EM-based maximum-likelihood channel estimation in multicarrier systems with phase distortion

In this paper, we address channel-impulse response (CIR) estimation in multicarrier systems with phase distortion, namely, phase noise (PHN) and carrier frequency offset (CFO). The estimation problem also considers the joint estimation of the channel noise variance, CFO, and PHN bandwidth. We develop a general state-space model for multicarrier systems, separating the complex signals into their real and imaginary parts. This provides a valid framework for any modulation scheme (proper or improper). We use the expectation-maximization (EM) algorithm to solve the maximum-likelihood (ML) estimation problem. Our approach exploits the linear and Gaussian structure associated with the transmitted signal. Due to the nonlinear nature of the PHN, sequential Monte Carlo (MC) techniques are considered. Our analysis includes general expressions under different training scenarios.We show, via simulation, the impact of PHN bandwidth estimation on overall parameter estimation, and we study the impact of different training levels. In addition, we consider the accuracy of the parameter estimates, providing expressions for the Fisher information matrix (FIM) and focusing on the estimation accuracy of the PHN bandwidth.