  We consider a multi-user multiple input single output (MU-MISO) system
assisted by a reconfigurable intelligent surface (RIS). For such a system, we
aim to optimally select the RIS phase shifts and precoding vectors for
maximizing the effective rank of the weighted channel covariance matrix which
in turn improves the channel capacity. For a low-complex transmitter design, we
employ maximum ratio transmission (MRT) and minimum-mean square error (MMSE)
precoding schemes along with water-filling algorithm-based power allocation.
Further, we show that MRT and MMSE exhibit equivalent performance and become
optimal when the channel effective rank is maximized by optimally configuring
the RIS consisting of a large number of elements.
