Ergodic Capacity of IRS-Assisted MIMO Systems with Correlation and Practical Phase-Shift Modeling

TL;DR

This paper derives a closed-form expression for the ergodic capacity of IRS-assisted MIMO systems considering practical correlation and phase-shift models, optimizing phase shifts with low overhead and validating results via simulations.

Contribution

It introduces a novel analytical framework for ergodic capacity considering realistic IRS element models and provides an efficient phase shift optimization method.

Findings

Closed-form PDF of cascaded channel derived

Ergodic capacity optimized with low overhead phase shifts

Monte-Carlo simulations confirm analytical accuracy

Abstract

We focus on the maximization of the exact ergodic capacity (EC) of a point-to-point multiple-input multiple-output (MIMO) system assisted by an intelligent reflecting surface (IRS). In addition, we account for the effects of correlated Rayleigh fading and the intertwinement between the amplitude and the phase shift of the reflecting coefficient of each IRS element, which are usually both neglected despite their presence in practice. Random matrix theory tools allow to derive the probability density function (PDF) of the cascaded channel in closed form, and subsequently, the EC, which depend only on the large-scale statistics and the phase shifts. Notably, we optimize the EC with respect to the phase shifts with low overhead, i.e., once per several coherence intervals instead of the burden of frequent necessary optimization required by expressions being dependent on instantaneous channel information. Monte-Carlo (MC) simulations verify the analytical results and demonstrate the insightful interplay among the key parameters and their impact on the EC.