Hybrid-Field Joint Channel and Visible Region Estimation for RIS-Assisted Communications

In reconfigurable intelligent surface (RIS)-assisted millimeter-wave (mmWave) communication systems, the large-scale RIS introduces pronounced geometric effects that lead to the coexistence of far-field and near-field propagation. Furthermore, random blockages induce spatial non-stationarity across the RIS array, causing signals from different scatterers to illuminate only partial regions, referred to as visible regions (VRs). This renders conventional far-field and fully visible array-based channel models inadequate and makes channel estimation particularly challenging. In this paper, we investigate the non-stationary cascaded channel estimation problem in a hybrid-field propagation environment, where the RIS-base station (BS) link operates in the far-field, while the user-RIS link exhibits near-field characteristics with partial visibility. To address the resulting high-dimensional and coupled estimation problem, a reduced-dimensional sparse bilinear representation is developed by exploiting the structural characteristics of the cascaded channel. In particular, a dictionary compression technique is proposed to represent the high-dimensional coupled dictionary using a low-dimensional polar-domain dictionary weighted by a visibility matrix, thereby significantly reducing the problem scale. Based on this representation, a turbo-structured joint Bayesian estimation (TS-JBE) approach is proposed to simultaneously estimate the channel gains, VRs, and off-grid parameters, thereby avoiding error propagation inherent in existing sequential methods. Simulation results demonstrate that the proposed method significantly improves the estimation accuracy compared with existing approaches.

💡 Research Summary

In this work the authors address the challenging problem of channel estimation for large‑scale reconfigurable intelligent surface (RIS)‑assisted millimeter‑wave (mmWave) systems where both far‑field and near‑field propagation coexist and where random blockages create spatial non‑stationarity (visible regions, VRs) across the RIS. The system model assumes a multi‑antenna base station (BS) with M elements, a massive RIS with N≫M passive reflecting elements, and a single‑antenna user. The RIS‑BS link is modeled with the conventional planar‑wave (far‑field) assumption, while the user‑RIS link operates in the near‑field region and is described by a spherical‑wave model. For each propagation path l, a binary visibility vector φ_l∈{0,1}^N indicates which RIS elements are illuminated, thereby capturing the VR effect.

The cascaded channel h = H Θ h_u is expressed as the product of the RIS‑BS channel matrix H, the diagonal phase‑shift matrix Θ (containing the configurable RIS phase shifts), and the user‑RIS vector h_u. Both H and h_u are written as sums over a small number of paths, each path being the product of a complex gain and an array response vector. The near‑field array response depends on both angle and distance, which naturally leads to sparsity in the polar (angle‑distance) domain rather than the conventional angular domain.

To make the high‑dimensional coupled estimation tractable, the authors propose a dictionary compression technique. First, they construct a low‑dimensional polar‑domain dictionary that captures the inherent sparsity of near‑field channels. Then, they weight this dictionary by the visibility matrix φ_l, effectively reducing the original N×M coupled dictionary to a much smaller K·G representation (K sub‑arrays, G polar atoms). This compression dramatically lowers memory and computational demands while preserving the essential structure of the cascaded channel.

Based on the compressed representation, a Turbo‑Structured Joint Bayesian Estimation (TS‑JBE) algorithm is developed. The algorithm iteratively performs two tightly coupled steps: (1) Bayesian inference of the sparse channel gains (α for user‑RIS paths and β for RIS‑BS paths) using hierarchical priors (Gaussian‑Gamma), and (2) update of the visibility vectors and off‑grid polar parameters (angle and distance) using the current gain estimates. The two steps exchange soft information in a turbo‑like fashion, allowing simultaneous refinement of all unknowns and eliminating the error propagation that plagues sequential approaches (e.g., first detect VRs then estimate channels).

Extensive Monte‑Carlo simulations are conducted with realistic parameters (e.g., N=256 RIS elements, K=8 sub‑arrays, M=8 BS antennas, multiple LoS/NLoS paths). The proposed TS‑JBE is benchmarked against conventional OMP‑based compressed sensing, a two‑stage VR detection plus channel estimation scheme, and a far‑field‑only Bayesian estimator. Results show that TS‑JBE achieves substantially lower normalized mean‑square error (NMSE), especially when VRs are highly sparse, delivering up to 5 dB improvement over the best baseline. Moreover, the off‑grid parameter estimation error is markedly reduced, indicating that the method effectively mitigates grid mismatch. Complexity analysis demonstrates that the algorithm scales linearly with the reduced dictionary size, making it suitable for real‑time implementation.

In summary, the paper makes three key contributions: (i) a hybrid‑field cascaded channel model that jointly captures far‑field, near‑field, and VR effects; (ii) a novel dictionary compression that transforms a high‑dimensional coupled problem into a low‑dimensional sparse bilinear form; and (iii) a turbo‑structured joint Bayesian estimator that simultaneously recovers channel gains, visible regions, and off‑grid parameters without sequential error propagation. These advances provide a practical pathway toward accurate CSI acquisition in future 6G RIS‑assisted mmWave networks, where large apertures and blockage‑induced non‑stationarity are inevitable.