A Gauss-Seidel approach to precoding design for joint transmission of distributed correlated sources

We consider the problem of transmitting multiple spatially distributed correlated sources to a common destination (e.g. a fusion center or an access point) in wireless sensor networks (WSNs). The correlated data from multiple sensors are jointly transmitted to the destination via orthogonal channels. We assume that the channel between each sensor and the receiver is multiple-input multiple-output (MIMO), with each sensor and the receiver equipped with multiple transmit/receive antennas. In this framework, we study the problem of joint design of linear precoders for all sensors by assuming the knowledge of the instantaneous channel state information (CSI), with the objective of maximizing the mutual information between the sources and the destination. We propose a Gauss-Seidel iterative approach which successively optimizes the precoding matrix associated with each sensor, while fixing the other precoding matrices. Numerical results show that the proposed algorithm that takes into account the spatial correlations across sensors can achieve higher capacity than conventional methods that neglect the spatial correlations.