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IEEE Transactions on Wireless Communications

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

Aymen Omri, Mazen O. Hasna

Published Apr 16, 2018• 39 citations
Publisher

Abstract

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.

DOI
10.1109/twc.2018.2816648

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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.
In this paper, we study important physical layer security metrics over wiretap channels with Rician fading. We derive the average secrecy outage rate (ASOR) expression to quantify the average secrecy zero level crossing rate, and the expression of the average secrecy outage duration (ASOD), which measures (in second) how long in average the system remains in the secrecy outage status. Simulation results are conducted to confirm and discuss the theoretical derived expressions. The results show that maximum Doppler frequency shift and signal to noise ratio (SNR) at the eavesdropper are the main factors that affect the ASOR and ASOD.
Securing information in future mobile networks is particularly challenging for devices with limited computational resources. In such contexts, physical layer security (PLS) offers a promising alternative by exploiting the inherent randomness of wireless channels. When full secrecy cannot be guaranteed, the partial secrecy regime provides a realistic and effective approach to system design. This study investigates the partial secrecy performance of wireless systems operating over the recently introduced generalized multicluster fluctuating two-ray (MFTR) fading model. This model is highly regarded for its adaptability in representing a broad range of propagation environments and includes various classical fading models as exceptional cases. We consider a secure communication setup involving a transmitter (A), an intended receiver (B), and an eavesdropper (E). Inspired by previous work showing the benefits and simplicity of diversity schemes for improving PLS, we assume that both B and E are equipped with antenna arrays and apply maximal ratio combining (MRC). The model also considers independently but not identically distributed (i.n.i.d.) fading conditions on the A → B and A → E links. We derive exact and closed-form approximate expressions for three central metrics in partial secrecy theory: generalized secrecy outage probability (GSOP), average fractional equivocation (AFE), and average information leakage rate (AILR). Unlike previous approaches based on simpler fading models, the proposed expressions maintain a constant computational complexity, irrespective of the number of diversity branches, and are compatible with standard mathematical tools. Validation via Monte Carlo simulations confirms the accuracy of the derived expressions and highlights the impact of key system parameters on secrecy performance. The flexible MFTR framework enables assessment across varied fading conditions. In particular, increasing the number of MRC branches at B improves the GSOP diversity order and alters PLS behavior based on the fading characteristics of the A → E link.
We investigate the physical layer security limits of Wyner's wiretap model over Fisher-Snedecor .T composite fading channels. .T fading conditions have been recently shown to provide an accurate characterization of multipath fading and shadowing effects in emerging wireless transmission scenarios such as body centric, cellular and vehicular communications. To this end, we utilize a redefined analytic expression for the Fisher-Snedecor .T distribution in order to ensure unconstrained validity and reliability when used in the analysis of various performance metrics of interest. In this context, we assume that the main channel (i.e., between the source and the legitimate destination) and the eavesdropper's channel (i.e., between the source and the illegitimate destination) undergo independent quasi-static Fisher-Snedecor .T composite fading. Novel exact analytic expressions are then derived for the corresponding average secrecy capacity (ASC), secure outage probability (SOP) and probability of strictly positive secrecy capacity (SPSC) along with their insightful asymptotic representations. In addition, analytical expressions for the ASC, SOP and SPSC over mixed fading channels such as Nakagami-m/Nakagami-m, Nakagami-m/Fisher-Snedecor .T and Fisher-Snedecor .T/Nakagami-m are derived. The new formulations are validated through comparisons with Monte-Carlo simulations and analyzed to gain useful insights into the impact of the fading parameters on the achievable accuracy and the overall system performance.
For secure communications over wireless fading channels, the secrecy outage probability is widely used as the performance measure. However, the current secrecy outage formulation has two major limitations in evaluating the secrecy performance: a) the amount of information leakage to the eavesdropper cannot be characterized when an outage occurs, b) the current formulation does not give insights into the eavesdropper's decodability of confidential messages. To overcome such limitations and obtain in-depth understanding of secrecy performance over wireless fading channels, this paper proposes three new secrecy measures for different practical aims, namely, 1) generalized secrecy outage probability, 2) asymptotic lower bound on eavesdropper's decoding error probability, and 3) average information leakage rate. A specific example of wireless transmissions with a fixed-rate wiretap code is given to illustrate the use of the proposed secrecy measures.
Theoretical studies on physical layer security often adopt the secrecy outage probability as the performance metric for wireless communications over quasi-static fading channels. The secrecy outage probability has two limitations from a practical point of view: 1) it does not give any insight into the eavesdropper's decodability of confidential messages and 2) it cannot characterize the amount of information leakage to the eavesdropper when an outage occurs. Motivated by the limitations of the secrecy outage probability, we propose three new secrecy metrics for secure transmissions over quasi-static fading channels. The first metric establishes a link between the concept of secrecy outage and the decodability of messages at the eavesdropper. The second metric provides an error-probability-based secrecy metric which is typically used for the practical implementation of secure wireless systems. The third metric characterizes how much or how fast the confidential information is leaked to the eavesdropper. We show that the proposed secrecy metrics collectively give a more comprehensive understanding of physical layer security over fading channels and enable one to appropriately design secure communication systems with different views on how secrecy is measured.
Theoretical studies on physical layer security often adopt the secrecy outage probability as the performance metric for wireless communications over quasi-static fading channels. The secrecy outage probability has two limitations from a practical point of view: 1) it does not give any insight into the eavesdropper's decodability of confidential messages and 2) it cannot characterize the amount of information leakage to the eavesdropper when an outage occurs. Motivated by the limitations of the secrecy outage probability, we propose three new secrecy metrics for secure transmissions over quasi-static fading channels. The first metric establishes a link between the concept of secrecy outage and the decodability of messages at the eavesdropper. The second metric provides an error-probability-based secrecy metric which is typically used for the practical implementation of secure wireless systems. The third metric characterizes how much or how fast the confidential information is leaked to the eavesdropper. We show that the proposed secrecy metrics collectively give a more comprehensive understanding of physical layer security over fading channels and enable one to appropriately design secure communication systems with different views on how secrecy is measured.