Distributed LCMV Beamforming in a Wireless Sensor Network With Single-Channel Per-Node Signal Transmission

Linearly constrained minimum variance (LCMV) beamforming is a popular spatial filtering technique for signal estimation or signal enhancement in many different fields. We consider distributed LCMV (D-LCMV) beamforming in wireless sensor networks (WSNs) with either a fully connected or a tree topology. In the D-LCMV beamformer algorithm, each node fuses its multiple sensor signals into a single-channel signal of which observations are then transmitted to other nodes. We envisage an adaptive/time-recursive implementation where each node adapts its local LCMV beamformer coefficients to changes in the local sensor signal statistics, as well as to changes in the statistics of the wirelessly received signals. Although the per-node signal transmission and computational power is greatly reduced compared to a centralized realization, we show that it is possible for each node to generate the centralized LCMV beamformer output as if it had access to all sensor signals in the entire network, without an explicit computation of the network-wide sensor signal covariance matrix. We provide sufficient conditions for convergence and optimality of the D-LCMV beamformer. The theoretical results are validated by means of Monte Carlo simulations, which demonstrate the performance of the D-LCMV beamformer.