Double-XL-IRS Aided Near-Field Communications

The existing works on double-intelligent reflecting surfaces (IRS) have mostly assumed the far-field channel model even for a large-size IRS. This, however, may over-estimate the IRS communication performance as the accurate near-field channel model is not considered. To address this issue, in this paper, we consider the extremely large-scale IRSs (XL-IRSs) and study the performance of double-XL-IRS aided near-field communication systems. Specifically, we first present the near-field channel model and then formulate an optimization problem to maximize its achievable rate by designing the cooperative beamforming. Due to the large-scale channel dimension, the existing methods based on semidefinite relaxation (SDR) are not applicable. Thus, we propose two efficient methods to obtain near-optimal solutions, where the first method is based on the alternative optimization (AO) technique, and the second method is based on the inter-IRS channel approximation. Finally, numerical results show that the single XL-IRS can outperform the double-XL-IRS aided system in the near-field channel case when the number of IRS elements is asymptotically large. This is expected since the SNR in the double-XL-IRS system will saturate, while the system suffers more severe path-loss than the single-XL-IRS system.