We study the rate-distortion function (RDF) for sampled cyclostationary Gaussian processes with memory, representing, e.g., the sampling of communications signals for the subsequent application of digital processing. Accounting for the inherent random jitter in local oscillators and keeping the sampling interval smaller than the memory length of the continuous-time (CT) source process to facilitate reliable modeling, induce a discrete-time (DT) wide-sense almost cyclostationary (WSACS) process with memory model upon the sampled signals. The main challenge follows from the information-instability of DT WSACS processes, which renders conventional information-theoretic approaches inapplicable. We use the information-spectrum framework to study the compression of incoming source sequences in two settings: when processing starts immediately upon reception and when a bounded delay exists between consecutive source sequences. Our analysis provides novel insights relating source memory, sampling frequency synchronization, and achievable compression rates.We show that, contrary to the sampled stationary case, the RDF for sampled cyclostationary processes is very sensitive to sampling rate synchronization. We also demonstrate that the RDF is not a monotonically decreasing function for the sampling rate and how introducing delay simplifies the compression scheme and lowers the rates.

We study the rate-distortion function (RDF) for the lossy compression of discrete-time (DT) wide-sense almost cyclo-stationary (WSACS) Gaussian processes with memory, arising from sampling continuous-time (CT) wide-sense cyclostationary (WSCS) Gaussian source processes. The importance of this problem arises as such CT processes represent communications signals, and sampling must be applied to facilitate the DT processing associated with their compression. Moreover, the physical characteristics of oscillators imply that the sampling interval is incommensurate with the period of the autocorrelation function (AF) of the physical process, giving rise to the DT WSACS model considered. In addition, to reduce the loss, the sampling interval is generally shorter than the correlation length, and thus, the DT process is correlated as well. The difficulty in the RDF characterization follows from the information-instability of WSACS processes, which renders the traditional information-theoretic tools inapplicable. In this work we utilize the information-spectrum framework to characterize the RDF when a finite and bounded delay is allowed between processing of subsequent source sequences. This scenario extends our previous works which studied settings without processing delays or without memory. Numerical evaluations reveal the impact of scenario parameters on the RDF with asynchronous sampling.

In this paper we consider the upper bound on the capacity of bandlimited linear, time-invariant (LTI) channels with additive white Gaussian noise (AWGN) in which the input signal is subject to a peak amplitude constraint. It has been shown that when the channel impulse response (CIR) is square-integrable, unit processes attain the largest achievable rate for this channel, [Ozarow et al., 1988], yet the characterization of such processes is associated with a high numerical complexity. In this work we use a characterization of the autocorrelation function for unit processes derived in [Quintanilla, 2008], which facilitates a simpler and structured numerical evaluation of necessary condition for the autocorrelation function of unit processes, originally characterized in [Mcmillan, 1955] and [Shepp, 1967]. We translate this characterization into spectral constraints on the input power spectral density (PSD), following the approach applied in [Shamai and Bar-David, 1989], to tighten their bound on the capacity of such channels.

High clock synchronization accuracy across the nodes in wireless networks is a prerequisite for facilitating high-rate data transmission. Accurate clock synchronization is a particularly challenging goal in networks implementing time division multiple access (tdma) via half-duplex (hd) communications, as in such networks the updates are temporally sparse, and consequently, clock frequency differences induce significant phase drifts between subsequent updates. Thus, accurate clock synchronization in hd tdma networks requires synchronizing both clock phases and clock frequencies across the nodes, which is the focus of this work. We consider pulse-coupling (pc)-based distributed clock synchronization, where each node implements its synchronization processing independently, based on its own received clock phases and power measurements. These measurements are then weighted to generate the phase and the frequency correction signals. We first analyze this synchronization framework and motivate decoupling the phase and frequency updates. We then analyze the resulting decoupled structure and derive the asymptotic synchronization accuracy, which is shown to be a function of the weighting coefficients and the unknown propagation delays. This motivates on-line learning of the optimal weights. To that aim, we introduce a novel initialization scheme with unsupervised online training. Simulation results show that the new scheme exhibits excellent synchronization accuracy, which is significantly better than previously proposed schemes, as well as robustness to clock resets and to node mobility.

Supporting increasingly higher rates in wireless networks requires highly accurate clock synchronization across the nodes. Motivated by this need, in this work we consider distributed clock synchronization for half-duplex (HD) TDMA wireless networks. We focus on pulse-coupling (PC)-based synchronization as it is practically advantageous for high-speed networks using low-power nodes. Previous works on PC-based synchronization for TDMA networks assumed full-duplex communications, and focused on correcting the clock phase at each node, without synchronizing clocks' frequencies. However, as in the HD regime corrections are temporally sparse, uncompensated clock frequency differences between the nodes result in large phase drifts between updates. Moreover, as the clocks determine the processing rates at the nodes, leaving the clocks' frequencies unsynchronized results in processing rates mismatch between the nodes, leading to a throughput reduction. Our goal in this work is to synchronize both clock frequency and clock phase across the clocks in HD TDMA networks, via distributed processing. The key challenges are the coupling between frequency correction and phase correction, and the lack of a computationally efficient analytical framework for determining the optimal correction signal at the nodes. We address these challenges via a deep neural network (DNN)-aided nested loop structure in which the DNNs are used for generating the weights applied to the loop input for computing the correction signal. This loop is operated in a sequential manner which decouples frequency and phase compensations, thereby facilitating synchronization of both parameters. Performance evaluation shows that the proposed scheme significantly improves synchronization accuracy compared to the conventional approaches.

Handling peak-to-average power ratio is a major challenge in the design of communications systems, as current signal designs constrain the power of the generated signal and therefore its peak amplitude is considered as an uncontrolled outcome of the power-constrained signal generation scheme. An alternative signal design approach would be to restrict the peak of the signal's amplitude. The capacity of continuous-time bandlimited linear channels with additive Gaussian noise and peak input amplitude constraint is unknown to date; however, if the channel impulse response has finite energy, then any rate achieved by peak-amplitude constrained waveforms can be achieved by binary waveforms (unit processes). This fact is the basis for the two major previous works that have derived lower bounds on the achievable rate of this channel for the ideal bandlimited case. In this work we propose a different approach for obtaining lower bounds on the capacity of this channel, particularly relevant for linear, time-invariant channels with non-ideal frequency responses. Our approach is based on modulating a subset of the Walsh basis functions and using a fundamental relationship between the peak amplitude and the power of such signals. This approach yields achievable rates for general linear channels.

We study the rate-distortion function (RDF) for lossy compression of discrete-time (DT) processes obtained by sampling continuous-time (CT) wide-sense cyclostationary (WSCS) Gaussian processes with memory. This problem was previously studied for the case in which the sampling interval is commensurate with the period of the cyclostationary statistics (referred to as synchronous sampling), hence we focus on the situation in which these parameters are incommensurate, referred to as asynchronous sampling. The sampling interval is also assumed to be smaller than the maximal autocorrelation length of the CT source process, which results in a DT process with memory, such that the overall DT process is modeled as a Gaussian wide-sense almost cyclostationary (WSACS) process with memory. This problem is motivated by the fact that communications signals are modelled as CT WSCS processes, thus, to facilitate DT processing, e.g., as in compress-and-forward relaying and in recording systems, sampling has to be applied first. The main challenge follows as DT WSACS processes are not information-stable which renders conventional information-theoretic arguments irrelevant, and hence, the characterization of the RDF is carried out within the information-spectrum framework. This work expands upon our previous work which addressed the special case in which the DT process is memoryless. The existence of dependence between the samples requires a new approach for characterizing the RDF.

In this work we study the capacity of interference-limited channels with memory. These channels model non-orthogonal communications scenarios, such as the non-orthogonal multiple access (NOMA) scenario and underlay cognitive communications, in which the interference from other communications signals is much stronger than the thermal noise. Interference-limited communications is expected to become a very common scenario in future wireless communications systems, such as 5G, WiFi6, and beyond. As communications signals are inherently cyclostationary in continuous time (CT), then after sampling at the receiver, the discrete-time (DT) received signal model contains the sampled desired information signal with additive sampled CT cyclostationary noise. The sampled noise can be modeled as either a DT cyclostationary process or a DT almost-cyclostationary process, where in the latter case the resulting channel is not information-stable. In a previous work we characterized the capacity of this model for the case in which the DT noise is memoryless. In the current work we come closer to practical scenarios by modelling the resulting DT noise as a finite-memory random process. The presence of memory requires the development of a new set of tools for analyzing the capacity of channels with additive non-stationary noise which has memory. Our results show, for the first time, the relationship between memory, sampling frequency synchronization and capacity, for interference-limited communications. The insights from our work provide a link between the analog and the digital time domains, which has been missing in most previous works on capacity analysis. Thus, our results can help improving spectral efficiency and suggest optimal transceiver designs for future communications paradigms.

We consider the problem of dynamic spectrum access (DSA) in cognitive wireless networks, consisting of primary users (PUs) and secondary users (SUs), where only partial observations are available at the SUs due to narrowband sensing and transmissions. The network operates in a time-slotted regime, where the traffic patterns of the PUs are modeled as finite-memory Markov chains, that are unknown to the SUs. Since observations are partial, then both channel sensing and access actions affect the throughput. Focusing on the case in which there is a single SU, our objective is to maximize the SU’s long-term throughput. To that aim, we develop a novel algorithm that learnsbothaccess and sensing policies via deep Q-learning, dubbed Double Deep Q-network for Sensing and Access (DDQSA). To the best of our knowledge, this is the first work that jointly optimizes both sensing and access policies for DSA via deep Q-learning. Next, we consider wireless networks with access policy which implements a fixed channel hopping dynamics, for which we analytically determine the optimal SU sensing and access policy and its associated throughput. Then, we demonstrate that indeed, the proposed DDQSA algorithm can achieve near-optimal performance for the considered network. Our results show that the proposed DDQSA algorithm learns a policy that implements both sensing and channel access, which significantly outperforms existing approaches, and can achieve the optimal performance in certain scenarios.

This paper is eligible for the Jack Keil Wolf ISIT Student Paper Award. In this paper we study dynamic spectrum access (DSA) in cognitive wireless networks, consisting of primary users (PUs) and a secondary user (SU) which has only partial observations. The traffic patterns of the PUs are modeled as finite-memory Markov chains, and are unknown to the SU. It is noted that as observations are partial, then both channel sensing and channel access actions affect the throughput. Our objective in this work is to design a DSA algorithm such that the SU’s long-term throughput is maximized. To that aim, we show theoretically that the DSA problem can be formulated as a single-agent problem with a single policy for both sensing and access, and propose a novel algorithm that learns both the optimal access policy and the optimal sensing policy via deep Q-learning, which is referred to as Double Deep Q-network for Sensing and Access (DDQSA). To the best of our knowledge, this is the first instance of a deep Q-learning-based DSA algorithm, which learns both sensing and access policies. Our results show that the DDQSA algorithm learns a policy that implements both sensing and channel access, and achieves significantly better performance compared to existing approaches.

Non-orthogonal communications play an important role in future digital communication architectures. In such scenarios, the received signal is corrupted by an interfering communications signal, which is much stronger than the thermal noise, and is often modeled as a cyclostationary process in continuous-time. To facilitate digital processing, the receiver typically samples the received signal synchronously with the symbol rate of the information signal. If the period of the statistics of the interference is synchronized with that of the information signal, then the sampled interference is modeled as a discrete-time (DT) cyclostationary random process. However, in the common interference scenario, the period of the statistics of the interference is not necessarily synchronized with that of the information signal. In such cases, the DT interference may be modeled as an almost cyclostationary random process. In this work we characterize the capacity of DT memoryless additive noise channels in which the noise arises from a sampled cyclostationary Gaussian process. For the case of synchronous sampling, capacity can be obtained in closed form. When sampling is not synchronized with the symbol rate of the interference, the resulting channel is not information stable, thus classic information-theoretic tools are not applicable. Using information spectrum methods, we prove that capacity can be obtained as the limit of a sequence of capacities of channels with additive cyclostationary Gaussian noise. Our results allow to characterize the effects of changes in the sampling rate and sampling time offset on the capacity of the resulting DT channel. In particular, it is demonstrated that minor variations in the sampling period, such that the resulting noise switches from being synchronously-sampled to being asynchronously-sampled, can substantially change the capacity.

Interference-limited communications plays an important role in future digital communication architectures. In such scenarios, the received signal is corrupted by an interfering communications signal, which is typically modeled as a cyclostationary process in continuous-time. To facilitate digital processing, the receiver typically samples the received signal synchronously with the symbol rate of the information signal. The sampled received signal thus contains an interference component which is either cyclostationary or almost cyclostationary in discrete-time (DT), depending on whether the symbol rate of the interference is synchronized with the sampling rate, or it is not. In this work we characterize the capacity of DT interference-limited communications channels, in which the interference is modeled as an additive sampled cyclostationary Gaussian noise. For the case of synchronous sampling, capacity can be obtained in closed form as a direct application of our previous work. When sampling is asynchronous, the resulting channel is not information stable, thus classic information-theoretic tools are not applicable. Using information spectrum methods, we prove that capacity can be obtained as the limit of a sequence of capacities of DT channels with additive cyclostationary noise. Our results facilitate the characterization of the impact of variations in the sampling rate and sampling time offset on the capacity of the resulting DT channel. In particular, it is demonstrated that minor variations in the sampling period can have a notable effect on capacity.

Communications over power lines in the frequency range above 2 MHz, commonly referred to as broadband (BB) power line communications (PLC), is a central communications scenario for smart power grids. BB-PLC channels are characterized by a dominant colored non-Gaussian additive noise, as well as by periodic variations of the channel impulse response and the noise statistics, induced by the mains voltage. In this work we study the fundamental rate limits for multiple input-multiple output (MIMO) BB-PLC channels, modeled as periodic channels with additive non-Gaussian noise and finite memory. We present bounds on the capacity of these channels by exploiting a bijection with time-invariant MIMO channels of extended dimensions. We illustrate the resulting fundamental limits in a numerical analysis corresponding to practical MIMO BB-PLC channels.

In many communications scenarios, the channel exhibits periodic characteristics, e.g., power line communications and interference-limited communications. Additionally, certain approximations for mobile radio channels over finite time intervals may result in periodic channel models. In this paper, we study pilot-aided joint estimation of the channel impulse response (CIR) and of the carrier frequency offset (CFO) for linear periodic channels, in which both the CIR and the noise statistics vary periodically in time. We first consider the joint maximum likelihood estimator (JMLE) for the CIR and the CFO, and discuss the practical drawbacks associated with this estimator. When the coefficients of the delay-Doppler spread function of the CIR are approximately sparse, we propose two estimation schemes with higher spectral efficiency and lower computational complexity compared with the JMLE, which are obtained by exploiting both the periodicity and the sparsity of the channel, without requiring a priori knowledge of the sparsity pattern. Finally, we study the design of pilot sequences aimed at improving the estimation performance in sparse periodic channels. Simulation studies corresponding to practical scenarios of the proposed estimators demonstrate that substantial benefits can be obtained by properly accounting for the sparsity and periodicity in the design of estimation schemes.

In[1], the first equation inTheorem 2on page 1195 contains an error, where$\rho $should be replaced with$N_{0} \cdot \rho $.

Communications over power lines in the frequency range above 2 MHz, commonly referred to as broadband (BB) power line communications (PLC), has been the focus of increasing research attention and standardization efforts in recent years. BB-PLC channels are characterized by a dominant colored non-Gaussian additive noise, as well as by periodic variations of the channel impulse response and of the noise statistics. In this paper, we study the fundamental rate limits for BB-PLC channels by bounding their capacity while accounting for the unique properties of these channels. We obtain explicit expressions for the derived bounds for several BB-PLC noise models, and illustrate the resulting fundamental limits in a numerical analysis.

In the phase retrieval problem, the observations consist of the magnitude of a linear transformation of the signal of interest (SOI) with additive noise, where the linear transformation is typically referred to as measurement matrix. The objective is then to reconstruct the SOI from the observations up to an inherent phase ambiguity. Many works on phase retrieval assume that the measurement matrix is a random Gaussian matrix, which in the noiseless scenario with sufficiently many measurements guarantees uniqueness of the mapping between the SOI and the observations. However, in many applications, e.g., optical imaging, the measurement matrix corresponds to the underlying physical setup, and is therefore a deterministic matrix with structure constraints. In this work we study the design of deterministic measurement matrices, aimed at maximizing the mutual information between the SOI and the observations. We characterize necessary conditions for the optimal measurement matrix, and propose a practical design method for measurement matrices corresponding to masked Fourier measurements. Simulation tests of the proposed method show that it achieves the same performance as random Gaussian matrices for various phase recovery algorithms.

Adaptive filters are commonly used in many signal processing and communications systems. In many practical digital communications scenarios, including, for example, interference-limited wireless and wireline communications, as well as narrowband power line communications, the considered signals are jointly cyclostationary. Yet, most works on adaptive filtering of cyclostationary signals used ad hoc application of adaptive algorithms designed for stationary signals, e.g., the least-mean-squares (LMS). It is known that these algorithms may not converge for jointly cyclostationary signals. In this paper, we rigorously study the optimal adaptive filtering of jointly cyclostationary signals. We first identify the relevant objective as the time-averaged mean-squared error criterion (TA-MSE), and obtain an adaptive algorithm as the stochastic approximation of the TA-MSE minimizer. When the considered signals are jointly stationary, the algorithm specializes to the standard LMS algorithm. We provide a comprehensive transient and steady-state performance analysis without imposing a specific distribution on the considered signals, and derive conditions for convergence and stability. The algorithm, which we call time-averaged LMS, is applied to practical scenarios in a simulations study, and an excellent agreement between the theoretical and the empirical performance is observed.

In this paper, we study linear encoding for a pair of correlated Gaussian sources transmitted over a two-user Gaussian broadcast channel in the presence of unit-delay noiseless feedback, abbreviated as the GBCF. Each pair of source samples is transmitted using a linear transmission scheme in a finite number of channel uses. We investigate three linear transmission schemes: A scheme based on the Ozarow-Leung (OL) code, a scheme based on the linear quadratic Gaussian (LQG) code of Ardestanizadeh et al., and a novel scheme derived in this paper using a dynamic programming (DP) approach. For the OL and LQG schemes we present lower and upper bounds on the minimal number of channel uses needed to achieve a target mean-square error (MSE) pair. For the LQG scheme in the symmetric setting, we identify the optimal scaling of the sources, which results in a significant improvement of its finite horizon performance, and, in addition, characterize the (exact) minimal number of channel uses required to achieve a target MSE. Finally, for the symmetric setting, we show that for any fixed and finite number of channel uses, the DP scheme achieves an MSE lower than the MSE achieved by either the LQG or the OL schemes.

In this paper, we study the secrecy capacity of Gaussian multiple-input multiple-output (MIMO) wiretap channels (WTCs) with a finite memory, subject to a per-symbol average power constraint on the MIMO channel input. MIMO channels with finite memory are very common in wireless communications as well as in wireline communications (e.g., in communications over power lines). To derive the secrecy capacity of the Gaussian MIMO WTC with finite memory, we first construct an asymptotically equivalent block-memoryless MIMO WTC, which is then transformed into a set of parallel, independent, memoryless MIMO WTCs in the frequency domain. The secrecy capacity of the Gaussian MIMO WTC with finite memory is obtained as the secrecy capacity of the set of parallel, independent, memoryless MIMO WTCs, and is expressed as maximization over the input covariance matrices in the frequency domain. Finally, we detail two applications of our result: First, we show that the secrecy capacity of the Gaussian scalar WTC with finite memory can be achieved by waterfilling, and obtain a closed-form expression for this secrecy capacity. Then, we use our result to characterize the secrecy capacity of narrowband powerline channels, thereby resolving one of the major open issues for this channel model.

Handling interference is one of the main challenges in the design of wireless networks. In this paper, we study the application of cooperation for interference management in the weak interference (WI) regime, focusing on the Z-interference channel with a causal relay (Z-ICR), in which the channel coefficients are subject to ergodic phase fading, all transmission powers are finite, and the relay is full-duplex. The phase fading model represents many practical communications systems in which the transmission path impairments mainly affect the phase of the signal, such as non-coherent wireless communications and fiber optic channels. In order to provide a comprehensive understanding of the benefits of cooperation in the WI regime, we characterize, for the first time, two major performance measures for the ergodic phase fading Z-ICR in the WI regime: the sum-rate capacity and the maximal generalized degrees-of-freedom (GDoF). In the capacity analysis, we obtain conditions on the channel coefficients, subject to which the sum-rate capacity of the ergodic phase fading Z-ICR is achieved by treating interference as noise at each receiver, and explicitly state the corresponding sum-rate capacity. In the GDoF analysis, we derive conditions on the exponents of the magnitudes of the channel coefficients, under which treating interference as noise achieves the maximal GDoF, which is explicitly characterized as well. It is shown that under certain conditions on the channel coefficients, relaying strictly increases both the sum-rate capacity and the maximal GDoF of the ergodic phase fading Z-interference channel in the WI regime. Our results demonstrate for the first time the gains from relaying in the presence of interference, when interference is weak and the relay power is finite, both in increasing the sum-rate capacity and in increasing the maximal GDoF, compared with the channel without a relay.

This work focuses on the minimum transmission energy required for communicating a pair of correlated Gaussian sources over a two-user Gaussian broadcast channel with noiseless and causal channel output feedback (GBCF). We study the fundamental limit on the required transmission energy for broadcasting a pair of source samples, such that each source can be reconstructed at its respective receiver to within a target distortion, when the source-channel bandwidth ratio is not restricted. We derive a lower bound and three distinct upper bounds on the minimum required energy. For the upper bounds we analyze three transmission schemes: Two schemes are based on separate source-channel coding, and apply coding over multiple samples of source pairs. The third scheme is based on joint source-channel coding obtained by extending the Ozarow-Leung (OL) transmission scheme, which applies uncoded linear transmission. Numerical simulations show that despite its simplicity, the energy-distortion tradeoff of the OL-based scheme is close to that of the better separation-based scheme, which indicates that the OL scheme is attractive for energy-efficient source transmission over GBCFs.

In many communications scenarios the channel exhibits periodic characteristics. Periodicity may be expressed as a periodically time-varying channel transfer function as well as an additive noise with periodically time-varying statistics. Examples for such scenarios include interference-limited communications, both wireless and wireline, and also power line communications (PLC). In this work, we characterize the capacity of discrete-time, finite-memory Gaussian multiple-input multiple-output (MIMO) channels with periodic characteristics. The derivation transforms the periodic MIMO channel into an extended time-invariant MIMO channel, for which we obtain a closed-form capacity expression. It is shown that capacity can be achieved by an appropriate waterfilling scheme. The capacity expression obtained is numerically evaluated for practical PLC scenarios, and compared to the achievable rate of an ad-hoc orthogonal frequency division multiplexing based scheme, and the gains from optimally handling the periodicity of the channel are quantified.

Abstract We study communications under slowly varying channels, and consider three cases of knowledge of the channel impulse response (CIR): full knowledge, no knowledge, and partial knowledge of the CIR. By partial knowledge, we refer to knowing only either the CIR magnitudes or the CIR phases. It is known that obtaining the exact joint maximum‐likelihood estimate (MLE) of the CFO and the SFO requires a two‐dimensional search. Here, we present a new estimation method which uses the Taylor expansion of the MLE cost function, combined with the best linear unbiased estimator, to obtain a method which does not require such a search. The computational complexity of the new method is evaluated. Numerical simulations demonstrate that the new method approaches the corresponding Cramér‐Rao bound for a wide range of signal‐to‐noise ratios, and has superior performance compared to all other existing methods for approximating the solution for the joint MLE, while maintaining a low computational complexity. Copyright © 2015 John Wiley & Sons, Ltd.

Narrowband power line communications (NB-PLC) is the central communications technology for the realization of smart power grids. For this reason, NB-PLC channels have been receiving substantial attention in recent years. These channels are characterized by periodic short-term variations of the channel transfer function (CTF) and strong noise with periodic statistics. In this work, we derive the capacity of discrete-time NB-PLC channels, accounting for the periodic properties of both the CTF and the noise. As part of the capacity derivation, we characterize the capacity achieving transmission scheme, which leads to guidelines for constructing a practical code that approaches the capacity as the blocklength increases. The capacity derived in this work is numerically evaluated and the results show that the optimal scheme achieves a substantial rate gain over previously proposed ad-hoc scheme. This gain is due to optimally accounting for the periodic properties of the channel and the noise.

Privacy is a critical issue when communicating over shared mediums. A fundamental model for the information-theoretic analysis of secure communications is the wiretap channel (WTC), which consists of a communicating pair and an eavesdropper. In this work we study the secrecy capacity of Gaussian multiple-input multiple-output (MIMO) WTCs with finite memory. These channels are very common in wireless communications as well as in wireline communications (e.g., in power line communications). We derive a closed-form expression for the secrecy capacity of the MIMO Gaussian WTC with finite memory via the analysis of an equivalent block-memoryless model, which is transformed into a set of parallel independent memoryless MIMO WTCs. The secrecy capacity is expressed as the maximization over the input covariance matrices in the frequency domain. Finally, we show that for the Gaussian scalar WTC with finite memory, the secrecy capacity can be obtained by waterfilling.

We study the uncoded transmission of a bivariate Gaussian source over a two-user symmetric Gaussian broadcast channel with a unit-delay noiseless feedback (GBCF), assuming that each (uncoded) source sample is transmitted using a finite number of channel uses, and that the transmission scheme is linear. We consider three transmission schemes: The scheme of Ardestanizadeh et al., which is based on linear quadratic Gaussian (LQG) control theory, the scheme of Ozarow and Leung (OL), and a novel scheme derived in this work designed using a dynamic programing (DP) approach. For the LQG scheme we characterize the minimal number of channel uses needed to achieve a specified mean-square error (MSE). For the OL scheme we present lower and upper bounds on the minimal number of channel uses needed to achieve a specified MSE, which become tight when the signal-to-noise ratio approaches zero. Finally, we show that for any fixed and finite number of channel uses, the proposed DP scheme achieves MSE lower than the MSE achieved by either the LQG or the OL schemes.

In this work, we consider linear-feedback schemes for the two-user Gaussian broadcast channel with noiseless feedback. We extend the transmission scheme of [Ozarow and Leung, 1984] by applying estimators with memory instead of the memoryless estimators used by Ozarow and Leung (OL) in their original work. A recursive formulation of the mean square errors achieved by the proposed estimators is provided, along with a proof for the existence of a fixed point. This enables characterizing the achievable rates of the extended scheme. Finally, via numerical simulations it is shown that the extended scheme can improve upon the original OL scheme in terms of achievable rates, as well as achieve a low probability of error after a finite number of channel uses.

Power line communications (PLC) is the central communications technology for the realization of smart power grids. As the designated band for smart grid communications is the narrowband (NB) power line channel, NB-PLC has been receiving substantial attention in recent years. Narrowband power line channels are characterized by cyclic short-term variations of the channel transfer function (CTF) and strong noise with periodic statistics. In this paper, modeling the CTF as a linear periodically time-varying filter and the noise as an additive cyclostationary Gaussian process, we derive the capacity of discrete-time NB-PLC channels. As part of the capacity derivation, we characterize the capacity achieving transmission scheme, which leads to a practical code construction that approaches capacity. The capacity derived in this work is numerically evaluated for several NB-PLC channel configurations taken from previous works, and the results show that the optimal scheme achieves a substantial rate gain over a previously proposed ad-hoc scheme. This gain is due to optimally accounting for the periodic properties of the channel and the noise.

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

Power line communications (PLC) has been drawing considerable interest in recent years due to the growing interest in smart grid implementation. In smart grids, network control and grid applications are allocated the frequency band of 0-500 kHz, commonly referred to as the narrowband PLC channel. This channel is characterized by strong periodic noise and low signal to noise ratio (SNR). In this work we propose a receiver which uses frequency shift filtering to exploit the cyclostationary properties of both the narrowband PLC noise, as well as the information signal, digitally modulated using orthogonal frequency division multiplexing. The results show that the new receiver obtains a substantial performance gain over previously proposed receivers, without requiring any coordination with the transmitter.

We study the generalized degrees of freedom (GDoF) of the phase fading Z-interference channel with a relay in the weak interference regime. We consider the scenario in which the relay node receives transmissions only from one of the sources but its transmissions are received at both destinations. We first derive two upper bounds on the achievable GDoF: the first bound is based on the genie-aided approach, and the second bound is based on the cut-set theorem. We then derive an achievable GDoF by employing the decode-and-forward strategy at the relay and by treating interference as noise at each receiver. Lastly, we derive conditions on the gains of the links, under which this simple scheme is GDoF-optimal. Our results support the application of relaying in scenarios in which the interference is weak.

This work studies the problem of jointly estimating the carrier frequency offset (CFO) and sampling frequency offset (SFO) in orthogonal frequency-division multiplexing (OFDM) systems. Two scenarios are considered: known channel impulse response (CIR) and unknown CIR. It was shown in previous works that the exact joint maximum-likelihood estimate (MLE) of the CFO and the SFO requires a two-dimensional search. In this work, we present a new estimation method which uses the Taylor expansion of the MLE cost function, combined with the best linear unbiased estimator, to obtain an estimator which does not require such a search. Numerical simulations demonstrate that the new method approaches the corresponding Cramér-Rao bound for a wide range of signal-to-noise ratios, and have superior performance compared to all other existing methods for approximating the joint MLE solution, while maintaining a low computational complexity.

Power line communications (PLC) has been drawing considerable interest in recent years due to the growing interest in smart grid implementation. Specifically, network control and grid applications are allocated the frequency band of 0-500 kHz, commonly referred to as the narrowband PLC channel. This frequency band is characterized by strong periodic noise which results in low signal to noise ratio (SNR). In this work we propose a receiver which uses frequency shift filtering to exploit the cyclostationary properties of both the narrowband power line noise, as well as the information signal, digitally modulated using orthogonal frequency division multiplexing. An adaptive implementation for the proposed receiver is presented as well. The proposed receiver is compared to existing receivers via analysis and simulation. The results show that the receiver proposed in this work obtains a substantial performance gain over previously proposed receivers, without requiring any coordination with the transmitter.

We study the transmission of correlated sources over discrete memoryless (DM) multiple-access-relay channels (MARCs), in which both the relay and the destination have access to side information arbitrarily correlated with the sources. As the optimal transmission scheme is an open problem, in this paper, we propose a new joint source-channel coding scheme based on a novel combination of the correlation preserving mapping (CPM) technique with Slepian-Wolf (SW) source coding, and obtain the corresponding sufficient conditions. The proposed coding scheme is based on the decode-and-forward strategy, and utilizes CPM for encoding information simultaneously to the relay and the destination, whereas the cooperation information from the relay is encoded via SW source coding. It is shown that there are cases in which the new scheme strictly outperforms the schemes available in the literature. This is the first instance of a source-channel code that uses CPM for encoding information to two different nodes (relay and destination). In addition to sufficient conditions, we present three different sets of single-letter necessary conditions for reliable transmission of correlated sources over DM MARCs. The newly derived conditions are shown to be at least as tight as the previously known necessary conditions.

The characterization of the optimal joint source-channel coding scheme for transmission of correlated sources over multiple-access-relay channels (MARCs) is an open problem. Here, this problem is studied in the presence of arbitrarily correlated side information at both the relay and the destination. Since each transmitter observes only one of the sources, the admissible joint distributions of the sources and channel inputs must satisfy a Markov relationship which constrains their statistical dependence. This observation is used together with the new data processing inequality derived by [Kang and Ulukus, 2011] to obtain two new sets of single-letter necessary conditions. These new conditions are shown to be at least as tight as the previously known ones, and strictly tighter than the cut-set bound.

We study the sum-rate capacity of the Z-interference channel with a relay (Z-ICR) in the weak interference regime, when the channel coefficients are subject to phase fading. This fading model represents many practical communication systems in which phase noise is a major concern, such as OFDM communications and line-of-sight microwave communications. We consider the case in which the relay receives transmissions from only one of the two transmitters, but the transmission of the relay is received at both destinations. We present conditions on the channel coefficients under which the sum-rate capacity of the phase fading Z-ICR is achieved by treating interference as noise at each receiver, and derive the corresponding sum-rate capacity. Our results show the benefits of relaying in the presence of interference when interference is weak and relay power is finite.

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

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

We study reliable transmission of arbitrarily correlated sources over multiple-access relay channels (MARCs) and multiple-access broadcast relay channels (MABRCs). In MARCs only the destination is interested in reconstructing the sources, while in MABRCs, both the relay and the destination want to reconstruct them. In addition to arbitrary correlation among the source signals at the users, both the relay and the destination have side information correlated with the source signals. Our objective is to determine whether a given pair of sources can be losslessly transmitted to the destination for a given number of channel symbols per source sample, defined as the source-channel rate. Sufficient conditions for reliable communication based on operational separation, as well as necessary conditions on the achievable source-channel rates are characterized. Since operational separation is generally not optimal for MARCs and MABRCs, sufficient conditions for reliable communication using joint source-channel coding schemes based on a combination of the correlation preserving mapping technique with Slepian-Wolf source coding are also derived. For correlated sources transmitted over fading Gaussian MARCs and MABRCs, we present conditions under which separation (i.e., separate and stand-alone source and channel codes) is optimal. This is the first time optimality of separation is proved for MARCs and MABRCs.

Reliable transmission of arbitrarily correlated sources over multiple-access relay channels (MARCs) and multiple-access broadcast relay channels (MABRCs) is considered. In MARCs, only the destination is interested in a reconstruction of the sources, while in MABRCs, both the relay and the destination want to reconstruct the sources. We allow an arbitrary correlation among the sources at the transmitters, and let both the relay and the destination have side information that are correlated with the sources. Two joint source-channel coding schemes are presented and the corresponding sets of sufficient conditions for reliable communication are derived. The proposed schemes use a combination of the correlation preserving mapping (CPM) technique with Slepian-Wolf (SW) source coding: the first scheme uses CPM for encoding information to the relay and SW source coding for encoding information to the destination; while the second scheme uses SW source coding for encoding information to the relay and CPM for encoding information to the destination.

The interference channel with a relay (ICR) is the fundamental building block of cooperation in wireless networks where there are multiple communicating pairs interfering with each other. This paper considers ICRs in which the links are subject to i.i.d. fading, and each node has channel state information (CSI) only on its incoming links (receive CSI). Two channel models are considered: phase fading and Rayleigh fading. Strong interference conditions are derived for the case where the links from the sources to the relay are good in the sense that the achievable region for decoding both messages at the relay contains the maximal achievable region at the destinations. This leads to the characterization of the capacity region for such scenarios. This is the first time the capacity region of the ICR is characterized for a nondegraded, noncognitive scenario, with a causal relay when all links are active.

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

Handling interference is one of the main challenges in the design of wireless networks. One of the key approaches to interference management is node cooperation, which can be classified into two main types: relaying and feedback. In this paper, we consider simultaneous application of both cooperation types in the presence of interference. We obtain exact characterization of the capacity regions for Rayleigh fading and phase fading interference channels with a relay and with feedback links, in the strong and very strong interference regimes. Four feedback configurations are considered: 1) feedback from both receivers to the relay, 2) feedback from each receiver to the relay and to one of the transmitters (either corresponding or opposite), 3) feedback from one of the receivers to the relay, and 4) feedback from one of the receivers to the relay and to one of the transmitters. Our results show that there is a strong motivation for incorporating relaying and feedback into wireless networks.

Handling interference is one of the main challenges in the design of wireless networks. One of the key approaches to interference management is node cooperation, which can be classified into two main types: relaying and feedback. In this work we consider simultaneous application of both cooperation types in the presence of interference. We obtain exact characterization of the capacity regions for Rayleigh fading and phase fading interference channels with a relay and with feedback links, in the strong and very strong interference regimes. Two feedback configurations are considered. In the first configuration there are feedback links from both receivers to the relay, and in the second configuration there are feedback links from both receivers to the relay and to their opposite transmitters.

The interference channel with a relay (ICR) is the fundamental building block of cooperation in wireless networks consisting of multiple communicating pairs. This work considers ICRs in which the links are subject to i.i.d. phase fading. Strong interference conditions are derived for the case where the links from the sources to the relay are good, leading to the characterization of the capacity region of the ICR for such scenarios. This is the first time the capacity region of this model is characterized for a non-degraded, non-cognitive scenario when all links are active and the SNRs are finite.

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

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

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

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

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

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

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

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

In this paper, we focus on the general relay channel. We investigate the application of the estimate-and-forward (EAF) relaying scheme to different scenarios. Specifically, we study assignments of the auxiliary random variable that always satisfy the feasibility constraints. We then consider the Gaussian relay channel with coded modulation, where we show that a three-level quantization outperforms the Gaussian quantization commonly used to evaluate the achievable EAF rates in this scenario. Last, we consider the cooperative general broadcast scenario with a multistep conference between the receivers. We first apply EAF to obtain a general achievable rate region with a multistep conference. We then use an explicit assignment for the auxiliary random variables to obtain an explicit rate expression for the single common message case with a two-step conference.

In this paper we consider the multiple-relay channel. For this scenario there are two well known results: the decode-and- forward (DAF) result of [Xie and Kumar, 2005] and the estimate-and forward (EAF) result of [Kramer et al., 2005]. However, the EAF result does not lend itself to numerical evaluation due to the large number of parameters to be determined and the non-convex nature of the optimization problem for finding the maximum rate. Therefore, for a given channel we cannot tell what is the EAF rate while keeping the expressions in their general form. We propose a specific assignment for the EAF auxiliary variables that satisfy the feasibility constraints and allow us to obtain an explicit EAF-based rate expression. This expression can be easily computed, and compared against the DAF- based rate. We give an example of a channel where this EAF rate is superior to both the DAF and the point-to-point rates.

In this work we consider the Gaussian relay channel with coded modulation at the transmitter and an orthogonal relay- destination link. We investigate the application of the estimate-and- forward (EAF) scheme with different mappings at the relay to this scenario. We show that in certain situations a three-level quantization outperforms the Gaussian mapping, which is the common practice in this scenario. We conclude that for the coded modulation scenario Gaussian quantization is good at low source-relay SNR, decode-and- forward is superior at high source-relay SNR and at intermediate SNR, methods that combine elements of both schemes are superior to these individual assignments. Another observation is that as the source-relay SNR increases, the cardinality of the auxiliary random variable can be decreased.

In this paper we consider the general broadcast channel with partially cooperating receivers having noiseless conference links of finite capacity between them. We present an explicit three-step conference scheme, which improves on the two-step scheme presented previously in [Dabora et al., ISIT 05]. The scheme achieves the full cooperation rate bounds at conference capacities that are less than the full cooperation capacities, i.e. C212|Y1) and C121|Y2). We also introduce a new relaying strategy for the general relay channel, which results in a rate increase for any non-degraded channel and does not require auxiliary random variables

We consider the problem of communicating over the general discrete memoryless broadcast channel (DMBC) with partially cooperating receivers. In our setup, receivers are able to exchange messages over noiseless conference links of finite capacities, prior to decoding the messages sent from the transmitter. In this paper, we formulate the general problem of broadcast with cooperation. We first find the capacity region for the case where the BC is physically degraded. Then, we give achievability results for the general broadcast channel, for both the two independent messages case and the single common message case

We consider the problem of communicating over the general discrete memoryless broadcast channel (BC) with partially cooperating receivers. In our setup, receivers are able to exchange messages over noiseless conference links of finite capacities, prior to decoding the messages sent from the transmitter. This problem comes up naturally in a sensor networking application, where a transmitter external to the sensor network wants to download data into the network, e.g., to configure the sensor array. In this paper, we extend the achievability results for the degraded broadcast channel derived in R. Dabora and S. Servetto (2004), to the general channel and present an upper bound on the rates

This paper describes the problem of communicating over broadcast channels (BCs) with partially cooperating receivers. In our setup receivers are able to exchange messages over conference links, prior to making their decisions. This problem comes up naturally in a sensor networking application, where a transmitter external to the sensor network wants to download data into the network to, e.g., configure the sensor array. We find the capacity region for the case where the BC is degraded. This region is a strict enlargement of the classical region for the degraded BC without cooperation in [T.M. Cover,(1998)].

In this paper, we consider training-based symbol timing synchronization for continuous phase modulation over channels subject to flat, Rayleigh fading. A high signal-to-noise-ratio maximum-likelihood estimator based on a simplified channel correlation model is derived. The main objective is to reduce algorithm complexity to a single-dimensional search on the delay parameter, similar to that of the static-channel (slow fading) estimator. The asymptotic behavior of the algorithm is evaluated, and comparisons are made with the Cramer-Rao lower bound for the problem. Simulation results demonstrate highly improved performance over the conventional, static-channel delay estimator.

In this paper we consider a time synchronization problem for a minimum shift keying (MSK) signal received over a time-selective, fast fading channel. We calculate the Cramer Rao bound (CRB) for the case when the transmitted data bits are a-priori known and examine the effects of parameters such as signal-to-noise ratio (SNR) and temporal correlation of the channel on the synchronization performance. In addition, we derive an explicit high SNR approximation to the CRB. Lastly, we use the bound to study how the choice of transmitted bits (the training sequence) influences synchronization performance thus enabling us to identify the best and worst case bit sequences.