| Summary: | 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.
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