Low-Overhead Channel Estimation Framework for Beyond Diagonal Reconfigurable Intelligent Surface Assisted Multi-User MIMO Communication

Abstract: Beyond diagonal reconfigurable intelligent surface (BD-RIS) refers to a family of RIS architectures characterized by scattering matrices not limited to being diagonal and enables higher wave manipulation flexibility and large performance gains over conventional (diagonal) RIS. To achieve those promising gains, accurate channel state information (CSI) needs to be acquired in BD-RIS assisted communication systems. However, the number of coefficients in the cascaded channels to be estimated in BD-RIS assisted systems is significantly larger than that in conventional RIS assisted systems, because the channels associated with the off-diagonal elements of the scattering matrix have to be estimated as well. Surprisingly, for the first time in the literature, this paper rigorously shows that the uplink channel estimation overhead in BD-RIS assisted systems is actually of the same order as that in the conventional RIS assisted systems. This amazing result stems from a key observation: for each user antenna, its cascaded channel matrix associated with one reference BD-RIS element is a scaled version of that associated with any other BD-RIS element due to the common RIS-base station (BS) channel. In other words, the number of independent unknown variables is far less than it would seem at first glance. Building upon this property, this paper manages to characterize the minimum overhead to perfectly estimate all the channels in the ideal case without noise at the BS, and propose a twophase estimation framework for the practical case with noise at the BS. Numerical results demonstrate outstanding channel estimation overhead reduction over existing schemes in BD-RIS assisted systems.

Low-Overhead Channel Estimation Framework for BD-RIS Assisted Multi-User MIMO Communication

The paper presents an innovative approach to channel estimation in communication systems assisted by Beyond Diagonal Reconfigurable Intelligent Surfaces (BD-RIS) in a multi-user MIMO setup. BD-RIS are proposed as a next-generation enhancement for RIS technology, moving beyond the traditional use of diagonal scattering matrices and allowing more versatile wave manipulation capabilities.

Concept and Importance

BD-RIS introduce non-diagonal scattering matrices that facilitate greater flexibility in beamforming and spatial audio coverage for 6G networks. This architecture potentially optimizes the Signal-to-Noise Ratio (SNR) and maximizes the capacities of wireless channels. They necessitate accurate Channel State Information (CSI), which is traditionally more complex due to the larger set of channel coefficients involved in non-diagonal RS structures compared to conventional RIS.

Key Insights

1. Channel Property Utilization:
   • The core contribution is the discovery of a fundamental correlation property between the cascaded user-RIS-BS channels. It is shown that for each user antenna, the cascaded channel matrix with one reference BD-RIS element is scaled from any other BD-RIS element due to the shared RIS-BS channel, drastically reducing the number of independent channel coefficients required for estimation.
2. Theoretical Efficiency:
   • By leveraging this correlation, the authors reduce the channel estimation overhead from an expected order of $KUM^2$ coefficients to the order equivalent to that required in conventional RIS systems, $M + \lceil \frac{M(KU-1)}{q} \rceil$.
3. Estimation Framework:
   • A two-phase estimation process is introduced:
     • Phase I focuses on estimating reference channels and their scaling coefficients using BD-RIS designed scattering properties while minimizing time instants without noise.
     • Phase II estimates other antennas' scaling coefficients, exploiting the redundancies discovered.
4. Algorithm Design:
   • In realistic conditions with noise, LMMSE-based estimators are applied in both phases to ensure precision in estimating scaling coefficients, allowing accurate construction of cascaded channel matrices.

Results and Implications

The framework results in significant quantitative reductions in estimation overhead, making BD-RIS a feasible solution for future communication systems. The reduced computational complexity due to minimized overhead can enhance real-time processing capabilities in high-density environments. Numerically, the developed methodology demonstrated much better NMSE performance against existing benchmark schemes.

Future Prospects

The approach provides a novel paradigm in channel estimation for BD-RIS-assisted systems, ensuring potential deployment in 6G and beyond scenarios that involve advanced ISAC applications, MIMO capacity optimization, and emerging non-terrestrial networks. Future research can expand upon these findings by integrating more sophisticated noise models and exploring real-time adaptive configurations under dynamic mobile network operations.

In conclusion, the work posits BD-RIS as an integral component for next-generation wireless communication networks, reconciling high-dimensional channel structures with practical, low-overhead estimation frameworks. This laid foundation reinforces the principles of scalable systems design and efficient spectrum utilization mandatory for advancing network technologies.