A Gram-Attention Learning Framework for Spatially Non-Stationary Channel Estimation

Abstract

As next-generation wireless systems migrate to high-frequency bands, extremely large-scale multiple-input multiple-output (XL-MIMO) is indispensable for combating severe path loss. However, the received path energy along the extremely large array aperture (ELAA) may exhibit spatial non-stationarity, rendering the conventional discrete Fourier transform (DFT) codebook inadequate for channel estimation (CE) due to its full-array angular representation. To address this mismatch, we propose a novel joint angle-subarray (JAS) codebook, where each codeword corresponds to an angular direction and a specific subarray. Spatially non-stationary CE is thus transformed into structured sparse support detection in the JAS domain. However, reliable support recovery remains challenging for conventional model-based methods. We therefore develop a signal processing and deep learning co-design framework, where data-driven JAS parallel support detection is followed by least-squares (LS)-based channel reconstruction. The matched filter response of each JAS grid is embedded into a high-dimensional feature vector. We then propose a Gram-attention module that incorporates the Gram matrix as a physical prior to guide feature purification, enabling the network to suppress leakage-related components while preserving support-relevant information of each grid. The purified features are passed to decoupled heads to infer the hierarchical sparse supports in the JAS domain. Finally, LS is performed over the low-dimensional dictionary constructed from the detected supports to retrieve path gains. Simulation results demonstrate that the proposed framework achieves the highest support detection F1-score and the lowest CE normalized mean square error (NMSE) among all baselines, while ablation studies verify the benefits of integrating the Gram-domain physical prior with data-driven representation learning.