Coverage Probability and Ergodic Capacity of Intelligent Reflecting Surface-Enhanced Communication Systems

TL;DR

This paper derives closed-form expressions for coverage probability and ergodic capacity of IRS-enhanced SISO systems under Rayleigh fading, providing insights into system performance with finite elements.

Contribution

It introduces new analytical formulas for coverage probability and ergodic capacity in IRS-assisted systems, including a scaling law relating coverage probability to phase shifts.

Findings

Closed-form coverage probability expression derived.

Ergodic capacity upper bound established.

Numerical results confirm accuracy of formulas.

Abstract

This paper studies the performance of a single-input single-output (SISO) system enhanced by the assistance of an intelligent reflecting surface (IRS), which is equipped with a finite number of elements under Rayleigh fading channels. From the instantaneous channel capacity, we compute a closed-form expression of the coverage probability as a function of statistical channel information only. A scaling law of the coverage probability and the number of phase shifts is further obtained. The ergodic capacity is derived, then a simple upper bound to simplify matters of utilizing the symbolic functions and can be applied for a long period of time. Numerical results manifest the tightness and effectiveness of our closed-form expressions compared with Monte-Carlo simulations.