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：智能反射表面（IRS）凭借其重构无线电环境的能力，成为无线通信领域的一项新兴技术。然而，在实际应用中，这一优势仅在无源IRS具有足够大尺寸时才能实现，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，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差异，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。结果表明：与传统UPW模型中信噪比随反射单元数量M呈无界二次增长不同，在新型非均匀球面波（NUSW）模型下，信噪比随M增长呈现递减收益，并最终收敛至某一极限。为获得更深入的见解，我们进一步研究了基于均匀线性阵列（ULA）的XL-IRS特例场景，推导了关于IRS尺寸及基站（BS）与用户位置的闭式SNR表达式。结果揭示：信噪比主要由BS/用户位置与IRS形成的两个几何角度及IRS维度共同决定。数值结果验证了理论分析，并表明对XL-IRS辅助无线通信进行合理近场建模的必要性。