We address the client-selection problem in federated learning over wireless networks under data heterogeneity. Existing client-selection methods often rely on server-side knowledge of client-specific information, thus compromising privacy. To overcome this issue, we propose a client self-selection strategy based solely on the comparison between locally computed training losses and a centrally updated selection threshold. Furthermore, to support robust aggregation of clients' updates over wireless channels, we integrate this client self-selection strategy into the recently proposed type-based unsourced multiple-access framework over distributed multiple-input multiple-output (D-MIMO) networks. The resulting scheme is completely unsourced: the server does not need to know the identity of the clients. Moreover, no channel state information is required, neither at the clients nor at the server side. Simulation results conducted over a D-MIMO wireless network show that the proposed self-selection strategy matches the performance of a comparable state-of-the-art server-side selection method and consistently outperforms random client selection.

We derive finite-blocklength bounds on the minimum achievable energy per bit over a Gaussian unsourced multiple access (UMA) channel in the presence of heterogeneous path-loss conditions. We consider a setting in which the path loss is known to the users, which enables the use of location-based codebook partitioning [Çakmak et al., 2025]. Through numerical simulations and a large-system analysis based on the replica method, we quantify the performance gain of this strategy relative to the conventional UMA approach in which all users employ a common codebook.

In many cases, federated learning (FL) has to take place in communication constrained scenarios, where we must select a small number of learning nodes to reduce bandwidth consumption. Furthermore, such nodes may also have computational constraints, i.e., they can store small datasets and process and perform as little data processing as possible. In this context, it is of paramount importance to make node selection decisions before the learning process begins, and without labeling information. We tackle this daunting task through a two-pronged approach, where we (i) introduce a new metric called loneliness, defined on unlabeled datasets, and (ii) propose a novel algorithm called Goldilocks to make node selection decisions and identify the data to be labeled. Through both a theoretical and an experimental analysis, we show that loneliness is strongly linked with learning performance (i.e., test accuracy). Furthermore, our performance evaluation, including three state-of-the-art datasets and a comparison against centralized learning, demonstrates that Goldilocks outperforms approaches based upon a balanced label distribution by providing over $70 \%$ accuracy improvement, in spite of being efficient to compute and not using labeling information.

We investigate accuracy and freshness of status updates from a large number of energy-harvesting devices that monitor two-state Markov processes and access the medium using slotted ALOHA without feedback. Using a Markovian framework, we analyze the average value of a generic state-dependent penalty function that grows whenever there is a state estimation error. The age of incorrect information (AoII) is an example of such penalty function. We propose an accurate and easy-to-compute approximation for the average penalty. Numerical results show the benefits of optimizing the transmission probabilities according to the process state transitions and current battery levels to minimize the average penalty. Minimizing a state-independent penalty function can be highly suboptimal when one of the process states is critical, i.e., entails a high penalty if wrongly estimated. Furthermore, minimizing the average penalty does not guarantee a low probability of misdetecting a critical state period.

In many scenarios of practical interest, labeled data from a target distribution are scarce while labeled data from a related source distribution are abundant. One particular setting of interest arises when the target label space is a subset of the source label space, leading to the framework of partial domain adaptation (PDA). Typical approaches to PDA involve minimizing a domain alignment term and a weighted empirical loss on the source data, with the aim of transferring knowledge between domains. However, a theoretical basis for this procedure is lacking, and in particular, most existing weighting schemes are heuristic. In this work, we derive generalization bounds for the PDA problem based on partial optimal transport. These bounds corroborate the use of the partial Wasserstein distance as a domain alignment term, and lead to theoretically motivated explicit expressions for the empirical source loss weights. Inspired by these bounds, we devise a practical algorithm for PDA, termed WARMPOT. Through extensive numerical experiments, we show that WARMPOT is competitive with recent approaches, and that our proposed weights improve on existing schemes.

We investigate a lossy source compression problem in which both the encoder and decoder are equipped with a pre-trained sequence predictor. We propose an online lossy compression scheme that, under a$0-1$loss distortion function, ensures a deterministic, per-sequence upper bound on the distortion (outage) level for any time instant. The outage guarantees apply irrespective of any assumption on the distribution of the sequences to be encoded or on the quality of the predictor at the encoder and decoder. The proposed method, referred to as online conformal compression (OCC), is built upon online conformal prediction-a novel method for constructing confidence intervals for arbitrary predictors. Numerical results show that OCC achieves a compression rate comparable to that of an idealized scheme in which the encoder, with hindsight, selects the optimal subset of symbols to describe to the decoder, while satisfying the overall outage constraint.

We derive an achievability bound to quantify the performance of a type-based unsourced multiple access system—an information-theoretic model for grant-free multiple access with correlated messages. The bound extends available achievability results for the per-user error probability in the unsourced multiple access framework, where, different from our setup, message collisions are treated as errors. Specifically, we provide an upper bound on the total variation distance between the type (i.e., the empirical probability mass function) of the transmitted messages and its estimate over a Gaussian multiple access channel. Through numerical simulations, we illustrate that our bound can be used to determine the message type that is less efficient to transmit, because more difficult to detect. We finally show that a practical scheme for type estimation, based on coded compressed sensing with approximate message passing, operates approximately 3 dB away from the bound, for the parameters considered in the paper.

Type-based unsourced multiple access (TUMA) is a recently proposed framework for type-based estimation in massive uncoordinated access networks. We extend the existing design of TUMA, developed for an additive white Gaussian channel, to a more realistic environment with fading and multiple antennas. Specifically, we consider a cell-free massive multipleinput multiple-output system and exploit spatial diversity to estimate the set of transmitted messages and the number of users transmitting each message. Our solution relies on a locationbased codeword partition and on the use at the receiver of a multisource approximate message passing algorithm in both centralized and distributed implementations. The proposed TUMA framework results in a robust and scalable architecture for massive machine-type communications.

Compared to the generations up to 4G, whose main focus was on broadband and coverage aspects, 5G has expanded the scope of wireless cellular systems toward embracing two new types of connectivity: massive machine-type communications (mMTCs) and ultrareliable low-latency communications (URLLCs). This article discusses the possible evolution of these two types of connectivity within the umbrella of 6G wireless systems. This article consists of three parts. The first part deals with the connectivity for a massive number of devices. While mMTC research in 5G predominantly focuses on the problem of uncoordinated access in the uplink for a large number of devices, the traffic patterns in 6G may become more symmetric, leading to closed-loop massive connectivity. One of the drivers for this type of traffic pattern is distributed/decentralized learning and inference. The second part of this article discusses the evolution of wireless connectivity for critical services. While latency and reliability are tightly coupled in 5G, 6G will support a variety of safety-critical control applications with different types of timing requirements, as evidenced by the emergence of metrics related to information freshness and information value. In addition, ensuring ultrahigh reliability for safety-critical control applications requires modeling and estimation of the tail statistics of the wireless channel, queue length, and delay. The fulfillment of these stringent requirements calls for the development of novel artificial intelligence (AI)-based techniques, incorporating optimization theory, explainable AI (XAI), generative AI, and digital twins (DTs). The third part analyzes the coexistence of massive connectivity and critical services. Specifically, we consider scenarios in which a massive number of devices need to support traffic patterns of mixed criticality. This is followed by a discussion about the management of wireless resources shared by services with different criticality.

We investigate the age of information (AoI) in a scenario where energy-harvesting devices send status updates to a gateway following the slotted ALOHA protocol and receive no feedback. We let the devices adjust the transmission probabilities based on their current battery level. Using a Markovian approach, we derive analytically the average AoI. We further provide an approximate analysis for accurate and easy-to-compute approximations of both the average AoI and the age-violation probability (AVP), i.e., the probability that the AoI exceeds a given threshold. We also analyze the average throughput. Via numerical results, we investigate two baseline strategies: transmit a new update whenever possible to exploit every opportunity to reduce the AoI, and transmit only when sufficient energy is available to increase the chance of successful decoding. The two strategies are beneficial for low and high update-generation rates, respectively. We show that an optimized policy that balances the two strategies outperforms them significantly in terms of both AoI metrics and throughput. Finally, we show the benefit of decoding multiple packets in a slot using successive interference cancellation and adapting the transmission probability based on both the current battery level and the time elapsed since the last transmission.

We analyze the trade-off between the undetected error probability (i.e., the probability that the channel decoder outputs an erroneous message without detecting the error) and the total error probability in the short blocklength regime. We address the problem by developing two new finite blocklength achievability bounds, which we use to benchmark the performance of two coding schemes based on polar codes with outer cyclic redundancy check (CRC) codes—also referred to as CRC-aided (CA) polar codes. The first bound is obtained by considering an outer detection code, whereas the second bound relies on a threshold test applied to the generalized information density. Similarly, in the first CA polar code scheme, we reserve a fraction of the outer CRC parity bits for error detection, whereas in the second scheme, we apply a threshold test (specifically, Forney’s optimal rule) to the output of the successive cancellation list decoder. Numerical simulations performed on the binary-input AWGN channel reveal that, in the short-blocklength regime, the threshold-based approach is superior to the CRC-based approach, both in terms of bounds and performance of CA polar code schemes. We also consider the case of decoding with noisy channel-state information, which leads to a mismatched decoding setting. Our results illustrate that, differently from the previous case, in this scenario, the CRC-based approach outperforms the threshold-based approach, which is more sensitive to the mismatch.

We propose a framework to evaluate the random coding union bound with parameter$s$(RCUs) on the achievable error probability in the finite-blocklength regime for a pilot-assisted transmission scheme operating over an imperfectly synchronized and memoryless block-fading waveform channel. Unlike previous results, which disregard the effects of imperfect synchronization, our framework utilizes pilots for both synchronization and channel estimation. Additionally, we utilize the saddlepoint approximation to provide a numerically efficient method for evaluating the RCUs bound in this scenario. Our numerical experiments verify the accuracy of the proposed approximation. Moreover, when transmission blocks are received synchronously, numerical results indicate that the number of pilot symbols needed to estimate the fading channel gains to the level of accuracy required in ultra-reliable low-latency communication is also sufficient to acquire sufficiently good synchronization. However, when the blocks are received asynchronously, there can be a significant SNR penalty compared to the synchronous case.

We analyze the uplink performance of a distributed massive multiple-input multiple-output (MIMO) architecture in which the remotely located access points (APs) are connected to a central processing unit via a fiber-optical fronthaul carrying a dithered and 1-bit quantized version of the received radio-frequency (RF) signal. The innovative feature of the proposed architecture is that no down-conversion is performed at the APs. This eliminates the need to equip the APs with local oscillators, which may be difficult to synchronize. Under the assumption that a constraint is imposed on the amount of data that can be exchanged across the fiber-optical fronthaul, we investigate the tradeoff between spatial oversampling, defined in terms of the total number of APs, and temporal oversampling, defined in terms of the oversampling factor selected at the central processing unit, to facilitate the recovery of the transmitted signal from 1-bit samples of the RF received signal. Using the so-called error-vector magnitude (EVM) as performance metric, we shed light on the optimal design of the dither signal, and quantify, for a given number of APs, the minimum fronthaul rate required for our proposed distributed massive MIMO architecture to outperform a standard co-located massive MIMO architecture in terms of EVM.

We investigate the coexistence of massive and critical Internet of Things (IoT) services in the context of the unsourced multiple access (UMA) framework introduced by Polyanskiy (2017), where all users employ a common codebook and the receiver returns an unordered list of decoded codewords. This setup is suitably modified to introduce heterogeneous traffic. Specifically, to model the massive IoT service, we assume that a standard message originates independently from each IoT device as in the standard UMA setup. To model the critical IoT service, we assume the generation of alarm messages that are common for all devices. This setup requires a significant redefinition of the error events, i.e., misdetections and false positives. We further assume that the number of active users in each transmission attempt is random and unknown. We derive a random-coding achievability bound on the misdetection and false positive probabilities of both standard and alarm messages on the Gaussian multiple access channel. Using our bound, we demonstrate that orthogonal network slicing enables massive and critical IoT to coexist under the requirement of high energy efficiency. On the contrary, we show that nonorthogonal network slicing is energy inefficient due to the residual interference from the alarm signal when decoding the standard messages.

We propose a framework to evaluate the so-called random-coding union bound with parameter s (RCUs) on the achievable error probability in the finite-blocklength regime for a pilot-assisted transmission scheme operating over an imperfectly synchronized and memoryless block-fading waveform channel. Unlike previous results, which disregard the effects of imperfect synchronization, our framework utilizes pilots for both synchronization and channel estimation. Specifically, we provide an algorithm to perform joint synchronization and channel estimation, and verify its accuracy by observing its tightness in comparison with the Cramer-Rao bound. Then, we develop an RCUs bound on the error probability, which applies for a receiver that treats the estimates provided by the algorithm as accurate. Additionally, we utilize the saddlepoint approximation to provide a numerically efficient method for evaluating the RCUs bound in this scenario. Our numerical experiments verify the accuracy of the proposed approximation. Moreover, when the delays are modeled as fully dependent across fading blocks, numerical results indicate that the number of pilot symbols needed to estimate the fading channel gains to the level of accuracy required in ultra-reliable low-latency communication is also sufficient to acquire sufficiently good synchronization. However, when the delays are modeled as independent across blocks, synchronization becomes the bottleneck for the system performance.

We examine the age of information (AoI) of a status update system that incorporates energy harvesting and uses the slotted ALOHA protocol. We derive analytically the average AoI and the probability that the AoI exceeds a given threshold. Via numerical results, we investigate two strategies to minimize the age of information (AoI): transmitting a new update whenever possible to exploit every chance to reduce the AoI, and transmitting only when sufficient energy is available to increase the chance of successful delivery. The two strategies are beneficial for low and high update generation rates, respectively. However, an optimized approach that balances the two strategies outperforms them significantly in terms of both AoI and throughput.

We propose an irregular repetition slotted ALOHA (IRSA) based random-access protocol for the binary adder channel (BAC). The BAC captures important physical-layer concepts, such as packet generation, per-slot decoding, and information rate, which are neglected in the commonly considered collision channel model. We divide a frame into slots and let users generate a packet, to be transmitted over a slot, from a given codebook. In a state-of-the-art scheme proposed by Paolini et al. (2022), the codebook is constructed as the parity-check matrix of a BCH code. Here, we construct the codebook from independent and identically distributed binary symbols to obtain a random-coding achievability bound. Our per-slot decoder progressively discards incompatible codewords from a list of candidate codewords, and can be improved by shrinking this list across iterations. In a regime of practical interests, our scheme can resolve more colliding users in a slot and thus achieves a higher average sum rate than the scheme in Paolini et al. (2022).

We propose a numerically efficient method for evaluating the random-coding union bound with parameter$s$on the error probability achievable in the finite-blocklength regime by a pilot-assisted transmission scheme employing Gaussian codebooks and operating over a memoryless block-fading channel. Our method relies on the saddlepoint approximation, which, differently from previous results reported for similar scenarios, is performed with respect to the number of fading blocks (a.k.a. diversity branches) spanned by each codeword, instead of the number of channel uses per block. This different approach avoids a costly numerical averaging of the error probability over the realizations of the fading process and of its pilot-based estimate at the receiver and results in a significant reduction of the number of channel realizations required to estimate the error probability accurately. Our numerical experiments for both single-antenna communication links and massive multiple-input multiple-output (MIMO) networks show that, when two or more diversity branches are available, the error probability can be estimated accurately with the saddlepoint approximation with respect to the number of fading blocks using a numerical method that requires about two orders of magnitude fewer Monte-Carlo samples than with the saddlepoint approximation with respect to the number of channel uses per block.

We study the dynamic behavior of frameless ALOHA, both in terms of throughput and age of information (AoI). In particular, differently from previous studies, our analysis accounts for the fact that the number of terminals contending the channel may vary over time, as a function of the duration of the previous contention period. The stability of the protocol is analyzed via a drift analysis, which allows us to determine the presence of stable and unstable equilibrium points. We also provide an exact characterization of the AoI performance, through which we determine the impact of some key protocol parameters, such as the maximum length of the contention period, on the average AoI. Specifically, we show that configurations of parameters that maximize the throughput may result in a degradation of the AoI performance.

To account for the massive uncoordinated random access scenario, which is relevant for the Internet of Things, Polyanskiy et al. (2017) proposed a novel formulation of the multiple-access problem, commonly referred to as unsourced multiple access, where all users employ a common codebook and the receiver decodes up to a permutation of the messages. In this paper, we extend this seminal work to the case where the number of active users is random and unknowna priori. We define a random-access code accounting for both misdetection (MD) and false alarm (FA), and derive a random-coding achievability bound for the Gaussian multiple access channel. Our bound captures the fundamental trade-off between MD and FA probabilities. It suggests that the lack of knowledge of the number of active users entails a small penalty in energy efficiency when the target MD and FA probabilities are high. However, as the target MD and FA probabilities decrease, the energy efficiency penalty becomes more significant. For example, in a typical IoT scenario with framelength 19200 complex channel uses and 25–300 active users in average, the required energy per bit to achieve both MD and FA probabilities below$10^{-1}$, predicted by our bound, is only 0.5–0.7 dB higher than that predicted by the bound in Polyanskiy et al. (2017) for a known number of active users. This gap increases to 3–4 dB when the target MD probability and/or FA probability is below$10^{-3}$. Taking both MD and FA into account, we use our bound to benchmark the energy efficiency of slotted-ALOHA with multi-packet reception, of a decoder that simply treats interference as noise, and of some recently proposed unsourced multiple access schemes. Numerical results suggest that, when the target MD and FA probabilities are high, it is effective to estimate the number of active users, then treat this estimate as the true value, and use a coding scheme that performs well for the case of known number of active users. However, this approach becomes energy inefficient when the requirements on MD and FA probabilities are stringent.

We present a general framework for the characterization of the packet error probability achievable in cell-free Massive multiple-input multiple output (MIMO) architectures deployed to support ultra-reliable low-latency (URLLC) traffic. The framework is general and encompasses both centralized and distributed cell-free architectures, arbitrary fading channels and channel estimation algorithms at both network and user-equipment (UE) sides, as well as arbitrary combining and precoding schemes. The framework is used to perform numerical experiments on specific scenarios, which illustrate the superiority of cell-free architectures compared to cellular architectures in supporting URLLC traffic in uplink and downlink. Also, these numerical experiments provide the following insights into the design of cell-free architectures for URLLC:${i}$) minimum mean square error (MMSE) spatial processing must be used to achieve the URLLC targets; ii) for a given total number of antennas per coverage area, centralized cell-free solutions involving single-antenna access points (APs) offer the best performance in the uplink, thereby highlighting the importance of reducing the average distance between APs and UEs in the URLLC regime; iii) this observation applies also to the downlink, provided that the APs transmit precoded pilots to allow the UEs to estimate accurately the precoded channel.

We present a new family of information-theoretic generalization bounds, in which the training loss and the population loss are compared through a jointly convex function. This function is upper-bounded in terms of the disintegrated, samplewise, evaluated conditional mutual information (CMI), an information measure that depends on the losses incurred by the selected hypothesis, rather than on the hypothesis itself, as is common in probably approximately correct (PAC)-Bayesian results. We demonstrate the generality of this framework by recovering and extending previously known information-theoretic bounds. Furthermore, using the evaluated CMI, we derive a samplewise, average version of Seeger's PAC-Bayesian bound, where the convex function is the binary KL divergence. In some scenarios, this novel bound results in a tighter characterization of the population loss of deep neural networks than previous bounds. Finally, we derive high-probability versions of some of these average bounds. We demonstrate the unifying nature of the evaluated CMI bounds by using them to recover average and high-probability generalization bounds for multiclass classification with finite Natarajan dimension.

Recent work has established that the conditional mutual information (CMI) framework of Steinke and Zakynthinou (2020) is expressive enough to capture generalization guarantees in terms of algorithmic stability, VC dimension, and related complexity measures for conventional learning (Harutyunyan et al., 2021, Haghifam et al., 2021). Hence, it provides a unified method for establishing generalization bounds. In meta learning, there has so far been a divide between information-theoretic results and results from classical learning theory. In this work, we take a first step toward bridging this divide. Specifically, we present novel generalization bounds for meta learning in terms of the evaluated CMI (e-CMI). To demonstrate the expressiveness of the e-CMI framework, we apply our bounds to a representation learning setting, with $n$ samples from $\hat n$ tasks parameterized by functions of the form $f_i \circ h$. Here, each $f_i \in \mathcal F$ is a task-specific function, and $h \in \mathcal H$ is the shared representation. For this setup, we show that the e-CMI framework yields a bound that scales as $\sqrt{ \mathcal C(\mathcal H)/(n\hat n) + \mathcal C(\mathcal F)/n} $, where $\mathcal C(\cdot)$ denotes a complexity measure of the hypothesis class. This scaling behavior coincides with the one reported in Tripuraneni et al. (2020) using Gaussian complexity.

Large amounts of data are collected by IoT devices, and transmitted wirelessly to cloud servers for aggregation. These data are often sensitive and need to remain secret. Moreover, the employed servers might be untrustworthy, and maliciously alter their results. To address this, public verifiability must be provided, i.e., anyone can check the result's correctness. Nevertheless, any such protocol must also cope with the limited battery capacity of the IoT devices.

Meta-learning automatically infers an inductive bias by observing data from a number of related tasks. The inductive bias is encoded by hyperparameters that determine aspects of the model class or training algorithm, such as initialization or learning rate. Meta-learning assumes that the learning tasks belong to a task environment, and that tasks are drawn from the same task environment both during meta-training and meta-testing. This, however, may not hold true in practice. In this paper, we introduce the problem of transfer meta-learning, in which tasks are drawn from a target task environment during meta-testing that may differ from the source task environment observed during meta-training. Novel information-theoretic upper bounds are obtained on the transfer meta-generalization gap, which measures the difference between the meta-training loss, available at the meta-learner, and the average loss on meta-test data from a new, randomly selected, task in the target task environment. The first bound, on the average transfer meta-generalization gap, captures the meta-environment shift between source and target task environments via the KL divergence between source and target data distributions. The second, PAC-Bayesian bound, and the third, single-draw bound, account for this shift via the log-likelihood ratio between source and target task distributions. Furthermore, two transfer meta-learning solutions are introduced. For the first, termed Empirical Meta-Risk Minimization (EMRM), we derive bounds on the average optimality gap. The second, referred to as Information Meta-Risk Minimization (IMRM), is obtained by minimizing the PAC-Bayesian bound. IMRM is shown via experiments to potentially outperform EMRM.

We consider a communication problem in which the receiver must first detect the presence of an information packet and, if detected, decode the message carried within it. We present general nonasymptotic upper and lower bounds on the maximum coding rate that depend on the blocklength, the probability of false alarm, the probability of misdetection, and the packet er-ror probability. The bounds, which are expressed in terms of binary-hypothesis-testing performance metrics, generalize finite-blocklength bounds derived previously for the scenario when a genie informs the receiver whether a packet is present. The bounds apply to detection performed either jointly with decoding on the entire data packet, or separately on a dedicated preamble. The results presented in this paper can be used to determine the block-length values at which the performance of a communication system is limited by its ability to perform packet detection satisfacto-rily, and to assess the difference in performance between preamble-based detection, and joint detection and decoding. Numerical re-sults pertaining to the binary-input AWGN channel are provided.

This paper presents a rigorous finite-blocklength framework for the characterization and the numerical evaluation of the packet error probability achievable in the uplink and downlink of Massive MIMO for ultra-reliable low-latency communications (URLLC). The framework encompasses imperfect channel-state information, pilot contamination, spatially correlated channels, and arbitrary linear signal processing. For a practical URLLC network setup involving base stations with M = 100 antennas, we show by means of numerical results that a target error probability of 10−5can be achieved with MMSE channel estimation and multicell MMSE signal processing, uniformly over each cell, only if orthogonal pilot sequences are assigned to all the users in the network. For the same setting, an alternative solution with lower computational complexity, based on least-squares channel estimation and regularized zero-forcing signal processing, does not suffice unless M is increased significantly.

We present a framework to derive bounds on the test loss of randomized learning algorithms for the case of bounded loss functions. Drawing from Steinke & Zakynthinou (2020), this framework leads to bounds that depend on the conditional information density between the output hypothesis and the choice of the training set, given a larger set of data samples from which the training set is formed. Furthermore, the bounds pertain to the average test loss as well as to its tail probability, both for the PAC-Bayesian and the single-draw settings. If the conditional information density is bounded uniformly in the size$n$of the training set, our bounds decay as 1/n, This is in contrast with the tail bounds involving conditional information measures available in the literature, which have a less benign 1/√n dependence. We demonstrate the usefulness of our tail bounds by showing that they lead to nonvacuous estimates of the test loss achievable with some neural network architectures trained on MNIST and Fashion-MNIST.

We extend the seminal work by Polyanskiy (2017) on massive uncoordinated access to the case where the number of active users is random and unknown a priori. We define a random-access code accounting for both misdetection (MD) and false-alarm (FA), and derive a random-coding achievability bound for the Gaussian multiple access channel. Our bound captures the fundamental trade-off between MD and FA probabilities. It suggests that lack of knowledge of the number of active users entails a small penalty in power efficiency. For a typical scenario, to achieve both MD and FA probabilities below 0.1, the required energy per bit predicted by our bound is 0.5–0.7 dB higher than that predicted by the bound in Polyanskiy (2017) for a known number of active users. Taking both MD and FA into account, we use our bound to benchmark the energy efficiency of some recently proposed massive random access schemes.

Meta-learning optimizes an inductive bias—typically in the form of the hyperparameters of a base-learning algorithm—by observing data from a finite number of related tasks. This paper presents an information-theoretic bound on the generalization performance of any given meta-learner, which builds on the conditional mutual information (CMI) framework of Steinke and Zakynthinou (2020). In the proposed extension to meta-learning, the CMI bound involves a training meta-supersample obtained by first sampling 2N independent tasks from the task environment, and then drawing 2M independent training samples for each sampled task. The meta-training data fed to the meta-learner is modelled as being obtained by randomly selecting N tasks from the available 2N tasks and M training samples per task from the available 2M training samples per task. The resulting bound is explicit in two CMI terms, which measure the information that the meta-learner output and the base-learner output provide about which training data are selected, given the entire meta-supersample. Finally, we present a numerical example that illustrates the merits of the proposed bound in comparison to prior information-theoretic bounds for meta-learning.

We present an upper bound on the error probability achievable using variable-length stop feedback (VLSF) codes, for a fixed size of the information payload and a given constraint on the maximum latency and the average service time. Differently from the bound proposed in Polyanskiy et al. (2011), which pertains to the scenario in which the stop signal is sent over a noiseless feedback channel, our bound applies to the practically relevant setup in which the feedback link is noisy. Numerical evaluation of our bound suggests that, for fixed latency and reliability constraints, noise in the feedback link may increase the minimum average service time for the VLSF scheme considered in this paper, to the extent that fixed-length codes without feedback may be preferable in some scenarios.

The fast adoption of Massive MIMO for high-throughput communications was enabled by many research contributions mostly relying on infinite-blocklength information-theoretic bounds. This makes it hard to assess the suitability of Massive MIMO for ultra-reliable low-latency communications (URLLC) operating with short-blocklength codes. This paper provides a rigorous framework for the characterization and numerical evaluation (using the saddlepoint approximation) of the error probability achievable in the uplink and downlink of Massive MIMO at finite blocklength. The framework encompasses imperfect channel state information, pilot contamination, spatially correlated channels, and arbitrary linear spatial processing. In line with previous results based on infinite-blocklength bounds, we prove that, with minimum mean-square error (MMSE) processing and spatially correlated channels, the error probability at finite blocklength goes to zero as the number$M$of antennas grows to infinity, even under pilot contamination. However, numerical results for a practical URLLC network setup involving a base station with$M=100$antennas, show that a target error probability of 10−5can be achieved with MMSE processing, uniformly over each cell, only if orthogonal pilot sequences are assigned to all the users in the network. Maximum ratio processing does not suffice.

Nxt-generation wireless systems are expected to combine millimeter-wave (mmWave) and massive multi-user multiple-input multiple-output (MU-MIMO) technologies to deliver high data-rates. These technologies require the basestations (BSs) to process high-dimensional data at extreme rates, which results in high power dissipation and system costs. Finite-alphabet equalization has been proposed recently to reduce the power consumption and silicon area of uplink spatial equalization circuitry at the BS by coarsely quantizing the equalization matrix. In this work, we improve upon finite-alphabet equalization by performing unbiased estimation and soft-output computation for coded systems. By simulating a massive MU-MIMO system that uses orthogonal frequency-division multiplexing and per-user convolutional coding, we show that soft-output finite-alphabet equalization delivers competitive error-rate performance using only 1 to 3 bits per entry of the equalization matrix, even for challenging mmWave channels.

We present a general approach to deriving bounds on the generalization error of randomized learning algorithms. Our approach can be used to obtain bounds on the average generalization error as well as bounds on its tail probabilities, both for the case in which a new hypothesis is randomly generated every time the algorithm is used-as often assumed in the probably approximately correct (PAC)-Bayesian literature-and in the single-draw case, where the hypothesis is extracted only once.For this last scenario, we present a novel bound that is explicit in the central moments of the information density. The bound reveals that the higher the order of the information density moment that can be controlled, the milder the dependence of the generalization bound on the desired confidence level.Furthermore, we use tools from binary hypothesis testing to derive a second bound, which is explicit in the tail of the information density. This bound confirms that a fast decay of the tail of the information density yields a more favorable dependence of the generalization bound on the confidence level.

We propose finite-alphabet equalization, a new paradigm that restricts the entries of the spatial equalization matrix to low-resolution numbers, enabling high-throughput, low-power, and low-cost hardware equalizers. To minimize the performance loss of this paradigm, we introduce FAME, short for finite-alphabet minimum mean-square error (MMSE) equalization, which is able to significantly outperform a naïve quantization of the linear MMSE matrix. We develop efficient algorithms to approximately solve the NP-hard FAME problem and showcase that near-optimal performance can be achieved with equalization coefficients quantized to only 1-3 bits for massive multi-user multiple-input multiple-output (MU-MIMO) millimeter-wave (mmWave) systems. We provide very-large scale integration (VLSI) results that demonstrate a reduction in equalization power and area by at least a factor of 3.9× and 5.8×, respectively.

This article concerns the maximum coding rate at which data can be transmitted over a noncoherent, single-antenna, Rayleigh block-fading channel using an error-correcting code of a given blocklength with a block-error probability not exceeding a given value. A high-SNR normal approximation of the maximum coding rate is presented that becomes accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals L over which we code tend to infinity. Numerical analyses suggest that the approximation is accurate at SNR values above 15dB and when the number of coherence intervals is 10 or more.

In recent years, the derivation of nonasymptotic converse and achievability bounds on the maximum coding rate as a function of the error probability and blocklength has gained attention in the information theory literature. While these bounds are accurate for many scenarios of interest, they need to be evaluated numerically for most wireless channels of practical interest, and their evaluation is computationally demanding. This paper presents saddlepoint approximations of state-of-the-art converse and achievability bounds for noncoherent, single-antenna, Rayleigh block-fading channels. These approximations can be calculated efficiently and are shown to be accurate for SNR values as small as 0 dB and blocklengths of 168 channel uses or more.

This paper presents saddlepoint approximations of state-of-the-art converse and achievability bounds for noncoherent, single-antenna, Rayleigh block-fading channels. These approximations can be calculated efficiently and are shown to be accurate for SNR values as small as 0 dB, blocklengths of 168 channel uses or more, and when the channel's coherence interval is not smaller than two. It is demonstrated that the derived approximations recover both the normal approximation and the reliability function of the channel.

We present an upper bound on the error probability achievable using variable-length stop-feedback codes, for a fixed size of the information payload and a given constraint on both the average and the maximum latency. Differently from the bound proposed in Polyanskiy et at. (2011), which pertains to the scenario in which the stop signal is sent over a noiseless feedback channel, our bound applies to the practically relevant scenario in which the feedback link is noisy. Through numerical results, we illustrate that, in scenarios in which the desired average latency is small, noise in the feedback link can deteriorate the performance of variable-length stop-feedback codes to the extent that it becomes inferior to that of fixed-length codes without feedback.

This paper investigates the probability that the delay and the peak-age of information exceed a desired threshold in a point-to-point communication system with short information packets. The packets are generated according to a stationary memoryless Bernoulli process, placed in a single-server queue and then transmitted over a wireless channel. A variable-length stop-feedback coding scheme-a general strategy that encompasses simple automatic repetition request (ARQ) and more sophisticated hybrid ARQ techniques as special cases-is used by the transmitter to convey the information packets to the receiver. By leveraging finite-blocklength results, the delay violation and the peak-age violation probabilities are characterized without resorting to approximations based on larg-deviation theory as in previous literature. Numerical results illuminate the dependence of delay and peak-age violation probability on system parameters such as the frame size and the undetected error probability, and on the chosen packet-management policy. The guidelines provided by our analysis are particularly useful for the design of low-latency ultra-reliable communication systems.

We present nonasymptotic upper and lower bounds on the maximum coding rate achievable when transmitting short packets over a Rician memoryless block-fading channel for a given requirement on the packet error probability. We focus on the practically relevant scenario in which there is no a priori channel state information available at the transmitter or at the receiver. An upper bound built upon the min-max converse is compared with two lower bounds: the first one relies on a noncoherent transmission strategy in which the fading channel is not estimated explicitly at the receiver and the second one employs pilot-assisted transmission (PAT) followed by maximum-likelihood channel estimation and scaled mismatched nearest-neighbor decoding at the receiver. Our bounds are tight enough to unveil the optimum number of diversity branches that a packet should span so that the energy per bit required to achieve a target packet error probability is minimized, for a given constraint on the code rate and the packet size. Furthermore, the bounds reveal that noncoherent transmission is more energy efficient than PAT, even when the number of pilot symbols and their power is optimized. For example, in Rayleigh fading, for the case when a coded packet of 168 symbols is transmitted using a channel code of rate 0.48-bits/channel use, over a block-fading channel with block size equal to eight symbols, PAT requires an additional 1.2 dB of energy per information bit to achieve a packet error probability of 10-3compared with a suitably designed noncoherent transmission scheme. Finally, we devise a PAT scheme based on punctured tail-biting quasi-cyclic codes and ordered-statistics decoding, whose performance is close (1-dB gap at 10-3packet error probability) to the ones predicted by our PAT lower bound. This shows that the PAT lower bound provides useful guidelines on the design of actual PAT schemes.

We consider the downlink of a massive multiuser (MU) multiple-input multiple-output (MIMO) system in which the base station (BS) is equipped with low-resolution digital-to-analog converters (DACs). In contrast to most existing results, we assume that the system operates over a frequency-selective wideband channel and uses orthogonal frequency division multiplexing (OFDM) to simplify equalization at the user equipments (UEs). Furthermore, we consider the practically relevant case of oversampling DACs. We theoretically analyze the uncoded bit error rate (BER) performance with linear precoders (e.g., zero forcing) and quadrature phase-shift keying using Bussgang's theorem. We also develop a lower bound on the information-theoretic sum-rate throughput achievable with Gaussian inputs, which can be evaluated in closed form for the case of 1-bit DACs. For the case of multi-bit DACs, we derive approximate, yet accurate, expressions for the distortion caused by low-precision DACs, which can be used to establish the lower bounds on the corresponding sum-rate throughput. Our results demonstrate that, for a massive MU-MIMO-OFDM system with a 128-antenna BS serving 16 UEs, only 3-4 DAC bits are required to achieve an uncoded BER of 10-4with a negligible performance loss compared to the infinite-resolution case at the cost of additional out-of-band emissions. Furthermore, our results highlight the importance of considering the inherent spatial and temporal correlations caused by low-precision DACs.

In this paper, we solve the sum mean-squared error (MSE)-optimal 1-bit quantized precoding problem exactly for small-to-moderate sized multiuser multiple-input multiple-output (MU-MIMO) systems via branch and bound. To this end, we reformulate the original NP-hard precoding problem as a tree search and deploy a number of strategies that improve the pruning efficiency without sacrificing optimality. We evaluate the error-rate performance and the complexity of the resulting 1-bit branch-and-bound (BB-1) precoder, and compare its efficacy to that of existing, suboptimal algorithms for 1-bit precoding in MU-MIMO systems.

Fifth-generation (5G) cellular systems will build on massive multi-user (MU) multiple-input multiple-output (MIMO) technology to attain high spectral efficiency. However, having hundreds of antennas and radio-frequency (RF) chains at the base station (BS) entails prohibitively high hardware costs and power consumption. This paper proposes a novel nonlinear precoding algorithm for the massive MU-MIMO downlink in which each RF chain contains an 8-phase (3-bit) constant-modulus transmitter, enabling the use of low-cost and power-efficient analog hardware. We present a high-throughput VLSI architecture and show implementation results on a Xilinx Virtex-7 FPGA. Compared to a recently-reported nonlinear precoder for BS designs that use two 1-bit digital-to-analog converters per RF chain, our design enables up to 3.75 dB transmit power reduction at no more than a 2.7× increase in FPGA resources.

This paper investigates the distribution of delay and peak age of information in a communication system where packets, generated according to an independent and identically distributed Bernoulli process, are placed in a single-server queue with first-come first-served discipline and transmitted over an additive white Gaussian noise (AWGN) channel. When a packet is correctly decoded, the sender receives an instantaneous error-free positive acknowledgment, upon which it removes the packet from the buffer. In the case of negative acknowledgment, the packet is retransmitted. By leveraging finite-blocklength results for the AWGN channel, we characterize the delay violation and the peak-age violation probability without resorting to approximations based on large deviation theory as in previous literature. Our analysis reveals that there exists an optimum blocklength that minimizes the delay violation and the peak-age violation probabilities. We also show that one can find two blocklength values that result in very similar average delay but significantly different delay violation probabilities. This highlights the importance of focusing on violation probabilities rather than on averages.

It is well known that matched filtering and sampling (MFS) demodulation together with minimum Euclidean distance (MD) detection constitute the optimal receiver for the additive white Gaussian noise channel. However, for a general nonlinear transmission medium, MFS does not provide sufficient statistics, and, therefore, is suboptimal. Nonetheless, this receiver is widely used in optical systems, where the Kerr nonlinearity is the dominant impairment at high powers. In this paper, we consider a suite of receivers for a two-user channel subject to a type of nonlinear interference that occurs in wavelength-division-multiplexed channels. The asymptotes of the symbol error rate (SER) of the considered receivers at high powers are derived or bounded analytically. Moreover, Monte-Carlo simulations are conducted to evaluate the SER for all the receivers. Our results show that receivers that are based on MFS cannot achieve arbitrary low SERs, whereas the SER goes to zero as the power grows for the optimal receiver. Furthermore, we devise a heuristic demodulator, which together with the MD detector yields a receiver that is simpler than the optimal one and can achieve arbitrary low SERs. The SER performance of the proposed receivers is also evaluated for some single-span fiber-optical channels via split-step Fourier simulations.

It is well known that the mutual information between two random variables can be expressed as the difference of two relative entropies that depend on an auxiliary distribution, a relation sometimes referred to as the golden formula. This paper is concerned with a finite-blocklength extension of this relation. This extension consists of two elements: 1) a finiteblocklength channel-coding converse bound by Polyanskiy and Verdú, which involves the ratio of two Neyman-Pearson β functions (beta-beta converse bound); and 2) a novel beta-beta channel-coding achievability bound, expressed again as the ratio of two Neyman-Pearson β functions. To demonstrate the usefulness of this finite-blocklength extension of the golden formula, the beta-beta achievability and converse bounds are used to obtain a finite-blocklength extension of Verdú's wideband-slope approximation. The proof parallels the derivation of the latter, with the beta-beta bounds used in place of the golden formula. The beta-beta (achievability) bound is also shown to be useful in cases where the capacity-achieving output distribution is not a product distribution due to, e.g., a cost constraint or structural constraints on the codebook, such as orthogonality or constant composition. As an example, the bound is used to characterize the channel dispersion of the additive exponential-noise channel and to obtain a finite-blocklength achievability bound (the tightest to date) for multiple-input multiple-output Rayleigh-fading channels with perfect channel state information at the receiver.

We investigate the maximum coding rate for a given average blocklength and error probability over a K-user discrete memoryless broadcast channel for the scenario where a common message is transmitted using variable-length stop-feedback codes. For the point-to-point case, Polyanskiy et al. (2011) demonstrated that variable-length coding combined with stop-feedback significantly increases the speed of convergence of the maximum coding rate to capacity. This speed-up manifests itself in the absence of a square-root penalty in the asymptotic expansion of the maximum coding rate for large blocklengths, i.e., zero dispersion. In this paper, we present nonasymptotic achievability and converse bounds on the maximum coding rate of the common-message K-user discrete memoryless broadcast channel, which strengthen and generalize the ones reported in Trillingsgaard et al. (2015) for the two-user case. An asymptotic analysis of these bounds reveals that zero dispersion cannot be achieved for certain common-message broadcast channels (e.g., the binary symmetric broadcast channel). Furthermore, we identify conditions under which our converse and achievability bounds are tight up to the second order. Through numerical evaluations, we illustrate that our second-order expansions approximate accurately the maximum coding rate and that the speed of convergence to capacity is indeed slower than for the point-to-point case.

We investigate the maximum coding rate achievable on a two-user broadcast channel for the case where a common message is transmitted with feedback using either fixed-blocklength codes or variable-length codes. For the fixed-blocklength-code setup, we establish nonasymptotic converse and achievability bounds. An asymptotic analysis of these bounds reveals that feedback improves the second-order term compared to the no-feedback case. In particular, for a certain class of antisymmetric broadcast channels, we show that the dispersion is halved. For the variable-length-code setup, we demonstrate that the channel dispersion is zero.

Massive multiuser (MU) multiple-input multiple- output (MIMO) is foreseen to be a key technology in future wireless communication systems. In this paper, we analyze the downlink performance of an orthogonal frequency division multiplexing (OFDM)-based massive MU-MIMO system in which the base station (BS) is equipped with 1-bit digital-to-analog converters (DACs). Using Bussgang's theorem, we characterize the performance achievable with linear precoders (such as maximal-ratio transmission and zero forcing) in terms of bit error rate (BER). Our analysis accounts for the possibility of oversampling the time-domain transmit signal before the DACs. We further develop a lower bound on the information-theoretic sum-rate throughput achievable with Gaussian inputs. Our results suggest that the performance achievable with 1-bit DACs in a massive MU-MIMO- OFDM downlink are satisfactory provided that the number of BS antennas is sufficiently large.

This paper concerns the maximal achievable rate at which data can be transmitted over a non-coherent, single-antenna, Rayleigh block-fading channel using an error-correcting code of a given blocklength with a block-error probability not exceeding a given value. In particular, a high-SNR normal approximation of the maximal achievable rate is presented that becomes accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals L over which we code tend to infinity. Numerical analyses suggest that the approximation is accurate already at SNR values of 15 dB.

We investigate the maximum coding rate achievable on a two-user broadcast channel for the case where a common-message is transmitted using fixed-blocklength codes with feedback. Specifically, we focus on a family of broadcast channels composed of two antisymmetric Z-channels. For this setup, we obtain matching upper and lower bounds on the dispersion term in the asymptotic expansion of the maximum coding rate. These bounds reveal that the dispersion is halved compared to the no-feedback case.

Massive multiuser (MU) multiple-input multiple-output (MIMO) is foreseen to be one of the key technologies in fifth-generation wireless communication systems. In this paper, we investigate the problem of downlink precoding for a narrowband massive MU-MIMO system with low-resolution digital-to-analog converters (DACs) at the base station (BS). We analyze the performance of linear precoders, such as maximal-ratio transmission and zero-forcing, subject to coarse quantization. Using Bussgang's theorem, we derive a closed-form approximation on the rate achievable under such coarse quantization. Our results reveal that the performance attainable with infinite-resolution DACs can be approached using DACs having only 3-4 bits of resolution, depending on the number of BS antennas and the number of user equipments (UEs). For the case of 1-bit DACs, we also propose novel nonlinear precoding algorithms that significantly outperform linear precoders at the cost of an increased computational complexity. Specifically, we show that nonlinear precoding incurs only a 3 dB penalty compared with the infinite-resolution case for an uncoded bit-error rate of 10-3, in a system with 128 BS antennas that uses 1-bit DACs and serves 16 single-antenna UEs. In contrast, the penalty for linear precoders is about 8dB.

We investigate the uplink throughput achievable by a multiple-user (MU) massive multiple-input multiple-output (MIMO) system, in which the base station is equipped with a large number of low-resolution analog-to-digital converters (ADCs). Our focus is on the case where neither the transmitter nor the receiver have any a priori channel state information. This implies that the fading realizations have to be learned through pilot transmission followed by channel estimation at the receiver, based on coarsely quantized observations. We propose a novel channel estimator, based on Bussgang's decomposition, and a novel approximation to the rate achievable with finite-resolution ADCs, both for the case of finite-cardinality constellations and of Gaussian inputs, that is accurate for a broad range of system parameters. Through numerical results, we illustrate that, for the 1-bit quantized case, pilot-based channel estimation together with maximal-ratio combing, or zero-forcing detection enables reliable multi-user communication with high-order constellations, in spite of the severe nonlinearity introduced by the ADCs. Furthermore, we show that the rate achievable in the infinite-resolution (no quantization) case can be approached using ADCs with only a few bits of resolution. We finally investigate the robustness of low-ADC-resolution MU-MIMO uplink against receive power imbalances between the different users, caused for example by imperfect power control.

We study the second-order asymptotics of information transmission using random Gaussian codebooks and nearest neighbor decoding over a power-limited stationary memoryless additive non-Gaussian noise channel. We show that the dispersion term depends on the non-Gaussian noise only through its second and fourth moments, thus complementing the capacity result (Lapidoth, 1996), which depends only on the second moment. Furthermore, we characterize the second-order asymptotics of point-to-point codes over K-sender interference networks with non-Gaussian additive noise. Specifically, we assume that each user's codebook is Gaussian and that NN decoding is employed, i.e., that interference from the K -1 unintended users (Gaussian interfering signals) is treated as noise at each decoder. We show that while the first-order term in the asymptotic expansion of the maximum number of messages depends on the power of the interfering codewords only through their sum, this does not hold for the second-order term.

This paper investigates the maximum coding rate over a K-user discrete memoryless broadcast channel for the scenario where a common message is transmitted using variable-length stop-feedback codes. Specifically, upon decoding the common message, each decoder sends a stop signal to the encoder, which transmits continuously until it receives all K stop signals. We present nonasymptotic achievability and converse bounds for the maximum coding rate, which strengthen and generalize the bounds previously reported in Trillingsgaard et al. (2015) for the two-user case. An asymptotic analysis of these bounds reveal that-contrary to the point-to-point case-the second-order term in the asymptotic expansion of the maximum coding rate decays inversely proportional to the square root of the average blocklength. This holds for certain nontrivial common-message broadcast channels, such as the binary symmetric broadcast channel. Furthermore, we identify conditions under which our converse and achievability bounds are tight up to the second order. Through numerical evaluations, we illustrate that our second-order asymptotic expansion approximates accurately the maximum coding rate and that the speed of convergence to capacity is indeed slower than for the point-to-point case.

A channel coding achievability bound expressed in terms of the ratio between two Neyman-Pearson β functions is proposed. This bound is the dual of a converse bound established earlier by Polyanskiy and Verdú (2014). The new bound turns out to simplify considerably the analysis in situations where the channel output distribution is not a product distribution, for example due to a cost constraint or a structural constraint (such as orthogonality or constant composition) on the channel inputs. Connections to existing bounds in the literature are discussed. The bound is then used to derive 1) the channel dispersion of additive non-Gaussian noise channels with random Gaussian codebooks, 2) the channel dispersion of an exponential-noise channel, 3) a second-order expansion for the minimum energy per bit of an additive white Gaussian noise channel, and 4) a lower bound on the maximum coding rate of a multiple-input multiple-output Rayleigh-fading channel with perfect channel state information at the receiver, which is the tightest known achievability result.

We present nonasymptotic achievability and converse bounds on the maximum coding rate (for a fixed average error probability and a fixed average blocklength) of variable-length full-feedback (VLF) and variable-length stop-feedback (VLSF) codes operating over a binary erasure channel (BEC). For the VLF setup, the achievability bound relies on a scheme that maps each message onto a variable-length Huffman codeword and then repeats each bit of the codeword until it is received correctly. The converse bound is inspired by the meta-converse framework by Polyanskiy, Poor, and Verdú (2010) and relies on binary sequential hypothesis testing. For the case of zero error probability, our achievability and converse bounds match. For the VLSF case, we provide achievability bounds that exploit the following feature of BEC: the decoder can assess the correctness of its estimate by verifying whether the chosen codeword is the only one that is compatible with the erasure pattern. One of these bounds is obtained by analyzing the performance of a variable-length extension of random linear fountain codes. The gap between the VLSF achievability and the VLF converse bound, when number of messages is small, is significant: 23% for 8 messages on a BEC with erasure probability 0.5. The absence of a tight VLSF converse bound does not allow us to assess whether this gap is fundamental.

Most of the recent advances in the design of high-speed wireless systems are based on information-theoretic principles that demonstrate how to efficiently transmit long data packets. However, the upcoming wireless systems, notably the fifth-generation (5G) system, will need to support novel traffic types that use short packets. For example, short packets represent the most common form of traffic generated by sensors and other devices involved in machine-to-machine (M2M) communications. Furthermore, there are emerging applications in which small packets are expected to carry critical information that should be received with low latency and ultrahigh reliability. Current wireless systems are not designed to support short-packet transmissions. For example, the design of current systems relies on the assumption that the metadata (control information) is of negligible size compared to the actual information payload. Hence, transmitting metadata using heuristic methods does not affect the overall system performance. However, when the packets are short, metadata may be of the same size as the payload, and the conventional methods to transmit it may be highly suboptimal. In this paper, we review recent advances in information theory, which provide the theoretical principles that govern the transmission of short packets. We then apply these principles to three exemplary scenarios (the two-way channel, the downlink broadcast channel, and the uplink random access channel), thereby illustrating how the transmission of control information can be optimized when the packets are short. The insights brought by these examples suggest that new principles are needed for the design of wireless protocols supporting short packets. These principles will have a direct impact on the system design.

Motivated by the current interest in ultra-reliable, low-latency, machine-type communication systems, we investigate the tradeoff between reliability, throughput, and latency in the transmission of information over multiple-antenna Rayleigh block-fading channels. Specifically, we obtain finite-blocklength, finite-SNR upper and lower bounds on the maximum coding rate achievable over such channels for a given constraint on the packet error probability. Numerical evidence suggests that our bounds delimit tightly the maximum coding rate already for short blocklengths (packets of about 100 symbols). Furthermore, our bounds reveal the existence of a tradeoff between the rate gain obtainable by spreading each codeword over all available time-frequency-spatial degrees of freedom, and the rate loss caused by the need of estimating the fading coefficients over these degrees of freedom. In particular, our bounds allow us to determine the optimal number of transmit antennas and the optimal number of time-frequency diversity branches that maximize the rate. Finally, we show that infinite-blocklength performance metrics such as the ergodic capacity and the outage capacity yield inaccurate throughput estimates.

Coarse quantization at the base station (BS) of a massive multi-user (MU) multiple-input multiple-output (MIMO) wireless system promises significant power and cost savings. Coarse quantization also enables significant reductions of the raw analog-to-digital converter data that must be transferred from a spatially separated antenna array to the baseband processing unit. The theoretical limits as well as practical transceiver algorithms for such quantized MU-MIMO systems operating over frequency-flat, narrowband channels have been studied extensively. However, the practically relevant scenario where such communication systems operate over frequency-selective, wideband channels is less well understood. This paper investigates the uplink performance of a quantized massive MU-MIMO system that deploys orthogonal frequency-division multiplexing (OFDM) for wideband communication. We propose new algorithms for quantized maximum a posteriori channel estimation and data detection, and we study the associated performance/quantization tradeoffs. Our results demonstrate that coarse quantization (e.g., four to six bits, depending on the ratio between the number of BS antennas and the number of users) in massive MU-MIMO-OFDM systems entails virtually no performance loss compared with the infinite-precision case at no additional cost in terms of baseband processing complexity.

This paper investigates the minimum energy required to transmit k information bits with a given reliability over a multiple-antenna Rayleigh block-fading channel, with and without channel state information (CSI) at the receiver. No feedback is assumed. It is well known that the ratio between the minimum energy per bit and the noise level converges to -1.59 dB as k goes to infinity, regardless of whether CSI is available at the receiver or not. This paper shows that the lack of CSI at the receiver causes a slowdown in the speed of convergence to -1.59 dB as k → ∞ compared with the case of perfect receiver CSI. Specifically, we show that, in the no-CSI case, the gap to -1.59 dB is proportional to ((log k)/k)1/3, whereas when perfect CSI is available at the receiver, this gap is proportional V to 1/√k. In both cases, the gap to -1.59 dB is independent of the number of transmit antennas and of the channel's coherence time. Numerically, we observe that, when the receiver is equipped with a single antenna, to achieve an energy per bit of -1.5 dB in the no-CSI case, one needs to transmit at least 7 × 107information bits, whereas 6 × 104bits suffice for the case of perfect CSI at the receiver.

In multiple antenna systems, phase noise due to instabilities of the radio-frequency (RF) oscillators, acts differently depending on whether the RF circuitries connected to each antenna are driven by separate (independent) local oscillators (SLO) or by a common local oscillator (CLO). In this paper, we investigate the high-SNR capacity of single-input multiple-output (SIMO) and multiple-output single-input (MISO) phase-noise channels for both the CLO and the SLO configurations. Our results show that the first-order term in the high-SNR capacity expansion is the same for all scenarios (SIMO/MISO and SLO/CLO), and equal to 0.5 ln(ρ), where ρ stands for the SNR. On the contrary, the second-order term, which we refer to as phase-noise number, turns out to be scenario-dependent. For the SIMO case, the SLO configuration provides a diversity gain, resulting in a larger phase-noise number than for the CLO configuration. For the case of Wiener phase noise, a diversity gain of at least 0.5 ln(M) can be achieved, where M is the number of receive antennas. For the MISO, the CLO configuration yields a higher phase-noise number than the SLO configuration. This is because with the CLO configuration one can obtain a coherent-combining gain through maximum ratio transmission (a.k.a. conjugate beamforming). This gain is unattainable with the SLO configuration.

We investigate the maximum coding rate achievable over a two-user broadcast channel for the scenario where a common message is transmitted using variable-length stop-feedback codes. Specifically, upon decoding the common message, each decoder sends a stop signal to the encoder, which transmits continuously until it receives both stop signals. For the point-to-point case, Polyanskiy, Poor, and Verdú (2011) recently demonstrated that variable-length coding combined with stop feedback significantly increases the speed at which the maximum coding rate converges to capacity. This speed-up manifests itself in the absence of a square-root penalty in the asymptotic expansion of the maximum coding rate for large blocklengths, a result a.k.a. zero dispersion. In this paper, we show that this speed-up does not necessarily occur for the broadcast channel with common message. Specifically, there exist scenarios for which variable-length stop-feedback codes yield a positive dispersion.

This paper investigates the minimum energy required to transmit, with a given reliability, k information bits over a stationary memoryless Rayleigh-fading channel, under the assumption that neither the transmitter nor the receiver have a priori channel state information (CSI). It is well known that the ratio between the minimum energy per bit and the noise level converges to -1.59 dB as k goes to infinity, regardless of whether CSI is available at the receiver or not. This paper shows that lack of CSI at the receiver causes a slowdown in the speed of convergence to -1.59 dB as k → ∞ compared to the case of perfect receiver CSI. Specifically, we show that in the noCSI case, the gap to -1.59 dB is proportional to ((log k)/k)1/3, whereas when perfect CSI is available at the receiver, this gap is '/ proportional to 1/√(k). Numerically, we observe that to achieve an energy per bit of -1.5 dB in the no-CSI case, one needs to transmit at least 7 × 107information bits, whereas 6 × 104bits suffice for the case of perfect CSI at the receiver (same number of bits as for nonfading AWGN channels). Interestingly, all results (asymptotic and numerical) are unchanged if multiple transmit antennas and/or block fading is assumed.

There exists a rich flora of channel models for optical fiber channels, which differ not only in the types of transmission scenario they describe but also in the type of analysis they support. In this tutorial paper, we review several channel models used in optical communications, and discuss their suitability for information-theoretic analyses. Key issues are how nonlinearity, channel memory, and multiuser interference are modeled.

We provide nonasymptotic upper and lower bounds on the sum-rate capacity of Rayleigh block-fading multiple-access channels for the set up where a priori channel state information is not available. The upper bound relies on a dual formula for channel capacity and on the assumption that the users can cooperate perfectly. The lower bound is derived assuming a noncooperative scenario where each user employs unitary space-time modulation (independently from the other users). Numerical results show that the gap between the upper and the lower bound is small already at moderate SNR values. This suggests that the sum-rate capacity gains obtainable through user cooperation are minimal for the scenarios considered in the paper.

In multiple antenna systems, phase noise due to instabilities of the radio-frequency (RF) oscillators, acts differently depending on whether the RF circuitries connected to each antenna are driven by separate (independent) local oscillators (SLO) or by a common local oscillator (CLO). In this paper, we investigate the high-SNR capacity of single-input multiple-output (SIMO) and multiple-output single-input (MISO) phase-noise channels for both the CLO and the SLO configurations. Our results show that the first-order term in the high-SNR capacity expansion is the same for all scenarios (SIMO/MISO and SLO/CLO), and equal to 0.5 ln(p), where p stands for the SNR. On the contrary, the second-order term, which we refer to as phase-noise number, turns out to be scenario-dependent. For the SIMO case, the SLO configuration provides a diversity gain, resulting in a larger phase-noise number than for the CLO configuration. For the case of Wiener phase noise, a diversity gain of at least 0.5 ln(M) can be achieved, where M is the number of receive antennas. For the MISO, the CLO configuration yields a higher phase-noise number than the SLO configuration. This is because with the CLO configuration one can obtain a coherent-combining gain through maximum ratio transmission (a.k.a. conjugate beamforming). This gain is unattainable with the SLO configuration.

This paper investigates the maximal channel coding rate achievable at a given blocklength n and error probability ϵ, when the codewords are subjected to a long-term (i.e., averaged-over-all-codeword) power constraint. The second-order term in the large-n expansion of the maximal channel coding rate is characterized both for additive white Gaussian noise (AWGN) channels and for quasi-static fading channels with perfect channel state information available at both the transmitter and the receiver. It is shown that in both the cases, the second-order term is proportional to (n-1ln n)1/2. For the quasi-static fading case, this second-order term is achieved by truncated channel inversion, namely, by concatenating a dispersion-optimal code for an AWGN channel subject to a short-term power constraint, with a power controller that inverts the channel whenever the fading gain is above a certain threshold. Easy-to-evaluate approximations of the maximal channel coding rate are developed for both the AWGN and the quasi-static fading case.

This paper investigates the maximal channel coding rate achievable at a given blocklength n and error probability ε, when the codewords are subject to a long-term (i.e., averaged-over-all-codeword) power constraint. The second-order term in the large-n expansion of the maximal channel coding rate is characterized both for AWGN channels and for quasi-static fading channels with perfect channel state information at the transmitter and the receiver. It is shown that in both cases the second-order term is proportional to √(log n)/n.

This paper analyzes the channel dispersion of quasi-static multiple-input multiple-output fading channels with no channel state information at the transmitter. We show that the channel dispersion is zero under mild conditions on the fading distribution. The proof of our result is based on Stokes' theorem, which deals with the integration of differential forms on manifolds with boundary.

We present bounds and a closed-form high-SNR expression for the capacity of multiple-antenna systems affected by Wiener phase noise. Our results are developed for the scenario where a single oscillator drives all the radio-frequency circuitries at each transceiver (common oscillator setup), the input signal is subject to a peak-power constraint, and the channel matrix is deterministic. This scenario is relevant for line-of-sight multiple-antenna microwave backhaul links with sufficiently small antenna spacing at the transceivers. For the 2×2 multiple-antenna case, for a Wiener phase-noise process with standard deviation equal to 6°, and at the medium/high SNR values at which microwave backhaul links operate, the upper bound reported in the paper exhibits a 3dB gap from a lower bound obtained using 64-QAM. Furthermore, in this SNR regime the closed-form high-SNR expression is shown to be accurate.

We analyze the capacity of a continuous-time, time-selective, Rayleigh block-fading channel in the high signal-to-noise ratio (SNR) regime. The fading process is assumed stationary within each block and to change independently from block to block; furthermore, its realizations are not known a priori to the transmitter and the receiver (noncoherent setting). A common approach to analyzing the capacity of this channel is to assume that the receiver performs matched filtering followed by sampling at symbol rate (symbol matched filtering). This yields a discrete-time channel in which each transmitted symbol corresponds to one output sample. Liang & Veeravalli (2004) showed that the capacity of this discrete-time channel grows logarithmically with the SNR, with a capacity pre-log equal to 1-Q/N. Here, N is the number of symbols transmitted within one fading block, and Q is the rank of the covariance matrix of the discrete-time channel gains within each fading block. In this paper, we show that symbol matched filtering is not a capacity-achieving strategy for the underlying continuous-time channel. Specifically, we analyze the capacity pre-log of the discrete-time channel obtained by oversampling the continuous-time channel output, i.e., by sampling it faster than at symbol rate. We prove that by oversampling by a factor two one gets a capacity pre-log that is at least as large as 1-1/N. Since the capacity pre-log corresponding to symbol-rate sampling is 1-Q/N, our result implies indeed that symbol matched filtering is not capacity achieving at high SNR.

We study the high-signal-to-noise-ratio capacity of generic multiple-input multiple-output (MIMO) Rayleigh block-fading channels in the noncoherent setting where neither transmitter nor receiver has a priori channel state information but both are aware of the channel statistics. In contrast to the well-established constant block-fading model, we allow the fading to vary within each block with a temporal correlation that is generic (in the sense used in the interference-alignment literature). We show that the number of degrees of freedom of a generic MIMO Rayleigh block-fading channel with T transmit antennas and block length N is given by T(1 - 1/N) provided that T <; N and the number of receive antennas is at least T(N - 1)/(N - T). A comparison with the constant block-fading channel (where the fading is constant within each block) shows that, for large block lengths, generic correlation increases the number of degrees of freedom by a factor of up to four.

This paper investigates the maximal achievable rate for a given blocklength and error probability over quasi-static multiple-input multiple-output fading channels, with and without channel state information at the transmitter and/or the receiver. The principal finding is that outage capacity, despite being an asymptotic quantity, is a sharp proxy for the finite-blocklength fundamental limits of slow-fading channels. Specifically, the channel dispersion is shown to be zero regardless of whether the fading realizations are available at both transmitter and receiver, at only one of them, or at neither of them. These results follow from analytically tractable converse and achievability bounds. Numerical evaluation of these bounds verifies that zero dispersion may indeed imply fast convergence to the outage capacity as the blocklength increases. In the example of a particular 1 × 2 single-input multiple-output Rician fading channel, the blocklength required to achieve 90% of capacity is about an order of magnitude smaller compared with the blocklength required for an AWGN channel with the same capacity. For this specific scenario, the coding/decoding schemes adopted in the LTE-Advanced standard are benchmarked against the finite-blocklength achievability and converse bounds.

We consider a multiple-input multiple-output (MIMO) AWGN channel affected by phase noise. Focusing on the 2 × 2 case, we show that no MIMO multiplexing gain is to be expected when the phase-noise processes at each antenna are independent, memoryless in time, and with uniform marginal distribution over [0, 2π] (strong phase noise), and when the transmit signal is isotropically distributed on the real plane. The scenario of independent phase-noise processes across antennas is relevant for microwave backhaul links operating in the 20-40 GHz range.

We study the high-SNR capacity of MIMO Rayleigh block-fading channels in the noncoherent setting where neither transmitter nor receiver has a priori channel state information. We show that when the number of receive antennas is sufficiently large and the temporal correlation within each block is “generic” (in the sense used in the interference-alignment literature), the capacity pre-log is given by T(1 - 1/N) for T <; N, where T denotes the number of transmit antennas and N denotes the block length. A comparison with the widely used constant block-fading channel (where the fading is constant within each block) shows that for a large block length, generic correlation increases the capacity pre-log by a factor of about four.

We investigate the maximal achievable rate for a given blocklength and error probability over quasi-static single-input multiple-output (SIMO) fading channels. Under mild conditions on the channel gains, it is shown that the channel dispersion is zero regardless of whether the fading realizations are available at the transmitter and/or the receiver. The result follows from computationally and analytically tractable converse and achievability bounds. Through numerical evaluation, we verify that, in some scenarios, zero dispersion indeed entails fast convergence to outage capacity as the blocklength increases. In the example of a particular 1×2 SIMO Rician channel, the blocklength required to achieve 90% of capacity is about an order of magnitude smaller compared to the blocklength required for an AWGN channel with the same capacity.

We characterize the capacity of Rayleigh block-fading multiple-input multiple-output (MIMO) channels in the noncoherent setting where transmitter and receiver have no a priori knowledge of the realizations of the fading channel. We prove that unitary space-time modulation (USTM) is not capacity-achieving in the high signal-to-noise ratio (SNR) regime when the total number of antennas exceeds the coherence time of the fading channel (expressed in multiples of the symbol duration), a situation that is relevant for MIMO systems with large antenna arrays (large-MIMO systems). This result settles a conjecture by Zheng & Tse (2002) in the affirmative. The capacity-achieving input signal, which we refer to as Beta-variate space-time modulation (BSTM), turns out to be the product of a unitary isotropically distributed random matrix, and a diagonal matrix whose nonzero entries are distributed as the square-root of the eigenvalues of a Beta-distributed random matrix of appropriate size. Numerical results illustrate that using BSTM instead of USTM in large-MIMO systems yields a rate gain as large as 13% for SNR values of practical interest.

We find the capacity pre-log of a temporally correlated Rayleigh block-fading single-input multiple-output (SIMO) channel in the noncoherent setting. It is well known that for block-lengthLand rank of the channel covariance matrix equal toQ, the capacity pre-log in the single-input single-output (SISO) case is given by 1-Q/L. Here,Q/Lcan be interpreted as the pre-log penalty incurred by channel uncertainty. Our main result reveals that, by adding only one receive antenna, this penalty can be reduced to 1/Land can, hence, be made to vanish for the block-lengthL→∞, even ifQ/Lremains constant asL→∞. Intuitively, even though the SISO channels between the transmit antenna and the two receive antennas are statistically independent, the transmit signal induces enough statistical dependence between the corresponding receive signals for the second receive antenna to be able to resolve the uncertainty associated with the first receive antenna's channel and thereby make the overall system appear coherent. The proof of our main theorem is based on a deep result from algebraic geometry known as Hironaka's Theorem on the Resolution of Singularities.

We analyze the capacity of Rayleigh block-fading multiple-input multiple-output (MIMO) channels in the noncoherent setting and prove that unitary space-time modulation (USTM) is not capacity-achieving when the total number of antennas exceeds the coherence time of the fading channel. This situation is relevant for MIMO systems with large antenna arrays (large-MIMO systems). Our result settles a conjecture by Zheng & Tse (2002) in the affirmative. The capacity-achieving input signal, which we refer to as Beta-variate space-time modulation (BSTM), turns out to be the product of a unitary isotropically distributed random matrix, and a diagonal matrix whose nonzero entries are distributed as the square-root of the eigenvalues of a Beta-distributed random matrix of appropriate size. Numerical results illustrate that using BSTM instead of USTM in large-MIMO systems yields a rate gain as large as 13% for SNR values of practical interest.

In this paper, we introduce a 1-bit compressive sensing reconstruction algorithm that is not only robust against bit flips in the binary measurement vector, but also does not require a priori knowledge of the sparsity level of the signal to be reconstructed. Through numerical experiments, we show that our algorithm outperforms state-of-the-art reconstruction algorithms for the 1-bit compressive sensing problem in the presence of random bit flips and when the sparsity level of the signal deviates from its estimated value.

We study the maximal achievable rate R*(n, ∈) for a given block-length n and block error probability o over Rayleigh block-fading channels in the noncoherent setting and in the finite block-length regime. Our results show that for a given block-length and error probability, R*(n, ∈) is not monotonic in the channel's coherence time, but there exists a rate maximizing coherence time that optimally trades between diversity and cost of estimating the channel.

The noncoherent capacity of stationary discrete-time fading channels is known to be very sensitive to the fine details of the channel model. More specifically, the measure of the support of the fading-process power spectral density (PSD) determines if noncoherent capacity grows logarithmically with the signal-to-noise ratio (SNR) or slower than logarithmically. Such a result is unsatisfactory from an engineering point of view, as the support of the PSD cannot be determined through measurements. The aim of this paper is to assess whether, for general continuous-time Rayleigh-fading channels, this sensitivity has a noticeable impact on capacity at SNR values of practical interest. To this end, we consider the general class of band-limited continuous-time Rayleigh-fading channels that satisfy the wide-sense stationary uncorrelated-scattering (WSSUS) assumption and are, in addition, under spread. We show that, for all SNR values of practical interest, the noncoherent capacity of every channel in this class is close to the capacity of an additive white Gaussian noise channel with the same SNR and bandwidth, independently of the measure of the support of the scattering function (the 2-D channel PSD). Our result is based on a lower bound on noncoherent capacity, which is built on a discretization of the channel input-output relation induced by projecting onto Weyl-Heisenberg sets. This approach is interesting in its own right as it yields a mathematically tractable way of dealing with the mutual information between certain continuous-time random signals.

We present an uncertainty relation for the representation of signals in two different general (possibly redundant or incomplete) signal sets. This uncertainty relation is relevant for the analysis of signals containing two distinct features each of which can be described sparsely in a suitable general signal set. Furthermore, the new uncertainty relation is shown to lead to im- proved sparsity thresholds for recovery of signals that are sparse in general dictionaries. Specifically, our results improve on the well-known (1 + 1/d)/2-threshold for dictionaries with coherence d by up to a factor of two. Furthermore, we provide probabilistic recovery guarantees for pairs of general dictionaries that also allow us to understand which parts of a general dictionary one needs to randomize over to "weed out" the sparsity patterns that prohibit breaking the square-root bottleneck.

We establish a lower bound on the noncoherent capacity pre-log of a temporally correlated Rayleigh block-fading single-input multiple-output (SIMO) channel. Our result holds for arbitrary rank Q of the channel correlation matrix, arbitrary block-length L >; Q, and arbitrary number of receive antennas R, and includes the result in Morgenshtern et al. (2010) as a special case. It is well known that the capacity pre-log for this channel in the single-input single-output (SISO) case is given by 1-Q/L, where Q/L is the penalty incurred by channel uncertainty. Our result reveals that this penalty can be reduced to 1/L by adding only one receive antenna, provided that L ≥ 2Q - 1 and the channel correlation matrix satisfies mild technical conditions. The main technical tool used to prove our result is Hironaka's celebrated theorem on resolution of singularities in algebraic geometry.

As shown by Tropp, 2008, for the concatenation of two orthonormal bases (ONBs), breaking the square-root bottleneck in compressed sensing does not require randomization over all the positions of the nonzero entries of the sparse coefficient vector. Rather the positions corresponding to one of the two ONBs can be chosen arbitrarily. The two-ONB structure is, however, restrictive and does not reveal the property that is responsible for allowing to break the bottleneck with reduced randomness. For general dictionaries we show that if a sub-dictionary with small enough coherence and large enough cardinality can be isolated, the bottleneck can be broken under the same probabilistic model on the sparse coefficient vector as in the two-ONB case.

We establish a lower bound on the noncoherent capacity pre-log of a temporally correlated Rayleigh block-fading single-input multiple-output (SIMO) channel. Surprisingly, when the covariance matrix of the channel satisfies a certain technical condition related to the cardinality of its smallest set of linearly dependent rows, this lower bound reveals that the capacity pre-log in the SIMO case is larger than that in the single-input single-output (SISO) case.

We derive bounds on the noncoherent capacity of wide-sense stationary uncorrelated scattering (WSSUS) channels that are selective both in time and frequency, and are underspread, i.e., the product of the channel's delay spread and Doppler spread is small. The underspread assumption is satisfied by virtually all wireless communication channels. For input signals that are peak constrained in time and frequency, we obtain upper and lower bounds on capacity that are explicit in the channel's scattering function, are accurate for a large range of bandwidth, and allow to coarsely identify the capacity-optimal bandwidth as a function of the peak power and the channel's scattering function. We also obtain a closed-form expression for the first-order Taylor series expansion of capacity in the infinite-bandwidth limit, and show that our bounds are tight in the wideband regime. For input signals that are peak constrained in time only (and, hence, allowed to be peaky in frequency), we provide upper and lower bounds on the infinite-bandwidth capacity. Our lower bound is closely related to a result by Viterbi (1967). We find cases where the bounds coincide and, hence, the infinite-bandwidth capacity is characterized exactly. The analysis in this paper is based on a discrete-time discrete-frequency approximation of WSSUS time- and frequency-selective channels. This discretization takes the underspread property of the channel explicitly into account.

The noncoherent capacity of stationary discrete-time fading channels is known to be very sensitive to the fine details of the channel model. More specifically, the measure of the set of harmonics where the power spectral density of the fading process is nonzero determines if capacity grows logarithmically in SNR or slower than logarithmically. An engineering-relevant problem is to characterize the SNR value at which this sensitivity starts to matter. In this paper, we consider the general class of continuous-time Rayleigh-fading channels that satisfy the wide-sense stationary uncorrelated-scattering (WSSUS) assumption and are, in addition, underspread. For this class of channels, we show that the noncoherent capacity is close to the AWGN capacity for all SNR values of practical interest, independently of whether the scattering function is compactly supported or not. As a byproduct of our analysis, we obtain an information-theoretic pulse-design criterion for orthogonal frequency-division multiplexing systems.

Bounds are derived on the noncoherent capacity of a very general class of multiple-input multiple-output fading channels that are selective in time and frequency as well as correlated in space. The bounds apply to peak-constrained inputs; they are explicit in the channel's scattering function, are useful for a large range of bandwidth, and allow one to coarsely identify the capacity-optimal combination of bandwidth and number of transmit antennas. Furthermore, a closed-form expression is obtained for the first-order Taylor series expansion of capacity in the limit of infinite bandwidth. From this expression, it is concluded that in the wideband regime: (i) it is optimal to use only one transmit antenna when the channel is spatially uncorrelated; (ii) rank-one statistical beamforming is optimal if the channel is spatially correlated; and (iii) spatial correlation, be it at the transmitter, the receiver, or both, is beneficial.

This paper presents bounds on the noncoherent capacity of a very general multiple-input multiple-output channel, which allows for selectivity in time and frequency as well as for spatial correlation. The bounds apply to peak-constrained inputs; they are explicit in the channelpsilas scattering function, are useful for a large range of bandwidth, and allow one to coarsely identify the capacity-optimal combination of bandwidth and number of transmit antennas. Furthermore, a closed-form expression is obtained for the first-order Taylor series expansion of capacity in the limit of infinite bandwidth. From this expression, it is concluded that in the wideband regime: (i) it is optimal to use only one transmit antenna when the channel is spatially uncorrelated; (ii) rank-one statistical beamforming is optimal if the channel is spatially correlated; and (iii) spatial correlation, be it at the transmitter, the receiver, or both, is beneficial.

We characterize the capacity of the general class of noncoherent underspread wide-sense stationary uncorrelated scattering (WSSUS) time-frequency-selective Rayleigh fading channels, under peak constraints in time and frequency and in time only. Capacity upper and lower bounds are found which are explicit in the channel's scattering function and allow to identify the capacity-maximizing bandwidth for a given scattering function and a given peak-to-average power ratio.

In this paper we discuss the design of linear time encodable extended irregular repeat-accumulate (eIRA) codes for bit-interleaved coded modulation (BICM) systems. We interpret eIRA codes as a particular instance of the recently introduced multi-edge type (MET) low-density parity-check (LDPC) codes. This allows us to take into account during the design step both the systematic nature of these codes and the different level of protection given to each bit by the choice of input alphabet and mapping function. Furthermore, we extend to the eIRA-BICM case the method used by Roumy et al., IEEE Trans. Inf. Theory, 2004, to optimize LDPC codes for the binary input AWGN (bi-AWGN) channel. This method is based on EXIT functions and leads to a linear program. Using this method we design capacity-approaching eIRA codes for 4PAM and 8PSK. For both short and long block lengths these codes have performance approximately 0.1 dB worse than LDPC codes optimized with density evolution and with similar decoding complexity.

We characterize the infinite bandwidth capacity behavior of the general class of underspread wide-sense stationary uncorrelated scattering (WSSUS) time-frequency selective Rayleigh fading channels. In particular, we propose a signaling scheme, termed time-frequency pulse position modulation (TF-PPM), which is shown to achieve AWGN channel capacity in the infinite bandwidth limit. As a trivial consequence of this result, the infinite bandwidth capacity of WSSUS underspread fading channels, irrespectively of the scattering function, equals the AWGN channel's infinite bandwidth capacity. The wideband slope achieved by TF-PPM is found to be zero, irrespectively of the channel's scattering function, even in the presence of perfect receive channel state information. Our proof techniques use the fact that underspread fading channels have a highly structured set of eigenfunctions and a property of orthogonal signaling schemes first presented in Butman and Klass, Jet Propulsion Lab., Tech. Rep., 1973.

We present results of two ultra-wideband (UWB) channel measurement campaigns in the 2-5 GHz frequency band, and use Akaike's Information Criterion (AIC) to determine suitable distributions for the channel impulse response taps. Despite the large bandwidth, AIC supports the complex Gaussian tap distribution, with mean depending on the measurement setting. We estimate the empirical covariance matrix of the channel impulse response, and demonstrate that the number of corresponding significant eigenvalues scales approximately linearly with bandwidth, albeit we find that channel taps are correlated

Abstract In this paper, we discuss the design issues of an ultra wide band (UWB) receiver targeting a single‐chip CMOS implementation for low data‐rate applications like ad hoc wireless sensor networks. A non‐coherent transmitted‐reference (TR) receiver is chosen because of its small complexity compared to other architectures. After a brief recapitulation of the UWB fundamentals and a short discussion on the major differences between coherent and non‐coherent receivers, we discuss issues, challenges and possible design solutions. Several simulation results obtained by means of a behavioral model are presented, together with an analysis of the trade‐off between performance and complexity in an integrated circuit implementation. Copyright © 2005 John Wiley & Sons, Ltd.

In this paper we present a comparison between coherent and noncoherent UWB receivers, under a realistic propagation environment, that takes into account also the effect of path-dependent pulse distortion. As far as coherent receivers are concerned, both maximal ratio combining (MRC) and equal gain combining (EGC) techniques are analyzed, considering a limited number of estimated paths. Furthermore, two noncoherent schemes are presented: a simple differential detector and its adaptive version. While the first receiver shows a significative performance loss, if compared to coherent detectors, the second one is able to guarantee probability of error similar to the one obtained employing a Rake receiver, equipped with up to 20 fingers, without requiring channel estimation.

A general method for the evaluation of the symbol error probability (SER) of both M-PAM and M-PPM UWB systems, in presence of multipath channel, multiuser and strong narrowband interference is presented. This method is shown to be able to include all the principal multiaccess techniques proposed so far for UWB, like time hopping and direct sequence. A comparison between the performance of three of these techniques is also presented, for both ideal RAKE receiver and MMSE equalizer, in an indoor communications scenario.

Ultra wideband system performance is analyzed in terms of error probability for different modulation and multi-access schemes over the AWGN channel. The analysis leads to closed-form expressions of the bit error probability under the hypothesis of chip-synchronous systems, allowing a comparison of different techniques in a possible scenario for UWB applications. The use of convolutional codes to improve the performance of time hopping systems is also addressed.