Multiple RISs-Aided Networks: Performance Analysis and Optimization
Mahmoud Aldababsa, Anas M. Salhab, Ali A. Nasir, Monjed H. Samuh, Daniel Benevides da Costa
Abstract
This paper analyzes the performance of multiple reconfigurable intelligent surfaces (RISs)-aided networks with opportunistic RIS scheduling. The paper also provides some optimization results on the number of reflecting elements on RISs and the optimal placement of RISs. We first derive accurate closed-form approximations for RIS channels' distributions assuming independent non-identically distributed (i.ni.d.) Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fading environment. Then, the approximate expressions for outage probability (OP) and average symbol error probability (ASEP) are derived in closed-form. Furthermore, to get more insights into the system performance, we derive the asymptotic OP at the high signal-to-noise ratio (SNR) regime and provide closed-form expressions for the system diversity order and coding gain. Finally, the accuracy of our theoretical analysis is validated through Monte-Carlo simulations. The obtained results show that the considered RIS scenario can provide a diversity order of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\frac{a}{2}K$</tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$a$</tex-math></inline-formula> is a function of the Nakagami fading parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> and the number of meta-surface elements <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> is the number of RISs.