SNR Coverage Probability Analysis of RIS-Aided Communication Systems

Abstract

The reconfigurable intelligent surface (RIS) technique has received many interests, thanks to its advantages of low cost, easy deployment, and high controllability. It is acknowledged that the RIS can significantly improve the quality of signal transmission, especially in the line-of-sight-blocked scenarios. Therefore, it is critical to analyze the corresponding signal-to-noise ratio (SNR) coverage probability of RIS-aided communication systems. In this correspondence, we consider many practical issues to analyze the SNR coverage probability. We employ the realistic path loss model and Rayleigh fading model as large-scale and small-scale channel models, respectively. Meanwhile, we take the number and size of the RIS elements, as well as the placement of the RIS plane into considerations. We first derive the exact closed-form SNR coverage probability for a single element. Afterward, with the moment matching method, a highly accurate approximation of SNR coverage probability is formulated as the ratio of the upper incomplete Gamma function and Gamma function, allowing an arbitrary number of elements in the RIS. Finally, we comprehensively evaluate the impacts of essential factors on the SNR coverage probability, such as the number and size of the element, the coefficients of fading channel, and the angles of incidence and RIS plane. Overall, this work provides a succinct and general expression of SNR coverage probability, which can be helpful in the performance evaluation and practical implementation of the RIS.