Sparse Multiple Relay Selection for Network Beamforming With Individual Power Constraints Using Semidefinite Relaxation

This paper deals with the multiple relay selection problem in two-hop wireless cooperative networks with individual power constraints at the relays. In particular, it addresses the problem of selecting the best subset of K cooperative nodes and their corresponding beamforming weights so that the signal-to-noise ratio (SNR) is maximized at the destination. This problem is computationally demanding and requires an exhaustive search over all the possible combinations. In order to reduce the complexity, a new suboptimal method is proposed. This technique exhibits a near-optimal performance with a computational burden that is far less than the one needed in the combinatorial search. The proposed method is based on the use of the l
₁
-norm squared and the Charnes-Cooper transformation and naturally leads to a semidefinite programming relaxation with an affordable computational cost. Contrary to other approaches in the literature, the technique exposed herein is based on the knowledge of the second-order statistics of the channels and the relays are not limited to cooperate with full power.