Optimal Phase Design for RIS Channel Estimation

TL;DR

This paper introduces an optimal two-stage channel estimation protocol for RIS-assisted channels using a modified DFT matrix, significantly improving estimation speed and robustness across various propagation conditions.

Contribution

It proposes a novel MDFT-based training phase design that minimizes channel estimation error and accelerates estimation, especially in highly correlated channel scenarios.

Findings

MDFT design outperforms prior methods in minimizing estimation error.

Channel estimation can be accelerated by a factor of up to 16 with high correlation.

Performance loss remains below 1.5 bits/sec/Hz compared to perfect CSI.

Abstract

We develop an optimal version of a prior two-stage channel estimation protocol for RIS-assisted channels. The new design uses a modified DFT matrix (MDFT) for the training phases at the RIS and is shown to minimize the total channel estimation error variance. In conjunction with interpolation (estimating fewer RIS channels), the MDFT approach accelerates channel estimation even when the channel from base station to RIS is line-of-sight. In contrast, prior two-stage techniques required a full-rank channel for efficient estimation. We investigate the resulting channel estimation errors by comparing different training phase designs for a variety of propagation conditions using a ray-based channel model. To examine the overall performance, we simulate the spectral efficiency with MRC processing for a single-user RIS-assisted system using an existing optimal design for the RIS transmission phases. Results verify the optimality of MDFT while simulations and analysis show that the performance is more dependent on the user-to-RIS channel correlation and the coarseness of the interpolation used, rather than the training phase design. For example, under a scenario with more highly correlated channels, the procedure accelerates channel estimation by a factor of 16, while the improvement is a factor of 5 in a less correlated case. The overall procedure is extremely robust, with a maximum performance loss of 1.5bits/sec/Hz compared to that with perfect channel state information for the considered channel conditions.