  This work focuses on distributed linear precoding when users transmit
correlated information over a fading Multiple-Input and Multiple-Output
Multiple Access Channel. 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. 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
semidefinite 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 SNRs and when the number of receive antennas is
lower than the number of transmitting nodes.
