Base Station Beamforming Design for Near-field XL-IRS Beam Training

Existing research on extremely large-scale intelligent reflecting surface (XL-IRS) beam training has assumed the far-field channel model for base station (BS)-IRS link. However, this approach may cause degraded beam training performance in practice due to the near-field channel model of the BS-IRS link. To address this issue, we propose two efficient schemes to optimize BS beamforming for improving the XL-IRS beam training performance. Specifically, the first scheme aims to maximize total received signal power on the XL-IRS, which generalizes the existing angle based BS beamforming design and can be resolved using the singular value decomposition (SVD) method. The second scheme aims to maximize the $\ell_1$-norm of incident signals on the XL-IRS, which is shown to achieve the maximum received power at the user. To solve the non-convex $\ell_1$-norm maximization problem, we propose an eficient algorithm by using the alternating optimization (AO) technique. Numerical results show that the proposed AO based BS beamforming design outperforms the SVD/angle based BS beamforming in terms of training accuracy and achievable received signal-to-noise ratio (SNR).