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We provide closed-form approximations to the performance gain achieved in aRIS-assisted communication. We then consider a network deployment of RIS andTransmitter-Receiver pairs and use these approximate expressions to provideequivalence models which state that the performance of a RIS-equipped networkis similar to the performance of an appropriately spatially scaled system. Weprovide a way of assigning available RIS to assist communication betweenseveral transmitter-receiver pairs. Several such approximations are expected tospawn from this study, with more clarity on structural aspects of the gainsachieved in RIS-assisted communications.

Dimensioning an Indoor SISO RIS-system: Approximations and Equivalence Models