In this letter, we investigate a simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) assisting a massive multiple-input multiple-output (mMIMO) system. In particular, we derive a closed-form expression for the coverage probability of a STAR-RIS assisted mMIMO system while accounting for correlated fading and phase-shift errors. Notably, the phase configuration takes place at every several coherence intervals by optimizing the coverage probability since the latter depends on statistical channel state information (CSI) in terms of large-scale statistics. As a result, we achieve a reduced complexity and overhead for the optimization of passive beamforming, which are increased in the case of STAR-RIS networks with instantaneous CSI. Numerical results corroborate our analysis, shed light on interesting properties such as the impact of the number of RIS elements and the effect of phase errors, along with affirming the superiority of STAR-RIS against reflective-only RIS.

中文翻译：

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具有相关性和相位误差的 STAR-RIS 辅助大规模 MIMO 系统的覆盖概率

在这封信中，我们研究了一种同时发射和反射的可重构智能表面 (STAR-RIS)，以协助大规模多输入多输出 (mMIMO) 系统。特别是，我们推导了 STAR-RIS 辅助 mMIMO 系统的覆盖概率的封闭式表达式，同时考虑了相关的衰落和相移误差。值得注意的是，通过优化覆盖概率，相位配置每隔几个相干间隔发生一次，因为后者依赖于大规模统计方面的统计信道状态信息（CSI）。因此，我们降低了被动波束成形优化的复杂性和开销，而在具有瞬时 CSI 的 STAR-RIS 网络的情况下，这些复杂性和开销会增加。数值结果证实了我们的分析，