Nir Shlezinger

On the Capacity of Narrowband PLC Channels

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.

Frequency-Shift Filtering for OFDM Signal Recovery in Narrowband Power Line Communications

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.

The Secrecy Capacity of Gaussian MIMO Channels With Finite Memory

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.

Adaptive Filtering Based on Time-Averaged MSE for Cyclostationary Signals

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.

Carrier frequency offset estimation for linear channels with periodic characteristics

Periodic characteristics arise in many communications scenarios. Two major examples are interference-limited communications and power line communications. The most general point-to-point periodic channel model includes periodic variations of the channel transfer function and of the noise statistics. In this work we study carrier frequency offset estimation for linear channels with periodic characteristics. We design a maximum likelihood estimator (MLE), analytically characterize its asymptotic performance, and provide guidelines for its low-complexity implementation. We compare the strengths and weaknesses of the new estimator to those of an ad-hoc extended estimator obtained by adapting an MLE, originally designed for time-invariant channels, to periodically time-varying channels via a time partitioning approach. We numerically evaluate the performance of the new estimator and of the ad-hoc estimator, and illustrate the gain of rigorously accounting for the periodic characteristics of the channel, as opposed to the currently prevailing ad-hoc approach.

On the derivation of the capacity of discrete-time narrowband PLC channels

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.

Measurement Matrix Design for Phase Retrieval Based on Mutual Information

In phase retrieval problems, a signal of interest (SOI) is reconstructed based on the magnitude of a linear transformation of the SOI observed with additive noise. The linear transform is typically referred to as a measurement matrix. 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 invertability of the transformation between the SOI and the observations, up to an inherent phase ambiguity. However, in many practical applications, the measurement matrix corresponds to an underlying physical setup, and is therefore deterministic, possibly with structural constraints. In this paper, we study the design of deterministic measurement matrices, based on maximizing the mutual information between the SOI and the observations. We characterize necessary conditions for the optimality of a measurement matrix, and analytically obtain the optimal matrix in the low signal-to-noise ratio regime. Practical methods for designing general measurement matrices and masked Fourier measurements are proposed. Simulation tests demonstrate the performance gain achieved by the suggested techniques compared to random Gaussian measurements for various phase recovery algorithms.

Adaptive LMS-type filter for cyclostationary signals.

Adaptive filters are employed in many signal pro- cessing and communications systems. Commonly, the design and analysis of adaptive algorithms, such as the least mean-squares (LMS) algorithm, is based on the assumptions that the signals are wide-sense stationary (WSS). However, in many cases, including, for example, interference-limited wireless communications and power line communications, the considered signals are jointly cyclostationary. In this paper we propose a new LMS-type algorithm for adaptive filtering of jointly cyclostationary signals using the time-averaged mean-squared error objective. When the considered signals are jointly WSS, the proposed algorithm specializes to the standard LMS algorithm. We characterize the performance of the algorithm without assuming specific distributions on the considered signals, and derive conditions for convergence. We then evaluate the performance of the proposed algorithm, called time-averaged LMS, in a simulation study of practical channel estimation scenarios. The results show a very good agreement between the theoretical and empirical performance measures.

The capacity of discrete-time Gaussian MIMO channels with periodic characteristics

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.

The secrecy capacity of MIMO Gaussian channels with finite memory

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.