Coverage Probability of RIS-Assisted Wireless Communication Systems With Random User Deployment Over Nakagami-$m$ Fading Channel

In beyond 5G (B5G), the higher directivity and attenuation make millimeter-wave (mmWave) very vulnerable to blockages that degrades the system performance. However, reconfigurable intelligent surface (RIS) is considered as a key enabler for B5G applications to avoid the blockages effect. In this paper, to accurately model real-world behavior, we investigate a new analytical framework model for a RIS-aided wireless communication system with a random user deployment over Nakagami-$m$ fading channel where the user's position distributes according to random waypoint (RWP) model, to characterize the performance of the system, considering direct and indirect links. As a result, new expressions for end-to-end signal-to-noise ratio (SNR), coverage probability, and ergodic capacity (EC) are derived. The impact of different metrics such as: blockages density ($\lambda _{b}$), number of RIS reflecting elements ($N$), fading parameter at the indirect link ($m_{R}$), and path loss parameter ($\alpha$) has been studied to evaluate the system performance. The results provide valuable insights into the performance of the system under these metrics. The coverage probability is degraded by increasing the blockage density and path loss parameter as they hinder the signal propagation and limit the signal strength at the MU. For example, at $-10$ dB, the coverage probability is degrading from $8\times 10^{-2}$ for blockage density $\lambda _{b}=3$ Blockes/$km^{2}$ to $5\times 10^{-5}$ at $\lambda _{b}=11$ Blockes/$km^{2}$. On the other hand, increasing the number of RIS reflecting elements ($N$) and fading parameter ($m_{R}$) at the indirect link, improves the coverage probability by enhancing the signal strength, reducing the effects of fading, and compensating for environmental challenges such as blockages. For example, the coverage probability, at $-10$ dB, increases from $3\times 10^{-1}$ at number of reflecting elements $N = 15$ to $8\times 10^{-1}$ at $N=40$. As well, the increasing of $N$ and $m_{R}$ can significantly boost the EC as the system can direct the signal more effectively, which improves the overall signal quality and system capacity. The accuracy of the analysis is validated using the Monte Carlo simulations, which shows excellent agreement with the derived expressions.