Design of Linear Precoders for Correlated Sources in MIMO Multiple Access Channels

Abstract

This paper focuses on distributed linear precoding when users transmit correlated information over a fading multiple-input and multiple-output multiple access channel. The precoders are optimized in order to minimize the sum-mean square error (MSE) between the source and the estimated symbols. When sources are correlated, minimizing the sum-MSE results in a non-convex optimization problem. The precoders for an arbitrary number of users and transmit and receive antennas are thus obtained via a projected steepest-descent algorithm and a low-complexity heuristic approach. For the more restrictive case of two single-antenna users, a closed-form expression for the minimum sum-MSE precoders is derived. Moreover, for the scenario with a single receive antenna and any number of users, a solution is obtained by means of a semi-definite relaxation. Finally, we also consider precoding schemes where the precoders are decomposed into complex scalars and unit norm vectors. Simulation results show a significant improvement when source correlation is exploited at precoding, especially for low signal-to-noise ratios and when the number of receive antennas is lower than the number of transmitting nodes.