Beamforming for Centralized Wireless Sensor Network with Noisy Observation

This paper focuses on joint beamforming design problem in a multi-antenna wireless sensor network comprised of one fusion center(FC) and multiple wireless sensors. We consider the scenario where the same source signal is observed by all sensors, with each sensor having independent observation noise and individual power constraint. Each sensor transmits its corrupted observation to the FC to perform further processing and data fusion. Rent literature have researched the joint beamforming design in this system to optimize the mean square error(MSE) and signal to noise ratio(SNR) performance. Here we consider the problem to maximize mutual information(MI) between the source and received signal. To attack this nonconvex problem, we first adopt the weighted minimum mean square error(WMMSE) method to complicate the original problem by introducing intermediate variables and then utilize the block coordinate ascent(BCA) method to decompose it into subproblems. We first develop a 3-block BCA algorithm, each of the three subproblems has closed form solution or can be proved convex. Based on that, we further decompose the problem into multiple atom problems, with closed form solution to each atom problem obtained, which decreases the complexity. Convergence of the proposed algorithms is discussed and numerical results are presented to test our algorithms.