On the Physical Layer Security of Untrusted Millimeter Wave Relaying Networks: A Stochastic Geometry Approach

Abstract

The physical layer security (PLS) of millimeter wave (mmWave) communication systems is investigated, where the secure source-to-destination communication is assisted by an untrusted relay selected from a group of them and there are also several passive eavesdroppers (Eves) in the network. In the considered system model, while the distributions of the untrusted relays and Eves follow a homogeneous Poisson Point Process (PPP). To maximize the instantaneous secrecy rate, a novel joint relay selection and power allocation (JRP) method is developed where the destination and source aim for jamming the reception of both the untrusted relays and passive Eves. New expressions of the optimal power allocation (OPA) are derived for both non-colluding Eves (NCE) and colluding Eves (CE). Subsequently, by considering the impact of potential blockages, new closed-form equations are derived for analyzing the system’s ergodic secrecy rate (ESR) and secrecy outage probability (SOP) for transmission over fading mmWave channels. Finally, numerical examples are provided for demonstrating the superiority of our proposed JRP method over the relevant benchmarks found in the literature. Interestingly, the ESR increases with the density of untrusted relays for both the NCE and CE scenarios, which is a benefit of the improved probability of selecting a relay with a stronger second-hop channel. Furthermore, in the low transmit power regime, employing relatively low mmWave frequencies achieves better ESR, while in the high transmit power regime, high mmWave frequencies provide higher ESR.