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The objective of this paper is to develop simple techniques to bound theoptimal uplink sum-rate of multi-user RIS-aided wireless systems. Specifically,we develop a novel technique called \textit{channel separation} which providesa new understanding as to how the RIS phases affect the sum-rate. Leveragingchannel separation, we derive upper and lower bounds on the optimal sum-rate.In addition, we propose a low-complexity alternating optimization algorithm toobtain near-optimal sum-rate results. Numerical results demonstrate thetightness of the bounds and show that the alternating optimization approachdelivers sum-rate values similar to the results of a full numericaloptimization procedure. Furthermore, in practical scenarios where hardwarelimitations cause the RIS phases to be quantized, our lower bound can still beapplied and shows that the sum-rate is robust to quantization, even with lowresolution.

Tight Bounds on the Optimal UL Sum-Rate of MU RIS-aided Wireless Systems