This paper studies proof-of-work Nakamoto consensus protocols under bounded network delays, settling two long-standing questions in blockchain security: What is the most effective attack on block safety under a given block confirmation latency? And what is the resulting probability of safety violation? A Markov decision process (MDP) framework is introduced to precisely characterize the system state (including the blocktree and timings of all blocks mined), the adversary's potential actions, and the state transitions due to the adversarial action and the random block arrival processes. An optimal attack, called bait-and-switch, is proposed and proved to maximize the adversary's chance of violating block safety by ''beating Nakamoto in the race''. The exact probability of this violation is calculated for any given confirmation depth using Markov chain analysis, offering fresh insights into the interplay of network delay, confirmation rules, and blockchain security.

This paper introduces a novel offline approach to power control in wireless networks using a multi-agent reinforcement learning (MARL) framework. We develop a multi-agent decision transformer method to optimize performance metrics including sum-rate or packet delay. In this distributed method, each agent controls an individual link and determines its power level based on its own measurements and information exchange with a few agents within a limited neighborhood.Numerical results demonstrate that the proposed method achieves quality of service performance comparable to centralized methods using global information, for both sum-rate maximization and traffic-driven packet delay minimization problems. As an offline learning solution, it can efficiently leverage knowledge from existing mature techniques and offers significant advantages in the safety, stability, and convergence rate over existing online methods. This work provides a promising alternative for learning-based resource management in wireless networks.

Hybrid analog/digital beamforming provides a critical trade-off for achieving high gains at millimeter-wave (mmWave) and mid-band frequencies while minimizing hardware costs and energy consumption, particularly due to the power demands of high-rate analog-to-digital converters (ADCs). However, the partial reliance on analog beamformers introduces inefficiencies, prolonging the channel estimation and beam acquisition process. This paper presents a novel receiver architecture that integrates full-dimension digital chains with 1-bit ADCs, enabling efficient signal capture for rapid and accurate angle-of-arrival (AoA) estimation and beam acquisition. Once the beamformers are established, a standard hybrid architecture is used for communicating multiple data streams for the remainder of the channel coherence time, ensuring energy efficiency. Simulation results show that the proposed method achieves mean square error (MSE) performance comparable to fully digital beamforming with perfect channel and transmit beamforming knowledge, while accelerating the beam acquisition process.

This paper investigates the downlink spectral efficiency of low Earth orbit (LEO) satellite constellations, where spectral efficiency refers to the entire network's total data rate per unit spectrum per unit area on the Earth's surface. For practicality, all links employ single-user codebooks and treat interference as noise. A key finding is that, unlike terrestrial networks, the spectral efficiency of LEO constellations does not increase indefinitely with satellite density. Under typical assumptions about antenna array beam widths, this study explores the satellite density that maximizes spectral efficiency. As a special case, a regular deployment of satellites and ground terminals is analyzed across various densities. Simulation results reveal that regular configurations achieve higher spectral efficiency compared to random configurations. Furthermore, while the total downlink capacity of any LEO constellation remains significantly lower than that of terrestrial networks, there is substantial potential for growth-up to a few orders of magnitude-compared to current capacity levels.

The increasing density of cellular access points (APs) and user devices necessitates efficient user association strategies to balance traffic loads and ensure quality of service. This paper presents a traffic-aware user association framework leveraging multi-agent reinforcement learning (MARL), where APs cooperatively learn association policies based on network conditions and traffic demands. A dual-timescale architecture is empolyed: a slow timescale for association decisions and a fast timescale for power allocation and packet-level transmissions, enabling precise evaluation of network performance. Extensive simulations demonstrate that packet delays are significantly reduced by this approach compared to conventional methods, including user association with the nearest AP or association that maximizes the signal-to-noise-and-interference ratio, particularly in scenarios marked by high traffic, heterogeneous traffic distributions, or uneven user densities. The trained policies also show robust scalability across diverse network sizes and traffic conditions.

Efficient and scalable radio resource allocation is essential for the success of wireless cellular networks. This paper presents a fully scalable multi-agent reinforcement learning (MARL) framework, where each agent manages spectrum, power allocation, and scheduling within a cell, using only locally available information. The objective is to minimize packet delays under stochastic traffic arrivals, applicable to both conflict graph models and cellular network configurations. This is formulated as a distributed learning problem and implemented using a multi-agent proximal policy optimization (MAPPO) algorithm. This traffic-driven MARL approach enables fully decentralized training and execution, ensuring scalability to arbitrarily large networks. Extensive simulations demonstrate that the proposed methods achieve quality of service (QoS) performance comparable to centralized algorithms that require global information, while the trained policies show robust scalability across diverse network sizes and traffic conditions.

This paper investigates the fundamental trade-offs between block safety, confirmation latency, and transaction throughput of proof-of-work (PoW) longest-chain fork-choice protocols, also known as PoW Nakamoto consensus. New upper and lower bounds are derived for the probability of block safety violations as a function of honest and adversarial mining rates, a block propagation delay limit, and confirmation latency measured in both time and block depth. The results include the first non-trivial closed-form finite-latency bound applicable across all delays and mining rates up to the ultimate fault tolerance. Notably, the gap between these upper and lower bounds is narrower than previously established bounds for a wide range of parameters relevant to Bitcoin and its derivatives, including Litecoin and Dogecoin, as well as Ethereum Classic. Additionally, the study uncovers a fundamental trade-off between transaction throughput and confirmation latency, ultimately determined by the desired fault tolerance and the rate at which block propagation delay increases with block size.

This paper studies the performance of a transmission and reception scheme for massive access under some practical challenges. One challenge is the near-far problem, i.e., an access point often receives signals from different transmitting devices at vastly different signal strengths. Another challenge is that the signals from different devices may be subject to arbitrary, analog, and heterogeneous delays. This paper considers a fully asynchronous model which is more realistic than the frame or symbol level synchrony needed in most existing work. A main theorem characterizes the asymptotic scaling of the codelength with the number of devices, a device delay upper bound, and the dynamic range of received signal strengths across devices. The scaling result suggests potential advantages of grouping devices with similar received signal strengths and letting the groups use time sharing. The performance of the proposed scheme is evaluated using simulations with and without grouping.

Spatia1 prediction of the radio propagation environment (henceforth ‘radio environment’ for brevity) of a transmitter can assist and improve various aspects of wireless networks. The majority of research in this domain can be categorized as ‘reactive’ spatial prediction, where the predictions are made based on a small set of measurements from an active transmitter whose radio environment is to be predicted. Emerging spectrum-sharing paradigms would benefit from ‘proactive’ spatial prediction of the radio environment, where the spatial predictions must be done for a transmitter for which no measurement has been collected. This paper proposes a novel, supervised deep learning-based framework, ProSpire, that enables spectrum sharing by leveraging the idea of proactive spatial prediction. We carefully address several challenges in ProSpire, such as designing a framework that conveniently collects training data for learning, performing the predictions in a fast manner, enabling operations without an area map, and ensuring that the predictions do not lead to undesired interference. ProSpire relies on the crowdsourcing of transmitters and receivers during their normal operations to address some of the aforementioned challenges. The core component of ProSpire is a deep learning-based image-to-image translation method, which we call RSSu-net. We generate several diverse datasets using ray tracing software and numerically evaluate ProSpire. Our evaluations show that RSSu-net performs reasonably well in terms of signal strength prediction, $\approx$ 5dB mean absolute error, which is comparable to the average error of other relevant methods. Importantly, due to the merits of RSSu-net, ProSpire creates proactive boundaries around transmitters such that they can be activated with $\approx$ 97% probability of not causing interference. In this regard, the performance of RSSu-net is 19% better than that of other comparable methods.

The fundamental communication problem in the wireless Internet-of-Things (IoT) is to discover a massive number of devices and to provide them with reliable access to shared channels. Oftentimes these devices transmit short messages randomly and sporadically. This paper proposes a novel signaling scheme for grant-free massive access, where each device encodes its identity and/or information in a sparse set of tones. Such transmissions are implemented in the form of orthogonal frequency-division multiple access (OFDMA). Under some mild conditions and assuming device delays to be bounded unknown multiples of sampling intervals, sparse OFDMA is proved to enable arbitrarily reliable asynchronous device identification and message decoding with a codelength that is$O(K(\log K+\log S + \log N))$, where$N$denotes the device population,$K$denotes the actual number of active devices, and$\log S$is essentially equal to the number of information bits each device can send. The computational complexity for discovery and decoding can be made to be$O(K(\log K)(\log K+\log S+\log N)+K^{2}\log K)$. As a proof of concept, a specific design is proposed to identify up to 200 active devices out of$N=2^{96}$possible devices with up to 20 samples of delay, moderate signal-to-noise ratios, and fading. If the device population is$N=2^{48}$instead, each active device can also transmit 48 bits to the access point at the same time. The codelength compares much more favorably with those of standard slotted ALOHA and carrier-sensing multiple access (CSMA) schemes.

Simple closed-form upper and lower bounds are developed for the security of the Nakamoto consensus as a function of the confirmation depth, the honest and adversarial block mining rates, and an upper bound on the block propagation delay. The bounds are exponential in the confirmation depth and apply regardless of the adversary's attack strategy. The gap between the upper and lower bounds is small for Bitcoin's parameters. For example, assuming an average block interval of ten minutes, a network delay bound of ten seconds, and 10% adversarial mining power, the widely used 6-block confirmation rule yields a safety violation between 0.11% and 0.35% probability.

Bitcoin is a peer-to-peer electronic cash system invented by Nakamoto in 2008. While it has attracted much research interest, its exact latency and security properties remain open. Existing analyses provide security and latency (or confirmation time) guarantees that are too loose for practical use. In fact the best known upper bounds are several orders of magnitude larger than a lower bound due to a well-known private-mining attack. This paper describes a continuous-time model for blockchains and develops a rigorous analysis that yields close upper and lower bounds for the latency-security trade-off. For example, when the adversary controls 10% of the total mining power and the block propagation delays are within 10 seconds, a Bitcoin block is secured with less than 10-3 error probability if it is confirmed after four hours, or with less than 10-9 error probability if confirmed after ten hours. These confirmation times are about two hours away from their corresponding lower bounds. To establish such close bounds, the blockchain security question is reduced to a race between the Poisson adversarial mining process and a renewal process formed by a certain species of honest blocks. The moment generation functions of relevant renewal times are derived in closed form. The general formulas from the analysis are then applied to study the latency-security trade-off of several well-known proof-of-work longest-chain cryptocurrencies. Guidance is also provided on how to set parameters for different purposes.

Picocellular architectures are essential for providing the spatial reuse required to satisfy the ever-increasing demand for mobile data. A key deployment challenge is to provide backhaul connections with sufficiently high data rate. Providing wired support (e.g., using optical fiber) to pico base stations deployed opportunistically on lampposts and rooftops is impractical, hence wireless backhaul becomes an attractive approach. A multihop mesh network comprised of directional millimeter (mm) wave links is considered here for this purpose. Such networks are well suited for scaling backhaul data rates due to the abundance of spectrum in the mm wave bands, and the ability to form highly directional, electronically steerable beams. The backhaul design problem is formulated as one of joint routing and resource allocation, accounting for mutual interference across simultaneously active links. A computationally tractable formulation is developed by leveraging the localized nature of interference and the provable existence of a sparse optimal allocation. Numerical results are provided for topologies modeling urban and suburban settings.

In cellular federated edge learning (FEEL), multiple edge devices holding local data jointly train a neural network by communicating learning updates with an access point without exchanging their data samples. With very limited communication resources, it is beneficial to schedule the most informative local learning updates. This paper focuses on FEEL with gradient averaging over participating devices in each round of communication. A novel scheduling policy is proposed to exploit both diversity in multiuser channels and diversity in the “importance” of the edge devices' learning updates. First, a new probabilistic scheduling framework is developed to yield unbiased update aggregation in FEEL. The importance of a local learning update is measured by its gradient divergence. If one edge device is scheduled in each communication round, the scheduling policy is derived in closed form to achieve the optimal trade-off between channel quality and update importance. The probabilistic scheduling framework is then extended to allow scheduling multiple edge devices in each communication round. Numerical results obtained using popular models and learning datasets demonstrate that the proposed scheduling policy can achieve faster model convergence and higher learning accuracy than conventional scheduling policies that only exploit a single type of diversity.

The neighbor discovery paradigm finds wide application in Internet of Things networks, where the number of active devices is orders of magnitude smaller than the total device population. Designing low-complexity schemes for asynchronous neighbor discovery has recently gained significant attention from the research community. Concurrently, a divide-and-conquer framework, referred to as coupled compressive sensing, has been introduced for the synchronous massive random access channel. This work adapts this novel algorithm to the problem of asynchronous neighbor discovery with unknown transmission delays. Simulation results suggest that the proposed scheme requires much fewer transmissions to achieve a performance level akin to that of state-of-the-art techniques.

This work demonstrates the potential of deep reinforcement learning techniques for transmit power control in wireless networks. Existing techniques typically find near-optimal power allocations by solving a challenging optimization problem. Most of these algorithms are not scalable to large networks in real-world scenarios because of their computational complexity and instantaneous cross-cell channel state information (CSI) requirement. In this paper, a distributively executed dynamic power allocation scheme is developed based on model-free deep reinforcement learning. Each transmitter collects CSI and quality of service (QoS) information from several neighbors and adapts its own transmit power accordingly. The objective is to maximize a weighted sum-rate utility function, which can be particularized to achieve maximum sum-rate or proportionally fair scheduling. Both random variations and delays in the CSI are inherently addressed using deep Q-learning. For a typical network architecture, the proposed algorithm is shown to achieve near-optimal power allocation in real time based on delayed CSI measurements available to the agents. The proposed scheme is especially suitable for practical scenarios where the system model is inaccurate and CSI delay is non-negligible.

This paper studies initial beam acquisition in a millimeter wave network consisting of multiple access points (APs) and mobile devices. A training protocol for joint estimation of transmit and receive beams is presented with a general frame structure consisting of an initial access sub-frame followed by data transmission sub-frames. During the initial subframe, APs and mobiles sweep through a set of beams and determine the best transmit and receive beams via a handshake. All pilot signals are narrowband (tones), and the mobiles are distinguished by their assigned pilot frequencies. Both non-coherent and coherent beam estimation methods based on, respectively, power detection and maximum likelihood (ML) are presented. To avoid exchanging information about beamforming vectors between APs and mobiles, a local maximum likelihood (LML) algorithm is also presented. An efficient fast Fourier transform implementation is proposed for ML and LML to achieve high-resolution. A system-level optimization is performed in which the frame length, training time, and training bandwidth are selected to maximize a rate objective taking into account blockage and mobility. Simulation results based on a realistic network topology are presented to compare the performance of different estimation methods and training codebooks, and demonstrate the effectiveness of the proposed protocol.

Location awareness will be crucial for many future wireless network applications, such as the Internet of Things and vehicular networks. Existing localization works typically propose sequential signaling schemes, where one pair of nodes communicates to range their distance at a time. This implies high ranging overhead for large networks, where many nodes are within range of each node. In this paper, a novel scheme is proposed which takes merely two frames of transmissions. In the first frame, all nodes transmit their respective signatures. In the second frame, all nodes basically repeat what they have received in the first frame multiplied by a scrambling sequence (assuming full duplexing). By the end of the second frame, every node can estimate not only its distance to all nodes within range, but also the distances between neighboring nodes which are within range of each other. It is shown that in a half-duplex setting the scheme can still be utilized to perform two-way ranging. Successive interference cancellation can also be leveraged with the scheme in order to improve performance for subsequent estimates in interference heavy scenarios. The proposed scheme is highly scalable, and is validated using simulation.

Both localization and synchronization of mobile nodes are of fundamental importance for wireless networks. With the emergence of full-duplex (FD) communication technology, inter-node distances and clock offsets among a set of nodes can be simultaneously obtained through only two frames of communications, thus significantly improving the efficiency of node localization and synchronization. In this paper, we propose a localization and synchronization scheme using FD radios, and characterize its performance. Our study derives the Cramér-Rao lower bounds (CRLBs) for inter-node distances and clock offsets, the former of which can be translated into the estimation error bounds for localization. Comparison to conventional frequency division duplex (FDD) or time division duplex (TDD) demonstrates the high efficiency of localization and synchronization using FD radios. Our results reveal the potential of full-duplex technology beyond data communications in future wireless networks.

Joint allocation of spectrum and user association is considered for a large cellular network. The objective is to optimize a network utility function such as average delay given traffic statistics collected over a slow timescale. A key challenge is scalability: given n access points (APs), there are O(2n) ways in which the APs can share the spectrum. The number of variables is reduced from O(2n) to O(nk), where k is the number of users, by optimizing over local overlapping neighborhoods, defined by interference conditions, and by exploiting the existence of sparse solutions in which the spectrum is divided into k+1 segments. We reformulate the problem by optimizing the assignment of subsets of active APs to those segments. An ℓoconstraint enforces a one-to-one mapping of subsets to spectrum segments, and an iterative (reweighted ℓ1) algorithm is used to find an approximate solution. Numerical results for a network with 100 APs serving several hundred users show the proposed method achieves a substantial increase in total throughput relative to benchmark schemes.

This work studies centralized slow-timescale spectrum management in metropolitan area networks with a very large number of access points (APs) and user equipments (UEs). The joint spectrum allocation and user association problem is first formulated as a convex optimization problem with an exponential number of variables in the network size. A scalable reformulation is obtained by exploiting the geometric graph nature of the network and provable sparsity of the optimal solution. A pattern pursuit algorithm with low complexity is proposed to solve the reformulated problem with guaranteed gap to the global optimum. Efficient algorithms are developed to obtain near-optimal allocations for a network with up to 1000 APs and 2500 active users. Numerical results show that the proposed solution achieves significant gains in terms of delay and throughput over existing schemes and is within 7% to the global optimum in a typical scenario.

In massive multiple-input multiple-output (MIMO) systems, acquisition of the channel state information at the transmitter side (CSIT) is crucial. In this paper, a practical CSIT estimation scheme is proposed for frequency division duplexing (FDD) massive MIMO systems. Specifically, each received pilot symbol is first quantized to one bit per dimension at the receiver side and then the quantized bits are fed back to the transmitter. A joint one-bit compressed sensing algorithm is implemented at the transmitter to recover the channel matrices. The algorithm leverages the hidden joint sparsity structure in the user channel matrices to minimize the training and feedback overhead, which is considered to be a major challenge for FDD systems. Moreover, the one-bit compressed sensing algorithm accurately recovers the channel directions for beamforming. The one-bit feedback mechanism can be implemented in practical systems using the uplink control channel. Simulation results show that the proposed scheme nearly achieves the maximum output signal-to-noise-ratio for beamforming based on the estimated CSIT.

Facing the challenge of meeting ever-increasing demand for wireless data, the industry is striving to exploit large swaths of unlicensed spectrum, which supports open access. Major standards bodies are currently considering a proposal to retool and deploy long term evolution (LTE) technologies in unlicensed bands. This paper studies the fundamental question of how the unlicensed spectrum can be shared by strategic operators to mitigate suffering from the tragedy of the commons. A class of general utility functions is considered. The spectrum sharing problem is formulated as a repeated game over a sequence of time slots. It is first shown that a simple static sharing scheme allows a given set of operators to reach a subgame perfect Nash equilibrium for mutually beneficial sharing. The question of how many operators will choose to enter the market is also addressed by studying an entry game. A sharing scheme, which allows dynamic spectrum borrowing and lending between operators, is then proposed to address time-varying traffic and proved to achieve perfect Bayesian equilibrium. Numerical results show that the proposed dynamic sharing scheme outperforms static sharing, which in turn achieves much higher revenue than uncoordinated full-spectrum sharing. Implications of the results for the standardization and deployment of LTE in unlicensed bands (LTE-U) are also discussed.

In future networks, an operator may employ a wide range of access points using diverse radio access technologies (RATs) over multiple licensed and unlicensed frequency bands. This paper studies centralized user association and spectrum allocation across many access points in such a heterogeneous network. Such centralized control is on a relatively slow timescale to allow information exchange and joint optimization over multiple cells. This is in contrast and complementary to distributed scheduling on a fast timescale. A queueing model is introduced to capture the lower spectral efficiency, reliability, and additional delays of data transmission over the unlicensed bands due to contention and/or listen-before-talk requirements. Two optimization-based spectrum allocation schemes are proposed along with efficient algorithms for computing the allocations. The proposed solutions take into account traffic loads, network topology, as well as external interference levels in the unlicensed bands. Packet-level simulation results show that the proposed schemes significantly outperform orthogonal and full-frequency-reuse allocations under all traffic conditions.

A scalable framework is developed to allocate radio resources across a large number of densely deployed small cells with given traffic statistics on a slow timescale. Joint user association and spectrum allocation is first formulated as a convex optimization problem by dividing the spectrum among all possible transmission patterns of active access points (APs). To improve scalability with the number of APs, the problem is reformulated using local patterns of interfering APs. To maintain global consistency among local patterns, inter-cluster interaction is characterized as hyper-edges in a hyper-graph with nodes corresponding to subcarriers allocated to APs. A scalable solution is obtained by iteratively solving a convex optimization problem for bandwidth allocation with reduced complexity and followed by a global spectrum allocation using hyper-graph coloring. Numerical results demonstrate the proposed solution for a network with 100 APs and several hundred user equipment. For a given quality of service, the proposed scheme can often increase the network capacity severalfold compared with assigning each user to the strongest AP with full-spectrum reuse.

Classical multiuser information theory studies the fundamental limits of models with a fixed (often small) number of users as the coding blocklength goes to infinity. This paper proposes a new paradigm, referred to as many-user information theory, where the number of users is allowed to grow with the blocklength. This paradigm is motivated by emerging systems with a massive number of users in an area, such as the Internet of Things. The focus of this paper is the many-access channel model, which consists of a single receiver and many transmitters, whose number increases unboundedly with the blocklength. Moreover, an unknown subset of transmitters may transmit in a given block and need to be identified as well as decoded by the receiver. A new notion of capacity is introduced and characterized for the Gaussian many-access channel with random user activities. The capacity can be achieved by first detecting the set of active users and then decoding their messages. The minimum cost of identifying the active users is also quantified.

Compressive sensing aims to recover a high-dimensional sparse signal from a relatively small number of measurements. In this paper, a novel design of the measurement matrix is proposed. The design is inspired by the construction of generalized low-density parity-check codes, where the capacity-achieving point-to-point codes serve as subcodes to robustly estimate the signal support. In the case that each entry of the n-dimensional ft-sparse signal lies in a known discrete alphabet, the proposed scheme requires only O(k log n) measurements and arithmetic operations. In the case of arbitrary, possibly continuous alphabet, an error propagation graph is proposed to characterize the residual estimation error. With O(k log2 n) measurements and computational complexity, the reconstruction error can be made arbitrarily small with high probability.

Millimeter wave provides a promising approach for meeting the ever-growing traffic demand in next generation wireless networks. It is crucial to obtain the channel state information in order to perform beamforming and combining to compensate for severe path loss in this band. In contrast to lower frequencies, a typical millimeter wave channel consists of a few dominant paths. Thus it is generally sufficient to estimate the path gains, angles of departure (AoDs), and angles of arrival (AoAs) of those paths. Proposed in this paper is a dual timescale model to characterize abrupt channel changes (e.g., blockage) and slow variations of AoDs and AoAs. This work focuses on tracking the slow variations and detecting abrupt changes. A Kalman filter based tracking algorithm and an abrupt change detection method are proposed. The tracking algorithm is compared with the adaptive algorithm due to Alkhateeb, Ayach, Leus and Heath (2014) in the case with a single radio frequency chain. Simulation results show that to achieve the same tracking performance, the proposed algorithm requires much lower signal-to-noise ratio (SNR) and much fewer pilots than the other algorithm. Moreover, the change detection method can always detect abrupt changes with moderate number of pilots and SNR.

Location awareness will be crucial for many future wireless network applications, such as the Internet of Things and vehicular networks. Existing localization works typically propose sequential signaling schemes where one pair of nodes communicate to range their distance at a time. This poses a significant problem for large networks where many nodes are within range of each node. In this work, a novel scheme is proposed which takes merely two frames of transmissions: In the first frame all nodes transmit their respective signatures; in the second frame all nodes basically repeat what they have received in the first frame (assuming full duplexing). By the end of the second frame, every node can estimate not only its distance to all nodes within range, but also the distances between neighboring nodes which are within range of each other. The proposed scheme is highly scalable, and is validated using simulation.

Next generation (5G) cellular networks are expected to be supported by an extensive infrastructure with many-fold increase in the number of cells per unit area compared to today. The total energy consumption of base transceiver stations (BTSs) is an important issue for both economic and environmental reasons. In this paper, an optimization-based framework is proposed for energy-efficient global radio resource management in heterogeneous wireless networks. Specifically, with stochastic arrivals of known rates intended for users, the smallest set of BTSs is activated with jointly optimized user association and spectrum allocation to stabilize the network. The average delay is subsequently minimized. The scheme can be carried out periodically on a relatively slow timescale to adapt to aggregate traffic variations and average channel conditions. Numerical results show that the proposed scheme significantly reduces energy consumption and increases quality of service compared to existing schemes.

In this paper, we propose algorithms for computing Walsh-Hadamard transform with arbitrary K-sparse support. When K is sublinear in the dimension N of the time-domain signal, the algorithms achieve vanishing error probability as K increases without bound and involve sublinear computational complexity. Specifically, under the noiseless setting, an algorithm based on random hashing and successive cancellation is proposed, where O (K log K log N/K) operations on O(K log N/K) samples of the signal suffice. Under the noisy setting, a fast algorithm using the same framework is also proposed, which needs O (K log3K log N/K) operations and O (K log2K log N/K) samples. The latter algorithm reduces the complexity from superlinear in existing work to sublinear. The enabling idea is to relate the random hashing design to coding over a binary symmetric channel or a binary-input additive white Gaussian noise channel, whose quality depends on the noise level of the observations. Such inherent connection allows us to leverage well-established capacity-approaching codes to obtain the transform-domain signal with sublinear complexity.

Next generation cellular networks will be heterogeneous with dense deployment of small cells in order to deliver high data rate per unit area. Traffic variations are more pronounced in a small cell, which in turn lead to more dynamic interference to other cells. It is crucial to adapt radio resource management to traffic conditions in such a heterogeneous network (HetNet). This paper studies the optimization of spectrum allocation in HetNets on a relatively slow timescale based on average traffic and channel conditions (typically over seconds or minutes). Specifically, in a cluster with n base transceiver stations (BTSs), the optimal partition of the spectrum into 2n segments is determined, corresponding to all possible spectrum reuse patterns in the downlink. Each BTS's traffic is modeled using a queue with Poisson arrivals, the service rate of which is a linear function of the combined bandwidth of all assigned spectrum segments. With the system average packet sojourn time as the objective, a convex optimization problem is first formulated, where it is shown that the optimal allocation divides the spectrum into at most n segments. A second, refined model is then proposed to address queue interactions due to interference, where the corresponding optimal allocation problem admits an efficient suboptimal solution. Both allocation schemes attain the entire throughput region of a given network. Simulation results show the two schemes perform similarly in the heavy-traffic regime, in which case they significantly outperform both the orthogonal allocation and the full-frequency-reuse allocation. The refined allocation shows the best performance under all traffic conditions.

Most work on wireless network resource allocation use physical layer performance such as sum rate and outage probability as the figure of merit. These metrics may not reflect the true user QoS in future heterogenous networks (HetNets) with many small cells, due to large traffic variations in overlapping cells with complicated interference conditions. This paper studies the spectrum allocation problem in HetNets using the average packet sojourn time as the performance metric. To be specific, in a HetNet with K base terminal stations (BTS's), we determine the optimal partition of the spectrum into 2Kpossible spectrum sharing combinations. We use an interactive queueing model to characterize the flow level performance, where the service rates are decided by the spectrum partition. The spectrum allocation problem is formulated using a conservative approximation, which makes the optimization problem convex. We prove that in the optimal solution the spectrum is divided into at most K pieces. A numerical algorithm is provided to solve the spectrum allocation problem on a slow timescale with aggregate traffic and service information. Simulation results show that the proposed solution achieves significant gains compared to both orthogonal and full spectrum reuse allocations with moderate to heavy traffic.

Classical multiuser information theory studies the fundamental limits of models with a fixed (often small) number of users as the coding blocklength goes to infinity. Motivated by emerging systems with a massive number of users, this paper studies the new many-user paradigm, where the number of users is allowed to grow with the blocklength. The focus of this paper is the degraded many-broadcast channel model, whose number of users may grow as fast as linearly with the blocklength. A notion of capacity in terms of message length is defined and an example of Gaussian degraded many-broadcast channel is studied. In addition, a numerical example for the Gaussian degraded many-broadcast channel with fixed transmit power constraint is solved, where every user achieves strictly positive message length asymptotically.

Classical multiuser information theory studies the fundamental limits of models with a fixed (often small) number of users as the coding blocklength goes to infinity. This work proposes a new paradigm, referred to as many-user information theory, where the number of users is allowed to grow with the blocklength. This paradigm is motivated by emerging systems with a massive number of users in an area, such as machine-to-machine communication systems and sensor networks. The focus of the current paper is the many-access channel model, which consists of a single receiver and many transmitters, whose number increases unboundedly with the blocklength. Moreover, an unknown subset of transmitters may transmit in a given block and need to be identified. A new notion of capacity is introduced and characterized for the Gaussian many-access channel with random user activities. The capacity can be achieved by first detecting the set of active users and then decoding their messages.

In recent years, a number of mathematical relationships have been established between information measures and estimation measures for various models, including Gaussian, Poisson and binomial models. In this paper, it is shown that the second derivative of the input-output mutual information with respect to the input scaling can be expressed as the expectation of a certain Bregman divergence pertaining to the conditional expectations of the input and the input power. This result is similar to that found for the Gaussian model where the Bregman divergence therein is the square distance. In addition, the Poisson, binomial and negative binomial models are shown to be similar in the small scaling regime in the sense that the derivative of the mutual information and the derivative of the relative entropy converge to the same value.

The memoryless additive inverse Gaussian noise channel model describing communication based on the exchange of chemical molecules in a drifting liquid medium is investigated for the situation of simultaneously an average-delay and a peak-delay constraint. Analytical upper and lower bounds on its capacity in bits per molecule use are presented. These bounds are shown to be asymptotically tight, i.e., for the delay constraints tending to infinity with their ratio held constant (or for the drift velocity of the fluid tending to infinity), the asymptotic capacity is derived precisely. Moreover, characteristics of the capacity-achieving input distribution are derived that allow accurate numerical computation of capacity. The optimal input appears to be a mixed continuous and discrete distribution.

The articles in this special issue focus on the technology and applications supported by in-band full duplex wireless services.

In-band full-duplex (IBFD) operation has emerged as an attractive solution for increasing the throughput of wireless communication systems and networks. With IBFD, a wireless terminal is allowed to transmit and receive simultaneously in the same frequency band. This tutorial paper reviews the main concepts of IBFD wireless. One of the biggest practical impediments to IBFD operation is the presence of self-interference, i.e., the interference that the modem's transmitter causes to its own receiver. This tutorial surveys a wide range of IBFD self-interference mitigation techniques. Also discussed are numerous other research challenges and opportunities in the design and analysis of IBFD wireless systems.

In recent years, a number of new connections between information measures and estimation have been found under various models, including, predominantly, Gaussian and Poisson models. This paper develops similar results for the binomial and negative binomial models. In particular, it is shown that the derivative of the relative entropy and the derivative of the mutual information for the binomial and negative binomial models can be expressed through the expectation of closed-form expressions that have conditional estimates as the main argument. Under mild conditions, those derivatives take the form of an expected Bregman divergence.

In many wireless communication systems, radios are subject to a duty cycle constraint, that is, a radio can only actively transmit signals over a fraction of the time. For example, it is desirable to have a small duty cycle in some low power systems; a half-duplex radio cannot keep transmitting if it wishes to receive useful signals; and a cognitive radio needs to listen and detect primary users frequently. This paper studies the capacity of point-to-point scalar discrete-time Gaussian channels subject to a duty cycle constraint as well as an average transmit power constraint. An idealized duty cycle constraint is first studied, which can be regarded as a requirement on the minimum fraction of nontransmissions or zero symbols in each codeword. Independent input with a unique discrete distribution is shown to achieve the channel capacity. In many situations, numerically optimized on-off signaling can achieve much higher rate than Gaussian signaling over a deterministic transmission schedule. This is in part because the positions of nontransmissions in a codeword can convey information. A more realistic duty cycle constraint is also studied, where the extra cost of transitions between transmissions and nontransmissions due to pulse shaping is accounted for. The capacity-achieving input is correlated over time and is hard to compute. A lower bound of the achievable rate as a function of the input distribution is shown to be maximized by a first-order Markov input process, whose stationary distribution is also discrete and can be computed efficiently. The results in this paper suggest that, under various duty cycle constraints, departing from the usual paradigm of intermittent packet transmissions may yield substantial gain.

A novel solution is proposed to undertake a frequent task in wireless networks, which is to let all nodes broadcast information to and receive information from their respective one-hop neighboring nodes. The contribution in this paper is twofold. First, as each neighbor selects one message-bearing codeword from its unique codebook for transmission, it is shown that decoding their messages based on a superposition of those codewords through the multiaccess channel is fundamentally a problem of compressed sensing. In the case where each message is designed to consist of a small number of bits, an iterative algorithm based on belief propagation is developed for efficient decoding. Second, to satisfy the half-duplex constraint, each codeword consists of randomly distributed on-slots and off-slots. A node transmits during its on-slots and listens to its neighbors only through its own off-slots. Over one frame interval, each node broadcasts a message to its neighbors and simultaneously receives the superposition of neighbors' signals through its own off-slots and then decodes all messages. The proposed solution fully exploits the multiaccess nature of the wireless medium and addresses the half-duplex constraint at the fundamental level. In a network consisting of Poisson distributed nodes, numerical results demonstrate that the proposed scheme often achieves several times the rate of slotted ALOHA and CSMA with the same packet error rate.

A nationwide interoperable public safety broadband network is being planned by the United States government. The network will be based on long term evolution (LTE) standards and use recently designated spectrum in the 700 MHz band. The public safety network has different objectives and traffic patterns than commercial wireless networks. In particular, the public safety network puts more emphasis on coverage, reliability and latency in the worst case scenario. Moreover, the routine public safety traffic is relatively light, whereas when a major incident occurs, the traffic demand at the incident scene can be significantly heavier than that in a commercial network. Hence it is prohibitively costly to build the public safety network using conventional cellular network architecture consisting of an infrastructure of stationary base transceiver stations. A novel architecture is proposed in this paper for the public safety broadband network. The architecture deploys stationary base stations sparsely to serve light routine traffic and dispatches mobile base stations to incident scenes along with public safety personnel to support heavy traffic. The analysis shows that the proposed architecture can potentially offer more than 75% reduction in terms of the total number of base stations needed.

In recent years, a number of results have been developed which connect information measures and estimation measures under various models, including, predominantly, Gaussian and Poisson models. More recent results due to Gil Taborda and Pérez-Cruz relate the relative entropy to certain mismatched estimation errors in the context of binomial and negative binomial models, where, unlike in the case of Gaussian and Poisson models, the conditional mean estimates concern models of different orders than those of the original model. In this paper, a different set of results in simple forms are developed for binomial and negative binomial models, where the conditional mean estimates are produced through the original models. The new results are consistent with previous results for Gaussian and Poisson models.

In a molecular communication system, molecules convey the information by traversing from the transmitter to the receiver through the medium, which is often liquid. The time for a molecule to travel a fixed distance according to Brownian motion with a constant drift has the inverse Gaussian distribution. Hence the molecular communication channel is modeled by an additive inverse Gaussian noise channel, the input of which is the release times of the molecules. This paper studies the capacity-achieving input distribution for such a channel, where the release time is subject to both peak and average constraints. Several properties of the capacity-achieving input are established. A numerical method for computing the optimal input distribution is developed. The result complements some existing bounds on the capacity of molecular channel.

This paper studies communication networks with a very large number of users simultaneously communicating with an access point. A new notion of many-access channel (MnAC) is introduced, which is the same as a multiaccess channel except that the number of users increases unboundedly with the coding block length. Unlike the conventional multiaccess channel with a fixed number of users, the joint typicality decoding technique is not directly applicable to establish the achievability of the capacity. It is shown that, as long as the number of users grows sublinearly with the coding block length, random coding with Feinstein's threshold decoding is sufficient to achieve the symmetric capacity of the Gaussian MnAC.

This paper addresses relay design for a wireless multiple-input-multiple-output (MIMO) switching scheme that enables data exchange among multiple users. Here, a multi-antenna relay linearly precodes the received (uplink) signals from multiple users before forwarding the signal in the downlink, where the purpose of precoding is to let each user receive its desired signal with interference from other users suppressed. The problem of optimizing the precoder based on sum-rate maximization criteria is typically non-convex and difficult to solve. The main contribution of this paper is that we show the sum-rate maximization problem can be converted to an equivalent weighted sum-MSE minimization problem and can therefore be solved using an iterative algorithm proposed in our previous work. Asymptotic analysis reveals that, with properly chosen initial values, the proposed iterative algorithms are asymptotically optimal in both high and low signal-to-noise-ratio (SNR) regimes for MIMO switching, either with or without self-interference cancellation (a.k.a., physical-layer network coding). Numerical results show that the optimized MIMO switching scheme based on the proposed algorithms significantly outperforms existing approaches in the literature.

The throughput and stability properties of wireless network coding are evaluated for an arbitrary number of terminals exchanging broadcast traffic with the aid of a relay. First, coding and scheduling schemes are derived that minimize the number of transmissions needed for each node to broadcast one packet. For stochastically varying traffic, the stable throughput is then compared under both digital and analog network coding schemes. The initial analysis focuses on a network with a single relay. Extensions to arbitrary terminal-relay configurations are then outlined for a general multihop network. Backpressure-like algorithms for jointly achieving throughput optimal scheduling and network coding are given for each network coding scheme.

This paper studies the error exponent of block coding over an additive white Gaussian noise channel where a fraction ($f$) of the channel output symbols are revealed to the transmitter through noiseless feedback. If the code rate exceeds$fC$, where$C$is the channel capacity, then the probability of decoding error cannot decay faster than exponentially with block length. However, if the code rate is below$fC$, the error probability can decrease faster than exponentially with the block length, as with full feedback ($f=1$). This is achieved by combining a feedback code and a forward error control code, and jointly decoding them at the receiver. This scheme can attain higher reliability than rate splitting in which feedback and forward codes independently encode separate source messages.

This paper addresses joint transceiver and relay design for a wireless multiple-input multiple-output (MIMO) switching scheme that enables data exchange among multiple users. Here, a multiantenna relay linearly precodes the received (uplink) signals from multiple users and forwards the signal in the downlink, where the purpose of precoding is to let each user receive its desired signal with interference from other users suppressed. The problem of optimizing the precoder based on various design criteria is typically nonconvex and difficult to solve. The main contribution of this paper is a unified approach to solve the weighted sum mean square error (MSE) minimization and weighted sum rate maximization problems in MIMO switching. Specifically, an iterative algorithm is proposed for jointly optimizing the relay's precoder and the users' receive filters to minimize the weighted sum MSE. It is also shown that the weighted sum rate maximization problem can be reformulated as an iterated weighted sum MSE minimization problem and can, therefore, be solved similarly to the case of weighted sum MSE minimization. With properly chosen initial values, the proposed iterative algorithms are asymptotically optimal in both high- and low-signal-to-noise-ratio regimes for MIMO switching, either with or without self-interference cancellation (a.k.a., physical-layer network coding). Numerical results show that the optimized MIMO switching scheme based on the proposed algorithms significantly outperforms existing approaches in the literature.

This paper studies the optimal use of limited-rate feedback of channel state information (CSI) in the case of a wideband multicarrier channel with multiple transmit antennas and a single receive antenna. With full knowledge of the CSI, the receiver should compute the optimal beamforming vectors, jointly quantize them, and feed them back to the transmitter. The achievable forward data rate depends on the rate of the feedback link. The optimal tradeoff between the forward and feedback rates is characterized using rate distortion theory in the limit of infinite number of subcarriers with fixed amount of feedback per subcarrier. The distortion metric is the difference between the forward rate achieved with limited feedback and the capacity with perfect CSI at the transmitter. The rate distortion function gives the forward rate as a function of the feedback rate. Numerical results show that to achieve a target forward rate, the required feedback rate can be substantially reduced by joint quantization of the beamformers across subcarriers. A simple quantizer amenable to practical implementation is shown to approach the rate distortion bound with near-linear computational complexity.

Multicell joint processing can mitigate inter-cell interference and thereby increase the spectral efficiency of cellular systems. Most previous work has assumed phase-aligned (coherent) transmissions from different base transceiver stations (BTSs) so that the signals superpose coherently at each receiver, which is difficult to achieve in practice. In this work, a noncoherent cooperative transmission scheme for the downlink is studied, which does not require phase alignment. The focus is on jointly serving two users in adjacent cells sharing the same resource block. The two BTSs partially share their messages through a backhaul link, and each BTS can transmit a superposition of two codewords, one for each receiver. Each receiver decodes its own message, and treats the signals for the other receiver as background noise. With narrowband transmissions the achievable rate region and maximum achievable weighted sum rate are characterized by optimizing the power allocation (and the beamforming vectors in the case of multiple transmit antennas) at each BTS between its two codewords. For a wideband (multicarrier) system, a dual formulation of the optimal power allocation problem across sub-carriers is presented, which can be efficiently solved by numerical methods. Results show that the proposed cooperation scheme can improve the sum rate substantially in the low to moderate signal-to-noise ratio (SNR) range.

In this paper, we show that the characterisation of all determinant inequalities for n × n positive definite matrices is equivalent to determining the smallest closed and convex cone containing all entropy functions induced by n scalar jointly Gaussian random variables. We have obtained inner and outer bounds on the cone by using representable functions and entropic functions. In particular, these bounds are tight and explicit for n ≤ 3, implying that determinant inequalities for 3 × 3 positive definite matrices are completely characterized by Shannon-type information inequalities.

Many wireless communication systems are subject to duty cycle constraint, that is, a radio only actively transmits signals over a fraction of the time. For example, it is desirable to have a small duty cycle in some low-power systems; a half-duplex radio cannot keep transmitting if it wishes to receive useful signals; and a cognitive radio needs to listen to the channel frequently to detect primary users. Zhang and Guo have shown that the capacity of a Gaussian channel subject to an idealized duty cycle constraint as well as average transmission power constraint is achieved by discrete independent and identically distributed (i.i.d.) on-off signaling in lieu of Gaussian signaling. This paper extends the previous results by considering a more realistic duty cycle constraint where the extra cost of transitions between transmissions and nontransmissions due to pulse shaping is accounted for. The capacity-achieving input is no longer independent over time and is hard to compute. A lower bound of the input-output mutual information as a function of the input distribution is developed, which is shown to be maximized by a first-order Markov process, the distribution of which is also discrete and can be computed efficiently. Simulation results show that the Markov input is superior to i.i.d. inputs for the Gaussian channel subject to the realistic duty cycle and average power constraints.

Two users at the two ends of a bidirectional channel wish to estimate the common state of the channel. The problem is usually treated as two separate one-way channel estimation problems: User 1 sends deterministic pilots to assist user 2 in estimating the channel, and vice versa. This paper questions whether such separation is optimal. In other words, is it beneficial to let a user choose pilots that adapt to what the user has learned about the channel? Two concrete models are studied and it is found that using adaptive pilots often improves the channel estimate. In the special case of a Gaussian channel with colored additive interference, an iterative bidirectional estimation scheme is proposed, which achieves significantly better performance than separate one-way estimation.

A wireless relay which forms a one-to-one mapping from the inputs (uplinks) to the outputs (downlinks) is called a multiple-input-multiple-output (MIMO) switch. The MIMO switch carries out precode-and-forward, where all users send their signals in the uplink and then the MIMO switch precodes the received vector signal for broadcasting in the downlink. Ideally, each user employs a receive filter to recover its desired signal from one other user with no or little interference from other users. We propose a joint design of the precoder and the receive filters to achieve the minimum-mean-square-error (MMSE), assuming full channel state information is available at the relay. Our results indicate that the proposed MMSE relaying scheme outperforms the existing ZF/MMSE schemes.

A wireless relay with multiple antennas is called a multiple-input-multiple-output (MIMO) switch if it maps its input links to its output links using "precode-and-forward." Namely, the MIMO switch precodes the received signal vector in the uplink using some matrix for transmission in the downlink. This paper studies the scenario of K stations and a MIMO switch, which has full channel state information. The precoder at the MIMO switch is either a zero-forcing matrix or a network-coding matrix. With the zero-forcing precoder, each destination station receives only its desired signal with enhanced noise but no interference. With the network-coding precoder, each station receives not only its desired signal and noise, but possibly also self-interference, which can be canceled. Precoder design for optimizing the received signal-to-noise ratios at the destinations is investigated. For zero-forcing relaying, the problem is solved in closed form in the two-user case, whereas in the case of more users, efficient algorithms are proposed and shown to be close to what can be achieved by extensive random search. For network-coded relaying, we present efficient iterative algorithms that can boost the throughput further.

Interference between nodes is a critical impairment in mobile ad hoc networks. This paper studies the role of multiple antennas in mitigating such interference. Specifically, a network is studied in which receivers apply zero-forcing beamforming to cancel the strongest interferers. Assuming a network with Poisson-distributed transmitters and independent Rayleigh fading channels, the transmission capacity is derived, which gives the maximum number of successful transmissions per unit area. Mathematical tools from stochastic geometry are applied to obtain the asymptotic transmission capacity scaling and characterize the impact of inaccurate channel state information (CSI). It is shown that, if each node cancels interferers, the transmission capacity decreases as as the outage probability vanishes. For fixed , as grows, the transmission capacity increases as where is the path-loss exponent. Moreover, CSI inaccuracy is shown to have no effect on the transmission capacity scaling as vanishes, provided that the CSI training sequence has an appropriate length, which we derive. Numerical results suggest that canceling merely one interferer by each node may increase the transmission capacity by an order of magnitude or more, even when the CSI is imperfect.

This paper fully determines the degree-of-freedom (DoF) region of two-user interference channels with arbitrary number of transmit and receive antennas in the case of isotropic and independent (or block-wise independent) fading, where the channel state information is available to the receivers but not to the transmitters. Thus, the DoF gap between previous upper and lower bounds due to the authors, Vaze and Varanasi, and Huang, Jafar, Shamai, and Vishwanath is closed. The DoF result characterizes the capacity region to the first order of the logarithm of the signal-to-noise ratio (SNR) in the high-SNR regime. The DoF region is achievable by using random Gaussian codebooks independent of the channel states, which implies that it is impossible to increase the DoF using beamforming and interference alignment in the absence of channel state information at the transmitters.

Distributed medium access control (MAC) protocols are proposed for wireless networks assuming that one-hop peers can exchange a small amount of state information periodically. Each station maintains a state and makes state transitions and transmission decisions based on its state and recent state information collected from its one-hop peers. A station can adapt its packet length and the size of its state space to the amount of traffic in its neighborhood. It is shown that these protocols converge to a steady state, where stations take turns to transmit in each neighborhood without collision. An important consequence of this work is that using such protocols, an efficient time-division multiple access (TDMA) like schedule can be formed in a distributed manner, as long as the topology of the network remains static or changes slowly with respect to the execution of the protocol.

In many wireless communication systems, radios are subject to duty cycle constraint, that is, a radio only actively transmits signals over a fraction of the time. For example, it is desirable to have a small duty cycle in some low power systems; a half-duplex radio cannot keep transmitting if it wishes to receive useful signals; and a cognitive radio needs to listen and detect primary users frequently. This work studies the capacity of scalar discrete-time Gaussian channels subject to duty cycle constraint as well as average transmit power constraint. The duty cycle constraint can be regarded as a requirement on the minimum fraction of nontransmission or zero symbols in each codeword. A unique discrete input distribution is shown to achieve the channel capacity. In many situations, numerical results demonstrate that using the optimal input can improve the capacity by a large margin compared to using Gaussian signaling over a deterministic transmission schedule, which is capacity-achieving in the absence of the duty cycle constraint. This is in part because the positions of the nontransmission symbol in a codeword can convey information. The results suggest that, under the duty cycle constraint, departing from the usual paradigm of intermittent packet transmissions may yield substantial gain.

This paper studies a problem frequently seen in wireless networks: Every node wishes to broadcast information to nodes within a single hop, which are referred to as its peers. We call this problem mutual broadcast. A novel solution is proposed, which exploits the multiaccess nature of the wireless medium and addresses the half-duplex constraint at the fundamental level. The defining feature of the scheme is to let all nodes send their messages at the same time, where each node broadcasts a codeword (selected from its unique codebook) consisting of on-slots and off-slots, where it transmits only during its on-slots, and listens to its peers through its own off-slots. Decoding can be viewed as a problem of sparse support recovery based on linear measurements. In case each message consists of a small number of bits, an iterative message-passing algorithm based on belief propagation is developed, the performance of which is characterized using a state evolution formula in the limit where each node has a large number of peers. Numerical results demonstrate that, to achieve the same reliability for mutual broadcast, the proposed scheme achieves three to five times the rate of ALOHA and carrier-sensing multiple-access (CSMA) in typical scenarios.

A novel scheme for full-duplex neighbor discovery in wireless networks is proposed. The scheme allows all nodes to simultaneously discover one-hop neighbors and identify their network interface addresses (NIAs) within a single frame of transmission, which typically consists of no more than a few thousand symbols. The key technique is to assign each node a unique on-off signature derived from a second-order Reed-Muller code and let all nodes simultaneously transmit their signatures. Despite that the radio is half-duplex, each node observes a superposition of its neighbors' signatures (partially) through its own off-slots. To identify its (small number of) neighbors out of a large network address space, each node solves a compressed sensing (or sparse recovery) problem using a chirp reconstruction algorithm. A network of over one million Poisson distributed nodes (with 20-bit NIAs) is studied numerically, where each node has 30 neighbors on average, and the channel between each pair of nodes is subject to path loss and Rayleigh fading. Within a single frame of 4,096 symbols, nodes can discover their respective neighbors with on average 99.9% accuracy at 16 dB signal-to-noise ratio (SNR). The algorithm is scalable to networks of virtually any size of practical interest due to its sub-linear complexity. The new scheme requires much fewer transmissions than conventional random-access discovery schemes to achieve the same performance.

Consider the minimum mean-square error (MMSE) of estimating an arbitrary random variable from its observation contaminated by Gaussian noise. The MMSE can be regarded as a function of the signal-to-noise ratio (SNR) as well as a functional of the input distribution (of the random variable to be estimated). It is shown that the MMSE is concave in the input distribution at any given SNR. For a given input distribution, the MMSE is found to be infinitely differentiable at all positive SNR, and in fact a real analytic function in SNR under mild conditions. The key to these regularity results is that the posterior distribution conditioned on the observation through Gaussian channels always decays at least as quickly as some Gaussian density. Furthermore, simple expressions for the first three derivatives of the MMSE with respect to the SNR are obtained. It is also shown that, as functions of the SNR, the curves for the MMSE of a Gaussian input and that of a non-Gaussian input cross at most once over all SNRs. These properties lead to simple proofs of the facts that Gaussian inputs achieve both the secrecy capacity of scalar Gaussian wiretap channels and the capacity of scalar Gaussian broadcast channels, as well as a simple proof of the entropy power inequality in the special case where one of the variables is Gaussian.

Assuming additive Gaussian noise, a general sufficient condition on the input distribution is established to guarantee that the ratio of mutual information to signal-to-noise ratio (SNR) goes to one half nat as SNR vanishes. The result allows SNR-dependent input distribution and side information.

This paper studies the capacity region of a two-user ergodic interference channel with fading, where only one user is subject to interference from the other user, and the channel state information (CSI) is only available at the receivers. A layered erasure model with arbitrary fading statistics is studied first, whose capacity region is completely determined as a polygon. Each dominant rate pair can be regarded as the outcome of a tradeoff between the rate of the interference-free user and the rate loss its interference causes the other user. Using insights from the layered erasure model, inner and outer bounds of the capacity region are provided for fading Gaussian Z-interference channels. The gap between the inner and outer bounds is no more than 12.8 bits per channel use per user, regardless of the signal-to-noise ratio (SNR) and fading statistics.

The design of a scheduling scheme is crucial for the efficiency and user-fairness of wireless networks. Assuming that the channel quality information (CQI) of all users is available to a central controller, a simple scheme which maximizes the sum-log utility function has been shown to guarantee proportional fairness. This work studies a more general problem which takes both the CQI acquisition and the user scheduling into account. First, in case the statistics of the channel quality is available to the controller, a joint channel probing and proportional fair scheduling scheme is developed based on the optimal stopping time theory. The convergence and optimality of the scheme is proved. Next, the problem is further studied in the case where the channel statistics are not available to the controller, and a joint learning, probing and scheduling scheme is designed by solving a generalized bandit problem. Furthermore, it is shown that the multiuser diversity gain does not always increase as the number of users increases. Numerical results demonstrate that the proposed scheduling schemes can provide significant gain over existing schemes.

Multicell joint processing can mitigate inter-cell interference and thereby increase the spectral efficiency of cellular systems. Most previous work has assumed phase-aligned (coherent) transmissions from different base stations (BSTs), which is difficult to achieve in practice. In this work, a noncoherent cooperative transmission scheme for the downlink is studied, which does not require phase alignment. We consider two adjacent cells each with a single user, and assume that the BSTs share their messages through a dedicated link. Each BST transmits a superposition of two codewords, one for each receiver. Each receiver decodes its own message, and treats the signals for the other receiver as background noise. With narrowband transmissions the achievable rate region and maximum achievable weighted sum rate are characterized by optimizing the power allocation at each BST between its two codewords. For a wideband (multicarrier) system, a dual formulation of the optimal power allocation problem across subcarriers is presented, which admits efficient numerical solution. Results show that the proposed cooperation scheme can improve the sum rate substantially at low to moderate signal-to-noise ratios.

The design of scheduling schemes for wireless communication systems has been driven by a compromise between the objectives of system throughput and fairness among users. In case the quality of all user channels is known to the controller, proportional fair scheduling has been well understood. However, to acquire the channel quality information may consume substantial amount of resources. In this work, it is assumed that probing for channel quality information takes a fraction of the coherence block, so that the amount of time for data transmission is reduced. A simple strategy for channel probing and scheduling is proposed, which achieves the maximum throughput under the proportional fairness constraint. It is found that when probing cost is taken into account, the multi-user diversity gain does not always increase as the number of users increases. Simulation results show that the proposed strategy significantly outperforms existing schemes when the channel probing cost is taken into account.

This paper studies medium access control (MAC) protocols for regular wireless networks, where only nearest-neighbor interactions are involved. Each station chooses a state in the current time slot, which determines whether it transmits or not, based on its own state and the states of all its nearest neighbors in the previous time slot. The dynamics of the network follow that of a Markov Chain of Markov Fields, which is shown to converge to a stationary distribution for certain types of interactions. It is found that this type of protocols can achieve the optimal one-hop broadcast throughput in regular wireless networks. In case each station can only distinguish between transmitting and idle neighbors, the interactions of the network can be described using the Ising model in statistical mechanics. For this case, a MAC protocol is designed that can achieve a throughput close to the optimum.

This work studies the capacity region of ergodic fading Gaussian interference channels, where only one of the users is subject to interference from the other user, and that channel state information is not available at transmitters (no CSIT). In particular, inner and outer bounds of the capacity region are obtained. The inner bound is achieved by artificially creating layers in the signaling of the interference-free user. The outer bound is developed by characterizing the trade-off between the rate gain of the interference-free user and the rate loss of the other user due to interference. Furthermore, the gap between the inner and outer bounds is no more than 12.772 bits per channel use per user, regardless of the signal-to-noise ratios and fading statistics.

The capacity of a fading channel can be substantially increased by feeding back channel state information from the receiver to the transmitter. If the feedback rate is limited, what state information to feed back and how to encode it are important questions. This paper studies power loading in a multicarrier system using no more than one bit of feedback per subchannel. The subchannels can be correlated and full channel state information is assumed at the receiver. First, a simple model withNparallel two-state (good/bad) memoryless subchannels is considered, where the channel state feedback is used to select a fixed number of subchannels to activate. The optimal feedback scheme is the solution to a vector quantization problem, and the associated performance for large N is characterized using a rate distortion function. As N increases, the loss in forward rate from the asymptotic (rate-distortion) value is shown to decrease as (logN)/N and √{(logN)/N} with optimal variable- and fixed-length feedback codes, respectively. These results are subsequently extended to parallel Rayleigh block fading subchannels, where the feedback designates a set of subchannels to be activated with equal power. Rate-distortion feedback codes are proposed for designating subsets of (good) subchannels with signal-to-noise ratios (SNRs) that exceed a threshold. The associated performance is compared with that of a simpler lossless source coding scheme, which designates groups of good subchannels, where both the group size and threshold are optimized. The rate-distortion codes can provide a significant increase in forward rate at low SNRs.

We consider the problem of signal estimation (denoising) from a statistical mechanical perspective, using a relationship between the minimum mean square error (MMSE), of estimating a signal, and the mutual information between this signal and its noisy version. The paper consists of essentially two parts. In the first, we derive several statistical-mechanical relationships between a few important quantities in this problem area, such as the MMSE, the differential entropy, the Fisher information, the free energy, and a generalized notion of temperature. We also draw analogies and differences between certain relations pertaining to the estimation problem and the parallel relations in thermodynamics and statistical physics. In the second part of the paper, we provide several application examples, where we demonstrate how certain analysis tools that are customary in statistical physics, prove useful in the analysis of the MMSE. In most of these examples, the corresponding statistical-mechanical systems turn out to consist of strong interactions that cause phase transitions, which in turn are reflected as irregularities and discontinuities (similar to threshold effects) in the behavior of the MMSE.

Transmitter preceding is a crucial technique for harnessing the potential of multiple-input multiple-output (MIMO) fading channels. In many practical wireless systems, a limited amount of feedback from the receiver is available at the transmitter, which can be used to direct the choice of the precoder from a codebook to match the channel state. Assuming noiseless, limited-rate feedback, this work studies the design of simple, efficient quantization and feedback schemes which achieve near-optimal ergodic channel capacity. In the case the precoder takes the form of a beamforming vector for modulating a single symbol stream, it is found that simple scalar quantization of the elements of the vector is nearly optimal over a wide range of feedback rates; it typically costs a fraction of a dB higher SNR to achieve the same capacity as that of far more sophisticated vector quantization schemes. In the case a precoding matrix consisting of multiple beams is used to modulate multiple symbol streams, separate encoding of the beams using scalar quantization also performs well. Roughly speaking, the rate loss due to separate encoding of the beams increases linearly with the number of beams but appears to be constant over a wide range of SNRs. The loss can be reduced substantially by more sophisticated encoding of each beam, e.g., two-state trellis coded quantization. The complexity of such quantization schemes is linear in the number of antennas and the number of feedback bits.

This paper establishes new information-estimation relationships pertaining to models with additive noise of arbitrary distribution. In particular, we study the change in the relative entropy between two probability measures when both of them are perturbed by a small amount of the same additive noise. It is shown that the rate of the change with respect to the energy of the perturbation can be expressed in terms of the mean squared difference of the score functions of the two distributions, and, rather surprisingly, is unrelated to the distribution of the perturbation otherwise. The result holds true for the classical relative entropy (or Kullback-Leibler distance), as well as two of its generalizations: Reacutenyi's relative entropy and the f-divergence. The result generalizes a recent relationship between the relative entropy and mean squared errors pertaining to Gaussian noise models, which in turn supersedes many previous information-estimation relationships. A generalization of the de Bruijn identity to non-Gaussian models can also be regarded as consequence of this new result.

The achievable rate of a wideband multi-input single-output channel with multi-carrier transmission is studied with limited feedback of channel state information (CSI). The set of sub-channel vectors are assumed to be jointly quantized and relayed back to the transmitter. Given a fixed feedback rate, the performance of an optimal joint quantization scheme can be characterized by the rate-distortion bound. The distortion metric is the average loss in capacity (forward rate) relative to the capacity with perfect channel state information at the transmitter and receiver. The corresponding rate distortion function gives the forward capacity as a function of feedback rate, and is determined explicitly by casting the minimization of mutual information in the rate-distortion problem as an optimal control problem. Numerical results show that when the feedback rate is relatively small, the rate-distortion bound significantly outperforms separate quantization of the state information of each sub-channel.

This paper studies power loading in a multicarrier system with channel state feedback of no more than one bit per sub-channel. Full channel state information is assumed known at the receiver. A simple model with parallel two-state (good/bad) memoryless sub-channels is considered first, where feedback is used to select a given fraction of sub-channels to activate. The optimal feedback scheme is the solution to a vector quantization problem, the performance of which is characterized by a rate distortion function in the limit of infinite number of sub-channels. Bounds for performance loss with finite number of sub-channels are also developed. We then consider a second model of a bank of block Rayleigh fading sub-channels with total power constraint, where the feedback describes which sub-channels to activate with equal power. A scheme based on rate distortion code is proposed to describe which sub-channels exceed a threshold in signal-to-noise ratio and should be activated. With optimized threshold and moderate amount of feedback, the resulting capacity is known to be of the same order in the number of sub-channels as that achieved by water-filling with full channel state information at the transmitter. This scheme performs more favorably than alternative schemes based on channel state reduction (such as by grouping them) and subsequent entropy coding.

This paper considers the problem of beamforming in multiple-input multiple-output (MIMO) wireless systems. Assuming perfect channel state information at the receiver, the choice of the beamforming vector is made possible through a noiseless limited-rate feedback of one or more bits per coefficient to the transmitter. This paper proposes the use of beamforming codebooks based on quadrature amplitude modulation (QAM) and phase-shift keying (PSK) constellations, which essentially eliminates the need for storage of the codebook. We show that such codebooks perform arbitrarily close to the perfect feedback case as the constellation size increases, and that full diversity order is achieved. We demonstrate an equivalence between the beamforming codebook search problem with that of noncoherent sequence detection. Based on this we propose fast beamforming vector search algorithms. Monte-Carlo simulations are presented to show that the performance is comparable to the best known codebooks, and that the search complexity can be reduced by several orders of magnitude.

This paper studies the entropy rate of hidden Markov processes (HMPs) which are generated by observing a discrete-time binary homogeneous Markov chain through an arbitrary memoryless channel. A fixed-point functional equation is derived for the stationary distribution of an input symbol conditioned on all past observations. While the existence of a solution to the fixed-point functional equation is guaranteed by martingale theory, its uniqueness follows from the fact that the solution is the fixed point of a contraction mapping. The entropy or differential entropy rate of the HMP can then be obtained through computing the average entropy of each input symbol conditioned on past observations. In absence of an analytical solution to the fixed-point functional equation, a numerical method is proposed in which the fixed-point functional equation is first converted to a discrete linear system using uniform quantization and then solved efficiently. The accuracy of the computed entropy rate is shown to be proportional to the quantization interval. Unlike many other numerical methods, this numerical solution is not based on averaging over a sample path of the HMP.

Channel uncertainty and co-channel interference are two major challenges in the design of wireless systems such as future generation cellular networks. This paper studies receiver design for a wireless channel model with both time-varying Rayleigh fading and strong co-channel interference of similar form as the desired signal. It is assumed that the channel coefficients of the desired signal can be estimated through the use of pilots, whereas no pilot for the interference signal is available, as is the case in many practical wireless systems. Because the interference process is non-Gaussian, treating it as Gaussian noise generally often leads to unacceptable performance. In order to exploit the statistics of the interference and correlated fading in time, an iterative message-passing architecture is proposed for joint channel estimation, interference mitigation and decoding. Each message takes the form of a mixture of Gaussian densities where the number of components is limited so that the overall complexity of the receiver is constant per symbol regardless of the frame and code lengths. Simulation of both coded and uncoded systems shows that the receiver performs significantly better than conventional receivers with linear channel estimation, and is robust with respect to mismatch in the assumed fading model.

Interference between nodes directly limits the capacity of mobile ad hoc networks. This paper focuses on spatial interference cancellation with perfect channel state information (CSI), and analyzes the corresponding network capacity. Specifically, by using multiple antennas, zero-forcing beamforming is applied at each receiver for canceling the strongest interferers. Given spatial interference cancellation, the network transmission capacity is analyzed in this paper, which is defined as the maximum transmitting node density under constraints on outage and the signal-to-interference-plus-noise ratio. Assuming that the locations of network nodes are Poisson distributed and spatially i.i.d. Rayleigh fading channels, mathematical tools from stochastic geometry are applied for deriving scaling laws for transmission capacity. Specifically, for a large number of antennas per node, the transmission capacity scales with the number of antennas raised to a fractional power, which depends only on the path-loss exponent. Moreover, for small target outage probability, transmission capacity is proved to increase following a power law, where the exponent is the inverse of the size of antenna array or larger depending on the pass-loss exponent. As shown by simulations, spatial interference cancellation increases transmission capacity by an order of magnitude or more even if only one extra antenna is added to each node.

Feedback of channel state information (CSI) enables a multi-carrier transmitter to optimize the power allocation across sub-channels. We consider a single user feedback scheme in which the entire set of sub-channels is evenly divided into smaller groups of sub-channels, and the receiver requests the use of a particular group if the gain of every sub-channel in the group is above a threshold. The transmit power is then uniformly spread across the requested sub-channel groups. The amount of feedback is therefore controlled by the group size and the threshold. For this scheme, given a total power constraint, we characterize how the channel capacity scales with the number of sub-channels N as a function of the feedback rate. We then consider transmission over a block fading channel, assuming that each coherence block contains both feedback and data transmission. We optimize the fraction of feedback overhead as a function of the number of feedback bits per channel use and coherence time. Numerical results show that the asymptotic (large-N) analysis accurately predicts the behavior of finite-size systems of interest.

This paper studies signal detection in wireless networks where the uncertainty is due to fading as well as a strong co-channel interference of the same form as that of the desired signal. In particular, unlike for the desired signal, no pilot for the interference signal is available for measuring its fading channel state. Still, the interference is a non-Gaussian process and treating it as Gaussian noise can lead to poor performance. We propose a joint channel estimation and interference mitigation scheme based on belief propagation, which is capable of fully exploiting the statistics of the interference. Simulation results show that the receiver performs significantly better compared to conventional receivers with linear channel estimation.

In a fading communication channel, it is often beneficial to feedback Channel State Information (CSI) and Receiver State Information (RSI) to the transmitter. The CSI generally refers to information about the channel condition available at the receiver, while the RSI in this work is defined as information about the receive’s estimate of the message. The RSI can be used to improve reliability, e.g., through retransmission. This paper considers multi-carrier transmission through a doubly-selective Rayleigh fading channel, and studies the trade-off between the feedback of CSI and RSI under total feedback constraint. In particular, the CSI feedback specifies which groups of sub-channels to activate with equal power, and the RSI feedback determines retransmissions of a codeword. The problem is how to allocate feedback bits between CSI and RSI in order to maximize the error probability exponent. It is found that the optimal trade-off exhibits phase transitions which depends critically on the coherence time and the total amount of feedback. Specifically, the first feedback bits should be CSI up to a critical amount. Additional feedback bits, if available, should be allocated to RSI first, and then to both CSI and RSI. For the model considered, as the amount of feedback exceeds a certain threshold, additional RSI feedback is not beneficial unless CSI feedback increases accordingly.

This work studies the properties of the minimum mean-square error (MMSE) of estimating an arbitrary random variable contaminated by Gaussian noise based on the observation. The MMSE can be regarded as a function of the signal-to-noise ratio (SNR), as well as a functional or transform of the input distribution. This paper shows that the MMSE is analytic in SNR for every random variable. Simple expressions for the derivatives of the MMSE as a function of the SNR are obtained. Since the input-output mutual information can be written as the integral of the MMSE as a function of SNR, the results also lead to higher derivatives of the mutual information. The MMSE and mutual informationpsilas convexity in the SNR and concavity in the input distribution are established. It is shown that there can be only one SNR for which the MMSE of a Gaussian random variable and that of a non-Gaussian random variable coincide. Application of the properties of the MMSE to the scalar Gaussian broadcast channel problem is presented.

Code-division multiple access (CDMA) is the basis of a family of advanced air interfaces in current and future generation networks. The benefits promised by CDMA have not been fully realized partly due to the prohibitive complexity of optimal detection and decoding of many users communicating simultaneously using the same frequency band. From both theoretical and practical perspectives, this paper advocates a new paradigm of CDMA with sparse spreading sequences, which enables near-optimal multiuser detection using belief propagation (BP) with low-complexity. The scheme is in part inspired by capacity-approaching low-density parity-check (LDPC) codes and the success of iterative decoding techniques. Specifically, it is shown that BP-based detection is optimal in the large-system limit under many practical circumstances, which is a unique advantage of sparsely spread CDMA systems. Moreover, it is shown that, from the viewpoint of an individual user, the CDMA channel is asymptotically equivalent to a scalar Gaussian channel with some degradation in the signal-to-noise ratio (SNR). The degradation factor, known as the multiuser efficiency, can be determined from a fixed-point equation. The results in this paper apply to a broad class of sparse, semi-regular CDMA systems with arbitrary input and power distribution. Numerical results support the theoretical findings for systems of moderate size, which further demonstrate the appeal of sparse spreading in practical applications.

This paper studies a nonlinear vector precoding scheme which inverts the wireless multiple-input multiple-output (MIMO) channel at the transmitter so that simple symbol-by-symbol detection can be used in lieu of sophisticated multiuser detection at the receiver. In particular, the transmit energy is minimized by relaxing the transmitted symbols to a larger alphabet for precoding, which preserves the minimum signaling distance. The so-called replica method is used to analyze the average energy savings with random MIMO channels in the large-system limit. It is found that significant gains can be achieved with complex-valued alphabets. The analysis applies to a very general class of MIMO channels, where the statistics of the channel matrix enter the result via the R-transform of the asymptotic empirical distribution of its eigenvalues. Moreover, we introduce polynomial-complexity precoding schemes for binary and quadrature phase-shift keying in complex channels by using convex rather than discrete relaxed alphabets. In case the number of transmit antennas is more than twice the number of receive antennas, we show that a convex precoding scheme, despite its polynomial complexity, outperforms NP-hard precoding using the popular Tomlinson-Harashima signaling.

Following the discovery of a fundamental connection between information measures and estimation measures in Gaussian channels, this paper explores the counterpart of those results in Poisson channels. In the continuous-time setting, the received signal is a doubly stochastic Poisson point process whose rate is equal to the input signal plus a dark current. It is found that, regardless of the statistics of the input, the derivative of the input-output mutual information with respect to the intensity of the additive dark current can be expressed as the expected difference between the logarithm of the input and the logarithm of its noncausal conditional mean estimate. The same holds for the derivative with respect to input scaling, but with the logarithmic function replaced by x log x. Similar relationships hold for discrete-time versions of the channel where the outputs are Poisson random variables conditioned on the input symbols.

A unified approach to power control is proposed for maximizing utility in terms of energy efficiency in code-division multiple access (CDMA) networks. The approach is applicable to a large family of multiuser receivers including the matched filter, the decorrelator, the linear minimum mean-square error (MMSE) receiver, and the (nonlinear) optimal detectors. It exploits the linear relationship between the transmit power and the output signal-to-interference-plus-noise ratio (SIR) for each user in the large-system limit. Suppose that each user seeks to selfishly maximize its own energy efficiency, a unique Nash equilibrium is shown to exist and be SIR-balanced, thus extending a previous result on linear receivers. A unified power control algorithm for reaching the Nash equilibrium is proposed, which adjusts transmit powers iteratively by computing the large-system multiuser efficiency, which is independent of instantaneous spreading sequences. The convergence of the algorithm is proved for linear receivers, and is demonstrated via simulation for the multiuser maximum likelihood detector. Moreover, the performance of the algorithm in finite-size systems is studied and compared with that of a conventional power control scheme, in which user powers depend on the instantaneous spreading sequences.

This paper proposes a new QAM based codebook for beamforming in multiple-input multiple-output (MIMO) wireless systems with a limited-rate feedback channel. We show that such codebooks perform arbitrarily close to the perfect feedback case as the constellation size increases, and that full diversity order is achieved. We demonstrate an equivalence between the problems of beamforming codebook search and noncoherent sequence detection. Based on this we propose a fast beamforming vector search algorithm. Monte-Carlo simulations are presented to show that the performance is comparable to the best known codebooks, and that the search complexity can be reduced by several orders of magnitude.

Abstract — We consider an additive white Gaussian noise (AWGN) channel with partial sequential feedback. Namely, for every fixed-length block of forward transmissions a fraction of the received symbols are fed back sequentially to the transmitter through a noiseless feedback link. It is well known that complete noiseless feedback can provide a dramatic improvement in reliability (i.e., double-exponential error rate with block length). We show that partial feedback can also provide a substantial improvement in error rate. Specifically, we propose a capacityachieving coding scheme with partial feedback, in which the feedback is used to induce a prior distribution for the decoding of random forward error control (FEC) codewords. The errorexponent for this scheme is larger than the error-exponent with FEC coding only at all rates. For rates greater than those achieved by transmissions with feedback alone, we give an upper bound on the error exponent. Exponents close to this bound can be achieved with both the proposed scheme and a simple ratesplitting scheme. With finite block lengths, the proposed coding scheme achieves lower error rates than rate-splitting. I.

This paper studies the problem of estimating the vector input to a sparse linear transformation based on the observation of the output vector through a bank of arbitrary independent channels. The linear transformation is drawn randomly from an ensemble with mild regularity conditions. The central result is a decoupling principle in the large-system limit. That is, the optimal estimation of each individual symbol in the input vector is asymptotically equivalent to estimating the same symbol through a scalar additive Gaussian channel, where the aggregate effect of the interfering symbols is tantamount to a degradation in the signal-to-noise ratio. The degradation is determined from a recursive formula related to the score function of the conditional probability distribution of the noisy channel. A sufficient condition is provided for belief propagation (BP) to asymptotically produce the a posteriori probability distribution of each input symbol given the output. This paper extends the authors' previous decoupling result for Gaussian channels to arbitrary channels, which was based on an earlier work of Montanari and Tse. Moreover, a rigorous justification is provided for the generalization of some results obtained via statical physics methods.

We apply the replica method to analyze vector pre-coding, a method to reduce transmit power in antenna array communications, in the limit of an infinite number of dimensions of the signal vector. The analysis applies to a very general class of channel matrices. The statistics of the channel matrix enter the transmitted energy per symbol via its R-transform. We specialize our result to inversion of an i.i.d. channel and two cases of signal point optimization (i) 2-point lattice pre-coding and (ii) compact relaxation. In the two cases the replica symmetric transmitted energy is found to be 4.3 dB and 9.6 dB above the orthogonal case for a square channel matrix, respectively.

This work studies the performance of multiuser detection and decoding in the downlink of cellular systems based on orthogonal frequency-division multiplexing (OFDM). Of particular interest is a worst case scenario where the desired user is at the cell boundary and subject to an equally strong interferer from a neighboring cell. A flexible iterative turbo decision-feedback equalizer (DFE) is proposed and studied numerically, which exhibits good error performance and resilience to fading, requires moderate training and low complexity, and accommodates multiple antennas easily. The scheme performs well without knowledge of the pilots of interfering signals from other cells, which is typically unavailable in practice, while such knowledge may improve the performance significantly. Furthermore, in the absence of knowledge of pilots for the out-of-cell interference, it is found that estimating the filter coefficients of the DFE directly is superior to deriving the coefficients from estimates of the instantaneous channel gains.

The differential entropy of a random variable (or vector) can be expressed as the integral over signal-to-noise ratio (SNR) of the minimum mean-square error (MMSE) of estimating the variable (or vector) when observed in additive Gaussian noise. This representation sidesteps Fisher's information to provide simple and insightful proofs for Shannon's entropy power inequality (EPI) and two of its variations: Costa's strengthened EPI in the case in which one of the variables is Gaussian, and a generalized EPI for linear transformations of a random vector due to Zamir and Feder.

This correspondence extends previous work on direct-sequence code-division multiple access (DS-CDMA) to give a single-user characterization of multicarrier (MC) CDMA systems. Results on the error performance and information rate of a family of multiuser detectors for MC-CDMA are obtained using the replica method, which was originally developed in statistical physics. The central result is the "decoupling principle", namely, an MC-CDMA channel with frequency-selective fading followed by a generic multiuser detection front end can be decoupled into a bank of single-user fading channels in the large-system limit. Thus, conditioned on one's fading coefficients, each user essentially experiences an equivalent single-user Gaussian channel with a degradation in the signal-to-noise ratio (SNR) in lieu of multiaccess interference. A set of joint equations is identified, which determines the degradation for each user, known as the multiuser efficiency. The spectral efficiencies under both optimal joint decoding and separate single-user decoding following multiuser detection are obtained analytically. The result applies to arbitrary input distribution and SNRs, and to optimal multiuser detection as well as various suboptimal schemes.

This correspondence gives a simple proof of Shannon's entropy-power inequality (EPI) using the relationship between mutual information and minimum mean-square error (MMSE) in Gaussian channels.

This paper extends a previous work on direct-sequence code-division multiple access (DS-CDMA) to multicarrier (MC) CDMA systems. New results on the error performance of a family of multiuser detectors for MC-CDMA are obtained using the replica method, which was originally developed in statistical physics. The central result is the "decoupling principle", namely, an MC-CDMA channel with frequency-selective fading followed by a generic multiuser detection front end can be decoupled into a bank of single-user fading channels in the large-system limit. Thus conditioned on one's fading coefficients, each user essentially experiences an equivalent single-user Gaussian channel with a degradation in the signal-to-noise ratio (SNR) in lieu of multiaccess interference. A set of joint equations is identified that determine the degradation for each user, known as the multiuser efficiency. The result applies to arbitrary input distribution and SNRs, and to optimal multiuser detection, as well as various other suboptimal schemes.

New results are reported on the performance of synchronous multirate code-division multiple access (CDMA) systems. It has been shown using a statistical physics approach that, under arbitrary inputs and signal-to-noise ratios (SNRs), a CDMA channel followed by a generic multiuser detection front end can be decoupled into a bank of Gaussian single-user channels in the large-system limit. This work extends the analysis to multirate CDMA where users may employ a combination of adaptive modulation, variable spreading factor, and multicode schemes to transmit at different data rates. It is found that the decoupling principle still holds, i.e., each user experiences an equivalent single-user Gaussian channel, where the degradation in the SNR, known as the multiuser efficiency, is obtained analytically by solving some fixed-point equations. This result applies to optimal multiuser detectors as well as many well-know suboptimal detectors. The simple large-system characterization of multirate CDMA encompasses many previous results as special cases

It has recently been shown that the derivative of the input-output mutual information of Gaussian noise channels with respect to the signal-to-noise ratio is equal to the minimum mean-square error. This paper considers general additive noise channels where the noise may not be Gaussian distributed. It is found that, for every fixed input distribution, the derivative of the mutual information with respect to the signal strength is equal to the correlation of two conditional mean estimates associated with the input and the noise respectively. Special versions of the result are given in the respective cases of additive exponentially distributed noise, Cauchy noise, Laplace noise, and Rayleigh noise. The previous result on Gaussian noise channels is also recovered as a special case

This paper deals with arbitrarily distributed finite-power input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the input-output mutual information and the minimum mean-square error (MMSE) achievable by optimal estimation of the input given the output. That is, the derivative of the mutual information (nats) with respect to the signal-to-noise ratio (SNR) is equal to half the MMSE, regardless of the input statistics. This relationship holds for both scalar and vector signals, as well as for discrete-time and continuous-time noncausal MMSE estimation. This fundamental information-theoretic result has an unexpected consequence in continuous-time nonlinear estimation: For any input signal with finite power, the causal filtering MMSE achieved at SNR is equal to the average value of the noncausal smoothing MMSE achieved with a channel whose SNR is chosen uniformly distributed between 0 and SNR.

This paper studies randomly spread code-division multiple access (CDMA) and multiuser detection in the large-system limit using the replica method developed in statistical physics. Arbitrary input distributions and flat fading are considered. A generic multiuser detector in the form of the posterior mean estimator is applied before single-user decoding. The generic detector can be particularized to the matched filter, decorrelator, linear minimum mean-square error (MMSE) detector, the jointly or the individually optimal detector, and others. It is found that the detection output for each user, although in general asymptotically non-Gaussian conditioned on the transmitted symbol, converges as the number of users go to infinity to a deterministic function of a "hidden" Gaussian statistic independent of the interferers. Thus, the multiuser channel can be decoupled: Each user experiences an equivalent single-user Gaussian channel, whose signal-to-noise ratio (SNR) suffers a degradation due to the multiple-access interference (MAI). The uncoded error performance (e.g., symbol error rate) and the mutual information can then be fully characterized using the degradation factor, also known as the multiuser efficiency, which can be obtained by solving a pair of coupled fixed-point equations identified in this paper. Based on a general linear vector channel model, the results are also applicable to multiple-input multiple-output (MIMO) channels such as in multiantenna systems.

Consider arbitrarily distributed input signals observed in additive Gaussian noise. A new fundamental relationship is found between the input-output mutual information and the minimum mean-square error (MMSE) of an estimate of the input given the output: The derivative of the mutual information (nats) with respect to the signal-to-noise ratio (SNR) is equal to half the MMSE. This identity holds for both scalar and vector signals, as well as for discrete- and continuous-time noncausal MMSE estimation (smoothing). A consequence of the result is a new relationship in continuous-time nonlinear filtering: Regardless of the input statistics, the causal MMSE achieved at snr is equal to the expected value of the noncausal MMSE achieved with a channel whose SNR is chosen uniformly distributed between 0 and snr

Following the recent discovery of new connections between information and estimation in Gaussian channels, this paper reports parallel results in the Poisson regime. Both scalar and continuous-time Poisson channels are considered. It is found that, regardless of the statistics of the input, the derivative of the input-output mutual information with respect to the dark current can be expressed in the expected difference between the logarithm of the input and the logarithm of its conditional mean estimate (noncausal in case of continuous-time). The same is true for the derivative with respect to input scaling, but with the logarithmic function replaced by x log x.

We present some new results on large-system CDMA obtained through the replica method developed in statistical physics. We find the spectral efficiency of randomly spread CDMA subject to Gaussian noise and flat fading in the large-system limit under arbitrary input distributions. Both joint decoding and single-user decoding are considered. In the latter case, a conditional mean estimator is first applied to separate the users and it is found that the resulting single-user channel for every user is equivalent to a Gaussian channel. The multiuser efficiency of that Gaussian channel is the same for all users and satisfies a fixed-point equilibrium equation. The additive decomposition by Shamai-Verdu of optimum capacity in terms of single-user capacity is shown to hold for arbitrary input distributions.

This paper proves large-system asymptotic normality of the output of a family of linear multiuser receivers that can be arbitrarily well approximated by polynomial receivers. This family of receivers encompasses the single-user matched filter, the decorrelator, the minimum mean square error (MMSE) receiver, the parallel interference cancelers, and many other linear receivers of interest. Both with and without the assumption of perfect power control, we show that the output decision statistic for each user converges to a Gaussian random variable in distribution as the number of users and the spreading factor both tend to infinity with their ratio fixed. Analysis reveals that the distribution conditioned on almost all spreading sequences converges to the same distribution, which is also the unconditional distribution. This normality principle allows the system performance, e.g., the multiuser efficiency, to be completely determined by the output signal-to-interference ratio (SIR) for large linear systems.

Linear parallel interference cancellation (PIC) schemes are described and analyzed using matrix algebra. It is shown that the linear PIC, whether conventional or weighted, can be seen as a linear matrix filter applied directly to the chip-matched filtered received signal vector. An expression for the exact bit-error rate (BER) is obtained, and conditions on the eigenvalues of the code correlation matrix and the weighting factors to ensure convergence are derived. The close relationship between the linear multistage PIC and the steepest descent method (SDM) for minimizing the mean squared error (MSE) is demonstrated. A modified weighted PIC structure that resembles the SDM is suggested which approaches the minimum MSE (MMSE) detector rather than the decorrelator. It is shown that for a K-user system, only K PIC stages are required for the equivalent matrix filter to be identical to the the MMSE filter. For fewer stages, techniques are devised for optimizing the choice of weights with respect to the MSE. One unique optimal choice of weights is found, which will lead to the minimum achievable MSE at the final stage. Simulation results show that a few stages are sufficient for near-MMSE performance.

Parallel interference cancellation (PIC) is a promising detection technique for code division multiple access (CDMA) systems. It has previously been shown that the weighted multistage PIC can be seen as an implementation of the steepest descent algorithm used to minimize the mean squared error (MSE). Following this interpretation, a unique set of weights, based on the eigenvalues of the correlation matrix, was found to lead to the minimum achievable MSE for a given number of stages in a short-code system. In this paper, we introduce a method for finding an appropriate set of time-invariant weights for systems using long codes. The weights are dependent on moments of the eigenvalues of the correlation matrix, exact expressions of which can be derived. This set of weights is optimal in the sense that it minimizes the ensemble averaged MSE over all code-sets. The loss incurred by averaging rather than using the optimal, time-varying weights is practically negligible, since the eigenvalues of sample correlation matrices are tightly clustered in most cases of interest. The complexity required for computing the weights increases linearly with the number of users but is independent of the processing gain, hence on-line weight updating is possible in a dynamic system. Simulation results show that a few stages is usually sufficient for near-MMSE performance.