Optimal random parameter EM based Kalman filter (REKF) for fast fading MIMO channel estimation

In this work, we propose a novel random parameter based approach of the expectation maximization (EM) algorithm which makes use of a data-aided Kalman filter (KF) to perform joint symbol detection and channel estimation in multiple-input multiple-output (MIMO) wireless systems. This integration of EM and data-aided KF provides a robust procedure for MIMO channel estimation in fast fading wireless scenarios. Employing the random parameter approach, we prove the optimality of an iterative procedure which employs an MMSE based Kalman update of the channel estimate in the E-step followed by a fast sphere-decoder based maximum likelihood (ML) data estimate in the M-step. Thus, we demonstrate that the random parameter based KF leads to a substantial reduction in complexity compared to the deterministic parameter based approach existing in current literature. We also present a Bayesian Cramer-Rao bound (BRCB) analysis for the channel estimation using the random parameter KF scheme and compare it with the mean squared error (MSE) of the channel estimate. Simulation results for a fast fading MIMO wireless channel are presented to demonstrate the superior performance of the proposed technique with respect to bit error rate (BER) of symbol detection.