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 multipleinput 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.INDEX TERMS Reconfigurable intelligent surfaces (RIS), multiple-input and multiple-output (MIMO), multi-user, simultaneous wireless information and power transfer (SWIPT), energy efficiency (EE).
I. INTRODUCTIONThe impending deployment of fifth-generation (5G) mobile communications around the world will be a major factor in driving productivity and will be the key enabler for longenvisaged verticals including personalised healthcare, manufacturing, smart energy grids, smart cities, finance, and transportation. However, realizing the ever-growing demand for a better communication network with improved quality of service (QoS) requirements such as lower power consumption, very high energy efficiency (EE), better spectral efficiency (SE), etc., researchers have already started to explore the evolution of 5G, commonly referred to as 5G and beyond (5GB) and sixth generation (6G) communications [1]. In this context, to enhance the experience of relaying in wireless communication networks, the idea of multiple passive reflecting surfaces/elements made of meta-materials has been floated to assist the communication between multiple devices such as base station (BS), users etc., [2]-[4]. This set of discrete reflecting elements is termed as reconfigurable intelligent surface (RIS) or intelligent reflecting surface (IRS),