Optimal beamforming in spectrum sharing cognitive non-regenerative multi-relay networks

An optimal beamforming design for spectrum sharing cognitive non-regenerative multi-relay networks that maximises the signal-to-noise ratio of the secondary user subject to the total transmit power constraint at the relays and the interference power constraint at the primary user is proposed. In the power-limited regime and the interference-limited regime, closed-form beamformers can be found. While in the intermediate operating regime, the beamforming problem is first transformed to a convex semidefinite programming (SDP) via rank-one relaxation and Charnes-Cooper transformation, and then the optimal beamformers are found by applying the rank-one decomposition theorem to the solution of the established SDP. Simulation results show that the proposed solution performs better than existing schemes.