (DES), where each sensor linearly encodes its observations before the transmission to the FC, which performs a minimum mean squared error (MMSE) estimation for the unknown vector signal based on the received messages. When the channels between sensors and the FC are orthogonal, it has been shown previously that the complexity of designing the optimal encoding matrices is NP-hard in general. In this paper, we study the optimal design of linear DES for the case of non- orthogonal multiple access channel (MAC) under both bandwidth and power constraints. We show that when the MAC between sensors and the FC is noiseless, the resulting problem has a closed-form solution, while in the noisy MAC case, the problem can be efficiently solved by semi-definite programming (SDP).

We investigate distributed estimation based on measurements from multiple wireless sensors. For the same target, different sensors have different observations, which are modeled by additive observation noises of different variances. The observations are transmitted using (analog) amplify-and-forward transmissions from the sensors over non-ideal wireless channels to a fusion center, where they are combined to generate an estimate of the observed target. Our goal is to minimize total end-to-end distortion under certain power constraints, assuming the Best Linear Unbiased Estimator (BLUE) is used. We analyze the system outage performance, and show an achievable diversity gain of order K, which is the number of sensors. We also show that by turning off bad sensors, i.e., sensors with bad channels, we achieve adaptive power gain without losing diversity gain, where the adaptive power gain is similar to the array gain achieved in Multiple Input Single Output (MISO) systems when channel conditions are known to the transmitter.

A substantial amount of research has focused on analyzing and achieving the diversity-multiplexing tradeoff in multiple antenna (MIMO) wireless communications. Recently, ARQ protocols have been added to these formulations and shown to perform as a type of diversity. Our goal in this paper is to find the optimal operating point in the diversity-multiplexing-ARQ tradeoff, with a particular focus on delay sensitive systems. Previous results in this area construct performance measures through the use of high SNR asymptotic approximations. While effective, these approximations tend to trivialize the delay performance of MIMO systems. We present a dynamic programming formulation for finding the optimal diversity gain, multiplexing gain, and ARQ window size, without relying on a high SNR approximation. Our results show that the a delay sensitive system requires one to adapt diversity and multiplexing to the time-requires workload in the system. We provide numerical examples that demonstrate the significant performance gains that can be achieved by choosing an adaptive policy over a static allocation of diversity and multiplexing.

Capacity gain from transmitter and receiver cooperation under channel fading are compared in a relay network where the cooperating nodes are close together. We assume a Rayleigh flat-fading environment in the high signal-to-noise ratio (SNR) regime where the transmitters only have channel distribution information (CDI) but not channel state information (CSI). When all nodes have equal average transmit power, we show that the decode-and-forward transmitter cooperation strategy is capacity-achieving and is superior to receiver cooperation. However, the compress-and-forward receiver cooperation strategy is shown to outperform transmitter cooperation when power is optimally allocated among the nodes. Furthermore, we show that cooperative systems provide resilience to channel fading. However, in a fading channel, capacity becomes more sensitive to power allocation, and the cooperating nodes need to be closer together. With respect to limits on cooperation, it is shown that in a large cluster of M cooperating nodes, transmitter cooperation without CSI at the transmitter (CSIT), or receiver cooperation under equal power allocation, provides no capacity gain in a static channel, and at most a constant capacity gain that fails to grow with M in a fading channel.

Adaptive modulation schemes for fading channels are usually required to fulfill certain long-term average BER targets. However, for simplicity and mathematical tractability, these schemes are often designed by fixing the short-term instantaneous BER to the target value. In this paper, the analysis and design of variable-rate variable-power QAM schemes with average BER constraints are tackled for a MIMO beamforming system with MRC and imperfect CSI. The SISO system is considered as a special case of these more general results. Approximate closed-form policies are derived for continuous rate and power adaptation which are compared to fully discrete policies designed numerically. Closed-form expressions for the ASE of the proposed policies are derived and evaluated. Our results indicate that imperfect CSI and discrete rate and power constraints do not significantly degrade performance.

Adaptive modulation schemes for fading channels are usually required to fulfill certain long-term average BER targets. However, for simplicity and mathematical tractability, these schemes are often designed by fixing the short-term instantaneous BER to the target value. In this paper, the analysis and design of variable-rate variable-power QAM schemes with average BER constraints are tackled for MIMO multiplexing with imperfect CSI. The SISO system is considered as a special case of these more general results. Approximate closed-form policies are derived for continuous rate and power adaptation which are compared to the fully discrete policies. Our results indicate that MIMO multiplexing is much more sensitive to imperfect CSI than MIMO beamforming due to the self-interference that arises from channel coupling. In particular, if interference between eigenchannels is large, MIMO multiplexing should utilize only one of its eigenchannels, in which case all multiplexing gain is lost.

We determine exact closed-form expressions for the outage probability of multiple-input/multiple-output systems in Rayleigh fading with maximal ratio diversity combining and co-channel interference. Our analysis generalizes prior work in that we place no restrictions on the number or power of the interferers, or on the number of antennas at the transmitter and receiver. We also present an alternative mathematical approach to performance analysis that leads to an undemanding expression for the SINR moment generating function, which can then be used to evaluate average probability of error and the moments of the SINR. Our numerical results indicate that, for a fixed total interference power, system performance degrades when there are dominant interferers. In addition, for a fixed total number of transmit and receive antennas, outage probability and average bit error rate decrease when the transmitter and receiver have the same number of antennas.

We consider channel coding with feedback for the general case where the feedback may be an arbitrary deterministic function of the output samples. Under the assumption that the channel states take values in a finite alphabet, we find an achievable rate and an upper bound on the capacity. We conclude by showing that when the channel is indecomposable, and has no intersymbol interference, its capacity is given by the limit of the maximum of the (normalized) directed information between the input XNand the output YN, i.e. C = limNrarrinfin/1N max I(XNrarr YN), where the maximization is over the causal conditioning probability Q(xN||kN-) defined in this paper

We analyze the sum-rate performance of a multi-antenna downlink system carrying more users than transmit antennas, with partial channel knowledge at the transmitter due to finite rate feedback. In order to exploit multiuser diversity, we show that the transmitter must have, in addition to directional information, information regarding the quality of each channel. Such information should reflect both the channel magnitude and the quantization error. Expressions for the SINR distribution and the sum-rate are derived, and tradeoffs between the number of feedback bits, the number of users, and the SNR are observed. In particular, for a target performance, having more users reduces feedback load

We compare the rate of a multiple-antenna relay channel to the capacity of multiple-antenna systems to characterize the cooperative capacity in different SNR regions. While it is known that in the asymptotic regime, at a high SNR or with a large number of cooperating nodes, cooperative systems lack full multiplexing gain, in this paper we consider cooperative capacity gain at moderate SNR with a fixed number of cooperating antennas. We show that up to a lower bound to an SNR threshold, a cooperative system performs at least as well as a MIMO system with isotropic inputs; whereas beyond an upper bound to the SNR threshold, the cooperative system is limited by its coordination costs, and the capacity is strictly less than that of a MIMO orthogonal channel. The SNR threshold depends on the network geometry (the power gain g between the source and relay) and the number of cooperating antennas M; when the relay is close to the source (g [unk] 1), the SNR threshold lower and upper bounds are approximately equal. As the cooperating nodes are closer, i.e., as g increases, the MIMO-gain region extends to a higher SNR. Whereas for a populous cluster, i.e., when M is large, the coordination-limited region sets in at a lower SNR.

We compare the rates of one-shot and iterative conferencing in a cooperative Gaussian relay channel. The relay and receiver cooperate via a conference, as introduced by Willems, in which they exchange a series of communications over orthogonal links. Under one-shot conferencing, decode-and-forward (DF) is capacity-achieving when the relay has a strong channel. On the other hand, Wyner-Ziv compress-and-forward (CF) approaches the cut-set bound when the conference link capacity is large. To contrast with one-shot conferencing, we consider a two-round iterative conference scheme; it comprises CF in the first round, and DF in the second. When the relay has a weak channel, the iterative scheme is disadvantageous. However, when the relay channel is strong, iterative cooperation, with optimal allocation of conferencing resources, outperforms one-shot cooperation provided that the conference link capacity is large. When precise allocation of conferencing resources is not possible, we consider iterative cooperation with symmetric conference links, and show that the iterative scheme still surpasses one-shot cooperation, albeit under more restricted conditions.

Although the capacity of multiple-input/multiple-output (MIMO) broadcast channels (BCs) can be achieved by dirty paper coding (DPC), it is difficult to implement in practical systems. This paper investigates if, for a large number of users, simpler schemes can achieve the same performance. Specifically, we show that a zero-forcing beamforming (ZFBF) strategy, while generally suboptimal, can achieve the same asymptotic sum capacity as that of DPC, as the number of users goes to infinity. In proving this asymptotic result, we provide an algorithm for determining which users should be active under ZFBF. These users are semiorthogonal to one another and can be grouped for simultaneous transmission to enhance the throughput of scheduling algorithms. Based on the user grouping, we propose and compare two fair scheduling schemes in round-robin ZFBF and proportional-fair ZFBF. We provide numerical results to confirm the optimality of ZFBF and to compare the performance of ZFBF and proposed fair scheduling schemes with that of various MIMO BC strategies.

The finite-state Markov channel (FSMC) is a time-varying channel having states that are characterized by a finite-state Markov chain. These channels have infinite memory, which complicates their capacity analysis. We develop a new method to characterize the capacity of these channels based on Lyapunov exponents. Specifically, we show that the input, output, and conditional entropies for this channel are equivalent to the largest Lyapunov exponents for a particular class of random matrix products. We then show that the Lyapunov exponents can be expressed as expectations with respect to the stationary distributions of a class of continuous-state space Markov chains. This class of Markov chains, which is closely related to the prediction filter in hidden Markov models, is shown to be nonirreducible. Hence, much of the standard theory for continuous state-space Markov chains cannot be applied to establish the existence and uniqueness of stationary distributions, nor do we have direct access to a central limit theorem (CLT). In order to address these shortcomings, we utilize several results from the theory of random matrix products and Lyapunov exponents. The stationary distributions for this class of Markov chains are shown to be unique and continuous functions of the input symbol probabilities, provided that the input sequence has finite memory. These properties allow us to express mutual information and channel capacity in terms of Lyapunov exponents. We then leverage this connection between entropy and Lyapunov exponents to develop a rigorous theory for computing or approximating entropy and mutual information for finite-state channels with dependent inputs. We develop a method for directly computing entropy of finite-state channels that does not rely on simulation and establish its convergence. We also obtain a new asymptotically tight lower bound for entropy based on norms of random matrix products. In addition, we prove a new functional CLT for sample entropy and apply this theorem to characterize the error in simulated estimates of entropy. Finally, we present numerical examples of mutual information computation for intersymbol interference (ISI) channels and observe the capacity benefits of adding memory to the input sequence for such channels

In this correspondence, we determine the feedback capacity region of a two user Gaussian multiple-access channel (MAC) with multiple antennas at the base station and a single antenna at each user. The vector MAC with a single antenna at the base station and multiple antennas at each user is shown to be equivalent to a scalar MAC. We also determine the capacity enhancement due to feedback at high signal-to-noise ratio (SNR) for the scalar and vector MAC for any number of users. Extensions of the high SNR results to the vector broadcast channel are also provided.

In this correspondence, we investigate the effect of channel estimation error on the capacity of multiple-input-multiple-output (MIMO) fading channels. We study lower and upper bounds of mutual information under channel estimation error, and show that the two bounds are tight for Gaussian inputs. Assuming Gaussian inputs we also derive tight lower bounds of ergodic and outage capacities and optimal transmitter power allocation strategies that achieve the bounds under perfect feedback. For the ergodic capacity, the optimal strategy is a modified waterfilling over the spatial (antenna) and temporal (fading) domains. This strategy is close to optimum under small feedback delays, but when the delay is large, equal powers should be allocated across spatial dimensions. For the outage capacity, the optimal scheme is a spatial waterfilling and temporal truncated channel inversion. Numerical results show that some capacity gain is obtained by spatial power allocation. Temporal power adaptation, on the other hand, gives negligible gain in terms of ergodic capacity, but greatly enhances outage performance.

We consider the joint optimal design of the physical, medium access control (MAC), and routing layers to maximize the lifetime of energy-constrained wireless sensor networks. The problem of computing lifetime-optimal routing flow, link schedule, and link transmission powers for all active time slots is formulated as a non-linear optimization problem. We first restrict the link schedules to the class of interference-free time division multiple access (TDMA) schedules. In this special case, we formulate the optimization problem as a mixed integerconvex program, which can be solved using standard techniques. Moreover, when the slots lengths are variable, the optimization problem is convex and can be solved efficiently and exactly using interior point methods. For general non-orthogonal link schedules, we propose an iterative algorithm that alternates between adaptive link scheduling and computation of optimal link rates and transmission powers for a fixed link schedule. The performance of this algorithm is compared to other design approaches for several network topologies. The results illustrate the advantages of load balancing, multihop routing, frequency reuse, and interference mitigation in increasing the lifetime of energy-constrained networks. We also briefly discuss computational approaches to extend this algorithm to large networks

We introduce two new medium access control (MAC) protocols for wireless ad hoc networks, the progressive backoff algorithm (PBOA) and the progressive ramp up algorithm (PRUA). Both protocols divide time in frames in which a contention slot is followed by a data slot. PBOA is integrated with a well known power control algorithm. PRUA performs no power control, and so is not as energy efficient, but can achieve a tight packing of transmissions by allowing nodes to make educated decisions during the contention period. Under both protocols, contenting nodes try to select their potential destinations so that spatial reuse is as high as possible, even if that means transmitting a packet that is not on the head of their routing buffer. We compare both protocols with carrier sense multiple access with collision avoidance (CSMA/CA), and also with the power control MAC (PCM) protocol. We also compare them with a hypothetical MAC protocol that would be able to make optimal decisions and so achieve the network capacity. We show that both protocols perform better than CSMA/CA and PCM in terms of throughput and robustness with respect to the choice of the routing protocol. Also, PRUA is more energy efficient than CSMA/CA, and PBOA is more energy efficient than both CSMA/CA and PCM. However, due to their distributed nature, our protocols still can not achieve the network capacity, even in simple network topologies

We consider a multi-user MIMO downlink system employing zero-forcing beamforming (ZFBF) as a spatial multiplexing strategy, and propose low-complexity user subset selection methods based on a clique (fully connected subgraph) search. The proposed algorithms, maximum weighted clique (MWC)-ZFBF and greedy weighted clique (GWC)-ZFBF, are shown to achieve the asymptotic sum-capacity of MIMO downlink channels as the number of users goes to infinity. Thus, clique search based ZFBF is an appealing strategy in MIMO downlink systems with a large number of users.

We consider sensor networks where energy is a limited resource so that energy consumption must be minimized while satisfying given throughput requirements. Moreover, energy consumption must take into account both the transmission energy and the circuit processing energy for short-range communications. In this context, we analyze energy-efficient joint routing and link scheduling to achieve the optimal tradeoff between energy and delay. For networks composed of multiple clusters of nodes, we propose and analyze the cooperative multiple-input multiple-output (MIMO) approach where multiple sensor nodes in the same cluster cooperate in signal transmission and/or reception. We show that local information exchange within the cluster is not necessary for node cooperation based on Alamouti diversity codes if the transmissions are properly scheduled. We further show that the routing optimization problem based on cooperative MIMO can be solved by designing an equivalent single-input single-output (SISO) system, where each cluster is treated as a super node. For both SISO-based and MIMO-based cases, we derive the best energy-delay tradeoff curves and show that the cooperative MIMO approach dramatically improves the energy-delay performance.

Sensor networks in which energy is a limited resource so that energy consumption must be minimized for the intended application are considered. In this context, an energy-efficient method for the joint estimation of an unknown analog source under a given distortion constraint is proposed. The approach is purely analog, in which each sensor simply amplifies and forwards the noise-corrupted analog observation to the fusion center for joint estimation. The total transmission power across all the sensor nodes is minimized while satisfying a distortion requirement on the joint estimate. The energy efficiency of this analog approach is compared with previously proposed digital approaches with and without coding. It is shown in our simulation that the analog approach is more energy-efficient than the digital system without coding, and in some cases outperforms the digital system with optimal coding.

We consider sensor networks where energy is a limited resource so that energy consumption must be minimized while satisfying given throughput requirements. Moreover, energy consumption must take into account both the transmission energy and the circuit processing energy for short-range communications. We emphasize that the energy efficiency must be supported across all layers of the protocol stack through a cross-layer design. In this context, we analyze energy-efficient joint routing, scheduling, and link adaptation strategies that maximize the network lifetime. We propose variable-length TDMA schemes where the slot length is optimally assigned according to the routing requirement while minimizing the energy consumption across the network. We show that the optimization problems can be transformed into or approximated by convex problems that can be efficiently solved using known techniques. The results show that multihop routing schemes are more energy-efficient when only transmission energy is considered, but single-hop transmissions may be more efficient when the circuit processing energy is considered.

We consider a wireless sensor network where the nodes have limited energy. We first analyze the delay performance of a transmission scheme based on time division multiple access (TDMA). We propose a simple link scheduling algorithm to find the minimum-delay schedule given the slot lengths for all the links. We then combine these results with our previous work on energy-optimal cross-layer design to minimize the delay in transferring a fixed number of bits from the source nodes to the sink, in an energy-constrained manner. We also study the tradeoff between the total energy consumption and delay. Pareto optimal energy-delay curves are computed by solving a series of convex optimization problems where each objective function is a weighted sum of the delay and the total energy consumption. The computation is done for networks with and without link adaptation capabilities.

Packet switching remains one of the bottlenecks in building fast Internet routers. Load balancing and switch scheduling are two important algorithms in the effort to maximize the throughput and minimize the latency of these packet switches. A load balancing algorithm regulates the traffic to conform to the service rates while a switch scheduling algorithm allocates the service rates adaptive to the arrival patterns. Many existing load balancing and switch scheduling algorithms are very similar. We show that load balancing and switch scheduling systems are dual systems based on the linear queue dynamics approximation. This allows us to cast a load balancing problem as a scheduling problem, and vice versa. We further show an example of designing a new algorithm for load balancing using an existing scheduling algorithm based on the duality. The duality perspective also allows us to solve unknown problems. We find the entropy rate of the randomized bandwidth allocation system with linear queue dynamics based on the knowledge of the entropy rate of the randomized load balancing system. For the general case, we find both an upper and a lower bound on the entropy rate. The joint use of dual load balancing and switch scheduling algorithms leads to performance gains as we show using mean field analysis.

In MIMO downlink channels, the capacity is achieved by dirty paper coding (DPQ). However, DPC is difficult to implement in practical systems. This work investigates if, for a large number of users, simpler schemes can achieve the same performance. Specifically, we show that a zero-forcing beamforming (ZFBF) strategy, while generally suboptimal, can achieve the same asymptotic sum-rate capacity as that of DPC, as the number of users goes to infinity. In proving this asymptotic result, we propose an algorithm for determining which users should be active in ZFBF transmission. These users are semi-orthogonal to one another, and when fairness among users is required, can be grouped for simultaneous transmissions to enhance the throughput of fair schedulers. We provide numerical results to confirm the optimality of ZFBF and to compare its performance with that of various MIMO downlink strategies.

We consider the joint optimal design of physical, medium access control (MAC), and routing layers to maximize the lifetime of energy-constrained wireless sensor networks. The problem of computing a lifetime-optimal routing flow, link schedule, and link transmission powers is formulated as a non-linear optimization problem. We first restrict the link schedules to the class of interference-free time division multiple access (TDMA) schedules. In this special case we formulate the optimization problem as a mixed integer-convex program, which can be solved using standard techniques. For general non-orthogonal link schedules, we propose an iterative algorithm that alternates between adaptive link scheduling and computation of optimal link rates and transmission powers for a fixed link schedule. The performance of this algorithm is compared to other design approaches for several network topologies. The results illustrate the advantages of load balancing, multihop routing, frequency reuse, and interference mitigation in increasing the lifetime of energy-constrained networks. We also describe a partially distributed algorithm to compute optimal rates and transmission powers for a given link schedule.

A significant amount of recent research has focused on characterizing the diversity-multiplexing tradeoff region in multiple antenna wireless systems. In this paper we focus on finding the point on this diversity-multiplexing region that minimizes an end-to-end distortion measure. Our goal is to find the optimal balance between the increased data rate provided by multiplexing versus the error protection provided by diversity. We first present analytical results for the distortion achieved by concatenating a vector quantizer with a MIMO channel. We show that in the high SNR regime we can find a closed form expression for the end-to-end distortion as a function of the optimal point on the diversity-multiplexing tradeoff curve. We also show that this framework can be used to minimize end-to-end distortion for a broad class of source and channel codes. We demonstrate this with a non-asymptotic example using progressive video encoding and space-time channel codes. Finally, we summarize a methodology for incorporating delay into the end-to-end distortion model and solving for the optimal tradeoff between diversity, multiplexing, and delay

Capacity gain from transmitter and receiver cooperation are compared in a relay network where the cooperating nodes are close together. When all nodes have equal average transmit power along with full channel state information (CSI), it is proved that transmitter cooperation outperforms receiver cooperation, whereas the opposite is true when power is optimally allocated among the nodes but only receiver phase CSI is available. In addition, when the nodes have equal average power with receiver phase CSI only, cooperation is shown to offer no capacity improvement over a non-cooperative scheme with the same average network power. When the system is under optimal power allocation with full CSI, the decode-and-forward transmitter cooperation rate is close to its cut-set capacity upper bound, and outperforms compress-and-forward receiver cooperation. Moreover, it is shown that full CSI is essential in transmitter cooperation, while optimal power allocation is essential in receiver cooperation

We propose a scalar upper bound on the capacity region of the isotropic fading vector broadcast channel in terms of the capacity region of a scalar fading broadcast channel. The scalar upper bound is applicable to the broad class of isotropic fading broadcast channels regardless of the distribution of the users' channel magnitudes, the distribution of the additive noise experienced by each user, or the amount of channel knowledge available at the receiver. Using this upper bound, we prove the optimality of the Alamouti scheme in a broadcast setting, extend the recent results on the capacity of nondegraded, fading scalar broadcast channels to nondegraded fading vector broadcast channels, and determine the capacity region of a fading vector Gaussian broadcast channel with channel magnitude feedback. We also provide an example of a Rayleigh-fading broadcast channel with no channel state information available to the receiver (CSIR), where the bound on the capacity region obtained by a naive application of the scalar upper bound is provably loose, because it fails to account for the additional loss in degrees of freedom due to lack of channel knowledge at the receiver. A tighter upper bound is obtained by separately accounting for the loss in degrees of freedom due to lack of CSIR before applying the scalar upper bound.

We compare the capacity of dirty-paper coding (DPC) to that of time-division multiple access (TDMA) for a multiple-antenna (multiple-input multiple-output (MIMO)) Gaussian broadcast channel (BC). We find that the sum-rate capacity (achievable using DPC) of the multiple-antenna BC is at most min(M,K) times the largest single-user capacity (i.e., the TDMA sum-rate) in the system, where M is the number of transmit antennas and K is the number of receivers. This result is independent of the number of receive antennas and the channel gain matrix, and is valid at all signal-to-noise ratios (SNRs). We investigate the tightness of this bound in a time-varying channel (assuming perfect channel knowledge at receivers and transmitters) where the channel experiences uncorrelated Rayleigh fading and in some situations we find that the dirty paper gain is upper-bounded by the ratio of transmit-to-receive antennas. We also show that min(M,K) upper-bounds the sum-rate gain of successive decoding over TDMA for the uplink channel, where M is the number of receive antennas at the base station and K is the number of transmitters.

In this correspondence, we consider the problem of maximizing sum rate of a multiple-antenna Gaussian broadcast channel (BC). It was recently found that dirty-paper coding is capacity achieving for this channel. In order to achieve capacity, the optimal transmission policy (i.e., the optimal transmit covariance structure) given the channel conditions and power constraint must be found. However, obtaining the optimal transmission policy when employing dirty-paper coding is a computationally complex nonconvex problem. We use duality to transform this problem into a well-structured convex multiple-access channel (MAC) problem. We exploit the structure of this problem and derive simple and fast iterative algorithms that provide the optimum transmission policies for the MAC, which can easily be mapped to the optimal BC policies.

We derive the outage capacity region of an M-user fading multiple-access channel (MAC) under the assumption that both the transmitters and the receiver have perfect channel side information (CSI). The outage capacity region is implicitly obtained by deriving the outage probability region for a given rate vector. Given a required rate and average power constraint for each user, we find a successive decoding strategy and a power allocation policy that achieves points on the boundary of the outage probability region. We discuss the scenario where an outage must be declared simultaneously for all users (common outage) and when outages can be declared individually (individual outage) for each user.

Wireless systems where the nodes operate on batteries so that energy consumption must be minimized while satisfying given throughput and delay requirements are considered. In this context, the best modulation strategy to minimize the total energy consumption required to send a given number of bits is analyzed. The total energy consumption includes both the transmission energy and the circuit energy consumption. For uncoded systems, by optimizing the transmission time and the modulation parameters, it is shown that up to 80% energy savings is achievable over nonoptimized systems. For coded systems, it is shown that the benefit of coding varies with the transmission distance and the underlying modulation schemes.

We analyze a mobile multiple input multiple output wireless link with M transmit and N receive antennas operating in a spatially correlated Rayleigh flat fading environment. Only the correlations between the channel coefficients are assumed to be known at the transmitter and the receiver. The channel coefficients are correlated in space and uncorrelated in time from one coherence interval to another. These coefficients remain constant for a coherence interval of T symbol periods after which they change to another independent realization according to the spatial correlation model. For this system we characterize the structure of the input signal that achieves capacity. The capacity achieving transmit signal is expressed as the product of an isotropically distributed unitary matrix, an independent nonnegative diagonal matrix and a unitary matrix whose columns are the eigenvectors of the transmit fade covariance matrix. For the case where the number of transmit antennas M is larger than the channel coherence interval T, we show that the channel capacity is independent of the smallest M-T eigenvalues of the transmit fade covariance matrix. In contrast to the previously reported results for the spatially white fading model where adding more transmit antennas beyond the coherence interval length (M>T) does not increase capacity, we find that additional transmit antennas always increase capacity as long as their channel fading coefficients are spatially correlated with the other antennas. We show that for fast hopping or fast fading systems (T=1) with only channel covariance information available to the transmitter and receiver, transmit fade correlations are beneficial. Mathematically, we prove this by showing that capacity is a Schur-convex function of the vector of eigenvalues of the transmit fade correlation matrix. We also show that the maximum possible capacity gain due to transmitter fade correlations is 10logM dB.

We consider radio applications in sensor networks where energy is a limited resource so that energy consumption must be minimized while satisfying given delay and throughput requirements. In this context, we analyze energy-efficient data collection strategies where we minimize the total energy consumption necessary for collecting a certain amount of data from multiple sensors. The total energy consumption includes both the transmission energy and the circuit energy consumption. We propose a variable-length TDMA scheme where the slot length is adaptively assigned according to the number of bits in the transmitting queues and the distance between the transmitting nodes and the collecting node. The underlying goal is to finish the collection of information bits from the multiple sensor nodes before a deadline T with minimum energy cost. We show that the problem can be efficiently solved by convex relaxation methods, and in some special cases simple analytical solutions can be derived.

This paper presents new distributed power and admission control algorithms for ad-hoc wireless networks in random channel environments. Previous work in this area has focused on distributed control for ad-hoc networks with fixed channels. We show that the algorithms resulting from such formulations do not accurately capture the dynamics of a time-varying channel. The performance of the network in terms of power consumption and generated interference can be severely degraded when power and admission control algorithms that are designed for deterministic channels are applied to random channels. In particular, some well-known optimality results for deterministic channels no longer hold. In order to address these problems we propose a new criterion for power optimality in ad-hoc wireless networks. We then show that the optimal power allocation for this new criterion can be found through an appropriate stochastic approximation algorithm. We also present a modified version of this algorithm for tracking nonstationary equilibria, which allows us to perform admission control. Ultimately, the iterations of the stochastic approximation algorithms can be decoupled to form fully distributed on-line power and admission control algorithms for ad-hoc wireless networks with time-varying channels.

We investigate ergodic capacities and optimal transmitter strategies in Rayleigh fading multiple input multiple output (MIMO) channels with spatial correlation, when there exist channel uncertainties arising from the combined effect of channel estimation error and limited feedback. We consider both covariance feedback and instantaneous feedback, and formulate optimization problems that determine the capacities and optimal transmitter designs for both cases. In the high SNR regime, the optimal solutions have simple closed form formulas that involve inverting the channel covariance and waterfilling over instantaneous channel gains. Numerical results show that instantaneous feedback gives large capacity gain at low SNR and is also helpful at high SNR. Covariance feedback, on the other hand, seems to give little gain at mid SNR, but is almost as good as instantaneous feedback at high SNR under a reasonable channel estimation quality.

We develop an upperbound on the capacity region of an isotropic fading vector broadcast channel in terms of the capacity region of a scalar fading broadcast channel. Using this upperbound we prove the optimality of the Alamouti scheme [1] in a broadcast setting and extend the recent results [2] on the capacity region of the fading scalar non-degraded broadcast channel to fading vector non-degraded broadcast channels. The upperbound is fundamental in that it makes no assumption regarding the distribution of the users' channel magnitudes, the distribution of the additive noise, or the amount of channel information available at the receiver. The scalar upperbound explicitly characterizes the loss of degrees of freedom in a vector broadcast channel when the transmitter has no information about the "direction" of the users' channel vectors.

In this paper we derive an upper bound on the sum-rate gain that dirty-paper coding provides over TDMA for MIMO broadcast channels. We find that the sum-rate capacity (achievable using dirty-paper coding) of the multiple-antenna broadcast channel is at most min(M;K) times the largest single-user capacity (i.e. the TDMA sum-rate) in the system, where M is the number of transmit antennas and K is the number of receivers. This result is independent of the number of receive antennas. We investigate the tightness of this bound in a time-varying channel (assuming perfect channel knowledge at receivers and transmitters) where the channel experiences uncorrelated Rayleigh fading and in some situations we find that the dirty paper gain is upper bounded by the ratio of transmit to receive antennas. We also show that min(M,K) upper bounds the sum rate gain of successive decoding over TDMA for the uplink, where M is the number of receive antennas at the base station and K is the number of transmitters.

In this paper, we investigate the effect of channel estimation error on the capacity of multiple input multiple output (MIMO) systems in i.i.d. Rayleigh flat-fading channels. We study lower and upper bounds of mutual information under channel estimation error, and show that the two bounds are tight for Gaussian inputs. It is seen that the mutual information increases with the. number of antennas, but is limited by channel estimation error at high SNR. We also derive tight lower bounds of ergodic and outage capacities and optimal transmitter power allocation strategies that achieve the bounds. For the ergodic capacity, the optimal strategy is a modified waterfilling over the spatial (subchannel) and temporal (fading) domain. For the outage capacity, it is a spatial waterfilling and temporal truncated channel inversion. Numerical results show that some capacity gain is obtained by spatial power allocation. Temporal power adaptation, on the other hand, gives negligible gain in terms of ergodic capacity, but greatly enhances outage performance.

We study wireless ad hoc networks with a large number of nodes. We first focus on a network of n immobile nodes, each with a destination node chosen in random. We develop a scheme under which, in the absence of fading, the network can provide each node with a traffic rate /spl lambda//sub 1/(n)=K/sub 1/(nlog n)/sup -1/ 2/. This result was first shown in J. Hightower and G. Borriello (2001) under a similar setting, however the proof presented here is shorter and uses only basic probability tools. We then proceed to show that, under a general model of fading, each node can send data to its destination with a rate /spl lambda//sub 2/(n)=K/sub 2/n/sup -1// /sup 2/(log n)/sup -3/2/. Next, we extend our formulation to study the effects of node mobility. We first develop a simple scheme under which each of the a mobile nodes can send data to a randomly chosen destination node with a rate /spl lambda//sub 3/(n)=K/sub 3/n/sup -1/2/(log n)/sup -3/2/, and with a fixed upper bound on the packet delay d/sub max/ that does not depend on n. We subsequently develop a scheme under which each of the nodes can send data to its destination with a rate /spl lambda//sub 4/(n)=K/sub 4/n/sup (d-1)/ 2/(log n)/sup -5/ 2 /provided that nodes are willing to tolerate packet delays smaller than d/sub max/(n)<K/sub 5/n/sup d/, where 0<d<1. With both schemes, a general model of fading is assumed. In addition, nodes require no global topology or routing information, and only need to coordinate locally. The above results hold for an appropriate choice of values for the constants K/sub i/, and with probability approaching 1 as the number of nodes n approaches infinity.

This paper presents new distributed power and admission control algorithms for ad-hoc wireless networks in random channel environments. Previous work in this area has focused on distributed control for ad-hoc networks with fixed channels. We show that the algorithms resulting from such formulations do not accurately capture the dynamics of a time-varying channel. Hence, algorithms designed for fixed channels may perform quite poorly in random channels. In order to address these issues, this work proposes new algorithms, based on stochastic approximation, for optimal distributed power and admission control in random channels

We consider a set of parallel, two-user scalar Gaussian broadcast channels, where the transmitter wishes to send independent information to each of the receivers and common information to both receivers. The capacity region of this channel is implicitly characterized in [A. El Gamal, (1980)]. Here, we provide an explicit characterization of the power and rate allocation schemes that achieve the boundary of the three-dimensional rate region. We also propose a dirty-paper coding achievable region for MIMO broadcast channels with common information.

This paper examines communication between a cluster of closely-packed nodes with another cluster of closely-packed nodes. The nodes within each cluster are separated by small distances, relative to the distance between the two clusters. The effect on capacity of cooperation between nodes in the transmitting cluster and cooperation between nodes in the receiving cluster is investigated.

We compare two strategies for lossy source description across a pair of unreliable channels. In the first strategy, we use a broadcast channel code to achieve a different rate for each possible channel realization, and then use a multiresolution source code to describe the source at the resulting rates. In the second strategy, we use a channel coding strategy for two independent channels coupled with a multiple description source code. In each case, we choose the coding parameters to minimize the expected end-to-end distortion in the source reconstruction. We demonstrate that in point-to-point communication across a pair of non-ergodic channels, multiple description coding can provide substantial gains relative to multiresolution and broadcast coding. We then investigate this comparison in a simple MIMO channel. We demonstrate the inferior performance of space time coding with multiresolution source coding and broadcast channel coding relative to multiple description codes and a time sharing channel coding strategy. These results indicate that for non-ergodic channels, the traditional definition of channel capacity does not necessarily lead to the best channel code from the perspective of end-to-end source distortion.

We investigate capacity and achievable rates for transmitter cooperation schemes in ad-hoc wireless networks. In addition to cooperative dirty paper coding, we propose two new cooperative transmission techniques: time-division successive broadcasting and time-division relaying. We show that transmitter cooperation can significantly increase capacity, even if one of the cooperating nodes is halfway between the transmit and receive node clusters. However, the best form of cooperation depends on the relative geometry of the transmit and receive clusters. When the transmitters are close together, cooperative dirty paper coding achieves the highest rates. However, if one of the transmitters is relatively close to the receive cluster, cooperative broadcasting or relaying achieves higher rates than dirty paper coding. That is because, at large separations, the exchange of messages between the transmitters required for dirty paper coding consumes a substantial amount of power. We show that in most cases transmitter cooperation provides a substantial capacity improvement over noncooperative techniques, especially under an equal rate constraint.

We propose a cross-layer design framework for supporting delay-critical traffic over ad hoc wireless networks and analyze its benefits for video streaming. In this framework, link capacities and traffic flows are jointly allocated to minimize the congestion experienced by video packets. The optimal solution, calculated via time sharing among different transmission schemes, concentrates resources only on active links. Experimental results on a simulated network illustrate the advantages of cross-layer design over another method based on oblivious layers. With one path, the cross-layer approach yields a 10-fold gain in supported data rate or equivalently 8.5 dB improvement in PSNR of achievable received video quality. Using 3 paths, the gain is 3-fold in rate or 5 dB in video quality. While multipath routing is essential to high data rate in oblivious-layered design, cross-layer design achieves efficient resource utilization regardless of the number of routes.

We consider the problem of optimal power scheduling for the decentralized estimation of a noise-corrupted signal in an inhomogeneous sensor network. Sensor observations are first quantized into discrete messages, then transmitted to the fusion center where a final estimate is generated. Based on the sensor noise levels and channel gains from sensors to the fusion center, optimal quantization levels and transmit power levels at the local sensors can be chosen to minimize the total transmitting power, while ensuring a given mean squared error (MSE) performance. The proposed optimal power scheduling scheme suggests that the sensors with bad channels or poor observation qualities should decrease their quantization resolutions or simply become inactive in order to conserve power. For the remaining active sensors, their optimal quantization and transmit power levels are determined jointly by individual channel gains, local observation noise variance, and the targeted MSE performance. Numerical examples show that up to 60% energy savings is possible when compared with the uniform quantization strategy.

We consider radio applications in sensor networks, where the nodes operate on batteries so that energy consumption must be minimized, while satisfying given throughput and delay requirements. In this context, we analyze the best modulation and transmission strategy to minimize the total energy consumption required to send a given number of bits. The total energy consumption includes both the transmission energy and the circuit energy consumption. We first consider multi-input-multi-output (MIMO) systems based on Alamouti diversity schemes, which have good spectral efficiency but also more circuitry that consumes energy. We then extend our energy-efficiency analysis of MIMO systems to individual single-antenna nodes that cooperate to form multiple-antenna transmitters or receivers. By transmitting and/or receiving information jointly, we show that tremendous energy saving is possible for transmission distances larger than a given threshold, even when we take into account the local energy cost necessary for joint information transmission and reception. We also show that over some distance ranges, cooperative MIMO transmission and reception can simultaneously achieve both energy savings and delay reduction.

We define a duality between Gaussian multiple-access channels (MACs) and Gaussian broadcast channels (BCs). The dual channels we consider have the same channel gains and the same noise power at all receivers. We show that the capacity region of the BC (both constant and fading) can be written in terms of the capacity region of the dual MAC, and vice versa. We can use this result to find the capacity region of the MAC if the capacity region of only the BC is known, and vice versa. For fading channels we show duality under ergodic capacity, but duality also holds for different capacity definitions for fading channels such as outage capacity and minimum-rate capacity. Using duality, many results known for only one of the two channels can be extended to the dual channel as well.

We solve the transmitter optimization problem and determine a necessary and sufficient condition under which beamforming achieves Shannon capacity in a linear narrowband point-to-point communication system employing multiple transmit and receive antennas with additive Gaussian noise. We assume that the receiver has perfect channel knowledge while the transmitter has only knowledge of either the mean or the covariance of the channel coefficients. The channel is modeled at the transmitter as a matrix of complex jointly Gaussian random variables with either a zero mean and a known covariance matrix (covariance information), or a nonzero mean and a white covariance matrix (mean information). For both cases, we develop a necessary and sufficient condition for when the Shannon capacity is achieved through beamforming; i.e., the channel can be treated like a scalar channel and one-dimensional codes can be used to achieve capacity. We also provide a waterpouring interpretation of our results and find that less channel uncertainty not only increases the system capacity but may also allow this higher capacity to be achieved with scalar codes which involves significantly less complexity in practice than vector coding.

We derive closed-form expressions for the single-user capacity of maximal ratio combining diversity systems taking into account the effect of correlation between the different branches. We consider a Rayleigh fading channel with two kinds of correlation: 1) equal branch signal-to-noise ratios (SNRs) and the same correlation between any pair of branches and 2) unequal branch SNRs and arbitrary correlation between branches such that the eigenvalues of the branch covariance matrix are all distinct. Three adaptive transmission schemes are analyzed: 1) optimal simultaneous power and rate adaptation; 2) optimal rate adaptation with constant transmit power; and 3) channel inversion with fixed rate.

We study different notions of capacity for time-slotted ALOHA systems. In these systems, multiple users synchronously send packets in a bursty manner over a common additive white Gaussian noise (AWGN) channel. The users do not coordinate their transmissions, which may collide at the receiver. For such a system, we define both single-slot capacity and multiple-slot capacity. We then construct a coding and decoding scheme for single-slot capacity that achieves any rate within this capacity region. This coding and decoding scheme for a single time slot combines aspects of multiple access rate splitting and of broadcast codes for degraded AWGN channels. This design allows some bits to be reliably received even when collisions occur and more bits to be reliably received in the absence of collisions. The exact number of bits reliably received under both of these scenarios is part of the code design process, which we optimize to maximize the expected rate in each slot. Next, we examine the behavior of the system asymptotically over multiple slots. We show that there exist coding and decoding strategies such that regardless of the burstiness of the traffic, the system is stable as long as the average rate of the users is within the multiple access capacity region of the channel. In other words, we show that bursty traffic does not decrease the Cover-Wyner capacity region of the multiple access channel. A vast family of codes, which includes the type of codes we introduce for the single-slot transmission, achieve the capacity region, in a sense we define, for multiple-slot transmissions. These codes are stabilizing, using only local information at each of the individual queues. The use of information regarding other queues or the use of scheduling does not improve the multiple-slot capacity region.

We consider radio applications where the nodes operate on batteries so that energy consumption must be minimized while satisfying given throughput and delay requirements. In this context, we analyze the best modulation strategy to minimize the total energy consumption required to send a given number of bits when error-control codes are used. The total energy consumption includes both the transmission energy and the circuit energy consumption. We show that for both MQAM and MFSK the total energy consumption may be reduced significantly if the transmission time T/sub on/ is optimized to reduce the sum of transmission energy and circuit energy consumption. Our optimization considers both delay and peak-power constraints. Numerical examples are given, where we exhibit up to 90% energy savings over modulation strategies that minimize the transmission energy alone. We also show that the benefit of coding varies with the transmission distance and the underlying modulation schemes.

A two transmitter two receiver channel where independent data is sent on each communication link of the system is considered. We consider a three-link system, termed the "Z" channel, in which one transmitter is connected to both receivers while the other transmitter is only connected to one of the receivers. Thus, the "Z" channel has a three dimensional capacity region. We characterize the capacity region of a special class of degraded "Z" channels and establish an achievable region for the Gaussian "Z" channels. Finally, we use genie-aided techniques previously used for the interference and broadcast channels to obtain an outer bound for general "Z" channels.

We consider radio applications where the nodes operate on batteries so that energy consumption must be minimized while satisfying given throughput and delay requirements. In this context, we analyze the best modulation strategy to minimize the total energy consumption required to send a given number of bits. The total energy consumption includes both the transmission energy and the circuit energy consumption. We show that for both MQAM and MFSK the transmission energy decreases with the BT/sub on/ product while the circuit energy consumption increases with T/sub on/, where B is the modulation bandwidth and T/sub on/ is the transmission time. Thus, in short-range applications where the circuit energy consumption is nonnegligible compared with the transmission energy, the total energy consumption is minimized by using the maximum system bandwidth along with an optimized transmission time T/sub on/. We derive this optimal T/sub on/ for MQAM and MFSK modulation in both AWGN channels and Rayleigh fading channels. Our optimization considers both delay and peak-power constraints. Numerical examples are given, where we exhibit up to 68% energy savings over modulation strategies that minimize the transmission energy alone.

We introduce a methodology for studying wireless ad hoc networks in a multihop traffic environment. Our approach is to use theoretical upper bounds on network performance for evaluating the effects of various design choices: we focus on power control, the queuing discipline, the choice of routing and media access protocols, and their interactions. Using this framework, we then concentrate on the problem of medium access for wireless multihop networks. We first study CSMA/CA, and find that its performance strongly depends on the choice of the accompanying routing protocol. We then introduce two protocols that outperform CSMA/CA, both in terms of energy efficiency and achievable throughput. The progressive back off algorithm (PBOA) performs medium access jointly with power control. The progressive rump up algorithm (PRUA) sacrifices energy efficiency in favor of higher throughput. Both protocols slot time, and are integrated with queuing disciplines that are more relaxed than the first in first out (FIFO) rule. They are totally distributed and the overhead they require does not increase with the size and node density of the network.

We provide an overview of the extensive results on the Shannon capacity of single-user and multiuser multiple-input multiple-output (MIMO) channels. Although enormous capacity gains have been predicted for such channels, these predictions are based on somewhat unrealistic assumptions about the underlying time-varying channel model and how well it can be tracked at the receiver, as well as at the transmitter. More realistic assumptions can dramatically impact the potential capacity gains of MIMO techniques. For time-varying MIMO channels there are multiple Shannon theoretic capacity definitions and, for each definition, different correlation models and channel information assumptions that we consider. We first provide a comprehensive summary of ergodic and capacity versus outage results for single-user MIMO channels. These results indicate that the capacity gain obtained from multiple antennas heavily depends on the available channel information at either the receiver or transmitter, the channel signal-to-noise ratio, and the correlation between the channel gains on each antenna element. We then focus attention on the capacity region of the multiple-access channels (MACs) and the largest known achievable rate region for the broadcast channel. In contrast to single-user MIMO channels, capacity results for these multiuser MIMO channels are quite difficult to obtain, even for constant channels. We summarize results for the MIMO broadcast and MAC for channels that are either constant or fading with perfect instantaneous knowledge of the antenna gains at both transmitter(s) and receiver(s). We show that the capacity region of the MIMO multiple access and the largest known achievable rate region (called the dirty-paper region) for the MIMO broadcast channel are intimately related via a duality transformation. This transformation facilitates finding the transmission strategies that achieve a point on the boundary of the MIMO MAC capacity region in terms of the transmission strategies of the MIMO broadcast dirty-paper region and vice-versa. Finally, we discuss capacity results for multicell MIMO channels with base station cooperation. The base stations then act as a spatially diverse antenna array and transmission strategies that exploit this structure exhibit significant capacity gains. This section also provides a brief discussion of system level issues associated with MIMO cellular. Open problems in this field abound and are discussed throughout the paper.

We consider a turbo-coded system employed on a flat-fading channel where the transmitter and receiver adapt the encoder, decoder, modulation scheme, and transmit power to the state of the channel. Assuming instantaneous and error-free channel gain and phase knowledge at the transmitter and the receiver, we determine the optimal adaptation strategy that maximizes the throughput of this system, while achieving a given bit-error rate under an average power constraint. Our optimized adaptive modulation strategy is based on an extensive set of existing turbo-coded modulation schemes. We find that adapting both the turbo encoder (rate) and the transmit power can achieve performance within 3 dB of the fading channel capacity.

We derive the capacity region and optimal power allocation scheme for a slowly fading broadcast channel in which minimum rates must be maintained for each user in all fading states, assuming perfect channel state information at the transmitter and at all receivers. We show that the minimum-rate capacity region can be written in terms of the ergodic capacity region of a broadcast channel with an effective noise determined by the minimum rate requirements. This allows us to characterize the optimal power allocation schemes for minimum-rate capacity in terms of the optimal power allocations schemes that maximize ergodic capacity of the broadcast channel with effective noise. Numerical results are provided for different fading broadcast channel models.

We consider a multiuser multiple-input multiple- output (MIMO) Gaussian broadcast channel (BC), where the transmitter and receivers have multiple antennas. Since the MIMO BC is in general a nondegraded BC, its capacity region remains an unsolved problem. We establish a duality between what is termed the "dirty paper" achievable region (the Caire-Shamai (see Proc. IEEE Int. Symp. Information Theory, Washington, DC, June 2001, p.322) achievable region) for the MIMO BC and the capacity region of the MIMO multiple-access channel (MAC), which is easy to compute. Using this duality, we greatly reduce the computational complexity required for obtaining the dirty paper achievable region for the MIMO BC. We also show that the dirty paper achievable region achieves the sum-rate capacity of the MIMO BC by establishing that the maximum sum rate of this region equals an upper bound on the sum rate of the MIMO BC.

We determine the optimal adaptive rate and power control strategies to maximize the total throughput in a multirate code-division multiple-access system. The total throughput of the system provides a meaningful baseline in the form of an upper bound to the throughput achievable with additional restrictions imposed on the system to guarantee fairness. Peak power and instantaneous bit energy-to-noise spectral density constraints are assumed at the transmitter with matched filter detection at the receiver. Our results apply to frequency selective fading in so far as the bit energy-to-equivalent noise power spectral density ratio definition can be used as the quality-of-service metric. The bit energy-to-equivalent noise power spectral density ratio metric coincides with the bit-error rate metric under the assumption that the processing gains and the number of users are high enough so that self-interference can be neglected. We first obtain results for the case where the rates available to each user are unrestricted, and we then consider the more practical scenario where each user has a finite discrete set of rates. An upper bound to the maximum average throughput is obtained and evaluated for Rayleigh fading. Suboptimal low-complexity schemes are considered to illustrate the performance tradeoffs between optimality and complexity. We also show that the optimum rate and power adaptation scheme with unconstrained rates is in fact just a rate adaptation scheme with fixed transmit powers, and it performs significantly better than a scheme that uses power adaptation alone.

We define and study capacity regions for wireless ad hoc networks with an arbitrary number of nodes and topology. These regions describe the set of achievable rate combinations between all source-destination pairs in the network under various transmission strategies, such as variable-rate transmission, single-hop or multihop routing, power control, and successive interference cancellation (SIC). Multihop cellular networks and networks with energy constraints are studied as special cases. With slight modifications, the developed formulation can handle node mobility and time-varying flat-fading channels. Numerical results indicate that multihop routing, the ability for concurrent transmissions, and SIC significantly increase the capacity of ad hoc and multihop cellular networks. On the other hand, gains from power control are significant only when variable-rate transmission is not used. Also, time-varying flat-fading and node mobility actually improve the capacity. Finally, multihop routing greatly improves the performance of energy-constraint networks.

We develop a general framework for optimizing link adaptation for multiuser CDMA systems in the wideband limit. The framework is then used to solve for the optimal power control policy that minimizes average transmit power while satisfying a constraint on the per-user probability of packet loss due to deadline expiration. The optimal link adaptation is found through an infinite horizon dynamic program. Typical dynamic programming formulations do not perform well for CDMA systems since the size of the problem grows exponentionally with the number of users. We show that in the limiting regime of long spreading codes and large numbers of, users the problem size collapses to that of a single user formulation, allowing us to solve previously intractable problems. In particular, we consider a concrete example of power control in a CDMA system with deadline constrained traffic. We solve for the optimal power control policy and examine the tradeoffs between power consumption, probability of deadline expiration, and number of users In the system. Finally we present simulation results evaluating the accuracy of the wideband limit when used as an approximation for finite bandwidth systems. We show that the optimal power control and resulting performance for the limiting regime is a reasonable approximation for the large bandwidths expected in next generation wireless systems.

A novel dynamic programming formulation is proposed for computing optimal power control, source coding, and channel coding policies when the source traffic has tight delay constraints. Our solution minimizes power consumption subject to constraints on delay for all channel gains. This provides a much tighter delay bound than an average delay constraint, averaged over time varying channel gains. We present numerical results that show the tighter delay constraints come at a significant cost in terms of power consumption. However, we also show this power penalty can be greatly mitigated through optimal source-channel coding.

We present an optimal power and rate control policy for delay constrained traffic in next generation TDMA wireless systems. Our solution minimizes average transmit power while satisfying a constraint on the distribution of packets lost to deadline expiration. We also provide a means to account for erroneous and delayed channel estimates. Our results show the optimal power and rate adaptation may change dramatically as mobile speed and channel estimate delay increase. Finally, we present results from a simulation of a GSM EDGE mobile. This simulation incorporates industry standard wireless channels and performance data available from the Third Generation Partnership Project. When compared to the standard fixed-SIR power control policy, our algorithm provides a significant reduction in power consumption and mitigates some of the negative effects of delayed channel estimates.

We study the optimal power allocation scheme for i.i.d. block-fading channels with a strict transmission delay constraint. In particular, we consider the maximization of the total throughput within a finite interval under a short-term average power constraint. When all the channel gains are known a priori, we demonstrate the mapping between the delay-constrained channel and the corresponding parallel channel for which both the single-user and multi-user channel results are well-known. The maximization problem becomes more complicated when only causal channel side information (CSI) is available. We show that under this assumption, constant power transmission is optimal in the limit of high signal-to-noise ratio (SNR). We also examine the optimal power policy and show that a simple linear power control scheme has near optimal performance. We next consider a two-user broadcast channel with a stringent delay constraint and causal feedback. We solve the optimal power control problem for this channel via dynamic programming. We discuss the solutions in the limit of both low and high SNR. Numerical results show the optimal scheme is approximately piecewise linear for general SNRs.

We define and study capacity regions for ad hoc wireless networks with an arbitrary number of nodes and topology. These regions describe the set of achievable rate combinations between all source-destination pairs in the network under various transmission strategies, such as variable rate transmission, single hop or multihop routing, power control, and successive interference cancellation. With slight modifications, the developed formulation can handle multihop cellular networks, time-varying flat-fading channels and node mobility. Numerical results indicate that multihop routing, spatial reuse, and successive interference cancellation significantly increase the capacity of the network. On the other hand, gains by power control are not significant when the transmission rate is adapted to the channel SINR. We also find that time-varying flat fading and node mobility improve the performance of the network. Similar trends are observed for the special case of multihop cellular networks.

We consider a multiuser multiple input multiple output (MIMO) Gaussian broadcast channel (BC), where the transmitter and receivers have multiple antennas. Since the MIMO broadcast channel is in general a non-degraded broadcast channel, its capacity region remains an unsolved problem. We establish a duality between what is termed the "dirty paper" achievable region (the Caire-Shamai achievable region) for the MIMO broadcast channel and the capacity region of the MIMO multiple-access channel (MAC), which is easy to compute. Using this duality, we greatly reduce the computational complexity required for obtaining the dirty paper achievable region for the MIMO BC. The duality also enables us to translate previously known results for the MIMO MAC to the MIMO BC. We also show that the dirty paper achievable region achieves the sum-rate capacity of the MIMO BC by establishing that the maximum sum rate of this region equals an upper-bound on the sum rate of the MIMO BC.

We derive upper bounds on the capacity of an additive Gaussian noise channel with continuous phase modulation (CPM). We propose an MMSE approximation to Laurent's (1986) linear decomposition using an arbitrary number of filtered, linearly modulated pulses. Using this linear modulation structure, we derive capacity bounds for both white and colored noise channels with CPM modulation by showing the system is equivalent to a multiple access channel (MAC) with intersymbol interference (ISI). The rate sum capacity of this cooperative MAC is used for the upper bound. Numerical results are presented for a channel using CPM with both white and colored noise. The bounds show a significant gap between a channel using CPM and a channel with unconstrained modulation.

Multicarrier signals are known to suffer from a high peak-to-average power ratio, caused by the addition of a large number of independently modulated subcarriers in parallel at the transmitter. When subjected to a peak-limiting channel, such as a nonlinear power amplifier, these signals may undergo significant spectral distortion, leading to both in-band and out-of-band interference, and an associated degradation in system performance. This paper characterizes the distortion caused by the clipping of multicarrier signals in a peak-limiting (nonlinear) channel. Rather than modeling the effects of distortion as additive noise, as is widespread in the literature, we identify clipping as a rare event and focus on evaluating system performance based on the conditional probability of bit error given the occurrence of such an event. Our analysis is based on the asymptotic properties of the large excursions of a stationary Gaussian process, and offers important insights into both the true nature of clipping distortion, as well as the consequent design of schemes to alleviate this problem.

We propose a decision-feedback decoder for coded signals transmitted over finite-state Markov channels. The decoder achieves maximum-likelihood sequence detection (in the absence of feedback errors) with very low complexity by exploiting previous bit decisions and the Markov structure of the channel. We also propose a similar decoder, the output-feedback decoder, that does not use previous bit decisions and therefore does not suffer from error propagation. The decoder performance is determined using a new sliding window analysis technique as well as by simulation. Both decoders exhibit excellent bit error rate performance with a relatively low complexity that is independent of the channel decorrelation time.

PRMA, a packetized multiple access scheme for transmitting over short range radio channels, is a promising scheme to implement in a cellular system. PRMA requires little central control and allows hand-overs with minimal base station intervention. However, when mobile voice terminals move from one cell to another, they forfeit the slots reserved for them and, in addition, encounter hand-off delays leading to dropping of voice packets. The main problem is that a mobile terminal can lose more packets even after having secured a reservation. In this paper we use a path enumeration technique using signal flow graphs combined with equilibrium point analysis to analyze the effect of terminal mobility on the performance of PRMA in a cellular environment.

We provide an information theoretic perspective on the problem of throughput maximization in a block flat fading wireless data system with codeword lengths restricted to be less than the fade block duration. We assume no channel state information at the transmitter (CSIT) and perfect channel state information at the receiver (CSIR). We explore the tradeoffs between using a single codebook vs. multiple codebooks (rate-splitting) on single input single output (SISO) channels, and scalar coding vs. vector coding for diagonal multiple input multiple output (MIMO) channels. For all log-concave scalar channel fade distributions, we show that using multiple codebooks increases the average throughput of the system when the multiple codewords are transmitted simultaneously in time, frequency and space over the same channel. Splitting the channel orthogonally in time, frequency, or among the inputs of a MIMO system and then transmitting different codewords on each orthogonal sub-channel significantly reduces the achievable average throughput.

We derive the capacity and optimal power allocation scheme for a multiuser fading broadcast channel in which minimum rates must be maintained for each user in all fading states, assuming perfect channel state information at the transmitter and at all receivers. We show that superposition coding can achieve the capacity of such channels and explicitly characterize the boundary of the capacity region. The optimal power allocation scheme is a two-step process: we first allocate the minimum power required to achieve the minimum rates in all fading states, and we then optimally allocate the excess power to maximize the ergodic rates averaged over all fading states in excess of the minimum rate requirements. The optimal allocation of the excess power is a multi-level water-filling relative to effective noise that incorporates the minimum rate constraints. Numerical results are provided for different fading broadcast channel models.

We obtain optimal resource allocation policies for a single user single-carrier system and a multiple-access multi-carrier-CDMA system when the transmitter adapts to the variations in the short-term mean (slow fade) in a combined slow and fast fading (composite fading) environment. For the single user system, we maximize the average throughput achieved by the user, while In the uplink MC-CDMA system, we maximize the sum of average rates of the users in the system. For each system, we find the optimal resource allocation policies for two scenarios. The first is when is system is designed for voice transmission, where the bit error rate (BER) of each user, averaged over the fast fade, is maintained at a desired value. The second is when the system is designed for data transmission, where the BER of each user is maintained below a desired value for a given percentage of time. We find that, for the single-user system, the solution for both the voice and data transmission cases is waterfilling, and that waterfilling is the asymptotically optimal solution to multi-user problems in both scenarios, i.e. is nearly optimal for a large number of users. We also find that, when dealing with a voice system, the solution is independent of the distributions of the slow and fast fades and similar to the solutions obtained for noncomposite fading environments (fast or slow fading).

We consider the capacity of a narrowband point to point communication system employing multiple-element antenna arrays at both the transmitter and the receiver with covariance feedback. Under covariance feedback the receiver is assumed to have perfect channel state information (CSI) while at the transmitter the channel matrix is modeled as consisting of zero mean complex jointly Gaussian random variables with known covariances. Specifically we assume a channel matrix with i.i.d. rows and correlated columns, a common model for downlink transmission. We determine the optimal transmit precoding strategy to maximize the Shannon capacity of such a system. We also derive closed form necessary and sufficient conditions on the spatial covariance for when the maximum capacity is achieved by beamforming. The conditions for optimality of beamforming agree with the notion of water-filling over multiple degrees of freedom.

We examine adaptive modulation schemes for flat-fading channels where the data rate, transmit power, and instantaneous BER are varied to maximize spectral efficiency, subject to an average power and BER constraint. Both continuous-rate and discrete-rate adaptation are considered, as well as average and instantaneous BER constraints. We find the general form of power, BER and data rate adaptation that maximizes spectral efficiency for a large class of modulation techniques and fading distributions. The optimal adaptation of these parameters is to increase the power and data rate and decrease the BER as the channel quality improves. Surprisingly, little spectral efficiency is lost when the power or rate is constrained to be constant. Hence, the spectral efficiency of adaptive modulation is relatively insensitive to which degrees of freedom are adapted.

We derive the capacity region for a broadcast channel with intersymbol interference (ISI) and colored Gaussian noise under an input power constraint. The region is obtained by first defining a similar channel model, the circular broadcast channel, which can be decomposed into a set of parallel degraded broadcast channels. The capacity region for parallel degraded broadcast channels is known. We then show that the capacity region of the original broadcast channel equals that of the circular broadcast channel in the limit of infinite block length, and we obtain an explicit formula for the resulting capacity region. The coding strategy used to achieve each point on the convex hull of the capacity region uses superposition coding on some or all of the parallel channels and dedicated transmission on the others. The optimal power allocation for any point in the capacity region is obtained via a multilevel water-filling. We derive this optimal power allocation and the resulting capacity region for several broadcast channel models.

In multiuser wireless systems, dynamic resource allocation between users and over time significantly improves efficiency and performance. In this two-part paper, we study three types of capacity regions for fading broadcast channels and obtain their corresponding optimal resource allocation strategies: the ergodic (Shannon) capacity region, the zero-outage capacity region, and the outage capacity region with nonzero outage. We derive the ergodic capacity region of an M-user fading broadcast channel for code division (CD), time division (TD), and frequency division (FD), assuming that both the transmitter and the receivers have perfect channel side information (CSI). It is shown that by allowing dynamic resource allocation, TD, FD, and CD without successive decoding have the same ergodic capacity region, while optimal CD has a larger region. Optimal resource allocation policies are obtained for these different spectrum-sharing techniques. A simple suboptimal policy is also proposed for TD and CD without successive decoding that results in a rate region quite close to the ergodic capacity region. Numerical results are provided for different fading broadcast channels.

For pt.I see ibid., vol.47, no.3, p.1083-1102 (2002). We study three capacity regions for fading broadcast channels and obtain their corresponding optimal resource allocation strategies: the ergodic (Shannon) capacity region, the zero-outage capacity region, and the capacity region with outage. In this paper, we derive the outage capacity regions of fading broadcast channels, assuming that both the transmitter and the receivers have perfect channel side information. These capacity regions and the associate optimal resource allocation policies are obtained for code division (CD) with and without successive decoding, for time division (TD), and for frequency division (FD). We show that in an M-user broadcast system, the outage capacity region is implicitly obtained by deriving the outage probability region for a given rate vector. Given the required rate of each user, we find a strategy which bounds the outage probability region for different spectrum-sharing techniques. The corresponding optimal power allocation scheme is a multiuser generalization of the threshold-decision rule for a single-user fading channel. Also discussed is a simpler minimum common outage probability problem under the assumption that the broadcast channel is either not used at all when fading is severe or used simultaneously for all users. Numerical results for the different outage capacity regions are obtained for the Nakagami-m (1960) fading model.

Using a recently developed moment generating function-based approach for the performance evaluation of digital communications over fading channels, we present a unified approach for the exact performance analysis of binary direct-sequence code division multiple access (DS-CDMA) systems operating over generalized frequency-selective fading channels. The results are applicable to single carrier systems employing RAKE reception as well as to multicarrier DS-CDMA systems with frequency diversity. Aside from simplifying previous results both analytically and computationally, the proposed approach also gives a solution for many situations which heretofore defied a simple form. Copyright © 2001 John Wiley & Sons, Ltd.

We analyze the performance of a link adaptation scheme in which a user, based on his SIR estimate, either transmits using a given modulation and coding scheme or does not transmit (backs off). The impact of channel correlation on the optimal back off SIR threshold is studied for a co-channel interference limited cellular system. Expressions are derived for the average packet waiting time given the basic system parameters like packet arrival statistics, channel fade statistics, number of users per cell, and link adaptation thresholds. Analysis results are shown to be in good agreement with the simulation results. We show that the optimal back-off threshold crucially depends on the channel correlation, a fact not considered by the formulae suggested in literature for determining the link adaptation thresholds. For channel correlation /spl rho/=0.82, the back-off mechanism could reduce average packet delay by up to 15%, as compared to the no back-off case. No such improvement was found for /spl rho/=0.41.

We study the performance of joint source and channel codes designed to minimize end-to-end distortion over a Rayleigh fading channel. We consider two joint code designs. The first joint code uses a sequential design: a standard vector quantizer (VQ) source code is designed for a perfect channel (noiseless and distortionless) and then an RCPC channel code is optimized relative to the VQ and the channel statistics. The second design jointly optimizes a channel optimized VQ (COVQ) and an RCPC channel code through an iterative design process. We consider both hard-decision and soft-decision decoding for the channel codes. In both designs the bit allocation between the source and channel codes is optimized. At this optimal bit allocation, the performance of the iterative joint design and the simpler sequential design are nearly the same over the range of SNR values that we considered. Both code designs outperform standard COVQ and by up to 6 dB, and this performance improvement is most pronounced at low SNRs.

This paper studies the decorrelation property of the constituent codes in space-time turbo codes (STTCs), where different constituent codes are transmitted over different antennas. We show that the time correlation between constituent codes falls of with respect to STTC block length N as 1//spl radic/N for large N, and hence goes to zero as N/spl rarr//spl infin/. We then use this result to obtain analytical expressions for the frame error rate (FER) of STTCs in flat fading. The decorrelation property of STTCs helps explain the exceptional performance of STTCs on slowly varying flat fading channels.

For a voice user in PRMA, a packet header error leads to the loss of slot reservation while a packet data error only causes a rejection of the transmitted packet. We use equilibrium point analysis and a path enumeration technique for signal flow graphs to analyze the effect of voice packet header and data errors on the performance of PRMA. The technique provides an improvement over the solutions previously suggested in literature. We also extend the analysis to model the effect of cochannel inter-cellular interference and error correction coding on PRMA over fading channels. Analytically obtained results for fixed packet error rates and for packet error rates that depend on the co-channel inter-cellular interference in the system are presented. The limitations of the analytical technique are also discussed.

We use equilibrium point analysis to analyze the effect of terminal mobility on the performance of PRMA in a cellular environment. We derive expressions for PRMA's throughput and packet dropping probability, in the presence of terminal mobility. We employ a path enumeration technique based on Mason's (1960) gain formula for signal flow graphs to evaluate the packet dropping probability. We present results showing the marginal effect that terminal mobility has on PRMA's performance.

We derive the outage capacity regions of an M-user fading multiple-access channel under the assumption that both the transmitters and the receiver have perfect channel side information. We show that the outage capacity region is implicitly obtained by deriving the outage probability region for a given rate vector. Given the average power constraint and the required rate of each user, we find a successive decoding strategy and a power allocation policy that bound the outage probability region. Also discussed is a simpler minimum common outage probability problem under the assumption that the multiple-access channel is either not used at all when fading is severe or is used simultaneously by all users. Iterative algorithms are proposed for obtaining the optimal decoding order and power allocation in each fading state under the given power constraint of each user.

We consider the capacity of time-slotted ALOHA systems, where multiple users synchronously send packets, which may collide at the receiver. Specific coding for ALOHA systems had previously been proposed to avoid complete loss of packets involved in collisions, but the capacity of ALOHA systems had not been previously determined. We consider capacity in terms of reliably received rate rather than transmitted rate. We consider capacity achieving strategies under AWGN for transmission of a single packet which is long enough to achieve capacity over the duration of the packet. We combine concepts from multi-access channels and broadcast channels to determine the capacity region for a single transmission of a packet in an ALOHA system. The coding for each user takes into account the possibility of collisions with other users in order to establish a capacity region. Next, we consider the case where we transmit several packets under a channel model where users receive the right to transmit the package according to independent Bernoulli processes. We can then apply the single-packet coding strategies in order to maximize the expected reliable received rate.

We propose a new adaptive modulation technique for simultaneous voice and data transmission over fading channels and study its performance. The proposed scheme takes advantage of the time-varying nature of fading to dynamically allocate the transmitted power between the inphase (I) and quadrature (Q) channels. It uses fixed-rate binary phase shift keying (BPSK) modulation on the Q channel for voice, and variable-rate M-ary amplitude modulation (M-AM) on the I channel for data. For favorable channel conditions, most of the power is allocated to high rate data transmission on the I channel. The remaining power is used to support the variable-power voice transmission on the Q channel. As the channel degrades, the modulation gradually reduces its data throughput and reallocates most of its available power to ensure a continuous and satisfactory voice transmission. The scheme is intended to provide a high average spectral efficiency for data communications while meeting the stringent delay requirements imposed by voice. We present closed-form expressions as well as numerical and simulation results for the outage probability, average allocated power, achievable spectral efficiency, and average bit error rate (BER) for both voice and data transmission over Nakagami-m fading channels. We also discuss the features and advantages of the proposed scheme. For example, in Rayleigh fading with an average signal-to-noise ratio (SNR) of 20 dB, our scheme is able to transmit about 2 bits/s/Hz of data at an average BER of 10/sup -5/ while sending about 1 bit/s/Hz of voice at an average BER of 10/sup -2/.

We present a unified analytical framework to determine the exact average symbol-error rate (SER) of linearly modulated signals over generalized fading channels. The results are applicable to systems employing coherent demodulation with maximal-ratio combining multichannel reception. The analyses assume independent fading paths, which are not necessarily identically distributed. In all cases, the proposed approach leads to an expression of the average SER involving a single finite-range integral, which can be easily computed numerically. In addition, as special cases, SER expressions for single-channel reception are obtained. These expressions reduce to well-known solutions, give alternative (often simpler) expressions for previous results, or provide new formulas that are either closed-form expressions or simple to compute numerically.

We determine the bit-error rate (BER) of multilevel quadrature amplitude modulation (M-QAM) in flat Rayleigh fading with imperfect channel estimates, Despite its high spectral efficiency, M-QAM is not commonly used over fading channels because of the channel amplitude and phase variation. Since the decision regions of the demodulator depend on the channel fading, estimation error of the channel variation can severely degrade the demodulator performance. Among the various fading estimation techniques, pilot symbol assisted modulation (PSAM) proves to be an effective choice. We first characterize the distribution of the amplitude and phase estimates using PSAM. We then use this distribution to obtain the BER of M-QAM as a function of the PSAM and channel parameters. By using a change of variables, our exact BER expression has a particularly simple form that involves just a few finite-range integrals. This approach can be used to compute the BER for any value of M. We compute the BER for 16-QAM and 64-QAM numerically and verify our analytical results by computer simulation. We show that for these modulations, amplitude estimation error leads to a 1-dB degradation in average signal-to-noise ratio and combined amplitude-phase estimation error leads to 2.5-dB degradation for the parameters we consider.

We present a unified analytical framework to determine the exact average symbol-error-rate (SER) of linearly modulated signals over generalized fading channels. The results are applicable to systems employing coherent demodulation with maximal-ratio combining multichannel reception. The analyses assume independent fading paths which are not necessarily identically distributed. In all cases the proposed approach leads to an expression of the average SER involving a single finite-range integral which can be easily computed numerically. In addition, as special cases, SER expressions for single channel reception are obtained. These expressions reduce to well-known solutions, give alternate (often simpler) expressions for previous results, or provide new formulas which are either closed-form expressions or simple to compute numerically.

We apply coset codes to adaptive modulation in fading channels. Adaptive modulation is a powerful technique to improve the energy efficiency and increase the data rate over a fading channel. Coset codes are a natural choice to use with adaptive modulation since the channel coding and modulation designs are separable. Therefore, trellis and lattice codes designed for additive white Gaussian noise (AWGN) channels can be superimposed on adaptive modulation for fading channels, with the same approximate coding gains. We first describe the methodology for combining coset codes with a general class of adaptive modulation techniques. We then apply this methodology to a spectrally efficient adaptive M-ary quadrature amplitude modulation (MQAM) to obtain trellis-coded adaptive MQAM. We present analytical and simulation results for this design which show an effective coding gain of 3 dB relative to uncoded adaptive MQAM for a simple four-state trellis code, and an effective 3.6-dB coding gain for an eight-state trellis code. More complex trellis codes are shown to achieve higher gains. We also compare the performance of trellis-coded adaptive MQAM to that of coded modulation with built-in time diversity and fixed-rate modulation. The adaptive method exhibits a power savings of up to 20 dB.

We propose three new design algorithms for jointly optimizing source and channel codes. Our optimality criterion is to minimize the average end-to-end distortion. For a given channel SNR and transmission rate, our joint source and channel code designs achieve an optimal allocation of bits between the source and channel coders. Our three techniques include a source-optimized channel code, a channel-optimized source code, and an iterative descent technique combining the design strategies of the other two codes. The joint designs use channel-optimized vector quantization (COVQ) for the source code and rate compatible punctured convolutional (RCPC) coding for the channel code. The optimal bit allocation reduces distortion by up to 6 dB over suboptimal allocations and by up to 4 dB relative to standard COVQ for the source data set considered. We find that all three code designs have roughly the same performance when their bit allocations are optimized. This result follows from the fact that at the optimal bit allocation the channel code removes most of the channel errors, in which case the three design techniques are roughly equivalent. We also compare the robustness of the three techniques to channel mismatch. We conclude the paper by relaxing the fixed transmission rate constraint and jointly optimizing the transmission rate, source code, and channel code.

The effects of Nakagami multipath fading and log-normal shadowing on the area spectral efficiency (ASE) of cellular systems with variable-rate transmission is studied. Results indicate that the ASE increases as fading on both the desired and interfering signals decreases. In addition, the ASE is predominantly affected by the channel quality of the desired users, rather than by the fading parameter of the interferers. Furthermore, depending on the interference configuration, the optimal spectral efficiency is achieved when frequencies are reused every one or two cells. Finally, shadowing reduces the system spectral efficiency but does not affect the ASE dependence on the reuse distance.

We propose a variable-power and variable-rate coded MQAM modulation technique for high-speed data transmission on fading channels. Coding gain is obtained by superimposing trellis codes designed for AWGN channels on the adaptive modulation, and we obtain the same coding gains as these codes exhibit in AWGN. We present analytical and simulation results which show a 3dB coding gain relative to uncoded adaptive modulation for a simple 4-state trellis code, and a 4 dB coding gain for an 8-state trellis code. More complex trellis codes achieve higher gains.

We propose an iterative design algorithm for jointly optimizing source and channel codes. The joint design combines channel-optimized vector quantization (COVQ) for the source code with rate-compatible punctured convolutional (RCPC) coding for the channel code. Our objective is to minimize the average end-to-end distortion. For a given channel SNR and transmission rate, our joint source and channel code design achieves an optimal allocation of bits between the source and channel coders. This optimal allocation can reduce distortion by up to 6 dB over suboptimal allocations for the source data set considered. We also compare the distortion of our joint iterative design with that of two suboptimal design techniques: COVQ optimized for a given channel bit-error-probability, and RCPC channel coding optimized for a given vector quantizer. We conclude by relaxing the fixed transmission rate constraint and jointly optimizing the transmission rate, source code, and channel code.

We consider the effects of imperfect average power measurements on adaptive MQAM modulation, where the transmit power and data rate are varied relative to the received signal power. The channel varies with both fast Rayleigh fading and slow log-normal shadowing. We assume that the fast fading is estimated perfectly, and that the estimation error of the shadowing is log-normally distributed. This estimation error leads to a change in the average transmit power and rate of the adaptive modulation. We characterize these changes for two adaptive modulation schemes: variable-rate variable-power MQAM, where the average data rate is maximized, and fixed-rate MQAM, where the transmit power is adapted to invert the signal fading. The shadowing estimation error affects these two modulation techniques in opposite ways: the data rate and dB power changes resulting from the error are positive for variable-rate variable-power MQAM, and negative for fixed-rate MQAM. In both cases, however, the changes are very small.

We propose a variable-rate and variable-power MQAM modulation scheme for high-speed data transmission over fading channels. We first review results for the Shannon capacity of fading channels with channel side information, where capacity is achieved using adaptive transmission techniques. We then derive the spectral efficiency of our proposed modulation. We show that there is a constant power gap between the spectral efficiency of our proposed technique and the channel capacity, and this gap is a simple function of the required bit-error rate (BER). In addition, using just five or six different signal constellations, we achieve within 1-2 dB of the maximum efficiency using unrestricted constellation sets. We compute the rate at which the transmitter needs to update its power and rate as a function of the channel Doppler frequency for these constellation sets. We also obtain the exact efficiency loss for smaller constellation sets, which may be required if the transmitter adaptation rate is constrained by hardware limitations. Our modulation scheme exhibits a 5-10-dB power gain relative to variable-power fixed-rate transmission, and up to 20 dB of gain relative to nonadaptive transmission. We also determine the effect of channel estimation error and delay on the BER performance of our adaptive scheme. We conclude with a discussion of coding techniques and the relationship between our proposed modulation and Shannon capacity.

We obtain the Shannon capacity of a fading channel with channel side information at the transmitter and receiver, and at the receiver alone. The optimal power adaptation in the former case is "water-pouring" in time, analogous to water-pouring in frequency for time-invariant frequency-selective fading channels. Inverting the channel results in a large capacity penalty in severe fading.

The finite-state Markov channel (FSMC) is a discrete time-varying channel whose variation is determined by a finite-state Markov process. These channels have memory due to the Markov channel variation. We obtain the FSMC capacity as a function of the conditional channel state probability. We also show that for i.i.d. channel inputs, this conditional probability converges weakly, and the channel's mutual information is then a closed-form continuous function of the input distribution. We next consider coding for FSMCs. In general, the complexity of maximum-likelihood decoding grows exponentially with the channel memory length. Therefore, in practice, interleaving and memoryless channel codes are used. This technique results in some performance loss relative to the inherent capacity of channels with memory. We propose a maximum-likelihood decision-feedback decoder with complexity that is independent of the channel memory. We calculate the capacity and cutoff rate of our technique, and show that it preserves the capacity of certain FSMCs. We also compare the performance of the decision-feedback decoder with that of interleaving and memoryless channel coding on a fading channel with 4PSK modulation.

The authors have performed data reductions on 900 MHz signal attenuations measured on numerous streets in Manhattan. The database consists of both local spatial averages of signal attenuation and the short-term fluctuations about this average. The former, which is termed the local mean attenuation (LMA), is the primary focus. The database is used to obtain contours of constant LMA for two neighborhoods. It is shown that the contours have the shapes of convex diamonds. The authors propose that squares inscribed within these contours be used as the building blocks of microcellular environments. A theory is developed that explains the contours and predicts, with reasonable accuracy, the sizes of the inscribed squares. It is also shown that the prediction method can be applied without the need for measured data. The short-term fluctuation statistics of the signal attenuation are examined. They are shown to be Rayleigh-like in the non-line-of-sight regions of a microcell and Rice-like in the line-of-sight region. Possible extensions to other frequency bands and other urban environments are discussed.>