Tri-timescale Beamforming Design for Tri-hybrid Architectures with Reconfigurable Antennas

Reconfigurable antennas possess the capability to dynamically adjust their fundamental operating characteristics, thereby enhancing system adaptability and performance. To fully exploit this flexibility in modern wireless communication systems, this paper considers a novel tri-hybrid beamforming architecture, which seamlessly integrates pattern-reconfigurable antennas with both analog and digital beamforming. The proposed tri-hybrid architecture operates across three layers: (\textit{i}) a radiation beamformer in the electromagnetic (EM) domain for dynamic pattern alignment, (\textit{ii}) an analog beamformer in the radio-frequency (RF) domain for array gain enhancement, and (\textit{iii}) a digital beamformer in the baseband (BB) domain for multi-user interference mitigation. To establish a solid theoretical foundation, we first develop a comprehensive mathematical model for the tri-hybrid beamforming system and formulate the signal model for a multi-user multi-input single-output (MU-MISO) scenario. The optimization objective is to maximize the sum-rate while satisfying practical constraints. Given the challenges posed by high pilot overhead and computational complexity, we introduce an innovative tri-timescale beamforming framework, wherein the radiation beamformer is optimized over a long-timescale, the analog beamformer over a medium-timescale, and the digital beamformer over a short-timescale. This hierarchical strategy effectively balances performance and implementation feasibility. Simulation results validate the performance gains of the proposed tri-hybrid architecture and demonstrate that the tri-timescale design significantly reduces pilot overhead and computational complexity, highlighting its potential for future wireless communication systems.