Optimal SNR Analysis for Single-user RIS Systems
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In this paper, we present an analysis of the optimal uplink SNR of a SIMO RIS-aided wireless link. We assume that the channel between base station and RIS is a rank-1 LOS channel while the user-RIS and user-base station 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 user-base station channel can have negative effects on the mean SNR, while correlation in the user-RIS channel improves system performance. For systems with a large number of RIS elements, this improvement saturates to a gain of approximately 27.32
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