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.

翻译：本文研究了当用户在衰落多输入多输出多址接入信道上传输相关信息时的分布式线性预编码问题。为最小化信源与估计符号之间的总均方误差，对预编码器进行了优化。当信源相关时，最小化总均方误差导致非凸优化问题。因此，通过投影最速下降算法和低复杂度启发式方法，获得了任意用户数及收发天线数下的预编码器。针对更受限的两个单天线用户场景，推导了最小总均方误差预编码器的闭式表达式。此外，对于单接收天线且任意用户数的场景，通过半定松弛方法获得了解。最后，我们还考虑了预编码器分解为复标量和单位范数向量的预编码方案。仿真结果表明，在预编码中利用信源相关性可带来显著性能提升，尤其在低信噪比以及接收天线数少于发射节点数的情况下。