  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.
