Performance Analysis of Randomly Distributed Reconfigurable Intelligent Surfaces with Different Phase Profiles

Future scenarios foresee the deployment of a large amount of reconfigurable intelligent surfaces (RISs) covering buildings and objects to control the propagation of waves and to realize smart radio environments (SREs). Several works have already investigated the possibility to have a large-scale deployment of RISs indoors and outdoors, providing insightful considerations about the coverage and outage probability, especially in the absence of a direct base station (BS)-user (UE) link. Unfortunately, such works typically consider simplified propagation channels and assume ideal or random phase profiles at the RIS, which do not always fit real scenarios. This paper proposes a communication outage analysis that accounts for realistic RIS selection mechanisms and phase shift profiles. Differently from the literature, we first discuss some RIS association mechanisms and provide a general outage analysis, which is then specialized to the cascaded double Rician fading channel BS-RIS-UE. Finally, we provide extensive numerical evaluation, validated through simulations, to corroborate the proposed model to allow discussing the trade-off in terms of the number of employable RIS antennas and the number of quantization bits for each RIS element, which should be accounted for in the system design.