Joint relay beamforming and power splitting ratio optimization in a multi-antenna relay network

This paper investigates simultaneous wireless information and power transfer (SWIPT) in a multi-antenna relay network. We consider robust transmit power minimization problem at the relay by jointly optimizing beamforming and adaptive power splitting subject to the signal-to-inference-plus-noise (SINR) and energy harvesting constraints by incorporating channel uncertainty model. We formulate the original non-convex problem into semidefinite programming problem (SDP) by relaxing rank-one constraint and we show the optimal solution of SDP is always rank-one. Simulation results are provided to validate the performance of the proposed robust algorithms.