Flexible Beamforming Design with Hierarchical Rotational 6DMA Systems

Reconfigurable antenna technology, such as movable antennas (MAs) and rotatable antennas (RAs), has emerged as a promising solution to enhance the communication performance of wireless systems by exploiting the new degree of freedom (DoF) in antenna reconfiguration. However, existing RA designs mostly consider the array-wise or antenna-wise rotation only, which constrain their great potential in the wide-range radiation pattern control. To overcome this limitation, we propose a new hierarchical rotational six-dimensional MA (HR-6DMA) architecture to improve downlink coverage, which exploits array-wise rotation for global orientation adjustment and individual antenna rotation for fine-grained radiation refinement. Based on this array architecture, we then formulate an optimization problem to maximize the minimum beamforming gain over a target region by jointly optimizing the two-level rotations and transmit beamforming. To solve this non-convex problem, an efficient algorithm is proposed, where the transmit beamforming and per-antenna rotation are optimized via alternating optimization under any feasible array rotation, followed by a low-complexity linear search to determine the optimal array rotation. Last, numerical results show that the proposed HR-6DMA significantly improves the minimum beamforming gain over fixed and single-level rotatable arrays.