Game-Theoretic Precoding for SWIPT in the DF-Based MIMO Relay Networks

In this paper, we study the distributed precoding problem for simultaneous wireless information and power transfer (SWIPT) in decode-and-forward (DF)-based multiple-input-multiple-output (MIMO) relay networks. The system model considered here consists of a source, a relay, an information decoding (ID) receiver, and an energy harvesting (EH) receiver, all mounted with multiple antennas. Since full channel state information (CSI) is usually unavailable, a practical scenario, where only local CSI is required, is considered in this paper. Such a practical scenario naturally constitutes a noncooperative game, where the source and the relay can be regarded as two rational game players. With properly designed utilities, it can be further shown that the existence and uniqueness of the pure-strategy Nash equilibrium (NE) of the proposed game can both be guaranteed under some mild conditions. Therefore, a distributed iterative precoding algorithm can be developed based on the best-response dynamic to obtain the unique NE solution for the proposed game. Moreover, a proximal-point-based regularization approach is also pursued to ensure the convergence of the proposed algorithm without requiring special restrictions on the channel ranks. Numerical simulations are also provided to demonstrate the proposed algorithm. Results show that our algorithm can converge quickly to a satisfactory solution with guaranteed convergence.