Energy-Efficient Tri-Hybrid Beamforming with Movable Pattern-Reconfigurable Antennas

Conventional hybrid precoding is confined to the digital/analog domains, leaving the spatial and radiation-pattern degrees-of-freedoms (DoFs) largely untapped. To unlock these, we propose a movable pattern-reconfigurable antenna (MPRA) and an energy-efficient tri-hybrid framework that jointly optimizes the precoders, antenna positions, and radiation-pattern states. We develop a hardware-inspired power model capturing the energy and transmission-time costs of antenna reconfiguration. The resulting mixed discrete-continuous fractional problem is solved via an alternating-optimization framework combining fractional programming, Riemannian optimization, and switching-aware pattern optimization. Simulations demonstrate near-exhaustive-search performance and consistent energy-efficiency (EE) gains, validating the complementary benefits of antenna movement, pattern reconfiguration, and tri-hybrid precoding under hardware-inspired power and latency costs.