Bayesian Cramér-Rao Bound for distributed vector estimation with linear observation model

In this paper we study the problem of distributed estimation of a random vector in wireless sensor networks (WSN) with linear observation model. Each sensor makes a noisy observation, quantizes its observation, maps it to a digitally modulated symbol, and transmits the symbol over erroneous wireless channels (subject to fading and noise) to a fusion center (FC), which is tasked with fusing the received signals and estimating the unknown vector. We derive the Bayesian Cramer-Rao Bound (CRB) matrix and study the behavior of its trace (through analysis and simulations), with respect to the system parameters, including observation and communication channel signal-to-noise ratios (SNRs). The derived CRB serves as a benchmark for performance comparison of different Bayesian estimators, including linear MMSE estimator.