TRACE: A Trilinear Channel Estimation Framework for Tri-Hybrid Architectures with Reconfigurable Antennas

Abstract

Tri-hybrid beamforming with reconfigurable antennas (RAs) adds an electromagnetic (EM)-domain degree of freedom to radio-frequency (RF) analog combining and baseband processing, but it also couples the EM angular response, the spatial steering matrix, and the path gains inside every received pilot. This letter develops TRACE, a trilinear channel estimation framework for the single-user uplink of a tri-hybrid receiver. Cycling the radiation pattern over the pilot dimension yields a third-order PARAFAC tensor of the received pilots, with factors corresponding to the EM-domain angular factor, the RF-projected steering factor, and the pilot-weighted fading factor. TRACE fits this tensor by alternating least squares and then recovers the physical channel parameters in closed form. Kruskal-based identifiability translates into design rules for the number of pilot slots, RF chains, and EM probing states. In a compressive configuration, TRACE attains the SNR slope of an oracle-support bound, staying within a factor of $1.4$ of it above $10$~dB, while outperforming a dictionary-based greedy baseline.