On Spatial Multiplexing Using Reconfigurable Intelligent Surfaces

We consider an uplink multi-user scenario and investigate the use of reconfigurable intelligent surfaces (RIS) to optimize spatial multiplexing performance when a linear receiver is used. We study two different formulations of the problem, namely maximizing the effective rank and maximizing the minimum singular value of the RIS-augmented channel. We employ gradient-based optimization to solve the two problems and compare the solutions in terms of the sum-rate achievable when a linear receiver is used. Our results show that the proposed criteria can be used to optimize the RIS to obtain effective channels with favorable properties and drastically improve performance even when the propagation through the RIS contributes a small fraction of the received power.