Cyclostationary Signal Processing For Narrowband Power Line Communications

The growing interest in smart grid applications has drawn considerable attention to power line communications (PLC) as a central communications medium for smart grids. Specifically, network control and grid applications are allocated the frequency band of 0 − 500 kHz, commonly referred to as the narrowband PLC channel. As this frequency band is characterized by strong cyclostationary noise, multipath signal propagation, and periodically time varying channel conditions, narrowband PLC channels fall into the class of periodic channels with finite memory. In this dissertation we study communications over periodic channels with finite memory, utilizing the theory of cyclostationary processes to address two major aspects: information-theoretic performance bounds, and practical algorithms for realizing the predicted performance gains. In the first part of the dissertation, we study the fundamental rate limits of periodic channels with finite memory, focusing on the capacity of point-to-point (PtP) periodic channels, i.e., without security constraints, as well as the secrecy capacity of periodic wiretap channels, i.e., with security constraints. By proving a bijection between PtP periodic channels and time-invariant multiple input-multiple output (MIMO) channels with finite memory, we characterize the capacity of periodic channels via the capacity of the equivalent time-invariant MIMO channels. As part of the capacity derivation, we characterize the capacity achieving transmission scheme, which leads to a practical code construction that approaches capacity. Motivated by the bijection between periodic channels and time-invariant MIMO channels with finite memory, we study the secrecy capacity of time-invariant Gaussian MIMO channels with finite memory. Although the time-invariant Gaussian MIMO channel with finite memory is a very common channel model in wireless communications, as well as in wireline communications, this is the first time that the secrecy capacity has been characterized for this channel model. As the resulting secrecy capacity expression is given by a non-convex optimization problem, we derive a simple necessary and sufficient condition for positive secrecy capacity, and obtain an explicit expression for the secrecy capacity in the scalar case. Then, we show how our result directly leads to the secrecy capacity of periodic channels. In the second part of the dissertation, we study practical algorithms which utilize the theory of cyclostationarity to approach the predicted performance gains in periodic channels. First, we propose a receiver algorithm for the recovery of orthogonal frequency division multiplexing (OFDM) modulated signals in periodic channels. The proposed receiver uses frequency-shift filtering to exploit the cyclostationary properties of both the additive channel noise and the information signal. We explicitly derive the coefficients of the filter which minimize the time-averaged mean-squared error (TA-MSE), and propose an adaptive implementation, which is based on the recursive least-squares (RLS) algorithm. Numerical simulations show that the proposed receiver demonstrates a substantial performance gain over previously proposed receivers. Finally, motivated by the fact that most adaptive algorithms, such as the least mean-squares (LMS) and the RLS, are designed for stationary signals, we rigorously study the optimal adaptive filtering of cyclostationary signals. We first identify the relevant objective as the TA-MSE, and obtain an adaptive algorithm, which we refer to as time-averaged LMS (TA-LMS), as the stochastic approximation of the TA-MSE minimizer. We provide a comprehensive transient and steady-state performance analysis, and derive conditions for convergence and stability, which are shown to accurately characterize the performance of the adaptive algorithm in a simulation study.-- abstract.