Physical Layer Security over Independent Fluctuating Two-Ray (IFTR) Fading Channels

Abstract

Underwater acoustic communications (UACs) are vulnerable to eavesdropping because of the broadcast nature of acoustic transmission. In this work, we analyze physical layer security over statistically independent fluctuating two-ray (IFTR) legitimate and eavesdropping links. For the full-CSI benchmark, a closed-form expression for the average secrecy capacity (ASC) is derived as the main analytical contribution. In addition, a closed-form lower bound on the secrecy outage probability (SOP) is obtained. The probability of strictly positive secrecy capacity (SPSC) follows as an exact corollary when the target secrecy rate is zero. The ASC expression is verified through direct numerical integration and independent Monte Carlo simulation using realizations, with a maximum deviation of 0.1336%. Moreover, the SOP lower bound is verified numerically and compared with the exact SOP. Its maximum deviation is 4.25% at a target secrecy rate of 0.1bit/s/Hz over the tested cases; however, larger deviations occur at higher target secrecy rates. A sensitivity analysis further shows the influence of the IFTR parameters on secrecy performance. Finally, three representative IFTR parameter configurations are considered for numerical comparison. Accordingly, these configurations are treated as statistical test cases rather than general representations of measured shallow-water, deep-water, or UWSN environments.