Non-Square UPA-Enabled XL-MIMO Systems: Anisotropic Near-Field Characterization, Fundamental Limits, and Channel Estimation

Yilong Liu, Xi Yang, Jing Xu, Jun Zhang, Shi jin

Extremely large-scale multiple-input multiple-output (XL-MIMO) is crucial for next-generation communication systems. In practice, the deployment of non-square uniform planar arrays (UPAs) fundamentally alters wavefront characteristics and induces anisotropic beamfocusing capability along different axes due to the aperture disparity originating from the non-square array geometry. To fully uncover the performance impact of such non-square geometry and thus unleash the potential of the non-square UPAs, we investigate the anisotropic near-field characteristics, fundamental limits, and channel estimation for non-square UPA-enabled XL-MIMO systems. First, we derive the effective beamfocusing distances for the long and short axes of the array. Interestingly, the radiation space of a non-square UPA can be partitioned into three regions, i.e., the fully near-field, the anisotropic near-field, and the far-field regions, and the anisotropic region asymptotically dominates the overall near-field space as the array aspect ratio increases. Then, the asymptotic effective degree of freedom for non-square UPA-enabled XL-MIMO systems is provided, which reveals that distance-domain multiplexing is governed by the long-axis aperture in the large array aspect ratio regime. Furthermore, the closed-form Cramer-Rao bound for distance estimation and the three-dimensional (3D) position error bound (PEB) are derived to reveal the geometry-induced performance trade-offs among distance, azimuth, and elevation estimation, based on which the optimal array aspect ratio that minimizes the 3D PEB is determined. Finally, by exploiting the anisotropic wavefront properties, we design a 3D anisotropic near-field codebook to facilitate low-complexity channel estimation for non-square UPAs. Numerical results validate that the proposed codebook achieves comparable accuracy to the 3D polar-domain codebook at reduced complexity.