  The objective of this paper is to develop simple techniques to enhance the
performance of multi-user RIS aided wireless systems. Specifically, we develop
a novel technique called \textit{channel separation} which provides a better
understanding of how the RIS phases affect the uplink sum rate and sum rates
for ZF and MMSE linear receivers. Leveraging channel separation, we propose a
simple iterative algorithm to improve the uplink sum rate and the sum rates of
ZF and MMSE linear receivers when discrete RIS phases are considered. For
continuous RIS phases, we derive simple closed form solutions to enhance the
uplink sum rate and reduce the total mean square error of the MMSE combiner.
The latter metric is a tractable alternative to maximizing sum rates for ZF and
MMSE. Numerical simulations are performed for all optimization techniques and
the effectiveness of each technique is compared to a full numerical
optimization procedure, namely an interior point (IP) algorithm.
