Performance Analysis of Reconfigurable Intelligent Surface-Assisted Wireless Systems and Comparison With Relaying

In this paper, we provide the theoretical framework for the performance comparison of reconfigurable intelligent surfaces (RISs) and amplify-and-forward (AF) relaying wireless systems. In particular, after statistically characterizing the end-to-end (e2e) wireless channel coefficient of the RIS-assisted wireless system, in terms of probability density function (PDF) and cumulative density function (CDF), we extract novel closed-form expressions for the instantaneous and average e2e signal-to-noise ratio (SNR) for both the RIS-assisted and AF-relaying wireless systems. Building upon these expressions, we derive the diversity gain of the RIS-assisted wireless system as well as the outage probability (OP) and symbol error rate (SER) for a large variety of Gray-mapped modulation schemes of both systems under investigation. Additionally, the diversity order of the RIS-assisted wireless system is presented as well as the ergodic capacity (EC) of both the RIS-assisted and AF-relaying wireless systems. Likewise, high-SNR and high-number of metasurfaces (MS) approximations for the SER and EC for the RIS-assisted wireless system are reported. Finally, for the sake of completeness, the special case in which the RIS is equipped with only one MS is also investigated. For this case, the instantaneous and average e2e SNR are derived, as well as the OP, SER and EC. Our analysis is verified through respective Monte Carlo simulations, which reveal the accuracy of the presented theoretical framework. Moreover, our results highlight that, in general, RIS-assisted wireless systems outperform the corresponding AF-relaying ones in terms of average SNR, OP, SER and EC.