This paper considers the relay subset selection problem in an underlay cognitive network in which two secondary users communicate assisted by a set of N potential relays. More specifically, this paper deals with the joint problem of choosing the best subset of L secondary relays and their corresponding weights which maximize the Signal-to-Interference-plus-Noise ratio (SINR) at the secondary user receiver, subject to per-relay power constraints and interference power constraints at the primary user. This problem is a combinatorial problem with a high computational burden. Nevertheless, we propose a sub-optimal technique, based on a convex relaxation of the problem, which achieves a near-optimal performance with a reduced complexity. Contrary to other approaches in the literature, the secondary relays are not limited to cooperate at full power.

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