Optimum Performance Boundaries of OSTBC Based AF-MIMO Relay System With Energy Harvesting Receiver

This paper studies the optimum performance boundaries of a two-hop multi-antenna amplify-and-forward (AF) relay system with a multi-antenna energy harvesting (EH) receiver. The source and relay nodes employ orthogonal space-time block codes for data transmission. When instantaneous channel state information (CSI) is available, we design joint optimal source and relay precoders to achieve different tradeoffs between the energy and information transfers, which are characterized by the boundary of the rate-energy (R-E) region. For this purpose, the optimization problem is formulated as a relaxed convex problem but its optimality is confirmed with a proof that rank-one optimal precoders can always be obtained. As a consequence, it is shown that the full-rate OSTBC, like the Alamouti code, can be employed for an arbitrary number of antennas at the transmit nodes (source and relay) and support up to seven simultaneously existing EH receivers. When only second order statistics of the CSI is available, the tradeoff between outage probability (OP) and energy is characterized by the boundary of the OP-energy (OP-E) region. In this case, the precoder design problem is formulated using a convex upper bound approximation to the OP, since the exact OP expression is difficult for tractable optimization. Numerical results show that the OP-E region obtained with the upper bound of the OP is better than that with the approach based on maximization of the long-term average signal-to-noise ratio (SNR). The role of the different parameters such as average SNR, numbers of antennas, and spatial correlation on the boundaries of the R-E and OP-E regions is demonstrated via simulations.