A Pricing-Based Approach for Energy-Efficiency Maximization in RIS-aided Multi-user MIMO SWIPT-enabled Wireless Networks

In this work, we investigate the performance of a reconfigurable intelligent surface (RIS)-aided multi-user simultaneous wireless information and power transfer (SWIPT) network, where a multiple-input multiple-output (MIMO) base station (BS) serves multiple MIMO information receivers (IRs) while ensuring a minimum harvested power at multiple MIMO energy receivers (ERs). In order to improve the energy efficiency (EE) of the network, we consider a pricing-based performance metric called network utility. We then establish an optimization framework to jointly optimize the transmit precoding matrix (TPM) and phase shift matrix (PSM) to maximize the network utility function with constraints on the available transmit power at BS, minimum harvested power required at each ER, and unit modulus phase shift condition at RIS. Due to the non-convex nature of this problem, we divide it into two sub-problems where a sub-optimal solution of TPM and PSM are obtained separately using successive convex approximation and bisection search-based algorithms. Further, we propose an EE maximization (EEM) algorithm based on the block coordinate descent method to achieve the optimal solution of the master problem by iteratively obtaining the sub-optimal TPM, PSM, and network price using their respective algorithms. Moreover, we also prove that the solution obtained for each problem using their respective algorithm converges to the Karush-Kuhn-Tucker (KKT) optimum point of that problem. We also show the efficacy of the proposed algorithm using simulation results. In particular, we highlight the importance of using RIS in a multi-user MIMO SWIPT network and demonstrate the effect of various parameters on the network’s EE performance.