Near-Optimal Near-Field Beam Training: From Searching to Inference

In extremely large-scale multiple input multiple output (XL-MIMO) systems, near-field beam training (NFBT) is an essential way to acquire channel state information (CSI) knowledge. To reduce the high training overhead caused by the distance dimension of the near-field codebook, some overhead-reduced NFBT schemes were proposed in the literature. However, existing schemes ignore the correlation between different near-field beams, which promises to provide prior knowledge for the reduction of training overhead. Aligned with this vision, this paper proposes a Bayesian regression (BAR)-based NFBT scheme, which fully utilizes the strong correlation between near-field codewords to achieve near-optimal and low-overhead NFBT. Specifically, inspired by Bayesian regression, we model the received signal corresponding to different codewords as a Gaussian process. Then, the optimal codeword can be determined by iteratively updating the posterior distribution and designing the codeword searching order. Besides, different codeword inference strategies are analyzed and compared. The proposed scheme only requires searching for a few codewords instead of the entire codebook thus avoiding the high training overhead. Simulation results verify that, compared to the existing schemes, the proposed scheme can significantly reduce the training overhead while maintaining a near-optimal achievable rate performance.