Stochastic Geometry Analysis of IRS-Assisted Downlink Cellular Networks

TL;DR

This paper develops a stochastic geometry framework to analyze the performance of IRS-assisted cellular networks, including coverage, capacity, and energy efficiency, considering various user types and interference effects.

Contribution

It introduces a novel analytical model capturing the impact of IRS phase shifts, interference, and deployment parameters on network performance metrics.

Findings

IRS deployment improves coverage and capacity.

Interference from multiple IRSs affects overall network performance.

Optimal IRS element number enhances energy efficiency.

Abstract

Using stochastic geometry tools, we develop a comprehensive framework to analyze the downlink coverage probability, ergodic capacity, and energy efficiency (EE) of various types of users (e.g., users served by direct base station (BS) transmissions and indirect intelligent reflecting surface (IRS)-assisted transmissions) in a cellular network with multiple BSs and IRSs. The proposed stochastic geometry framework can capture the impact of channel fading, locations of BSs and IRSs, arbitrary phase-shifts and interference experienced by a typical user supported by direct transmission and/or IRS-assisted transmission. For IRS-assisted transmissions, we first model the desired signal power from the nearest IRS as a sum of scaled generalized gamma (GG) random variables whose parameters are functions of the IRS phase shifts. Then, we derive the Laplace Transform (LT) of the received signal power in a closed form. Also, we model the aggregate interference from multiple IRSs as the sum of normal random variables. Then, we derive the LT of the aggregate interference from all IRSs and BSs. The derived LT expressions are used to calculate coverage probability, ergodic capacity, and EE for users served by direct BS transmissions as well as users served by IRS-assisted transmissions. Finally, we derive the overall network coverage probability, ergodic capacity, and EE based on the fraction of direct and IRS-assisted users, which is defined as a function of the deployment intensity of IRSs, as well as blockage probability of direct transmission links. Numerical results validate the derived analytical expressions and extract useful insights related to the number of IRS elements, large-scale deployment of IRSs and BSs, and the impact of IRS interference on direct transmissions.