Optimal transmit precoding for distributed estimation in correlated wireless sensor networks

In this paper we present optimal transmit precoding schemes for distributed estimation in a correlated wireless sensor network. The presented schemes employ linear preprocessing with multiple transmit antennas and are based on a coherent MAC between the multiple sensors and the fusion center. In this context, we derive the closed form expression for the optimal transmit processing scheme which minimizes the variance of the estimate at the fusion center. Further, we also develop a low complexity transmit scheme for scenarios with partial Channel State Information (CSI) availability. Closed form expressions are also derived to characterize the asymptotic variance of the optimal full CSI, partial CSI and other suboptimal transmit processing schemes. Simulation results are presented to demonstrate the performance of the proposed schemes for distributed estimation in a wireless sensor network.