Performance Analysis of Active RIS-Aided Wireless Communication Systems Over Nakagami-$m$ Fading Channel

Reconfigurable Intelligent Surfaces (RISs) have emerged as a promising solution to enhance the security and reliability of wireless communication systems by intelligently reshaping the propagation environment. Although conventional passive RIS improves signal's strength through phase-shift control, its inability to amplify signals limits the overall system's performance. This limitation is addressed by the active RIS, which integrates amplification capabilities to offer significant performance enhancements. With the help of novel recursive integrals, this paper presents accurate yet analytically tractable closed-form solutions for the outage probability (OP) and the secrecy outage probability (SOP) for active RIS-aided wireless communication systems under Nakagami-$m$ fading conditions. To achieve the same level of target reliability of 0.4, we demonstrate that under certain degrees of the fading severity, and at some constant value of the receiver's signal-to-noise ratio (SNR), an active RIS-aided structure with amplification gain of 10 dB help in reducing the required number of reflecting elements by nearly 90% compared to its passive counterpart. This underscores the practical and economic advantages of active RIS in terms of reduced hardware complexity and deployment cost. The number of elements needed can be further reduced by increasing the amplification gain of the active reflecting elements. Additionally, the asymptotic receiver SNR analysis is carried out which further provides an insight into the advantages of incorporating active reflecting elements into the system's design as compared to the corresponding passive elements. Precisely, for the same number of elements, the active RIS-aided systems achieve a considerable user's SNR of 40 dB as compared to the passive RIS-aided systems; for all values of the Nakagami-$m$ fading parameters. All the analytical results are validated through extensive Monte-Carlo simulations.