On Performance of Distributed RIS-aided Communication in Random Networks

TL;DR

This paper analyzes the performance of distributed RIS-assisted wireless networks with randomly placed RISs, deriving a closed-form ergodic rate expression, optimizing RIS deployment, and characterizing the impact of phase errors on rate loss.

Contribution

It provides a novel closed-form expression for the ergodic rate in distributed RIS networks with phase errors and offers optimal deployment strategies based on network parameters.

Findings

Larger RISs with fewer deployments are optimal for bounded phase errors.

Spreading out reflecting elements is best under random phase shifts.

Rate loss due to phase errors is bounded or scales logarithmically with N.

Abstract

This paper evaluates the geometrically averaged performance of a wireless communication network assisted by a multitude of distributed reconfigurable intelligent surfaces (RISs), where the RIS locations are randomly dropped obeying a homogeneous Poisson point process. By exploiting stochastic geometry and then averaging over the random locations of RISs as well as the serving user, we first derive a closed-form expression for the spatially ergodic rate in the presence of phase errors at the RISs in practice. Armed with this closed-form characterization, we then optimize the RIS deployment under a reasonable and fair constraint of a total number of RIS elements per unit area. The optimal configurations in terms of key network parameters, including the RIS deployment density and the array sizes of RISs, are disclosed for the spatially ergodic rate maximization. Our findings suggest that deploying larger-size RISs with reduced deployment density is theoretically preferred to support extended RIS coverages, under the cases of bounded phase shift errors. However, when dealing with random phase shifts, the reflecting elements are recommended to spread out as much as possible, disregarding the deployment cost. Furthermore, the spatially ergodic rate loss due to the phase shift errors is quantitatively characterized. For bounded phase shift errors, the rate loss is eventually upper bounded by a constant as $N\rightarrow\infty$, where $N$ is the number of reflecting elements at each RIS. While for random phase shifts, this rate loss scales up in the order of $\log N$. These analytical observations are validated through numerical results.