How Should IRSs Scale to Harden Multi-Antenna Channels?

TL;DR

This paper analyzes how intelligent reflecting surfaces (IRSs) can be scaled to improve channel hardening in multi-antenna systems, providing theoretical approximations and confirming them with numerical experiments.

Contribution

It extends channel hardening theory to IRS-assisted multi-antenna channels and derives an accurate distribution approximation for large IRSs.

Findings

Channel hardening improves with IRS size if physical dimensions grow.

Asymptotic analysis holds for sub-linear growth of IRS elements.

Numerical results confirm the analytical approximation.

Abstract

This work extends the concept of channel hardening to multi-antenna systems that are aided by intelligent reflecting surfaces (IRSs). For fading links between a multi-antenna transmitter and a single-antenna receiver, we derive an accurate approximation for the distribution of the input-output mutual information when the number of reflecting elements grows large. The asymptotic results demonstrate that by increasing the number of elements on the IRS, the end-to-end channel hardens as long as the physical dimensions of the IRS grow as well. The growth rate however need not to be of a specific order and can be significantly sub-linear. The validity of the analytical result is confirmed by numerical experiments.