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We present an analysis of the optimal uplink (UL) SNR of a SIMOReconfigurable Intelligent Surface (RIS)-aided wireless link. We assume thatthe channel between base station (BS) and RIS is a rank-1 LOS channel while theuser (UE)-RIS and UE-BS channels are correlated Ricean. For the optimal RISmatrix, we derive an exact closed form expression for the mean SNR and anapproximation for the SNR variance leading to an accurate gamma approximationto the distribution of the UL SNR. Furthermore, we analytically characterisethe effects of correlation and the Ricean K-factor on SNR, showing thatincreasing the K-factor and correlation in the UE-BS channel can have negativeeffects on the mean SNR, while increasing the K-factor and correlation in theUE-RIS channel improves system performance. We also present favourable andunfavourable channel scenarios which provide insight into the sort ofenvironments that improve or degrade the mean SNR. We also show that therelative gain in the mean SNR when transitioning from an unfavourable to afavourable environment saturates to $(4-\pi)/\pi$ as $N \rightarrow \infty $

Optimal SNR Analysis for Single-user RIS Systems in Ricean and Rayleigh Environments