Liujia Yao

In this paper, we study efficient codebook design for limited feedback in extremely large-scale multiple-input-multiple-output (XL-MIMO) frequency division duplexing (FDD) systems. It is worth noting that existing codebook designs for XL-MIMO, such as the polar-domain codebook, have not well taken into account user (location) distribution in practice, thereby incurring excessive feedback overhead. To address this issue, we propose in this paper a novel and efficient feedback codebook tailored to the user distribution. To this end, we first consider a typical scenario where users are uniformly distributed within a specific polar-region, based on which a sum-rate maximization problem is formulated to jointly optimize angle-range samples and bit allocation among angle/range feedback. This problem is challenging to solve due to the lack of a closed-form expression for the received power in terms of angle and range samples. By leveraging a Voronoi partitioning approach, we show that uniform angle sampling is optimal for received power maximization. For the more challenging range sampling design, we obtain a tight lower bound on the received power and show that geometric sampling, where the ratio between adjacent samples is constant, can maximize the lower bound and thus serves as a high-quality suboptimal solution. We then extend the proposed framework to accommodate more general non-uniform user distribution via an alternating sampling method. Furthermore, theoretical analysis reveals that as the array size increases, the optimal allocation of feedback bits increasingly favors range samples at the expense of angle samples. Finally, numerical results validate the superior rate performance and robustness of the proposed codebook design under various system setups, achieving significant gains over benchmark schemes, including the widely used polar-domain codebook.

Movable antenna (MA) is a promising technology for improving the performance of wireless communication systems by providing new degrees-of-freedom (DoFs) in antenna position optimization. However, existing works on MA systems have mostly considered element-wise single-layer MA (SL-MA) arrays, where all the MAs move within a prescribed movable region, hence inevitably incurring high control complexity and hardware cost in practice. To address this issue, we propose in this letter a new two-layer MA array (TL-MA), where the positions of MAs are jointly determined by the large-scale movement of multiple subarrays and the small-scale fine-tuning of per-subarray MAs. In particular, an optimization problem is formulated to maximize the sum-rate of the TL-MA-aided communication system by jointly optimizing the subarray-positions, per-subarray (relative) MA positions, and receive beamforming. To solve this non-convex problem, we propose an alternating optimization (AO)-based particle swarm optimization (PSO) algorithm, which alternately optimizes the positions of subarrays and per-subarray MAs, given the optimal receive beamforming. Numerical results verify that the proposed TL-MA significantly reduces the sum-displacement of MA motors (i.e., the total moving distances of all motors) of element-wise SL-MA, while achieving comparable rate performance.