Downlink beamforming for SWIPT multi-user MISO underlay cognitive radio networks

This letter investigates downlink beamforming for simultaneous wireless information and power transfer in multi-user multi-input single-output underlay cognitive radio networks. Under the assumption of the integrated power splitting (PS) receiver architecture at the secondary receivers, we aim to minimize the total transmission power from the secondary base station by jointly optimizing the beamforming vectors and the PS ratios. We first exploit the structure of the relaxed problem to provide a closed form expression for the optimal solution. Since the underlying optimization problem is non-convex, we resort to semidefinite programming relaxation and we analytically prove that the relaxation is in fact tight and yields optimal beamforming solution