Joint Transceiver Design for Linear MMSE Data Fusion in Coherent MAC Wireless Sensor Networks

This paper considers the design of minimal mean square error (MMSE) transceivers in a wireless sensor network. The problem is nonconvex and challenging, and previous results (with partial solutions and/or with convergence unproved) left much to be desired. Here we propose several approaches - 2 block coordinate descent (BCD), essentially cyclic multi-block method and its variants and distributive method to solve this problem. The proposed 2-BCD approach formulates the subproblem of joint beamformer optimization as a general second-order cone programming problem, which lends itself to standard numerical solvers and which requires no extra assumptions like previous works do. The proposed essentially cyclic multi-block approach further decomposes the joint beamformer design subproblem into multiple blocks, and rigorously solves each with semi-closed-form solution. The distributive algorithm optimizes transmitters in a decentralized manner and has never been considered in existing literature. The distributive algorithm has time complexity independent of number of sensors and is especially suitable for large-scale networks. All the previous BCD-based approaches left some singularity issue unattended as well as the convergence property unaddressed, our proposals are the first to provide a complete and provably-converging analytical solution. Extensive analysis and simulations demonstrate the merits of the novel approaches relative to existing alternatives.