Stochastic Geometry Analysis of IRS-Assisted Downlink Cellular Networks

Using stochastic geometry tools, we develop a comprehensive framework to analyze the downlink performance 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. For the proposed users, we provide the approximate expressions for the performance in terms of coverage probability, ergodic capacity, and energy efficiency (EE). 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 approximate 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 approximate 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 density 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.

I. Introduction

Intelligent reflecting surfaces (IRSs) are considered as a key enabling technology for the sixth generation (6G) wireless communications systems. IRSs enable a smart manipulation of the wireless propagation environment [1], [2]. Each IRS consists of many antenna elements (a.k.a IRS elements) [3] and each IRS element is controlled via a controller that assists each IRS element to steer the incident signal into the desired direction [4]. Also, with the advances in the wireless technology and extravagant demand of higher data rate to millions of indoor/outdoor devices, it has become inevitable to utilize the resources wisely to enable massive connectivity. In this context, IRSs operate as a low cost solution to extend the communication range and to provide service to more users. In order to achieve this goal, the transmissions can happen in three modes, i.e., (i) Joint Transmission: in which a user receives the IRS signals combined with the direct signal from the base-stations (BSs), (ii) IRS-only Transmission: in which a user receives only IRS transmissions and the direct transmissions get blocked, and (iii) Direct Transmission: in which a user is served only through direct transmissions.