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This paper considers the joint transceiver design in a wireless sensornetwork where multiple sensors observe the same physical event and transmittheir contaminated observations to a fusion center, with all nodes equippedwith multiple antennae and linear filters. Under the mean square error (MSE)criterion, the joint beamforming design problem can be formulated as anonconvex optimization problem. To attack this problem, various blockcoordinate descent (BCD) algorithms are proposed with convergence beingcarefully examined. First we propose a two block coordinate descent (2-BCD)algorithm that iteratively designs all the beamformers and the linear receiver,where both subproblems are convex and the convergence of limit points tostationary points is guaranteed. Besides, the thorough solution to optimizingone single beamformer is given, which, although discussed several times, isusually incomplete in existing literature. Based on that, multiple blockcoordinate descent algorithms are proposed. Solving the joint beamformers'design by cyclically updating each separate beamformer under the 2-BCDframework gives birth to a layered BCD algorithm, which guarantees convergenceto stationary points. Besides that, a wide class of multiple BCD algorithmsusing the general essentially cyclic updating rule has been studied. As will beseen, by appropriately adjusting the update of single beamformer, fastconverging, highly efficient and stationary point achieving algorithms can beobtained. Extensive numerical results are presented to verify our findings.

Joint Transceiver Design for Wireless Sensor Networks through Block Coordinate Descent Optimization