Hybrid CD‐MMSE Two‐Timescale Channel Estimation for RIS‐Assisted 6G Systems

ABSTRACT

Reconfigurable intelligent surfaces (RIS) represent a transformative technology for enhancing coverage and energy efficiency in sixth‐generation (6G) wireless networks. However, the substantial pilot overhead required to estimate cascaded channels remains a critical bottleneck, particularly in low signal‐to‐noise ratio (SNR) environments where conventional estimation techniques degrade significantly. This paper proposes a robust two‐timescale channel estimation framework that decomposes the cascaded channel into a quasi‐static base station (BS)‐to‐RIS link estimated via coordinate descent (CD) and a rapidly varying RIS‐to‐User Equipment (UE) link estimated via a bias‐aware minimum mean square error (MMSE) filter. We prove rigorously, via a majorization‐minimization (MM) surrogate construction, that each CD coordinate subproblem is strictly convex under the bilinear observation model arising from hardware phase noise and mutual coupling, guaranteeing monotone cost reduction and convergence to a stationary point. The proposed MMSE estimator explicitly absorbs the residual error covariance of the CD estimate into a Woodbury‐structured filter, formally distinguishing it from standard Wiener filtering and eliminating the high‐SNR bias floor present in prior art. We provide a comprehensive comparison with recent works (2020–2024), including least squares (LS), minimum variance unbiased (MVU), orthogonal matching pursuit (OMP)‐based compressive sensing (CS), and a deep learning (DL) benchmark, under identical hardware‐realistic conditions: 2‐bit phase quantization,  dBc phase noise, and  dB mutual coupling. Ablation studies isolate the individual contributions of the CD and MMSE components. Sensitivity analyses with respect to RIS size and phase quantization bits are reported. We further provide a detailed discussion of implementation complexity, real‐time feasibility on modern FPGAs and ASICs, and hardware deployment challenges to support practical adoption. The results confirm that CD‐MMSE maintains superior normalized mean square error (NMSE) performance while drastically reducing pilot overhead, offering a scalable, spectrally efficient solution for massive multiple‐input multiple‐output (MIMO) and Internet of Things (IoT) deployments in future 6G networks.