Joint MMSE transceiver design for noisy MIMO channel with erasures

This paper investigates the design of optimal precoder for multiple input multiple output (MIMO) channel subjected to channel erasure and additive noise with known covariance. The subchannel erasure process is modeled as an independent Bernoulli process with known loss probabilities. The MIMO channel is known to the transmitter and receiver. But instantaneous erasure states are only known to receiver while transmitter has the statistical information of the erasures. We search for the optimal redundant linear correlating transform coding to combat against channel impairments due to erasure and noise by minimizing mean square error (MSE). While the transmitter is designed to accommodate all the channel scenarios, the minimum MSE (MMSE) receiver reconstructs the source for each channel realization. We propose a method based on linear matrix inequities (LMI) to solve for optimal precoder which can be efficiently computed by well known convex optimization toolbox. Effectiveness of this method is demonstrated by simulation examples.