Hybrid-Field-Aware Two-Stage Beamforming Scheme for XL-MIMO Systems

In this article, we propose a hybrid-field-aware two-stage beamforming (HFA-TSB) scheme for extremely large-scale MIMO (XL-MIMO) systems. The HFA-TSB scheme can reduce the high pilot overhead associated with channel estimation by leveraging statistical channel state information (SCSI). Utilizing our derived ergodic spectral efficiency (SE), which relies solely on SCSI, we can eliminate the interference resulting from the nonorthogonality of near-field polar domain codewords. Specifically, the HFA-TSB scheme comprises two stages: 1) pre-beamforming and 2) precoding. In the pre-beamforming stage, we use SCSI to design the pre-beamforming matrix, focusing on eliminating interference among asymptotically orthogonal channels. This can establish an equivalent reduced-dimensional channel matrix, which can be estimated using less pilot overhead. Additionally, to address the interference caused by the nonorthogonality of near-field codewords, we derived an ergodic SE that relies solely on SCSI. Using this as an optimization objective, the pre-beamforming matrix design problem is formulated as a 0-1 integer nonlinear programming problem, which is challenging to solve. To address this, we propose a constraint-driven two-phase greedy beam selection algorithm for identifying effective beams. In the precoding stage, we design the precoder based on the estimated equivalent sparse channel to effectively mitigate any residual interuser interference. Simulations validate the superior performance of our proposed HFA-TSB scheme in terms of net SE.