Codebook Design for Extremely Large-Scale MIMO Systems: Near-Field and Far-Field

Extremely large-scale multiple-input multiple-output (XL-MIMO) communication systems introduce a new communication paradigm called near-field communications, which identifies users’ location within the near-field (Fresnel’s region). In the near-field, beams can be steered in the angle and distance dimensions, resulting in an enormous codebook and a prolonged two-dimensional beam alignment (BA) process. To keep a low BA overhead while achieving low BA error, in this paper, we design a novel hierarchical codebook and a BA scheme for near-field XL-MIMO systems. Specifically, we first propose a novel spatial partition where the angle-offset effect is revealed and leveraged to improve the beam gain inside the coverage area. Based on the partition, we design distance-coarse and focusing beams. Distance-coarse beams are leveraged to construct the high level of the codebook for angle dimension alignment. In contrast, focusing beams construct the last level codebook for distance dimension alignment. Corresponding to the proposed codebook structure, our BA scheme is a tree search consisting of two stages: the angle aligning stage and the distance aligning stage. Next, we formulate the desired codebook design problem as difference convex optimization problems, where three beam design guidelines are considered to minimize the BA error rate raised by the near-field angle-offset effect. After that, the proposed optimization problem is solved by the constrained concave-convex procedure. Numerical simulations verify the angle offset effect and our designed near-field beam. Furthermore, we show that our BA scheme only utilizes one percent of overhead but achieves a lower BA error rate than exhaustive searching.