We investigate the impact of multiple distributed intelligent reflecting surfaces (IRSs), which are deployed and optimized by a mobile operator (MO), on the performance of user equipments (UEs) served by other co-existing out-of-band (OOB) MOs that do not control the IRSs. We show that, under round-robin scheduling, in mmWave frequencies, the ergodic sum spectral efficiency (SE) of an OOB MO increases logarithmically in the total number of IRS elements with a pre-log factor that increases with the ratio of the number of OOB paths through the IRS to the number of elements at an IRS. We further show that the maximum achievable SE of the OOB MO scales log-linearly with the total IRS elements, with a pre-log factor of $1$. Then, we specify the minimum number of IRSs as a function of the channel parameters and design a distributed IRS system in which an OOB MO almost surely obtains the maximum SE. Finally, we prove that the outage probability at an OOB UE decreases exponentially as the number of IRSs increases, even though they are randomly configured from the OOB UE's viewpoint. We numerically verify our theory and conclude that distributed IRSs always help every MO, but the MO controlling the IRSs benefits the most.

翻译：本研究探讨了由某一移动运营商部署与优化的多个分布式智能反射表面对其他共存且不控制IRS的带外移动运营商所服务用户设备性能的影响。我们证明，在毫米波频段采用轮询调度机制时，带外移动运营商的遍历和频谱效率随IRS总单元数呈对数增长，其对数前系数随IRS反射的带外路径数与单IRS单元数之比增大而增加。进一步研究表明，带外移动运营商可达的最大频谱效率随IRS总单元数呈对数线性增长，其对数前系数为$1$。随后，我们根据信道参数确定了所需IRS的最小数量，并设计了一种分布式IRS系统，使得带外移动运营商几乎必然能获得最大频谱效率。最后，我们证明尽管从带外用户设备视角看IRS是随机配置的，但其中断概率仍随IRS数量增加呈指数下降。数值实验验证了理论结果，表明分布式IRS始终对所有移动运营商有益，但控制IRS的运营商获益最大。