  In this paper, we present an analysis of the optimal uplink SNR of a SIMO
Reconfigurable Intelligent Surface (RIS)-aided wireless link. We assume that
the channel between base station and RIS is a rank-1 LOS channel while the user
(UE)-RIS and UE-base station (BS) channels are correlated Rayleigh. We derive
an exact closed form expression for the mean SNR and an approximation for the
SNR variance leading to an accurate gamma approximation to the distribution of
the UL SNR. Furthermore, we analytically characterise the effects of
correlation on SNR, showing that correlation in the UE-BS channel can have
negative effects on the mean SNR, while correlation in the UE-RIS channel
improves system performance. For systems with a large number of RIS elements,
correlation in the UE-RIS channel can cause an increase in the mean SNR of up
to 27.32% relative to an uncorrelated channel.
