Transceiver Design for AF MIMO Relay Systems With a Power Splitting Based Energy Harvesting Relay Node

In this article, a dual-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay communication system is studied. With a splitting (PS) protocol, the relay node harvests the radio frequency (RF) energy in the signals sent by the source node and utilizes the harvested energy to forward signals from the source node to the destination node. We aim at maximizing the source-destination mutual information (MI) through a joint design of the source matrix, the relay matrix, and the PS ratios under the source node power constraint and the relay node harvested energy constraint. We consider a general sum energy constraint at the relay node with different PS ratios across relay antennas, which includes existing works based on uniform PS or per data stream energy constraint as special cases. Moreover, a practical nonlinear energy harvesting (EH) model is adopted, where the harvested energy is bounded as the incident RF signal power increases. We establish the structure of the source matrix and the relay matrix, which simplifies the complicated transceiver design problem with matrix variables to a power distribution problem with scalar variables. Three approaches are proposed to efficiently solve the optimal power distribution problem. In particular, the first proposed algorithm solves the original nonconvex power allocation problem using the sequential quadratic programming, while the other two algorithms convert the original problem to convex problems by exploiting a tight upper bound and a tight lower bound of the objective function, respectively. Numerical simulations demonstrate that when the EH circuit works in the linear region, the proposed algorithms have a larger system MI than existing PS and TS based MIMO AF relay systems. The peak harvest power constraint plays an important role in choosing the location of the relay node.