This paper aims to make a comparison between decode-and-forward (DF) relays and reconfigurable intelligent surfaces (RISs) in the case where only one relay or RIS is selected based on the maximization of the signal-to-noise-ratio (SNR). Our study accounts for the spatial distribution of RISs and relays, which is assumed to follow a Poisson point process (PPP). It considers two different path loss models corresponding to RIS/relays randomly located in the near-field and the far-field of the transmitter. Based on the Gamma distribution moment matching method and tools from stochastic geometry, we derive approximations for the outage probability (OP) as well as the energy efficiency (EE) of the RISs-assisted system in the near-field and the far-field scenarios separately. Under the same conditions as RIS, the expressions for OP and EE of the half-duplex and the full-duplex DF relays-assisted systems are also derived. Simulation results are presented to corroborate the proposed analysis and compare between the three technologies. Our results show that RIS is the best choice in the near-field case, regardless of the OP or EE criterion. Compared to half-duplex relays and full-duplex relays, the RIS based system is the most energy-efficient solution to assist communication. Moreover, RIS allows for an improvement in both OP and EE when equipped with more reflecting elements or more densely deployed.

中文翻译：

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空间分布的RIS与中继辅助系统：公平的比较

本文旨在在基于信噪比（SNR）最大化的情况下仅选择一个继电器或RIS的情况下，对解码转发（DF）继电器和可重构智能表面（RIS）进行比较。 ）。我们的研究考虑了RIS和中继的空间分布，假定遵循Poisson点过程（PPP）。它考虑了两个不同的路径损耗模型，分别对应于随机位于发射机近场和远场的RIS /继电器。基于随机几何的Gamma分布矩匹配方法和工具，我们得出了RISs辅助系统在近场和远场场景中的中断概率（OP）和能效（EE）的近似值分别地。在与RIS相同的条件下，还推导了半双工和全双工DF中继辅助系统的OP和EE表达式。给出了仿真结果，以证实所提出的分析并在这三种技术之间进行比较。我们的结果表明，无论采用OP还是EE标准，RIS在近场情况下都是最佳选择。与半双工继电器和全双工继电器相比，基于RIS的系统是协助通信的最节能解决方案。此外，当配备更多反射元件或部署得更密集时，RIS可以改善OP和EE。不论OP或EE标准如何。与半双工继电器和全双工继电器相比，基于RIS的系统是协助通信的最节能解决方案。此外，当配备更多反射元件或部署得更密集时，RIS可以改善OP和EE。不论OP或EE标准如何。与半双工继电器和全双工继电器相比，基于RIS的系统是协助通信的最节能解决方案。此外，当配备更多反射元件或部署得更密集时，RIS可以改善OP和EE。