Blind Distributed Beamforming via Matrix Completion

Abstract

In this paper, we consider the problem of distributed beamforming, where the relays are able to cooperate with each other, in order to obtain the optimal beamforming vector based on the second-order statistics of the involved channels. We investigate the case where, the communication among the relays is imperfect, thus, the inter-relay network can be represented by a graph, where an edge represents a low distortion link. In this scenario, only a limited number of correlation quantities can be computed. On this premise, we propose a technique which overcomes the problem of the incomplete covariance matrices via matrix completion. Through simulation results, we show that, after a number of iterations, the proposed technique converges to the true covariance matrices.