Average Secrecy Outage Rate and Average Secrecy Outage Duration of Wireless Communication Systems With Diversity Over Nakagami-m Fading Channels

This paper presents an analytical methodology for the evaluation of two important physical layer security metrics in wiretap channels. Specifically, we first introduce the concept and the expression of average secrecy outage rate (ASOR) to quantify the average secrecy level crossing rate at a predefined secrecy threshold level. Then, we derive the expression of a new metric, namely, average secrecy outage duration (ASOD), which is a measure (in seconds) that describes how long on average the system remains in the secrecy outage status. The results are quite general and account for diversity-based systems operating over independent and identically distributed (i.i.d.) Nakagami-m fading channels. Monte Carlo simulations are conducted to confirm and discuss the analytical results. These results show that the ASOR and the ASOD are essentially affected by the diversity order, and the maximum Doppler frequency shift. In particular, and unlike the ASOD, the ASOR has a maximum value that should be considered in designing systems that are sensitive to secrecy level drops, even for short periods of time. In addition, the proposed new metric of ASOD might have large values even if the currently used metric of average fade duration shows low values on the communication link under consideration.