Outage Analysis of Energy Efficiency in a Finite-Element-IRS Aided Communication System

TL;DR

This paper analyzes the outage probability of energy efficiency in IRS-assisted wireless systems without instantaneous CSI, deriving approximate solutions for different channel models and optimizing transmit power.

Contribution

It provides the first analysis of outage probability of energy efficiency in IRS-assisted systems, including closed-form solutions and power optimization methods.

Findings

Derived approximate closed-form OP of EE for Rician and Rayleigh channels.

Validated analytical results with Monte-Carlo simulations.

Proved OP of EE is a pseudo-convex function with a unique minimum.

Abstract

In this paper, we study the performance of an energy efficient wireless communication system, assisted by a finite-element-intelligent reflecting surface (IRS). With no instantaneous channel state information (CSI) at the transmitter, we characterize the system performance in terms of the outage probability (OP) of energy efficiency (EE). Depending upon the availability of line-of-sight (LOS) paths, we analyze the system for two different channel models, viz. Rician and Rayleigh. For an arbitrary number of IRS elements $(N)$, we derive the approximate closed-form solutions for the OP of EE, using Laguerre series and moment matching methods. The analytical results are validated using the Monte-Carlo simulations. Moreover, we also quantify the rate of convergence of the derived expressions to the central limit theorem (CLT) approximations using the \textit{Berry-Esseen} inequality. Further, we prove that the OP of EE is a strict pseudo-convex function of the transmit power and hence, has a unique global minimum. To obtain the optimal transmit power, we solve the OP of EE as a constrained optimization problem. To the best of our knowledge, the OP of EE as a performance metric, has never been previously studied in IRS-assisted wireless communication systems.