Intelligent reflecting surface (IRS) is an emerging technology for wireless communications, thanks to its powerful capability to engineer the radio environment. However, in practice, this benefit is attainable only when the passive IRS is of sufficiently large size, for which the conventional uniform plane wave (UPW)-based far-field model may become invalid. In this paper, we pursue a near-field modelling and performance analysis for wireless communications with extremely large-scale IRS (XL-IRS). By taking into account the directional gain pattern of IRS's reflecting elements and the variations in signal amplitude across them, we derive both the lower- and upper-bounds of the resulting signal-to-noise ratio (SNR) for the generic uniform planar array (UPA)-based XL-IRS. Our results reveal that, instead of scaling quadratically and unboundedly with the number of reflecting elements M as in the conventional UPW-based model, the SNR under the new non-uniform spherical wave (NUSW)-based model increases with $M$ with a diminishing return and eventually converges to a certain limit. To gain more insights, we further study the special case of uniform linear array (ULA)-based XL-IRS, for which a closed-form SNR expression in terms of the IRS size and locations of the base station (BS) and the user is derived. Our result shows that the SNR is mainly determined by the two geometric angles formed by the BS/user locations with the IRS, as well as the dimension of the IRS. Numerical results validate our analysis and demonstrate the necessity of proper near-field modelling for wireless communications aided by XL-IRS.

翻译：智能反射面（IRS）作为一种新兴无线通信技术，因其塑造无线电环境的强大能力而备受关注。然而在实践中，该优势仅在无源IRS尺寸足够大时方能实现，此时传统的基于均匀平面波（UPW）的远场模型可能失效。本文针对超大规模IRS（XL-IRS）辅助的无线通信系统，开展近场建模与性能分析。通过考虑IRS反射单元的方向增益模式及其信号幅度的非均匀分布，我们推导了基于均匀平面阵列（UPA）的通用XL-IRS系统信噪比（SNR）的下界与上界。研究结果表明：与传统UPW模型中SNR随反射单元数M呈无界二次增长不同，在新型非均匀球面波（NUSW）模型下，SNR随M增长的边际收益递减，最终收敛至某一极限值。为获得更深入的认知，我们进一步研究了基于均匀线性阵列（ULA）的XL-IRS特例，推导出关于IRS尺寸、基站（BS）和用户位置的闭式SNR表达式。结果显示SNR主要由BS/用户位置与IRS形成的两个几何角度以及IRS维度共同决定。数值结果验证了理论分析，并揭示了XL-IRS辅助无线通信中进行合理近场建模的必要性。