  Reconfigurable intelligent surface (RIS) is a promising technology to enhance
the spectral and energy efficiency in a wireless communication system. The
design of the phase shifts of an RIS in every channel coherence interval
demands a huge training overhead, making its deployment practically infeasible.
The design complexity can be significantly reduced by exploiting the
second-order statistics of the channels. This paper is the extension of our
previous work to the design of an RIS for the multi-user setup, where we employ
maximisation of the lower bound of the achievable sum-rate of the users. Unlike
for the single-user case, obtaining a closed-form expression for the update of
the filters and phase shifts is more challenging in the multi-user case. We
resort to the fractional programming (FP) approach and the non-convex block
coordinate descent (BCD) method to solve the optimisation problem. As the phase
shifts of the RIS obtained by the proposed algorithms are based on the
statistical channel knowledge, they do not need to be updated in every channel
coherence interval.
