Robust Precoding and Beamforming Design of OSTBC Based CR AF-MIMO Relay System with Energy Harvesting Receiver

In this paper, we investigate the robust precoding and beamforming design problem for orthogonal space–time block code (OSTBC) based cognitive radio amplify-and-forward multiple-input–multiple-output relay systems with simultaneous wireless information and power transfer which consists of a primary receiver, a secondary source, a secondary relay, a secondary destination and an energy harvesting receiver. The secondary source and the secondary relay employ OSTBC based precoding and beamforming. The secondary relay and the secondary destination employ maximum-ratio combining for signal detecting and decoding. Our objective is to maximize the worst-case achievable rate under the sum transmit power constraint, the worst-case sum harvested power constraint and the worst-case interference power constraint. We transform the objective function into a convex function and convert the semi-infinite constraints into linear matrix inequalities by using \({\mathcal {S}}\)-Lemma and the extension of \({\mathcal {S}}\)-Lemma. Simulation results demonstrate that our proposed robust precoding and beamforming design has significant performance gain over the non-robust one.