This paper focuses on enhancing the energy efficiency (EE) of a cooperative network that features a miniature unmanned aerial vehicle (UAV) operating at terahertz (THz) frequencies and equipped with holographic surfaces to improve network performance. Unlike traditional reconfigurable intelligent surfaces (RIS), which serve as passive relays for signal reflection, this work introduces a novel concept: energy harvesting (EH) using reconfigurable holographic surfaces (RHS). These surfaces provide more powerful and focused energy delivery during wireless power transfer than RIS and are mounted on the miniature UAV. In this system, a source node enables the UAV to simultaneously receive both information and energy signals, with the harvested energy powering data transmission to a specific destination. The EE optimization problem involves adjusting non-orthogonal multiple access (NOMA) power coefficients and the UAV’s flight path while accounting for the unique characteristics of the THz channel. The problem is solved in two stages to maximize EE and meet a target transmission rate. The UAV trajectory is optimized using a successive convex approximation (SCA) method, followed by the adjustment of NOMA power coefficients through a quadratic transform technique. Simulation results demonstrate the effectiveness of the proposed algorithm, showing significant improvements over baseline methods.

We focus on designing error-correcting codes for the symmetric Gaussian broadcast channel with feedback. Feedback not only expands the capacity region of the broadcast channel but also enhances transmission reliability. In this work, we study the construction of learned finite blocklength codes for broadcast channels with feedback. Learned error-correcting codes, in which both the encoder and decoder are jointly trained, have shown impressive performance in point-to-point channels, particularly with noisy feedback. However, few learned schemes exist for multi-user channels. Here, we develop a lightweight code for the broadcast channel with feedback that performs well and operates effectively at short blocklengths.

The KO (Kronecker Operation) code is a recent deep-learned error-correcting code using a neural network architecture to generalize a Reed-Muller code with Dumer decoding. Analyzing the encoder modules and using ablation techniques, we give interpretations of the KO encoder which significantly reduce the number of parameters. We also discuss interpretability aspects of the KO decoder. The interpretation opens up possibilities to give an explicit representation of KO codes, which could be useful for more efficient learning of KO codes and explaining the learning mechanism underlying the empirical observations made about its performance in previous work.

Several researchers have used deep learning to obtain novel feedback codes. Two such codes for AWGN channels with passive (possibly noisy) output feedback are Deepcode which employs a bit-by-bit rate 1/3 encoder, and Lightcode, which is a symbol-by-symbol code inspired by the Schalkwijk-Kailath (SK) scheme. Here, we build on prior work to interpret these codes by 1) providing the optimal maximum a posteriori (MAP) decoder for our simple non-linear interpretable encoder of a single-bit, two-round code that accurately approximates both single-bit Deepcode and Lightcode. This non-linear interpretable coding scheme, which mimics these codes, turns out to resemble both the functional form and performance of the Polyanskiy-Poor-Verdu (PPV) single bit feedback scheme that minimizes energy transmission asymptotically. 2) We extend our non-linear interpretable code to support more than one bit and two rounds, again providing an optimal MAP decoder. This remarkably simple and power-efficient nonlinear scheme provides insight into Lightcode.

Arbiter-based Physically Unclonable Functions (APUFs) utilize the variability in manufacturing to create distinct digital identifiers for integrated circuits (ICs). Essentially, the input-output functions / truth-tables / full set of "responses" to "challenges", serve as potential hardware security primitives. To fulfill this role, every APUF batch from the same design should exhibit specific features; two of the most important are the response bias and uniqueness. A faulty APUF batch with a μ-fault from the design phase fails to achieve desired uniqueness levels and sometimes exhibits undesired response bias as well, hence is unqualified for security purposes. Instead of discarding such faulty APUFs and re-designing, we present a novel method to salvage a faulty APUF batch with the presence of multiple μ-faults, so that the desired uniqueness and bias are restored. This is done by carefully selecting challenges that can mitigate the impact of the faults. Such a salvaging strategy via challenge selection is intrinsically difficult, due to the enormous size of the challenge set, the black-box nature of APUFs, and the need to perform such tasks efficiently. To overcome these problems, we propose a simple yet effective way to estimate the intensity of the multiple faults and use them to guide the challenge selection process. The proposed method can efficiently find large challenge sets that achieve the desired response bias and uniqueness, thus salvaging a faulty APUF batch in the post-production phase.

In classical capacity analysis for point-to-point (P2P) channels, all transmitted data is equally protected. Transmitted data will be recovered if and only if transmitted at a rate below the channel's capacity. When a P2P channel is studied in the Finite Blocklength (FBL) regime the inclusion of a reliability term suggests the possibility of constructing codes that protect portions of the data differently. In this paper, we present an FBL achievable bound for the utilization of superposition (SUP) coding with successive interference cancellation (SIC) in the realization of Unequal Bit Protection (UBP) in transmission over a static, scalar additive white Gaussian noise (AWGN) channel. We also present a converse bound for the problem. Through our numerical analysis we show that in cases where data to be transmitted has known and differing reliability requirements, the use of superposition coding can increase the achievable sum rate of transmission of all classes of data protection over a uniform protection coding scheme and orthogonalization over time. However, the (SUP-SIC) achievable region and converse are not tight, and the FBL UBP capacity remains an open problem.

Deep learning methods have recently been used to construct non-linear codes for the additive white Gaussian noise (AWGN) channel with feedback. However, there is limited understanding of how these black-box-like codes with many learned parameters use feedback. This study aims to uncover the fundamental principles underlying the first deep-learned feedback code, known as Deepcode, which is based on an RNN architecture. Our interpretable model based on Deepcode is built by analyzing the influence length of inputs and approximating the non-linear dynamics of the original black-box RNN encoder. Numerical experiments demonstrate that our interpretable model - which includes both an encoder and a decoder - achieves comparable performance to Deepcode while offering an interpretation of how it employs feedback for error correction.11This work was supported by NSF under awards 1900911, 2217023, and 2240532, and by the AI National Laboratory Program (RRF-2.3.1-21-2022- 00004). The contents of this article are solely the responsibility of the authors and do not necessarily represent the official views of the NSF.

Arbiter Physically Unclonable Functions (APUFs) are low-cost hardware security primitives that may serve as unique digital fingerprints for ICs. To fulfill this role, it is critical for manufacturers to ensure that a batch of PUFs coming off the same design and production line have different truth tables, and uniqueness / inter-PUF-distance metrics have been defined to measure this. This paper points out that a widely-used uniqueness metric fails to capture some special cases, which we remedy by proposing a modified uniqueness metric. We then look at two fundamental APUF-native production line fault models that severely affect uniqueness: the$\mu$(abnormal mean of a delay difference element) and (abnormal variance of a delay difference element) faults. We propose test and diagnosis methods aimed at these two APUF production line faults, and show that these low-cost techniques can efficiently and effectively detect such faults, and pinpoint the element of abnormality, without the (costly) need to directly measure the uniqueness metric of a PUF batch.

Modeling attacks, in which an adversary uses machine learning techniques to model a hardware-based Physically Unclonable Function (PUF) pose a great threat to the viability of these hardware security primitives. In most modeling attacks, a random subset of challenge-response-pairs (CRPs) are used as the labeled data for the machine learning algorithm. Here, for the arbiter-PUF, a delay based PUF which may be viewed as a linear threshold function with random weights (due to manufacturing imperfections), we investigate the role of active learning in Support Vector Machine (SVM) learning. We focus on challenge selection to help SVM algorithm learn “fast” and learn “slow”. Our methods construct challenges rather than relying on a sample pool of challenges as in prior work. Using active learning to learn “fast” (less CRPs revealed, higher accuracies) may help manufacturers learn the manufactured PUFs more efficiently, or may form a more powerful attack when the attacker may query the PUF for CRPs at will. Using active learning to select challenges from which learning is “slow” (low accuracy despite a large number of revealed CRPs) may provide a basis for slowing down attackers who are limited to overhearing CRPs.

As new deep-learned error-correcting codes continue to be introduced, it is important to develop tools to interpret the designed codes and understand the training process. Prior work focusing on the deep-learned TurboAE has both interpreted the learned encoders post-hoc by mapping these onto nearby "interpretable" encoders, and experimentally evaluated the performance of these interpretable encoders with various decoders. Here we look at developing tools for interpreting the training process for deep-learned error-correcting codes, focusing on: 1) using the Goldreich-Levin algorithm to quickly interpret the learned encoder; 2) using Fourier coefficients as a tool for understanding the training dynamics and the loss landscape; 3) reformulating the training loss, the binary cross entropy, by relating it to encoder and decoder parameters, and the bit error rate (BER); 4) using these insights to formulate and study a new training procedure. All tools are demonstrated on TurboAE, but are applicable to other deep-learned forward error correcting codes (without feedback).

This paper considers the single antenna, static, scalar Gaussian broadcast channel in the finite blocklength regime. Second order achievable and converse rate regions are presented. Both a global reliability and per-user reliability requirements are considered. The two-user case is analyzed in detail, and generalizations to the$K$-user case are also discussed. The largest second order achievable regions presented here require both superposition and rate splitting in the code construction, as opposed to the (infinite blocklength, first order) capacity region which does not require rate splitting. Indeed, the finite blocklength penalty causes superposition alone to under-perform other coding techniques in some parts of the region. In addition, the proposed scheme uses joint simultaneous decoding as opposed to successive interference cancellation. Interestingly, in the two-user case with per-user reliability requirements, the capacity achieving superposition encoding order (with the codeword intended for the user with the smallest received SNR as cloud center) does not necessarily give the largest second order region. Instead, the message of the user with the smallest point-to-point second order capacity should be encoded in the cloud center in order to obtain the largest second order region for the proposed scheme.

Arbiter Physically Unclonable Functions (APUFs) are hardware security primitives that exploit manufacturing random-ness to generate unique digital fingerprints for ICs. This paper theoretically and numerically examines the impact of faults native to APUFs - mask parameter faults from the design phase, or process variation (PV) during the manufacturing phase. We model them statistically, and explain quantitatively how these faults affect the resulting APUF bias and uniqueness. On a single APUF instance, these faults manifest as some outlier delta elements in magnitude, thus we focus on such abnormal delta elements when addressing APUF faults. To detect such bad APUF instances and diagnose the abnormal delta elements, we propose a testing methodology which partitions a random set of challenges so that a specific delta element can be targeted, forming a perceivable bias in the responses over these sets. This low-cost approach is highly effective in detecting and diagnosing bad APUFs with abnormal delta element(s).

We consider the design of practical codes for a symmetric two-user fading Gaussian Broadcast Channel (BC) with feedback. We construct a two-phase coding scheme with the help of deep Neural Networks (NNs) that seeks to optimize the encoder and decoders jointly. Interpreting a communication system as an autoencoder (denoted by AE), we train the AE under various scenarios of noiseless feedback signals. Performance evaluation is presented for Rayleigh distributed channel state, which reveals the existence of a trained NN-based two-phase model that outperforms state-of-the-art codes in the low SNR regime. Considering the availability of feedback signals, we train the AE with different inputs, and observe that feedback consisting of received signals appears to be more beneficial than channel states to boost reliability under the proposed scheme. We provide initial interpretations of the encoding scheme which uses channel state feedback.

Deep learning has been used recently to learn error-correcting encoders and decoders which may improve upon previously known codes in certain regimes. The encoders and decoders are learned "black-boxes", and interpreting their behavior is of interest both for further applications and for incorporating this work into coding theory. Understanding these codes provides a compelling case study for Explainable Artificial Intelligence (XAI): since coding theory is a well-developed and quantitative field, the interpretability problems that arise differ from those traditionally considered. We develop post-hoc interpretability techniques to analyze the deep-learned, autoencoder-based encoders of TurboAE-binary codes, using influence heatmaps, mixed integer linear programming (MILP), Fourier analysis, and property testing. We compare the learned, interpretable encoders combined with BCJR decoders to the original black-box code.

A longstanding problem in statistics pertains to the estimation of probability density functions of continuous random variables from a finite set of their samples. In this paper, we propose a new parametric probability density function estimator based on convex programming. Our formulation decomposes the unknown distribution as a Gaussian penalty function plus an error function, which is then expanded by multi-scale wavelet functions (specifically frames) such as B-Spline and Mexican Hat wavelets. To recover the wavelet coefficients in the error function, a convex quadratic program is formulated which takes into account the positivity of the probability density function-through a linear constraint. The proposed decomposition model is shown to facilitate an accurate estimation of the probability density functions of interest.

This paper proposes a linear coding scheme for the two-user fading additive white Gaussian noise broadcast channel, under the assumptions that: (i) perfect Channel State Information (CSI) is available at the receivers; and (ii) unit delayed CSI along with channel output feedback (COF) is available at the transmitter. The proposed scheme is derived from a control-theoretic perspective that generalizes the communication scheme for the point-to-point (P2P) fading Gaussian channel under the same assumptions by Liu et al. [1]. The proposed scheme asymptotically achieves the rates of a posterior matching scheme, from the same authors, for a certain choice of parameters.

We present achievable error exponent regions for the Two-Way AWGN channel under an expected block power constraint and variable-length coding (VLC). We propose an achievability scheme that allows terminals to cooperate via interaction to detect decoding errors and request re-transmissions. Under this scheme, in certain rate-pair regimes both directions are able to simultaneously attain error exponent pairs larger than the feedback-free point-to-point random coding error exponents1.

Achievable error exponents for the one-way with noisy feedback and two-way AWGN channels are derived for the transmission of a finite number of messages M under almost sure (AS) and expected block (EXP) transmit power constraints. In the one-way setting under noisy AWGN feedback, under an AS power constraint, known linear and non-linear passive schemes are modified to incorporate AS constraints in the feedback link as well. In addition, a new active feedback scheme is presented in which the receiver feeds back the most likely pair of codewords, and the transmitter re-transmits which of these two was originally sent. This active feedback scheme outperforms one of the passive feedback schemes for all channel parameters; the linear scheme outperforms the others for low feedback noise variance. Under the EXP constraint, a known achievable error exponent for the transmission of two messages is generalized to any arbitrary but finite number of messages M through the use of simplex codes and erasure decoding. In the two-way AWGN setting, each user has its own message to send in addition to (possibly) aiding in the transmission of feedback for the opposite direction. Two-way error exponent regions are defined and achievable error exponent regions are derived for the first time under both AS and EXP power constraints. For the presented achievability schemes, feedback or interaction leads to error exponent gains in one direction, possibly at the expense of a decrease in the error exponents attained in the other direction. The relationship between M and n supported by our achievable strategies is explored.

We investigate the feasibility of second-order statistics-based blind channel estimation in the context of two-hop full-duplex relay systems. To that end, the performance of blind and traditional pilot-based (training sequence based) channel estimation approaches are compared. This is accomplished by deriving the Cramer-Rao Lower Bound (CRLB) expressions for both blind and pilot-based schemes, and comparing them to each other and to the mean-squared error (MSE) values measured via simulation. Post-equalization SINR expressions are also derived for both blind and pilot-based methods. Furthermore, a modified post-equalization SINR expression, where the channel estimation error is replaced by the inverse of the Fisher information matrix (FIM) is proposed, providing an upper bound for the post-equalization SINR. These analytically-predicted SINR values for the blind approach are compared to the SINR measured via link simulation. The performance of the two channel estimation methods is analyzed by comparing the CRLB, post-equalization SINR, and BER performance for two significantly different transmission packet sizes. All of the above metrics indicate that blind estimation provides clear performance advantages relative to the pilot-based counterpart. Additionally, the blind approach eliminates the overhead associated with the pilot-based method, where a portion of the system resources is allocated to the pilot sequence. To quantify this, the spectral efficiency of the FD relay system employing blind and pilot-based channel estimation methods are compared, indicating that at high SNR, the blind approach provides around 2-bps/Hz spectral efficiency gain relative to a typical pilot-based method. Finally, the computational complexity of the two channel estimation techniques are evaluated and compared. The blind approach has a clear computational advantage for larger packet sizes.

The fading broadcast channel (BC) with additive white Gaussian noise (AWGN) channel, channel output feedback (COF) and channel state information (CSI) is considered. Perfect CSI is available at the receivers, and unit delayed CSI along with COF at the transmitter. Under the assumption of memoryless fading, a posterior matching scheme that incorporates the additional CSI feedback into the coding scheme is presented. With COF, the achievable rates depend on the joint distribution of the fading process. Numerical examples show that the capacity region of two-user fading AWGN-BC is enlarged by COF. The coding scheme is however suboptimal since some parts of the achievable rate region are outperformed by superposition coding without COF.

We investigate error exponent regions for the parallel two-way DMC in which each terminal sends its own message and provides feedback to the other terminal. Various error exponents are presented in different rate-region regimes based on the relative rates and zero-error capacities of both directions. The schemes employed are extensions of error exponents for one-way DMCs with noiseless, rate-limited and noisy feedback1.

In this paper the capacity region of the Layered Packet Erasure Broadcast Channel (LPE-BC) with Channel Output Feedback (COF) available at the transmitter is investigated. The LPE-BC is a high-SNR approximation of the fading Gaussian BC recently proposed by Tse and Yates, who characterized the capacity region for any number of users and any number of layers when there is no COF. This paper derives capacity inner and outer bounds for the LPE-BC with COF for the case of two users and any number of layers. The inner bounds generalize past results for the two-user erasure BC, which is a special case of the LPE-BC with COF with only one layer. The novelty lies in the use of inter-user & inter-layer network coding retransmissions (for those packets that have only been received by the unintended user), where each random linear combination may involve packets intended for any user originally sent on any of the layers. Analytical and numerical examples show that the proposed outer bound is optimal for some LPE-BCs.

Achievable error exponents for two-way parallel discrete memoryless channels (DMC) using variable block length coding (VLC) are presented. First, Forney's erasure decoding error exponent is shown to be achievable for both directions simultaneously. Next, for some rate-pairs, it is shown that the error exponent of the direction with a smaller capacity may be further increased by allocating feedback resources to it in the other direction, at the price of a decreased error exponent for the other terminal. The presented two-way communication scheme builds upon Draper-Sahai's one-way DMC achievability scheme with noisy feedback under VLC. Both achievable error exponent regions demonstrate that the use of VLC and interaction between the terminals may benefit both directions' error exponents over fixed block length and feedback free transmission.1

A one-way additive white Gaussian noise (AWGN) channel with active feedback sent over another AWGN feedback channel is considered. Achievable error exponents are presented in the finite message / zero-rate regime for a variable length coding (VLC) scheme. This coding scheme uses a form of round-robin scheduling of messages, and a simplex-based feedback code to obtain reliable feedback and remain synchronized, despite the noise in the feedback link. Our results show that this new VLC scheme under an almost-sure power constraint achieves an error exponent similar to an achievable exponent attained using a fixed block length scheme under a much more relaxed expected block power constraint, and is larger than that achieved by schemes without feedback.

This paper considers the problem of code design for a channel where communications and radar systems coexist, modeled as having both Additive White Gaussian Noise (AWGN) and Additive Radar Interference (ARI). The issue of how to adapt or re-design convolutional codes (decoded by the Viterbi algorithm) and LDPC codes (decoded by the sum-product algorithm and optimized by using the EXIT chart method) to effectively handle the overall non-Gaussian ARI noise is investigated. A decoding metric is derived from the non-Gaussian ARI channel transition probability as a function of the Signal-to-Noise Ratio (SNR) and Interference-to-Noise Ratio (INR). Two design methodologies are benchmarked against a baseline "unaltered legacy system", where a code designed for AWGN-only noise, but used on the non-Gaussian ARI channel, is decoded by using the AWGN-only metric (i.e., as if INR is zero). The methodologies are: M1) codes designed for AWGN-only noise, but decoded with the new metric that accounts for both SNR and INR; and M2) codes optimized for the overall non-Gaussian ARI channel. Both methodologies give better average Bit Error Rate (BER) in the high INR regime compared to the baseline. In the low INR regime, both methodologies perform as the baseline since in this case the radar interference is weak. Interestingly, the performance improvement of M2 over M1 is minimal. In practice, this implies that specifications in terms of channel error correcting codes for commercially available wireless systems need not be changed, and that it suffices to use an appropriate INR-based decoding metric in order to effectively cope with the ARI.

This paper studies the Layered Packet Erasure Broadcast Channel (LPE-BC) with Channel Output Feedback (COF), which is a high-SNR approximation of the fading Gaussian BC, proposed by Tse and Yates in 2012 for the case without COF. This model is also a multi-layer generalization of the Binary Erasure Channel (BEC). In a past work, the Authors derived inner and outer bounds to the rate region (set of achievable rates with backlogged arrivals) of the LPE-BC with COF; here, the arrival region (set of exogenous arrival rates for which packet arrival queues are stable) for the same model is analyzed. For the case of K=2 users and Q ≥ 1 layers, the known achievable rate region and the derived arrival region coincide; both strategically employ a. For the case of Q = 2 layers, sufficient conditions are given for the achievable arrival region to coincide with the known converse rate region, thus showing that in those cases the optimal rate and arrival regions coincide.

This paper, motivated by mission-critical and latency-constrained traffic, focuses on delivering different messages to various end-users within hard deadlines on the downlink of a wireless system. A novel deadline outage performance criterion is introduced, which accounts for both the violation of the hard deadline by any of the messages as well as for channel decoding errors due to finite block-length. This formulation allows for the study of scheduling policies under a more refined model of the physical layer channel than is usually assumed in the networking literature. Different scheduling polices under hard deadline constraints are proposed, and the corresponding deadline outage probabilities evaluated. The main result is that, to reduce the deadline outage probability, a scheduling policy should cleverly combine time-sharing and concatenate-and- code.

A primitive relay channel (PRC) has one source (S) communicating a message to one destination (D) with the help of a relay (R). The link between R and D is considered to be noiseless, of finite capacity, and parallel to the link between S and (R,D). Prior work has established, for any fixed number of channel uses, the minimal R-D link rate needed so that the overall S-D message rate equals the zero-error single-input multiple output outer bound (Problem 1). The zero-error relaying scheme was expressed as a coloring of a carefully defined “relaying compression graph”. It is shown here that this relaying compression graph for$n$channel uses is not obtained as a strong product from its$n$= 1 instance. Here we define a new graph, the “primitive relaying graph” and a new “special strong product” such that the n-channel use primitive relaying graph corresponds to the n-fold special strong product of the$n$= 1 graph. We show how the solution to Problem 1 can be obtained from this new primitive relaying graph directly. Further study of this primitive relaying graph has the potential to highlight the structure of optimal codes for zero-error relaying.

Achievable error exponent regions of a two-way additive white Gaussian noise (AWGN) channel, where two terminals exchange a fixed number of messages M, are derived. In particular, error exponent regions for M = 2 messages under expected power and M = 3 messages under almost sure power constraints are considered. For M = 2 messages the use of active feedback is shown to lead to an error exponent gain over that when feedback / interaction is ignored. For M = 3 messages and asymmetric channels, it is shown that the error exponent of the weaker channel may be improved through active feedback, at the expense of a decreased error exponent of the stronger direction. This may, for sufficiently asymmetric channel gains, outperform the error exponent region achieved by having both terminals operate independently of one another (ignoring the possibility of sending feedback for the other).

Finding the underlying probability distributions of a set of observed sequences under the constraint that each sequence is generated i.i.d by a distinct distribution is considered. The number of distributions, and hence the number of observed sequences, are let to grow with the observation blocklength n. Asymptotically matching upper and lower bounds on the probability of error are derived.

Increasing demands for spectrum have necessitated the coexistence of communications and radar systems within the same band. This paper investigates how an unaltered radar system affects the performance of a communications receiver. For a single-carrier communications system, it is shown that a low power radar signal can be treated as Gaussian noise while a strong radar signal can be subtracted off the received signal, but in doing so one of the two signal dimensions is lost. Complex-valued constellation design problems are next proposed, with the goal of either minimizing the error rate under a power constraint, or maximizing the transmission rate under both error rate and power constraints. Numerically, the designed constellation is shaped as a concentric hexagon for weak radar interference while it morphs into an uneven pulse amplitude modulation for strong interference. A multi-carrier orthogonal frequency division multiplexing communications system is lastly considered. Due to the radar interference, the received signal becomes correlated over time and across carriers. To reduce the complexity of the optimal receiver, several suboptimal decoders are analyzed, among which the one that discards the correlations between subcarriers is numerically found to perform close to the optimal one.

This paper investigates the capacity of a communications channel that, in addition to additive white Gaussian noise, also suffers from interference caused by a co-existing radar transmission. The radar interference (of short duty-cycle and of much wider bandwidth than the intended communication signal) is modeled as an additive term whose amplitude is known and constant, but whose phase is independent and identically uniformly distributed at each channel use. The capacity achieving input distribution, under the standard average power constraint, is shown to have independent modulo and phase. The phase is uniformly distributed in [0, 2π]. The modulo is discrete with countably infinite many mass points, but only finitely many in any bounded interval. From numerical evaluations, a proper-complex Gaussian input is seen to perform quite well for weak radar interference. We also show that for very large radar interference, and for signal to noise ratio equal to S, the capacity is equal to (1/2) log(1+S) and a proper-complex Gaussian input achieves it. It is concluded that the presence of the radar interference results in a loss of half of the degrees of freedom compared with an AWGN channel without radar interference.

This paper considers a Gaussian channel with one transmitter and two receivers. The goal is to maximize the communication rate at the intended/primary receiver subject to a disturbance constraint at the unintended/secondary receiver. The disturbance is measured in terms of the minimum mean square error (MMSE) of the interference that the transmission to the primary receiver inflicts on the secondary receiver. This paper presents a new upper bound for the problem of maximizing the mutual information subject to an MMSE constraint. The new bound holds for vector inputs of any length and recovers a previously known limiting (when the length of the vector input tends to infinity) expression from the work of Bustin et al. The key technical novelty is a new upper bound on the MMSE. This bound allows one to bound the MMSE for all signal-to-noise ratio (SNR) values below a certain SNR at which the MMSE is known (which corresponds to the disturbance constraint). The bound also complements the “single-crossing point property” of the MMSE that upper bounds the MMSE for all SNR values above a certain value at which the MMSE value is known. The MMSE upper bound provides a refined characterization of the phase-transition phenomenon, which manifests, in the limit as the length of the vector input goes to infinity, as a discontinuity of the MMSE for the problem at hand. For vector inputs of size n = 1, a matching lower bound, to within an additive gap of order O(log log(1/MMSE)) (where MMSE is the disturbance constraint), is shown by means of the mixed inputs technique recently introduced by Dytso et al.

In this paper we analyze the performance of a full-duplex relay system in the presence of residual self-interference (SI) and frequency-selective fading. In particular, the residual SI channel estimation performance is evaluated both analytically and via simulation. The bit error rate (BER) performance at the destination is also characterized via simulation. Two schemes are considered for the equalization of the source-to-relay (SR) and relay-to-destination (RD) channels: end-point equalization and distributed equalization. In the first approach, channel equalization is performed only at the destination and is similar to an amplify-and-forward model. In the second approach, equalization of the SR channel is performed at the relay, while the RD channel equalization is performed at the destination. We show that at the cost of a modest complexity increase at the relay, the distributed scheme provides more robust performance than its end-point counterpart.

The slotted strongly asynchronous channel with a bursty user consists of a window of An= enαblocks of length n channel uses. A user transmits a randomly selected message among Mn= enRdifferent ones in exactly Kn= envrandomly selected but distinct blocks in the window. The receiver must locate and decode, with vanishing error probability in n, each one of the transmitted messages. The optimal tradeoff between (R, α, ν) is derived.

In a primitive relay channel, a new one-shot relaying scheme termed color-and-forward is proposed that guarantees a probability of error equal to zero. This relaying scheme constructs a relaying compression graph of relay outputs based on the joint conditional distribution of the relay and destination outputs, and forwards a minimum coloring of this graph. The n-letter extension of the proposed color-and-forward scheme is shown to be optimal in the sense that it results in the smallest needed out-of-band relay to destination link rate for the overall message rate to equal the single-input multiple-output outer bound for any fixed number of channel uses. This is used to obtain an upper bound on the asymptotic minimal relay to destination link rate needed to achieve the single-input multiple-output outer bound.

In the near future, radar and communication systems will share the spectrum. This motivates the study of how the two systems, which have traditionally operated in different bands, may co-exist. This paper investigates the effect of radar interference (unaltered, beyond the communication system designer's control) on an uncoded communication system, using complex-valued modulation schemes when the Maximum-A-Posteriori (MAP) detector is used. For all commonly used higher order modulation schemes, the Symbol Error Rate (SER) exhibits an "error floor" for the radar interference much larger than the signal power, which can be exactly characterized; in this regime the optimal MAP detector behaves like an interference canceller; interestingly, in this regime the channel behaves as a real-valued phase- fading AWGN channel with receiver CSI, thus indicating a loss of one of the two complex dimensions compared to the complex-valued interference-free channel.

The problem of estimating an arbitrary random vector from its observation corrupted by additive white Gaussian noise, where the cost function is taken to be the minimum mean pth error (MMPE), is considered. The classical minimum mean square error (MMSE) is a special case of the MMPE. Several bounds, properties, and applications of the MMPE are derived and discussed. The optimal MMPE estimator is found for Gaussian and binary input distributions. Properties of the MMPE as a function of the input distribution, signal-to-noiseratio (SNR) and order p are derived. The “single-crossing-point property” (SCPP) which provides an upper bound on the MMSE, and which together with the mutual information-MMSE relationship is a powerful tool in deriving converse proofs in multiuser information theory, is extended to the MMPE. Moreover, a complementary bound to the SCPP is derived. As a first application of the MMPE, a bound on the conditional differential entropy in terms of the MMPE is provided, which then yields a generalization of the Ozarow-Wyner lower bound on the mutual information achieved by a discrete input on a Gaussian noise channel. As a second application, the MMPE is shown to improve on previous characterizations of the phase transition phenomenon that manifests, in the limit as the length of the capacity achieving code goes to infinity, as a discontinuity of the MMSE as a function of SNR. As a final application, the MMPE is used to show new bounds on the second derivative of mutual information, or the first derivative of the MMSE.

This paper studies the impact of block asynchronism on the capacity of a slotted Multiple Access Channel (MAC) whose number of users Knincreases with the blocklength n. In a slotted strong-asynchronous MAC, the Knusers have independent transmission start times that are integer multiples of n (slotted) which are uniformly distributed on a window of length An= enα(strong-asynchronism). All users' messages as well as transmission times need to be reliably decoded at the single receiver. We show that for Kn= enνwith ν > α, not even synchronization is possible when transmitting a single message per user. We also show that for Kn= eνwith ν = o(n), each user can achieve its point-to-point asynchronous capacity, which is a trivial upper bound for the capacity of the MAC. Finally, achievable rates for Kn= enν. with 0 <; ν <; α/2 are derived.

This paper considers the minimum mean p-th error (MMPE) estimation problem: estimating a random vector in the presence of additive white Gaussian noise (AWGN) in order to minimize an Lpnorm of the estimation error. The MMPE generalizes the classical minimum mean square error (MMSE) estimation problem. This paper derives basic properties of the optimal MMPE estimator and MMPE functional. Optimal estimators are found for several inputs of interests, such as Gaussian and binary symbols. Under an appropriate p-th moment constraint, the Gaussian input is shown to be asymptotically the hardest to estimate for any p ≥ 1. By using a conditional version of the MMPE, the famous “MMSE single-crossing point” bound is shown to hold for the MMPE too for all p ≥ 1, up to a multiplicative constant. Finally, the paper develops connections between the conditional differential entropy and the MMPE, which leads to a tighter version of the Ozarow-Wyner lower bound on the rate achieved by discrete inputs on AWGN channels.

We consider an L-user multiple access channel where transmitter m has access to the linear equation um= ⊕l=1Lfmlwlof independent messages wl∈ Fpkl with fml∈ Fp, and the destination wishes to recover all L messages. This problem may be motivated as the last hop in a network where relay nodes employ the compute-and-forward strategy and decode linear equations of messages; we seek to do the reverse and extract messages from sums over a multiple access channel. In particular, we exploit the particular form of dependencies between the equations at the different relays to improve the reliable communication rates beyond those achievable by simply forwarding all equations to the destination independently. The presented achievable rate region for the discrete memoryless channel model is shown to be capacity for the additive white Gaussian noise channel.

This paper shows that for the two-user Gaussian interference channel (G-IC) treating interference as noise without time sharing (TINnoTS) achieves the closure of the capacity region to within either a constant gap, or to within a gap of the order O(log(ln(min(S, I))/y)) up to a set of Lebesgue measure γ ∈ (0, 1], where S is the largest signal to noise ratio on the direct links and I is the largest interference to noise ratio on the cross links. As a consequence, TINnoTS is optimal from a generalized degrees of freedom (gDoF) perspective for all channel gains except for a subset of zero measure. TINnoTS with Gaussian inputs is known to be optimal within 1/2 bit for a subset of the weak interference regime. Rather surprisingly, this paper shows that TINnoTS is gDoF optimal in all parameter regimes, even in the strong and very strong interference regimes where joint decoding of Gaussian inputs is optimal. For approximate optimality of TINnoTS in all parameter regimes, it is critical to use non-Gaussian inputs. This paper thus proposes to use mixed inputs as channel inputs for the G-IC, where a mixed input is the sum of a discrete and a Gaussian random variable. Interestingly, with reference to the Han-Kobayashi achievable scheme, the discrete part of a mixed input is shown to effectively behave as a common message in the sense that, although treated as noise, its effect on the achievable rate region is as if it were jointly decoded together with the desired messages at a non-intended receiver. The practical implication is that a discrete interfering input is a friend, while an Gaussian interfering input is in general a foe. This paper also discusses other practical implications of the proposed TINnoTS scheme with mixed inputs. Since TINnoTS requires neither explicit joint decoding nor time sharing, the results of this paper are applicable to a variety of oblivious or asynchronous channels, such as the block asynchronous G-IC (which is not an information stable channel) and the G-IC with partial codebook knowledge at one or more receivers.

In a full-duplex bidirectional interference network with 2K transceivers, there are K communication pairs: each user transmits a message to and receives a message from one intended user and interferes with and experiences interference from all other users. All nodes may interact, or adapt inputs to past received signals, and may thus co-operate with each other. We derive a new outer bound, and use interference alignment to demonstrate that the optimal degrees of freedom (DoF, also known as the multiplexing gain) is K: full-duplex operation doubles the DoF, but interaction and co-operation does not further increase the DoF. We next characterize the DoF of a full-duplex bidirectional interference network with a MIMO full-duplex relay. If the relay is noncausal/instantaneous (at time k forwards a function of its received signals up to time k) and has 2K antennas, we demonstrate a one-shot scheme where the relay mitigates all interference to achieve the interference-free 2K DoF. In contrast, if the relay is causal (at time k forwards a function of its received signals up to time k - 1), we show that a full-duplex MIMO relay cannot increase the DoF of the full-duplex bidirectional interference network beyond K, as if no relay or interaction is present.

Signal outage, due to shadowing and blockage, is expected to be the main bottleneck in millimeter wave (mmWave) networks. Moreover, the anticipated dense deployment of base stations in mmWave networks is expected to increase the interference from strong line-of-sight base stations too, thus further increasing the probability of outage. To address the issue of reducing outage, this paper explores the possibility of base station co-operation in the downlink of mmWave heterogenous networks. The main focus of this work is showing that, in a stochastic geometry framework that incorporates blockage, co-operation from randomly located base stations decreases the probability of outage/increases the coverage probability. Coverage probabilities are derived accounting for: blockage, different fading distributions on the direct links (but always Rayleigh fading on the interference links), antenna directionality, and different tiers. Numerical results suggest that coverage with base station co-operation in dense mmWave systems (i.e., with high average number of base stations per square meter), without small scale fading on the direct communications links, and with any probability of signal blockage, considerably exceeds coverage without co-operation. In contrast, a small increase in coverage is reported when mmWave networks are less dense, have a high probability of signal blockage and the direct communications links are affected by Rayleigh fading.

Recently a new “Colour-and-Forward” relaying strategy was proposed for the zero-error primitive relay channel, a relay channel in which the relay to destination link is out of band and of fixed, error-free capacity. This “Colour-and-Forward” scheme forwards the colour (from a minimum colouring) of the node corresponding to its received signal. This colouring is of a carefully designed graph based on the joint distribution of the relay and destination outputs given the transmit signal. This scheme was used to provide a non-trivial upper bound on the minimum required conference link capacity to allow the overall network to achieve the single-input multi-output (SIMO) upper bound. In this paper, we strengthen the result and show that this upper bound is tight if one wants to achieve the SIMO bound in the overall network for any fixed number of channel uses.

While a multi-letter limiting expression of the capacity region of the two-user Gaussian interference channel is known, capacity is generally considered to be open as this is not computable. Other computable capacity outer bounds are known to be achievable to within 1/2 bit using Gaussian inputs and joint decoding in the simplified Han and Kobayashi (single-letter) achievable rate region. This work shows that the simple scheme known as “treating interference as noise” without time-sharing attains the capacity region outer bound of the symmetric Gaussian interference channel to within either a constant gap, or a gap of order O(log log(SNR)), for all parameter regimes. The scheme is therefore optimal in the generalized Degrees of Freedom (gDoF) region sense almost surely. The achievability is obtained by using i.i.d. mixed inputs (i.e., a superposition of discrete and Gaussian random variables) in the multi-letter capacity expression, where the optimal number of points in the discrete part of the inputs, as well as the optimal power split among the discrete and continuous parts of the inputs, are characterized in closed form. An important practical implication of this result is that the discrete part of the inputs behaves as a “common message” whose contribution can be removed from the channel output, even though joint decoding is not employed. Moreover, time-sharing may be mimicked by varying the number of points in the discrete part of the inputs.

Motivated by the ongoing discussion of spectrum scarcity, this paper considers the K-user cognitive interference channel with K - 1 primary/licensed users and one cognitive/secondary user who has non-causal knowledge of the messages of all primary users. This message sharing mechanism is referred to as cognitive-only message sharing. For certain parameter regimes, the sum-capacity of the symmetric Gaussian noise channel is characterized to within an additive constant gap from an outer bound originally derived for a channel model with cumulative message sharing, which consists of one primary user and K-1 cognitive users where cognitive transmitter i ∈ [2 : K] has non-causal knowledge of the messages of the users with index less than i. The approximately optimal achievability scheme is a combination of simultaneous interference neutralization at the primary receivers, dirty-paper coding to remove the effect of interference at the cognitive receiver, and rate-splitting, where the power splits are chosen such that the signals treated as noise are received below the noise floor of the receiver. This shows that “distributed cognition” may not be necessary in the considered network model since (approximately) the same sum-capacity can be achieved by having only one “globally cognitive” user whose role is to manage all the interference in the network.

The study of the two-user Gaussian Interference Channel (IC) where one receiver lacks knowledge of the interfering codebook, also dubbed the IC with an oblivious receiver (IC-OR), is motivated by: (1) in heterogeneous, cognitive, distributed or dynamic networks, assuming that every node posses codebooks of every other node may not be practical, and (2) it is not clear whether and how much lack of codebook knowledge would affect the Han and Kobayashi (HK) achievable scheme, which involves joint decoding of intended and interfering messages and which appears not possible if nodes do not possess all codebooks. To address these issues, we evaluate a simplified HK (where the oblivious receiver treats interference as noise) with mixed inputs at the non-oblivious transmitter, i.e., a mixture of discrete and Gaussian random variables, where the power split between the two and the number of points of the discrete part are carefully chosen as a function of the channel parameters. The oblivious transmitter uses a purely Gaussian input. Surprisingly, for this choice of inputs, the capacity region of the symmetric Gaussian IC-OR is shown to be within 1 over 2 log (12πe) ≈ 3.34 bits of the best known outer bound for the classical Gaussian IC with full codebook knowledge at both receivers. Interestingly, this shows that a simplified HK where one receiver is restricted to treat interference as noise loses at most 1 over 2 log (12πe) ≈ 3.34 bits in performance. Moreover, the discrete part of the input behaves like a “common message” even though it is not jointly decoded (together with the intended messages) at the oblivious receiver.

In multiuser information theory, it is often assumed that every node in the network possesses all codebooks used in the network. This assumption may be impractical in distributed ad hoc, cognitive, or heterogeneous networks. This paper considers the two-user interference channel with one oblivious receiver (IC-OR), i.e., one receiver lacks knowledge of the interfering cookbook, whereas the other receiver knows both codebooks. This paper asks whether, and if so how much, the channel capacity of the IC-OR is reduced compared with that of the classical IC where both receivers know all codebooks. A novel outer bound is derived and shown to be achievable to within a gap for the class of injective semideterministic IC-ORs; the gap is shown to be zero for injective fully deterministic IC-ORs. An exact capacity result is shown for the general memoryless IC-OR when the nonoblivious receiver experiences very strong interference. For the linear deterministic IC-OR that models the Gaussian noise channel at high SNR, nonindependent identically distributed. Bernoulli(1/2) input bits are shown to achieve points not achievable by i.i.d. Bernoulli(1/2) input bits used in the same achievability scheme. For the real-valued Gaussian IC-OR, the gap is shown to be at most 1/2 bit per channel use, even though the set of optimal input distributions for the derived outer bound could not be determined. Toward understanding the Gaussian IC-OR, an achievability strategy is evaluated in which the input alphabets at the nonoblivious transmitter are a mixture of discrete and Gaussian random variables, where the cardinality of the discrete part is appropriately chosen as a function of the channel parameters. Surprisingly, as the oblivious receiver intuitively should not be able to jointly decode the intended and interfering messages (whose codebook is unavailable), it is shown that with this choice of input, the capacity region of the symmetric Gaussian IC-OR is to within 1/2 log (12πe)≈ 3.34 bits (per channel use per user) of an outer bound for the classical Gaussian IC with full codebook knowledge at both receivers.

This paper characterizes the sum-capacity of the ergodic fading Gaussian overlay cognitive interference channel (EGCIFC), a time-varying channel with two source-destination pairs in which a primary/licensed transmitter and a secondary/cognitive transmitter share the same spectrum and where the cognitive transmitter has noncausal knowledge of the primary user's message. The throughput/sum-capacity is characterized under the assumption of perfect knowledge of the instantaneous fading states at all terminals, which are assumed to form an ergodic process. A genie-aided outer bound on the sum-capacity is developed and then matched with an achievable scheme, thereby completely characterizing the sum-capacity of the EGCIFC. The power allocation policy that maximizes the sum-capacity is derived. It is shown that the sum-capacity achieving scheme for an EGCIFC is “separable” in all regimes (i.e., coding across fading states is not necessary), as opposed to the classical interference channel. Extensions to the whole capacity region are discussed. As a capacity achieving scheme for the EGCIFC under certain channel gain conditions, and as a topic of independent interest, the ergodic capacity of a point-to-point multiple-input-single-output channel with per-antenna power constraints and with perfect channel state information at all terminals is also derived.

In a K-pair-user two-way interference channel (TWIC), 2K messages and 2K transmitters/receivers form a K-user IC in the forward direction (K messages) and another K-user IC in the backward direction which operate in full-duplex. All nodes may interact, or adapt inputs to past received signals. The optimal degrees of freedom (DoF, also known as the multiplexing gain) is known to be K [1]: full-duplex operation doubles the DoF, but interaction does not further increase the DoF. In this paper, we characterize the DoF of the K-pair-user TWIC with a MIMO, full-duplex relay. If the relay is noncausal/ instantaneous (at time k forwards a function of its received signals up to time k) and has 2K antennas, we demonstrate a one-shot scheme where the relay mitigates all interference to achieve the interference-free 2K DoF. In contrast, if the relay is causal (at time k forwards a function of its received signals up to time k - 1), we show that a full-duplex MIMO relay cannot increase the DoF of the K-pair-user TWIC beyond K, as if no relay or interaction is present.

This paper studies the sum-rate of a class of memoryless, real-valued additive white Gaussian noise interference channels (IC) achievable by treating interference as noise (TIN). We develop and analytically characterize the rates achievable by a new strategy that uses superpositions of Gaussian and discrete random variables as channel inputs. Surprisingly, we demonstrate that TIN is sum-generalized degrees of freedom optimal and can achieve to within an additive gap of O(1) or O(log log(SNR)) to the symmetric sum-capacity of the classical IC. We also demonstrate connections to other channels such as the IC with partial codebook knowledge and the block asynchronous IC.

This paper characterizes the ergodic capacity of the fading multiple-input single-output (MISO) channel with per-antenna power constraints (PerPC) with perfect Channel State Information (CSI) at all terminals. This turns out to be the sum-capacity achieving strategy for the ergodic fading Gaussian overlay cognitive interference channel (EGCIFC) in the strong interference regime. The EGCIFC is a two-user time-varying interference channel in which a primary / licensed transmitter and a secondary / cognitive transmitter share the same spectrum and where the cognitive transmitter has non-causal knowledge of the primary user's message. The MISO and the EGCIFC results are verified numerically for the case of independent Rayleigh fading gains. Different achievable strategies, corresponding to different amount of CSI, are compared to show the performance of the derived PerPC optimal power allocation.

Full-duplex allows for the simultaneous flow of information in two directions and, in point-to-point Gaussian two-way channels, doubles capacity. A two-way line network where two sources exchange messages through multiple serial relays is considered. It is shown that when all nodes are full duplex, one may achieve to within a constant gap, independent of the number of relays, of the capacity of two one-way line networks. This shows that, even in the presence of relays that carry information in two directions, full duplex is able to approximately double capacity. A novel lattice coding scheme is developed for the two-way line network with two relays, which may be extended to an arbitrary number of relays and to half-duplex scenarios. The key technical contribution is the achievability strategy, where each relay decodes the sum of several signals (using lattice codes) and then re-encodes it into another lattice codeword. This allows other nodes to again decode sums of codewords. The presented lattice-coding-based scheme ensures that both directions simultaneously fully utilize the relays' powers, even for asymmetric channels. The symmetric rate achieved by the proposed scheme is within 0.5 log 5 bit/Hz/s of the symmetric rate capacity regardless of the number of relays.

Most wireless communication networks are two-way, where nodes act as both sources and destinations of messages. This allows for adaptation at or interaction between the nodes-a node's channel inputs may be functions of its message(s) and previously received signals allowing for potentially larger rates than those achievable in feedback-free one-way channels where inputs are functions of messages only. However, examples exist of channels where adaptation is not beneficial from a capacity perspective. We ask whether analogous results hold for several multiuser two-way networks. We first consider deterministic two-way channel models: the binary modulo-2 addition channel and a generalization of this, and the linear deterministic channel, which models Gaussian channels at high SNR. For these deterministic models, we obtain the capacity region for the two-way multiple access/broadcast channel (MAC/BC), the two-way Z channel, and the two-way interference channel (under certain partial adaptation constraints in some regimes). We permit all nodes to adapt their channel inputs to past outputs (except for portions of the linear high-SNR two-way interference channel where we only permit two of the four nodes to fully adapt). However, we show that the two-way fully or partially adaptive capacity region consists of two parallel one-way regions operating simultaneously in opposite directions, i.e., adaptation is useless. We next consider two noisy channel models: 1) the Gaussian two-way MAC/BC, where we show that adaptation can at most increase the sum-rate by (1/2) bit in each direction and 2) the two-way interference channel, where partial adaptation is shown to be useless when the interference is very strong. In the strong and weak interference regimes, we show that the nonadaptive Han and Kobayashi scheme utilized in parallel in both directions achieves to within a constant gap for the symmetric rate of the fully (for some regimes) or partially (for the remaining regimes) adaptive models. The central technical contribution is the derivation of new, computable outer bounds which allow for adaptation.

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.

This paper considers a variation of the classical two-user interference channel where the communication of two interfering source-destination pairs is aided by an additional node that has a priori knowledge of the messages to be transmitted, which is referred to as the cognitive relay. For this interference channel with a cognitive relay (ICCR), novel outer bounds and capacity region characterizations are derived. In particular, for the class of injective semi-deterministic ICCRs, a sum-rate upper bound is derived for the general memoryless ICCR and further tightened for the linear deterministic approximation (LDA) of the Gaussian noise channel at high SNR, which disregards the noise and focuses on the interaction among the users' signals. The capacity region of the symmetric LDA is completely characterized except for the regime of moderately weak interference and weak links from the CR to the destinations. The insights gained from the analysis of the LDA are then translated back to the symmetric Gaussian noise channel (GICCR). For the symmetric GICCR, an approximate characterization (to within a constant gap) of the capacity region is provided for a parameter regime where capacity was previously unknown. The approximately optimal scheme suggests that message cognition at a relay is beneficial for interference management as it enables simultaneous over the air neutralization of the interference at both destinations.

We characterize the degrees of freedom (DoF) of the full-duplex two-way interference channel with a non causal multi-antenna relay and time-varying channels. In a two-way interference channel (IC), 4 messages and 4 transmitters/receivers form an IC in the forward direction (2 messages) and another IC in the backward direction (2 messages) which operate simultaneously in full-duplex mode. Furthermore, all nodes are permitted to interact, i.e. adapt current channel inputs to past received signals. We propose a novel block Markov coding scheme combining the ideas of interference alignment and successive decoding to achieve the full, maximal, 4 degrees of freedom asymptotically. All source/destination nodes have a single antenna while 4 antennas at the relay are sufficient to achieve the full DoF. Interestingly, this implies that the non causal relay is able to effectively mitigate interference in this two way setting - i.e. each user in the two-way interference channel is able to exchange information with its desired user at interference-free rates thanks to the relay.

Time-reversal (TR) techniques have been shown to lead to gains in detection and enable super-resolution focusing. These gains have thus far mainly been demonstrated for time invariant channels, where the channel remains constant between the initial and time-reversed signal transmissions. Here, we are interested in determining whether TR techniques may be beneficial in time-varying channels. We approach this problem by comparing the mutual information between the channel and the received signals over two time slots of a radar system which does / does not use TR. Besides evaluating this mutual information, and showing that for this setup it is equal to directed information which might be of interest in feedback-like channels, we also provide a low-rank interpretation of this mutual information for Gaussian channels. Numerical evaluations suggest that if the channels are non-stationary yet correlated, TR may still provide information gains over non time-reversed systems.

In urban scenarios, target localization may be achieved using a single sensor via multipath exploitation. The multipath generating mechanisms such as building walls creates virtual radar sensors aiding in localization. For a wide class of radar-target geometries, specialized functions termed multipath preservers are derived to ensure that multipath is physically observable in the radar returns, and therefore these functions assist in evaluating the potential of multipath exploitation in urban sensing. The single sensor system performance is studied by deriving the Cramér-Rao and the Bayesian Cramér-Rao bounds (BCRBs). Given a reflecting geometry, these lower bounds and multipath preservers allow the radar operator to anticipate blind spots, place confidence levels on the localization results, and permit sensor positioning to optimally aid in exploiting multipath for target localization. It is shown here that Cramér-Rao bounds (CRBs) on the location parameters improve with additional multipath.

In this paper, we study ARQ feedback in the context of two-way wireless communications. In particular, we consider two nodes which wish to exchange data over a frequency division duplex, time-varying wireless additive white Gaussian noise with Rayleigh fading, channel. In two-way scenarios, unlike the more well studied one-way data scenarios, the data and resources allocated to feedback and channel estimation may share the same link, leading to interesting tradeoffs. To analyze these, we present a two-way framework in which 1) training (estimation of channel state), 2) feedback (in the form of ARQ), and 3) data are taken into account, and share the same noisy fading channel. We obtain an expression which captures the tradeoffs between allocating resources for these three tasks on the overall throughput achievable in each direction, which we numerically evaluate. In particular, we obtain the optimal resource allocations corresponding to different channel conditions, SNR regimes, and receiver feedback protocols under fast and slow fading conditions.

We consider a three user multiple access channel where transmitter m has access to the linear equation um= Σ3l = 1fmlwlof independent messages w1ϵ Fpk1, w2 ϵ Fpk2, w3 ϵ Fpk3(and fmlϵ Fp), and the destination wishes to recover all three messages. This problem is motivated as the last hop in a network where relay nodes employ the Compute-and-Forward strategy and decode linear equations of messages; we seek to do the reverse and extract messages from sums over a multiple access channel. An achievable rate region for the two user problem was previously derived; here we extend and strengthen this work to show capacity for the two and three user Gaussian channel models subject to invertability conditions on the matrix of coefficients describing the given linear equations of messages. The optimal transmission scheme is not to independently send the three equations umover the MAC but rather to exploit their special correlation structure.

Shannon theoretic multi-user capacity problems are traditionally formulated under the assumption that all decoding nodes possess all codebooks. However, for certain networks such as cognitive ones, this may be an unrealistic assumption. We work towards understanding the impact of lack of codebook knowledge at some decoding nodes in the network. We do so by considering a two-user interference channel in which one of the receivers has no information about the codebook of the interfering transmitter, while the other receiver has both codebooks. We derive a novel outer bound for the special class of injective semi-deterministic interference channels which incorporates this codebook knowledge explicitly. For the linear deterministic channel, which models the Gaussian channel at high SNR, we demonstrate the surprising fact that non i.i.d. Bernoulli(1/2) points achieve points on the outer bound not achievable by Bernoulli(1/2) inputs. We then show that this is achievable to within a constant gap by a modified Han-Kobayashi scheme. We characterize the capacity region of the Gaussian noise channel to within 1/2 bit, even though we could not determine the set of optimal input distributions. Numerical evaluations suggest that if the non-oblivious transmitter uses a discrete input a larger sum-rate is achievable compared to the case where both users employ Gaussian codebooks or use time division in strong interference regime at high SNR.

This paper considers the K-user cognitive interference channel with one primary and K - 1 secondary/cognitive transmitters with a cumulative message sharing structure, i.e., cognitive transmitter i, i ϵ [2 : K], non-causally knows all messages of the users with index less than i. We first propose a computable outer bound valid for any memoryless channel and show the sum-rate to be achievable for the symmetric K-user Linear Deterministic Channel. Interestingly, for the K-user channel having only the K-th transmitter know all other messages is sufficient to achieve the sum-capacity, i.e., cognition at transmitters 2 to K-1 is not needed. Next, the sum-capacity of the symmetric Gaussian noise channel is characterized to within a constant additive and multiplicative gap, which depend on K. As opposed to other interference channel models, a single scheme suffices for both the weak and strong interference regimes. Moreover it is only required for transmitters 2 to K-1 to have, in addition to their own message, non-causal message knowledge of the transmitter 1's message.

We develop a novel lattice coding scheme for the Two-way Two-relay Channel: 1 ↔ 2 ↔ 3 ↔ 4, where Node 1 and 4 communicate with each other through two relay nodes 2 and 3. Each node only communicates with its neighboring nodes. The key technical contribution is the lattice-based achievability strategy, where each relay is able to remove the noise while decoding the sum of several signals in a Block Markov strategy and then re-encode the signal into another lattice codeword using the so-called “Re-distribution Transform”. This allows nodes further down the line to again decode sums of lattice codewords. The symmetric rate achieved by the proposed lattice coding scheme is within 1/2 log 3 bit/Hz/s of the symmetric rate capacity.

This work considers different K-user extensions of the two-user cognitive interference channel model. The models differ by the cognitive abilities of the transmitters. In particular, the primary message sharing model, in which only one user is cognitive and knows all messages, and the cumulative message sharing model, in which a user knows the messages of all users with lesser index, are analyzed. The central contribution is the characterization of the sum-capacity of both models under a strong interference condition, which amounts to having one receiver in the network that can decode all transmitted signals without loss of optimality. The sum-capacity is evaluated for the Gaussian noise channel, as well as the conditions on the channel gains that grant strong interference.

It has been shown that time-reversal (TR) techniques focus energy back to the dominant scatters, lead to super-resolution focusing, and gains in detection. Time reversal has so far mainly been studied when the channel remains invariant between the initial and time-reversed signal transmission times. In this letter, we relax this assumption and study the benefits of TR over time-varying channels. To do so, we compare a time-reversed and a non time-reversed system by comparing the mutual information between the channel impulse response and channel outputs given the transmitted signals. We present analytical results for a simple scalar problem which illustrates the impact of nonstationary channels on TR, and for general channels, numerically evaluate the difference in mutual informations, which demonstrate that, if the channels are nonstationary yet correlated, TR may still provide mutual information gains over non time-reversed systems.

Lattice codes are known to achieve capacity in the Gaussian point-to-point channel, achieving the same rates as i.i.d. random Gaussian codebooks. Lattice codes are also known to outperform random codes for certain channel models that are able to exploit their linearity. In this paper, we show that lattice codes may be used to achieve the same performance as known i.i.d. Gaussian random coding techniques for the Gaussian relay channel, and show several examples of how this may be combined with the linearity of lattices codes in multisource relay networks. In particular, we present a nested lattice list decoding technique in which lattice codes are shown to achieve the decode-and-forward (DF) rate of single source, single destination Gaussian relay channels with one or more relays. We next present two examples of how this DF scheme may be combined with the linearity of lattice codes to achieve new rate regions which for some channel conditions outperform analogous known Gaussian random coding techniques in multisource relay channels. That is, we derive a new achievable rate region for the two-way relay channel with direct links and compare it to existing schemes, and derive a new achievable rate region for the multiple access relay channel. We furthermore present a lattice compress-and-forward (CF) scheme for the Gaussian relay channel which exploits a lattice Wyner-Ziv binning scheme and achieves the same rate as the Cover-El Gamal CF rate evaluated for Gaussian random codes. These results suggest that structured/lattice codes may be used to mimic, and sometimes outperform, random Gaussian codes in general Gaussian networks.

The capacity of the Interference Channel with a Cognitive Relay, a channel model which generalizes the broadcast, interference and cognitive interference channels, is still an open question. Towards understanding this complex channel, we first consider the binary linear deterministic model that approximates the Gaussian channel at high SNR. We consider symmetric channel gains and show achievability of a tightened version of a previously known outer bound for almost all channel parameters. Of particular interest in this channel model is how the cognitive relay may be used to simultaneously relay as well as cancel/neutralize interference at the two receivers. The achievability schemes used to prove capacity use combinations of three main strategies at the cognitive relay that we term bit cancellation, bit sharing, and bit (self)cleaning. We highlight the capacity achieving schemes in the different regimes, pointing out some of the interesting new behaviors seen at the cognitive relay.

In multi-user two-way channels nodes are both sources and destinations of messages. This allows for “adaptation” at or “interaction” between the nodes - the next channel inputs may be a function of the past received signals at a particular node. How to best adapt is key to two-way communication problems, rendering them complex and challenging. However, examples exist of channels where adaptation is not beneficial from a capacity perspective; it is known that for the point-to-point two-way modulo 2 adder and Gaussian channels, adaptation does not increase capacity. Recently, it was shown that the two-way modulo-2 additive versions of the multiple-access / broadcast (MAC/BC respectively, in the two directions), the Z channel and the interference channel also have capacity regions equal to two parallel one-way versions of the channels. In this work we show that the same is true for the linear deterministic multi-user two-way channels which approximate their Gaussian counterparts at high SNR, which include the two-way MAC/BC channel, the two-way Z channel, and the two-way interference channel under some adaptation constraints. For all three channel models we obtain the capacity region, which is that of two one-way channels in each direction, which may be achieved without the use of adaptation.

Inspired by cognitive networks, we consider the linear deterministic three-user cognitive interference channel with one primary and two secondary/cognitive transmitters which approximates the Gaussian channel at high SNR. Outer bounds on the sum-rate are derived and matching transmission schemes are provided in all interference regimes, thereby completely characterizing the sum-capacity. Significant increase in the sum-capacity is demonstrated when comparing the three-user cognitive channel to the classical (non-cognitive) three-user interference channel and to the two-user cognitive channel. The paper discusses extensions to an arbitrary number of users, the relationship between the cognitive channel and the (fully cooperative) broadcast channel, and observations on the behavior of the cognitive transmitters in the different interference scenarios.

The capacity of the Gaussian cognitive interference channel, a variation of the classical two-user interference channel where one of the transmitters (referred to as cognitive) has knowledge of both messages, is known in several parameter regimes but remains unknown in general. This paper provides a comparative overview of this channel model as it proceeds through the following contributions. First, several outer bounds are presented: (a) a new outer bound based on the idea of a broadcast channel with degraded message sets, and (b) an outer bound obtained by transforming the channel into channels with known capacity. Next, a compact Fourier-Motzkin eliminated version of the largest known inner bound derived for the discrete memoryless cognitive interference channel is presented and specialized to the Gaussian noise case, where several simplified schemes with jointly Gaussian input are evaluated in closed form and later used to prove a number of results. These include a new set of capacity results for: (a) the “primary decodes cognitive” regime, a subset of the “strong interference” regime that is not included in the “very strong interference” regime for which capacity was known, and (b) the “S-channel in strong interference” in which the primary transmitter does not interfere with the cognitive receiver and the primary receiver experiences strong interference. Next, for a general Gaussian channel the capacity is determined to within one bit/s/Hz and to within a factor two regardless of the channel parameters, thus establishing rate performance guarantees at high and low SNR, respectively. The paper concludes with numerical evaluations and comparisons of the various simplified achievable rate regions and outer bounds in parameter regimes where capacity is unknown, leading to further insight on the capacity region.

The cognitive interference channel (C-IFC) consists of a classical two-user interference channel in which the message of one user (the "primary" user) is non-causally available at the transmitter of the other user (the "cognitive" user). We obtain the capacity of the semi-deterministic C-IFC: a discrete memoryless C-IFC in which the cognitive receiver output is a noise-less deterministic function of the channel inputs. We then use the insights obtained from the capacity-achieving scheme for the semi-deterministic model to derive new, unified and tighter constant gap results for the complex-valued Gaussian C-IFC. We prove: (1) a constant additive gap (difference between inner and outer bounds) of half a bit/sec/Hz per real dimension, of relevance at high SNRs, and (b) a constant multiplicative gap (ratio between outer and inner bounds) of a factor two, of relevance at low SNRs.

We consider a cellular network inspired channel model which consists of the bi-directional exchange of information between a base-station and M terminal nodes with the help of a relay. The base-station has a message for each of M terminals, and conversely, each terminal node has a message for the base-station. A single relay assists the bi-directional communication endeavor. We assume an AWGN channel model with direct links (omitted in previous studies) between the base-station, relay, and half-duplex nodes. In this scenario, we derive achievable rate regions for two temporal protocols - needed in half-duplex networks - which indicate which users transmit when. These achievable rate regions are based on a novel lattice encoding and decoding strategy which outperforms previously derived regions using random-coding based decode-and-forward strategies under certain channel conditions. The terminal nodes employ nested lattice codes, and the relay decodes a series of codeword combinations - one of the main novelties of our scheme - from which it deduce the sum-codewords of the base-station to terminal node i, which it then broadcasts. This scheme differs markedly from previously considered successive-decoding based lattice strategies and provides a more general framework for the joint decoding of lattice codewords in a MAC. Numerical evaluations of our lattice-based inner bounds are shown to improve upon previous random-coding based schemes under certain channel conditions, and are compared to half-duplex cut-set outer bounds. We further demonstrate a constant sum-rate gap result using this lattice-based scheme for symmetric channels for one of the two protocols.

This work proposes a novel outer bound for the Gaussian cognitive interference channel in strong interference at the primary receiver based on the capacity of a multi-antenna broadcast channel with degraded message set. It then shows that for the Z-channel, i.e., when the secondary receiver experiences no interference and the primary receiver experiences strong interference, the proposed outer bound not only is the tightest among known bounds but is actually achievable for sufficiently strong interference. The latter is a novel capacity result that from numerical evaluations appears to be generalizable to a larger (i.e., non-Z) class of Gaussian channels.

The InterFerence Channel with a Cognitive Relay (IFC-CR) consists of a classical two-user interference channel in which the two independent messages are also non-causally known at a cognitive relay node. In this work a special class of IFC-CRs in which the sources do not create interference at the non-intended destinations is analyzed. This special model results in a channel with two non-interfering point-to-point channels whose transmission is aided by an in-band cognitive relay, which is thus referred to as the Parallel Channel with a Cognitive Relay (PC-CR). We determine the capacity of the PC-CR channel to within 3 bits/s/Hz for all channel parameters. In particular, we present several new outer bounds which we achieve to within a constant gap by proper selection of Gaussian input distributions in a simple rate-splitting and superposition coding-based inner bound. The inner and outer bounds are numerically evaluated to show that the actual gap can be far less than 3 bits/s/Hz.

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 consider the transmission of independent messages over a Gaussian relay network with interfering links. Using the compute-and-forward framework, relays can efficiently decode equations of the transmitted messages. The relays can then send their collected equations to the destination, which solves for its desired messages. Here, we study a special case of the inverse compute-and-forward problem: transmitting the equations to a single destination over a multiple-access channel. We observe that if the underlying messages have unequal rates, the set of possible values of an equation is constrained by the value of the other equations. We use this fact to improve the rate region for downloading equations. Interestingly, the rate region achieved over relay networks with interfering links using a combination of compute-and-forward and inverse compute-and-forward is larger than the best rate region achievable in the absence of interfering links. This verifies that interference may be used to beneficially “mix” messages over a wireless network.

We present a nested lattice-code-based strategy that achieves the random-coding based Compress-and-Forward (CF) rate for the three node Gaussian relay channel. To do so, we first outline a lattice-based strategy for the (X + Z1, X + Z2) Wyner-Ziv lossy source-coding with side-information problem in Gaussian noise, a re-interpretation of the nested lattice-code-based Gaussian Wyner-Ziv scheme presented by Zamir, Shamai, and Erez. We use the notation (X + Z1, X + Z2) Wyner-Ziv to mean that the source is of the form X + Z1and the side-information at the receiver is of the form X+Z2, for independent Gaussian X, Z1and Z2. We use this (X + Z1, X + Z2) Wyner-Ziv scheme to implement a “structured” or lattice-code-based CF scheme for the Gaussian relay channel which achieves the same rate as the Cover-El Gamal CF rate achieved by random Gaussian codebooks.

Two distinct, but overlapping, networks that operate at the same time, space, and frequency is considered. The first network consists ofnrandomly distributed primary users, which form an ad hoc network. The second network again consists ofmrandomly distributed ad hoc secondary users or cognitive users. The primary users have priority access to the spectrum and do not need to change their communication protocol in the presence of the secondary users. The secondary users, however, need to adjust their protocol based on knowledge about the locations of the primary users to bring little loss to the primary network's throughput. By introducing preservation regions around primary receivers, a modified multihop routing protocol is proposed for the cognitive users. Assumingm=nβwith β >; 1, it is shown that the secondary network achieves almost the same throughput scaling law as a stand-alone network while the primary network throughput is subject to only a vanishingly small fractional loss. Specifically, the primary network achieves the sum throughput of ordern1/2and, for any δ >; 0, the secondary network achieves the sum throughput of orderm1/2-δwith an arbitrarily small fraction of outage. Thus, almost all secondary source-destination pairs can communicate at a rate of orderm-1/2-δ.

In a bi-directional relay channel, two nodes wish to exchange independent messages over a shared wireless half-duplex channel with the help of a relay. In this paper, we derive achievable rate regions for four new half-duplex protocols and compare these to four existing half-duplex protocols and outer bounds. In time, our protocols consist of either two or three phases. In the two phase protocols, both users simultaneously transmit during the first phase and the relay alone transmits during the second phase, while in the three phase protocol the two users sequentially transmit followed by a transmission from the relay. The relay may forward information in one of four manners; we outline existing amplify and forward (AF), decode and forward (DF), lattice based, and compress and forward (CF) relaying schemes and introduce the novel mixed forward scheme. The latter is a combination of CF in one direction and DF in the other. We derive achievable rate regions for the CF and Mixed relaying schemes for the two and three phase protocols. We provide a comprehensive treatment of eight possible half-duplex bi-directional relaying protocols in Gaussian noise, obtaining their relative performance under different SNR and relay geometries.

The cognitive interference channel is a two-user interference channel in which one transmitter is non-causally provided with the message of the other transmitter. This channel model has been extensively studied in the past years and capacity results have been proved for certain classes of channels. This paper presents new inner and outer bounds for the capacity region of the cognitive interference channel, as well as new capacity results. Previously proposed outer bounds are expressed in terms of auxiliary random variables for which no cardinality constraint of their alphabet is known. Consequently, it is not possible to evaluate such outer bounds explicitly for a given channel. The outer bound derived in this work is based on an idea originally devised by Sato for channels without receiver cooperation and results in an outer bound that does not contain auxiliary random variables, thus allowing it to be more easily evaluated. The inner bound presented in this work-which includes rate splitting, superposition coding, a broadcast channel-like binning scheme and Gel'fand Pinsker coding-is the largest known to date and is explicitly shown to include all previously proposed achievable rate regions. The novel inner and outer bounds are shown to coincide in certain cases. In particular, capacity is proved for a class of channels in the so-called “better cognitive decoding” regime, which includes the regimes in which capacity was known. Finally, the capacity region of the semi-deterministic cognitive interference channel, in which the signal at the cognitive receiver is an arbitrary deterministic function of the channel inputs, is established.

This paper analyzes the impact and benefits of infrastructure support in improving the throughput scaling in networks ofnrandomly located wireless nodes. The infrastructure uses multiantenna base stations (BSs), in which the number of BSs and the number of antennas at each BS can scale at arbitrary rates relative ton. Under the model, capacity scaling laws are analyzed for both dense and extended networks. Two BS-based routing schemes are first introduced in this study: an infrastructure-supported single-hop (ISH) routing protocol with multiple-access uplink and broadcast downlink and an infrastructure-supported multihop (IMH) routing protocol. Then, their achievable throughput scalings are analyzed. These schemes are compared against two conventional schemes without BSs: the multihop (MH) transmission and hierarchical cooperation (HC) schemes. It is shown that a linear throughput scaling is achieved in dense networks, as in the case without help of BSs. In contrast, the proposed BS-based routing schemes can, under realistic network conditions, improve the throughput scaling significantly in extended networks. The gain comes from the following advantages of these BS-based protocols. First, more nodes can transmit simultaneously in the proposed scheme than in the MH scheme if the number of BSs and the number of antennas are large enough. Second, by improving the long-distance signal-to-noise ratio (SNR), the received signal power can be larger than that of the HC, enabling a better throughput scaling under extended networks. Furthermore, by deriving the corresponding information-theoretic cut-set upper bounds, it is shown under extended networks that a combination of four schemes IMH, ISH, MH, and HC is order-optimal in all operating regimes.

The issue of efficiency and fairness in resource allocation will continue to be of significant importance in scheduler designs for future wireless systems. Of particular importance is the development of distributed techniques for achieving desired efficiency and fairness tradeoffs. We will focus on the the design of selfishly efficient and as well as different fair policies through the use of a virtual timer. This virtual timer unifies various previously considered fairness methods including Round-Robin, Max-Min and Proportional fairness, which are rigorously investigated. The performance of the presented techniques are compared using extensive simulations.

The multi-pair bi-directional relay network under consideration consists of one base-station, multiple (say m) terminal nodes and one relay, all of which are half-duplex, in which, contrary to prior work, each node has a direct link with every other node. Each of the m terminal nodes exchanges messages with the base-station in a bi-directional fashion, leading to 2m total messages to be communicated with the (possible) help of the relay. Our contributions are: 1) the introduction of three new temporal protocols which fully exploit the two-way nature of the data, over-heard side-information through network coding, random binning, and compress-and-forward terminal node cooperation, 2) derivations of achievable rate regions and 3) cut-set based outer bounds for the multi-pair network, and 4) a numerical evaluation of the derived regions in Gaussian noise which illustrate the performance of the proposed protocols.

In this paper, we first present an outer bound for a general interference channel with a cognitive relay, i.e., a relay that has non-causal knowledge of both independent messages transmitted in the interference channel. This outer bound reduces to the capacity region of the deterministic broadcast channel and of the deterministic cognitive interference channel the through nulling of certain channel inputs. It does not, however, reduce to that of certain deterministic interference channels for which capacity is known. As such, we subsequently tighten the bound for channels whose outputs satisfy an “invertibility” condition. This second outer bound now reduces to the capacity of the special class of deterministic interference channels for which capacity is known. The second outer bound is further tightened for the high-SNR deterministic approximation of the Gaussian channel by exploiting the special structure of the interference. We provide an example that suggests that this third bound is tight in at least some parameter regimes for the high-SNR deterministic approximation of the Gaussian channel. Another example shows that the third bound is capacity in the special case where there are no direct links between the non-cognitive transmitters.

This letter analyzes the impact, from a network-layer perspective, of having a single cognitive radio transmitter-receiver pair share the spectrum with multiple primary users wishing to communicate to a single receiver in a multi-access channel (MAC). In contrast to previous work which assumes a time division multi-access strategy, here, we assume the set of primary users simultaneously access the channel to deliver their packets to a common destination. We derive the symmetric stable throughput regions, consisting of maximal arrival rates for primary and secondary (or cognitive radio) users under two investigated protocols. The first protocol is a conventional MAC scheme where the primary and secondary nodes operate independenly. The second protocol corresponds to a multi-access relay channel (MARC) which exploits user cooperation between primary and secondary nodes. We prove that cooperation is beneficial in the considered MARC as it enables higher throughputs for both primary and secondary users.

In a bi-directional relay channel, two nodes wish to exchange independent messages over a shared wireless half-duplex channel with the help of relays. Recent work has considered information theoretic limits of the bi-directional relay channel with a single relay. In this work we consider bi-directional relaying with multiple relays. We derive achievable rate regions and outer bounds for half-duplex protocols with multiple decode and forward relays and compare these to the same protocols with amplify and forward relays in an additive white Gaussian noise channel. We consider three novel classes of half-duplex protocols: the (m, 2) 2 phase protocol with m relays, the (m, 3) 3 phase protocol with m relays, and general (m, t) Multiple Hops and Multiple Relays (MHMR) protocols, where m is the total number of relays and 3 < t ¿ m + 2 is the number of temporal phases in the protocol. Finally, we provide a comprehensive treatment of the MHMR protocols with decode and forward relaying and amplify and forward relaying in Gaussian noise, obtaining their respective achievable rate regions, outer bounds and relative performance at different SNRs. The (m,m+2) DF MHMR protocol achieves the largest rate region under simulated channel conditions.

We study two distinct, but overlapping, networks which operate at the same time, space and frequency. The first network consists of n randomly distributed primary users, which form either an ad hoc network, or an infrastructure supported ad hoc network in which l additional base stations support the primary users. The second network consists of m randomly distributed secondary or cognitive users. The primary users have priority access to the spectrum and do not change their communication protocol in the presence of secondary users. The secondary users, however, need to adjust their protocol based on knowledge about the locations of the primary users so as not to harm the primary network's scaling law. Base on percolation theory, we show that surprisingly, when the secondary network is denser than the primary network, both networks can simultaneously achieve the same throughput scaling as a standalone ad hoc network.

We propose a low-complexity equalizer whose performance approaches that of the optimal maximum-likelihood estimators in wideband multiple-input multiple-output (MIMO) channels. The proposed algorithm makes use of a bit-flipping refinement procedure preceded by a frequency-domain equalizer and is based on local-optima searching algorithms. Through performance evaluations, it is demonstrated that the proposed equalizer can perform well when a large number of diversity branches are available in severely dispersive fading channels.

We study a cognitive network consisting of a single primary transmitter and multiple secondary, or cognitive, users. The primary transmitter, located at the center of the network, communicates with primary receivers within a disc called the primary exclusive region (PER). Inside the PER, no cognitive users may transmit, in order to guarantee an outage probability for the primary receivers within. Outside the PER, uniformly distributed cognitive users may transmit, provided they are at a certain protected radius from a primary receiver. We analyze the aggregated interference from the cognitive transmitters to a primary receiver within the PER. Based on this interference and the outage guarantee, we derive bounds on the radius of the PER, showing its interdependence on the receiver protected distance and other system parameters. We also extend the analysis to allowing the cognitive users to scale their power according to the distance from the primary transmitter. These studies provide a closed-form, theoretical analysis of such a network geometry with PER, which may be relevant in the upcoming spectrum sharing actions.

In this paper, we consider a cognitive network in which a single primary transmitter communicates with primary receivers within an area of radius RO, called the primary exclusive region (PER). Inside this region, no cognitive users may transmit. Outside the PER, provided that the cognitive transmitters are at a minimal distance isinpfrom a primary receiver, they may transmit concurrently with the primary user. We determine bounds on the primary exclusive radius ROand the guard band isinpto guarantee an outage performance for the primary user. Specifically, for a desired rate COand an outage probability beta, the probability that the primary user's rate falls below COis less than beta. This performance guarantee holds even with an arbitrarily large number of cognitive users uniformly distributed with constant density outside the primary exclusive region.

We analyze the benefits of infrastructure support in improving the throughput scaling in networks of n randomly located wireless nodes. The infrastructure uses multi-antenna base stations (BSs), in which the number of BSs and the number of antennas at each BS can scale at arbtrary rates relative to n. We introduce two multi-antenna BS-based routing protocols and analyze their throughput scaling laws. Two conventional schemes not using BSs are also shown for comparison. In dense networks, we show that the BS-based routing schemes do not improve the throughput scaling. In contrast, in extended networks, we show what our BS-based routing schemes can, under certain network conditions, improve the throughput scaling significantly.

Wireless relays extend coverage, improve spectral efficiency, and enhance reliability and rates of wireless cellular communication systems. In this work, we introduce the fundamental notion of asymmetric cooperation among cooperating relays in cellular downlinks - different relays are party to different but overlapping knowledge about the messages transmitted from the base station. We argue that asymmetric cooperation arises naturally in most two-phase protocols in which the base station first transmits information to multiple relays that then cooperatively forward the information to the recipient mobile stations in the cell. For a system in which two relays are of the decode-and-forward type and cooperate using linear precoding to communicate with two mobile stations, we formulate the general, but complicated, throughput optimization problem and derive several results that considerably simplify the optimization. We show that under different channel configurations and fairness criteria, asymmetric cooperation is often the throughput-maximizing option. Under typical configurations, a 20-30% throughput enhancement is achieved compared to conventional full-cooperation systems.

Fixed and mobile relays are used, among other applications, in the downlink of cellular communications systems. Cooperation between relays can greatly increase their benefits in terms of extended coverage, increased reliability, and improved spectral efficiency. In this paper, we introduce the fundamental notion of asymmetric cooperation. For this, we consider a two-phase transmission protocol where, in the first phase, the base station (BS) sends several available messages to the relays over wireless links. But, depending on the channel state and the duration of the BS transmission, not all relays decode all messages. In a second phase, the relays, which may now have asymmetric message knowledge, use cooperative linear precoding for the transmission to the mobile stations. We show that for many channel configurations, asymmetric cooperation, although (slighlty) sub-optimum for the second phase, is optimum from a total-throughput point of view, as it requires less time and energy in the first phase. We give analytical formulations for the optimum operating parameters and the achievable throughput, and show that under typical circumstances, 20-30% throughput enhancement can be achieved over conventional systems.

In this paper, we obtain the scaling laws of the sum-rate capacity of a MIMO X-channel, a 2 independent sender, 2 independent receiver channel with messages from each transmitter to each receiver, at high signal to noise ratios (SNR). The X-channel has sparked recent interest in the context of cooperative networks and it encompasses the interference, multiple access, and broadcast channels as special cases. Here, we consider the case with partially cooperative transmitters in which asymmetric side-information (in the form of a codeword) is available at one of the transmitters. It is proved that when there are M antennas at all four nodes, the sum-rate scales like 2M log SNR which is in sharp contrast to lceillfloor4M/3rfloor, 4M/3rceil log SNR for non-cooperative X-channels [M. Maddah-Ali et al., 2006], [S.A. Jafar]. This further proves that, in terms of sum-rate scaling at high SNR, partial side-information at one of the transmitters and full side-information at both transmitters are equivalent in the MIMO X-channel.

Cognitive radio promises a low-cost, highly flexible alternative to the classic single-frequency band, single-protocol wireless device. By sensing and adapting to its environment, such a device is able to fill voids in the wireless spectrum and can dramatically increase spectral efficiency. In this paper, the cognitive radio channel is defined as a two-sender, two-receiver interference channel in which sender 2 obtains the encoded message sender 1 plans to transmit. We consider two cases: in the genie-aided cognitive radio channel, sender 2 is noncausally presented the data to be transmitted by sender 1 while in the causal cognitive radio channel, the data is obtained causally. The cognitive radio at sender 2 may then choose to transmit simultaneously over the same channel, as opposed to waiting for an idle channel as is traditional for a cognitive radio. Our main result is the development of an achievable region which combines Gel'fand-Pinkser coding with an achievable region construction for the interference channel. In the additive Gaussian noise case, this resembles dirty-paper coding, a technique used in the computation of the capacity of the Gaussian multiple-input multiple-output (MIMO) broadcast channel. Numerical evaluation of the region in the Gaussian noise case is performed, and compared to an inner bound, the interference channel, and an outer bound, a modified Gaussian MIMO broadcast channel. Results are also extended to the case in which the message is causally obtained.

Costa has proved that for noncausally known Gaussian interference at a power constrained transmitter communicating over an additive white Gaussian noise channel there is no capacity loss when compared to a scenario where interference is not present. For the case of a transmitter communicating over a quasistatic (i.e., nonergodic) fading channel, his method does not apply. In this correspondence, we derive upper and lower bounds on the capacity of compound channels with side information at the transmitter, first for finite alphabet channels and then, based on this result, for channels on standard alphabets (this includes real alphabets). For the special case of a degenerate compound channel with only one possible realization, our bounds are equivalent to the well-known capacity with side-information formula of Gel'fand and Pinsker. For the quasistatic fading channel, when fading is Ricean, we suggest a scheme based on our lower bound for which the performance is found to be relatively good even for moderate K-factor. As K/spl rarr//spl infin/, the uncertainty on the channel vanishes and our scheme obtains the performance of dirty paper coding, namely that the interference is perfectly mitigated. As K/spl rarr/0, the proposed scheme treats the interferer as additional noise. These results may be of importance for the emerging field of cognitive radios where one user may be aware of another user's intended message to a common receiver, but is unaware of the channel path gains.

A cognitive radio can sense the transmission of other users in its environment and possibly extract the corresponding messages. It can use this information to transmit over the same channel while reducing interference from, and to other users. In this paper, we define inter/intra-cluster competitive, cooperative, and cognitive behavior in wireless networks. We define intercluster cognitive behavior as simultaneous transmissions by two or more clusters in which some clusters know the messages to be transmitted by other clusters, and so can act as relays or use a Gel'fand-Pinsker coding-like technique to mitigate interference. We construct an achievable region for the inter-cluster behavior of two multiple access channels. In the Gaussian case, we compare our achievable region to that of competitive behavior as well as that of cooperative behavior