  In this correspondence, we propose a movable antenna (MA)-aided multi-user
hybrid beamforming scheme with a sub-connected structure, where multiple
movable sub-arrays can independently change their positions within different
local regions. To maximize the system sum rate, we jointly optimize the digital
beamformer, analog beamformer, and positions of subarrays, under the
constraints of unit modulus, finite movable regions, and power budget. Due to
the non-concave/non-convex objective function/constraints, as well as the
highly coupled variables, the formulated problem is challenging to solve. By
employing fractional programming, we develop an alternating optimization
framework to solve the problem via a combination of Lagrange multipliers,
penalty method, and gradient descent. Numerical results reveal that the
proposed MA-aided hybrid beamforming scheme significantly improves the sum rate
compared to its fixed-position antenna (FPA) counterpart. Moreover, with
sufficiently large movable regions, the proposed scheme with sub-connected MA
arrays even outperforms the fully-connected FPA array.
