Beamforming for Centralized Wireless Sensor Network with Noisy Observation

This paper focuses on joint beamforming design towards maximizing mutual information (MI) in a coherent multiple access channel (MAC) wireless sensor network (WSN) with nodes equipped with multiple antennae. We consider the scenario where the same source signal is observed by all sensors, with each sensor having independent noisy observation and individual power constraint. All the sensors transmit their observations to a preassigned node, called fusion center (FC), to perform further processing and data fusion. To attack this nonconvex hard problem, we adopt the weighted minimum mean square error(WMMSE) method to transform the original problem by introducing intermediate variables and then consult to the block coordinate ascent (BCA) methodology to develop iterative algorithms for solutions. Specifically, we design a 3-block BCA algorithm with each of its three subproblems having closed form solutions or being efficiently solvable by standard numerical solvers. As will be shown, this proposed 3-BCA algorithm exhibits a satisfactory convergence property. Besides that, a multiple block BCA algorithm is also developed, which has closed form solution to each subproblem (possibably up to a simple bisection search). This multiple block BCA algorithm cherishes low complexity, does not depend on numerical solver and can even give out fully analytical update in special circumstance. Extensive numerical results are presented to test our algorithms.