Robust Optimum and Near-Optimum Beamformers for Decode-and-Forward Full-Duplex Multi-Antenna Relay With Self-Energy Recycling

In this paper, we consider the full-duplex decode-and-forward wireless-powered relaying system, which employs energy harvesting protocol with power splitting. The robust joint optimum relay transmit beamformer and power splitting factor are obtained for the quality of service (QoS)-aware problem for the first time in the literature. The optimum solution is found by analyzing the Karush-Kuhn-Tucker conditions, thanks to the effective reformulation of the problem in an equivalent and simplified manner. In addition, the signal-to-interference-plus-noise ratio (SINR) maximization problem is investigated in order to find the robust optimum solution. The simulation results verify the optimality of the proposed method compared with the sub-optimum one which is presented by Zhao et al.. In the next part of this paper, the considered system is generalized by employing multiple receive antennas at the relay. Both QoS-aware and SINR maximization problems are considered. The near-optimum relay transmit and receive beamformers as well as power splitting factor are found by optimizing the variables alternately. First, transmit beamformer and power splitting factor are found optimally for a given initial receive beamformer. Then, the optimum receive beamformer is obtained. Relay with multiple-receive antennas is shown to perform better than the single receive antenna relay in terms of SINR and transmission power