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 is monotonic in the total number of IRS elements with a pre-log factor that depends on the channel properties of the OOB UE. We further show that the maximum achievable SE of OOB MO scales log-linearly in IRS elements. Then, by specifying the minimum number of IRSs as a function of the channel parameters, we 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 in the number of IRSs, even though they are randomly configured from the 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：我们研究了多个分布式智能反射表面（IRS）对非控制IRS的共存带外（OOB）移动运营商所服务用户设备（UE）性能的影响，这些IRS由某移动运营商部署并优化。研究表明，在毫米波频段采用轮询调度时，OOB运营商的遍历和频谱效率（SE）随IRS单元总数单调递增，其前对数因子取决于OOB UE的信道特性。进一步证明，OOB运营商的最大可达SE与IRS单元数量呈对数线性关系。随后，通过将最小IRS数量表示为信道参数的函数，我们设计了一种分布式IRS系统，使得OOB运营商几乎必然获得最大SE。最后，我们证明，尽管从UE视角看IRS配置具有随机性，但OOB UE的中断概率随IRS数量呈指数级下降。数值实验验证了理论结论，并表明分布式IRS始终有益于所有运营商，但控制IRS的运营商获益最多。