Subset relay selection in wireless cooperative networks using sparsity-inducing norms

This paper addresses the problem of multiple relay selection in a two-hop wireless cooperative network. In particular, the proposed technique selects the best subset of relays, in a distributed beamforming scheme, which maximizes the signal-to-noise ratio at the destination node subject to individual power constraints at the relays. The selection of the best subset of K relays out of a set of N potential relay nodes, under individual power constraints, is a hard combinatorial problem with a high computational burden. The approach considered herein consists in relaxing this problem into a convex one by considering a sparsity-inducing norm. The method exposed in this paper is based on the knowledge of the second-order statistics of the channels and achieves a near-optimal performance with a computational burden which is far less than the one needed in the combinatorial search. Furthermore, in the proposed technique, contrary to other approaches in the literature, the relays are not limited to cooperate with full power.