On Secrecy Performance of RIS-Assisted MISO Systems over Rician Channels with Spatially Random Eavesdroppers

TL;DR

This paper investigates the physical-layer security of RIS-assisted MISO systems with spatially random eavesdroppers modeled by a Poisson point process and RIS-to-ground links subject to Rician fading. Using stochastic geometry, it derives exact distributions for the SNRs at the legitimate user and the eavesdroppers, leading to closed-form expressions for the secrecy outage probability (SOP) and the ergodic secrecy capacity (ESC); a high-SNR analysis yields a secrecy diversity order of $d_s=\frac{2}{\alpha_2}$, showing the diversity is dictated by the RIS-to-ground path-loss exponent. The results reveal that secrecy performance is mainly driven by the number of RIS elements $N$, with the transmit antennas $K$ and transmit power having only marginal effects; in the unknown-eavesdropper-positions scenario, placing the RIS closer to the legitimate user improves secrecy, and the asymptotic ESC scales additively with $\log_2(1/\lambda_e)$. Numerical simulations corroborate the theoretical findings and provide practical guidelines for RIS deployment, highlighting the trade-offs between RIS size, placement, and security in realistic stochastic scenarios.

Abstract

Reconfigurable intelligent surface (RIS) technology is emerging as a promising technique for performance enhancement for next-generation wireless networks. This paper investigates the physical layer security of an RIS-assisted multiple-antenna communication system in the presence of random spatially distributed eavesdroppers. The RIS-to-ground channels are assumed to experience Rician fading. Using stochastic geometry, exact distributions of the received signal-to-noise-ratios (SNRs) at the legitimate user and the eavesdroppers located according to a Poisson point process (PPP) are derived, and closed-form expressions for the secrecy outage probability (SOP) and the ergodic secrecy capacity (ESC) are obtained to provide insightful guidelines for system design. First, the secrecy diversity order is obtained as $\frac{2}{α_2}$, where $α_2$ denotes the path loss exponent of the RIS-to-ground links. Then, it is revealed that the secrecy performance is mainly affected by the number of RIS reflecting elements, $N$, and the impact of the number of transmit antennas and transmit power at the base station is marginal. In addition, when the locations of the randomly located eavesdroppers are unknown, deploying the RIS closer to the legitimate user rather than to the base station is shown to be more efficient. Moreover, it is also found that the density of randomly located eavesdroppers, $λ_e$, has an additive effect on the asymptotic ESC performance given by $\log_2{\left({1}/{λ_e}\right)}$. Finally, numerical simulations are conducted to verify the accuracy of these theoretical observations.

Figures (13)

• Figure 1: System model of an RIS-assisted MISO communication system in the presence of spatially random eavesdroppers.
• Figure 2: The CDF of the received SNRs at the legitimate user $D$ and the eavesdroppers $E$, respectively.
• Figure 3: The SOP versus $\rho_d$, with $K=16$, $\alpha_1=\alpha_2=2$, $\epsilon=2$, $d_{S\!R}=30~{\rm m}$, $d_{R\!D}=40~{\rm m}$, $r_e=200~{\rm m}$, $\lambda_e=10^{-3}$, $C_{\rm th}=0.05$, and $\rho_e= 30~{\rm dB}$.
• Figure 4: The SOP versus $\rho_d$, with $N=16$, $\alpha_1=\alpha_2=2$, $\epsilon=2$, $d_{S\!R}=30~{\rm m}$, $d_{R\!D}=40~{\rm m}$, $r_e=200~{\rm m}$, $\lambda_e=10^{-3}$, $C_{\rm th}=0.05$, and $\rho_e= 30~{\rm dB}$.
• Figure 5: The SOP versus $\epsilon$ and $\lambda_e$, with $K=16$, $N=36$, $\alpha_1=\alpha_2=2$, $d_{S\!R}=30~{\rm m}$, $d_{R\!D}=40~{\rm m}$, $r_e=200~{\rm m}$, $C_{\rm th}=0.05$, $\rho_d= 20~{\rm dB}$, and $\rho_e= 30~{\rm dB}$.