Optimization of a robust collaborative-relay beamforming design for simultaneous wireless information and power transfer

We investigate a collaborative-relay beamforming design for simultaneous wireless information and power transfer. A non-robust beamforming design that assumes availability of perfect channel state information (CSI) in the relay nodes is addressed. In practical scenarios, CSI errors are usually inevitable; therefore, a robust collaborative-relay beamforming design is proposed. By applying the bisection method and the semidefinite relaxation (SDR) technique, the non-convex optimization problems of both non-robust and robust beamforming designs can be solved. Moreover, the solution returned by the SDR technique may not always be rank-one; thus, an iterative sub-gradient method is presented to acquire the rank-one solution. Simulation results show that under an imperfect CSI case, the proposed robust beamforming design can obtain a better performance than the non-robust one.