Secrecy Performance Analysis in FD Relay-Assisted ISAC Systems Under Dual Eavesdropping Threats

In the era of integrated sensing and communication (ISAC) systems, protecting privacy has become increasingly challenging as eavesdroppers target both information and sensing signals. To address this issue, we propose a downlink multi-user full-duplex decode-and-forward (FD-DF) relay-assisted ISAC architecture. This system comprises a macro base station (MaBS), a micro base station (MiBS) acting as a relay, several cooperative users, a sensing target, and two types of eavesdroppers: one focused on communication signals and the other on sensing data. We derive new statistical expressions for the probability density function (PDF) and cumulative distribution function (CDF) of the signal-to-noise ratio for both legitimate and eavesdropping channels. Using these derived PDF and CDF, we obtain closed-form expressions for the intercept probability (IP), the probability of non-zero secrecy capacity (PNZSC), and the sensing secrecy outage probability (SSOP). Monte Carlo simulations confirm the accuracy of the derived analytical expressions. The results highlight the impact of eavesdropping and transmit diversity on the secrecy of ISAC systems.