Separate Channel Estimation for Transmissive RIS Based on Antenna-Side Favorable Propagation

In this paper, a novel three-stage separate channel estimation framework is proposed for transmissive reconfigurable intelligent surface (TRIS) wireless communication systems. TRIS communication systems achieve multi-stream communication capabilities equivalent to traditional large-scale antenna systems equipping only a single radio frequency (RF) link, but face significant challenges in channel estimation. However, the single-RF constraint and the passivity of TRIS elements pose significant challenges for high-dimensional channel estimation, often resulting in phase ambiguity when estimating the cascaded channel directly. To address these issues, the designed scheme is characterized by low complexity, low storage requirements, and high accuracy. First, the composite channel is constructed and estimated through uplink and downlink pilot transmission, where favorable propagation simplifies signal processing via dimension reduction, facilitating separate estimation and resolving the inherent phase ambiguity. Second, the antenna-to-TRIS channel is acquired with low complexity by exploiting the geometric prior of the TRIS, using a limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm tailored for large-scale optimization under the single-RF constraint. Thirdly, a subframe estimation scheme is introduced to formulate a sparse recovery problem for the TRIS-to-user channel. A lookahead orthogonal matching pursuit (LAOMP) algorithm is designed to enhance sparse channel recovery accuracy without requiring prior knowledge of sparsity.Simulation results demonstrate that, compared to least absolute shrinkage and selection operator (LASSO) for normalized mean square error (NMSE) and gradient descent (GD) for convergence metrics, this approach reduces channel estimation NMSE by 42.46%, convergence iterations by 92.73%, and computational time by 85.97%, while exhibiting strong robustness under diverse noise distributions, TRIS phase errors, and Doppler effects.