In this paper, we focus on the coverage probability of a double-intelligent reflecting surface (IRS) assisted wireless network and study the impact of multiplicative beamforming gain and correlated Rayleigh fading. In particular, we obtain a novel closed-form expression of the coverage probability of a single-input single-output (SISO) system assisted by two large IRSs while being dependent on the corresponding arbitrary reflecting beamforming matrices (RBMs) and large-scale statistics in terms of correlation matrices. Taking advantage of the large-scale statistics, i.e., statistical channel state information (CSI), we perform optimization of the RBMs of both IRSs once per several coherence intervals rather than at each interval. Hence, we achieve a reduction of the computational complexity, otherwise increased in multi-IRS-assisted networks during their RBM optimization. Numerical results validate the analytical expressions even for small IRSs, confirm enhanced performance over the conventional single-IRS counterpart, and reveal insightful properties.

翻译：在本文中,我们侧重于反映表面(IRS)辅助无线网络的双灵性反应双向反应的概率,并研究倍增波束增益和雷利益退缩相关关系的影响,特别是,我们获得了由两个大型IRS协助的单一投入单产出(SISO)系统的覆盖概率的新型封闭式表达方式,同时依赖于相应的任意反映波束矩阵(RBMS)和相关矩阵方面的大规模统计。我们利用大规模统计,即统计渠道国家信息(CSI),对两种IRS的成果管理制进行优化,一次是在若干一致性间隔期间,而不是每个间隔期间。因此,我们实现了计算复杂性的减少,否则在成果管理制优化期间,多IRS协助的网络会增加。数字结果验证了即使是小型IRS的分析表达方式,证实常规的单一IRS对口单位的性能提高,并揭示了有洞察力的特性。