Game-Theoretic Precoding for Cooperative MIMO SWIPT Systems with Secrecy Consideration

In this paper, we study the secrecy precoding problem for simultaneous wireless information and power transfer (SWIPT) in a multiple-input multiple-output (MIMO) relay network. The problem is formulated as a noncooperative game, where the network utility, defined as the nonnegative sum of the achievable secrecy rate and the harvested energy, is regarded as the common payoff, and the source and the relay are assumed as two rational game players. The formulated game is proven to be a potential game, which always processes at least one pure-strategy Nash equilibrium (NE), and the optimal transmit strategy profile that maximizes the network utility also constitutes a pure-strategy NE of it. Since the best-response problems of the proposed game constitute difference convex (DC)-type programming problems, we solve them by employing a successive convex approximation (SCA) method. With the SCA method, the two best-response problems can be iteratively solved through successive convex programming of their convexified versions. Then, based on the best-response dynamic, a distributed precoding algorithm is developed to obtain a feasible NE solution the proposed game. Numerical simulations are further provided to demonstrate it. Results show that our algorithm can converge fast to a near-optimal solution with guaranteed convergence.