Movable Antenna-Assisted Secret Key Generation over Temporally Correlated Channels

Physical-layer key generation (PLKG) exploits reciprocal channel dynamics to generate symmetric keys, addressing the key distribution problem in wireless communications. However, strong temporal correlation in slow-fading environments limits fresh randomness and results in low key generation rates. Movable antennas (MAs) introduce spatial degrees of freedom through antenna repositioning, providing a new approach to addressing the limitation. This paper investigates MA-assisted PLKG over temporally correlated channels. A first-order Gauss-Markov process is utilized to characterize the temporal correlation of multipath gains. We characterize the full-sequence mutual information (MI) over temporally correlated channels. For fixed antenna positions and beamforming, we establish a finite-horizon approximation error bound that vanishes as both effective signal-to-noise ratios (SNRs) increase. We derive a closed-form expression for the one-step conditional MI and adopt it as a tractable key-information metric. A nonconvex problem is formulated to jointly optimize antenna positions and per-slot beamforming under transmit-power and minimum-spacing constraints. We develop an alternating optimization algorithm, combining an exact principal-eigenvector beamforming solution with feasible SCA-based projected gradient position updates. Simulation results demonstrate that the MA-assisted scheme outperforms the fixed-position antenna baseline. At a high temporal correlation coefficient, position optimization achieves approximately $51\%$ higher rates than fixed antennas. Joint position and beamforming optimization provides a further $106\%$ gain over position optimization alone, demonstrating more pronounced gains under strong temporal correlation.