Level Crossing Rate Analysis for Optimal Single-user RIS Systems

TL;DR

This paper derives an exact analytical expression for the level crossing rate of RIS-assisted systems, showing that RIS does not significantly increase channel variability, which benefits channel estimation.

Contribution

It provides a novel, exact LCR expression for RIS systems with a new stable approximation for direct channels, addressing numerical issues in existing methods.

Findings

LCR drops more rapidly with more RIS or BS elements and lower correlation.

RIS systems do not significantly amplify channel temporal variations.

The new approximation improves numerical stability for large systems.

Abstract

We analyse the level crossing rate (LCR) of an uplink single-user (SU) reconfigurable intelligent surface (RIS) aided system. It is assumed that the RIS to base station (RIS-BS) channel is deployed as line-of-sight (LoS), and the user (UE)-RIS and UE-BS channels are correlated Rayleigh. For the optimal RIS reflection matrix, we derive a novel and exact analytical LCR expression for when the direct (UE-BS) channel is blocked, i.e. the RIS-only channel. Also, the existing exact expression for the direct-only channel (equivalent to classical maximal-ratio-combining (MRC)) suffers from extreme numerical precision problems when the BS has many elements. Therefore, we propose a new stable and accurate approximation to the LCR of the direct channel. The approximation is based on replacing any small similar eigenvalues of the channel correlation matrix by their average. We show that increasing the number of elements at the RIS or BS and decreasing channel correlation makes the LCR drop more rapidly for thresholds away from the mean SNR. Crucially, we find that RIS systems do not significantly amplify temporal variations in the channel. This is particularly beneficial for RIS systems considering the difficulty in acquiring channel state information (CSI).