Linear MMSE Precoder Combiner Designs for Decentralized Estimation in Wireless Sensor Networks

This work considers the design of linear minimum mean square error (MMSE) precoders and combiners for the estimation of an unknown vector parameter in a coherent multiple access channel (MAC)-based multiple-input multiple-output (MIMO) wireless sensor network. The proposed designs that minimize the mean squared error (MSE) of the parameter estimate at the fusion center are based on majorization theory, which leads to non-iterative closed-form solutions for the precoders and combiners. Various scenarios are considered for parameter estimation such as networks with ideal high precision sensors as well as noisy non-ideal sensors. Moreover, inter parameter correlation is also incorporated, which makes the analysis comprehensive. The Bayesian Cramer-Rao bound (BCRB) and centralized MMSE bound are determined to characterize the estimation performance. Simulation results demonstrate the improved performance and also corroborate our analytical formulations.