Two-Wave With Diffuse Power Channel Modeling and Two-Timescale Design for Movable Antenna Aided Multiuser Communications

Movable antenna (MA) has emerged as a promising technology to enhance communication performance via allowing antennas to flexibly adjust their positions to fully exploit the spatial degrees of freedom (DoFs). This paper focuses on the MA-aided multiuser communications under the two-wave with diffuse power (TWDP) model with statistical channel state information (CSI). With the extended TWDP channel model, a two-timescale optimization problem is formulated to jointly optimize the MA positions and beamforming matrix for the maximization of the ergodic minimum rate among multiple users. Then, we develop a log-barrier gradient descent (LGD) algorithm to optimize the MA positions based on the slowly varying statistical CSI over a large timescale, which can reduce the MA movement overhead and power consumption, while zero-forcing (ZF) beamforming is utilized based on the instantaneous CSI for any given fixed MA positions. For the LGD algorithm, two methods, namely Monte-Carlo method and deterministic equivalent method, are employed to construct the surrogate function, in which the proposed deterministic equivalent method can achieve a reduced computational complexity for the optimization of MA positions. Finally, simulation results show that the ergodic minimum rates achieved by the MA systems with antenna positions optimized based on statistical CSI significantly surpass their fixed-position antenna (FPA) counterparts, and approach their upper bound for MA systems with antenna positions optimized based on instantaneous CSI under both the TWDP and Rician fading channel models.