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IEEE Systems Journal

Asymptotic Secrecy Analysis of Random Networks With Colluding Eavesdroppers

Satyanarayana Vuppala, Giuseppe Thadeu Freitas de Abreu

Published Apr 29, 2016• 5 citations
Publisher

Abstract

We perform an analysis of the secrecy outage and transmission capacity of random networks under Nakagami-m fading with colluding eavesdroppers, in the asymptotic case of large reference signal-to-noise ratios. In literature, secrecy analysis from the perspective of collusion pool has still not been well characterized. Considering a network model that accounts for uncertainties both in node locations and channel coefficients, we approximate the distribution of the aggregate path gain received by a collusion of eavesdroppers. Using this result, the asymptotic secrecy rate distribution, the secrecy outage probability, and the secrecy transmission capacity of random networks with colluding eavesdroppers are obtained, with basic factors such as density of nodes, the guarding distance, and the fading figure all accounted for by explicit parameters. Since secrecy in low-outage random networks are found to be most significant when the density of active nodes is small, the expressions derived can be seen as upper-bounds on the three aforementioned secrecy performance metrics in random networks, offering particular insight on the impact of fading, density, and guarding distances, while taking into account cooperation among eavesdroppers. Furthermore, we give a bound on colluding pool size, which is pragmatic in creating a nonprotected communication zone for the typical destination.

DOI
10.1109/jsyst.2016.2524582

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We perform an analysis of the secrecy outage and transmission capacity of random networks under Nakagami-m fading with colluding eavesdroppers, in the asymptotic case of large reference signal-to-noise ratios. In literature, secrecy analysis from the perspective of collusion pool has still not been well characterized. Considering a network model that accounts for uncertainties both in node locations and channel coefficients, we approximate the distribution of the aggregate path gain received by a collusion of eavesdroppers. Using this result, the asymptotic secrecy rate distribution, the secrecy outage probability, and the secrecy transmission capacity of random networks with colluding eavesdroppers are obtained, with basic factors such as density of nodes, the guarding distance, and the fading figure all accounted for by explicit parameters. Since secrecy in low-outage random networks are found to be most significant when the density of active nodes is small, the expressions derived can be seen as upper-bounds on the three aforementioned secrecy performance metrics in random networks, offering particular insight on the impact of fading, density, and guarding distances, while taking into account cooperation among eavesdroppers. Furthermore, we give a bound on colluding pool size, which is pragmatic in creating a nonprotected communication zone for the typical destination.
We perform an analysis of the secrecy outage of random networks under Nakagami-m fading with multiple transmit antennas. Specifically, using a network model that accounts for uncertainties both in node locations (distances) and channel coefficients (fading), we derive the distribution of the best path gain of eavesdroppers using Probability Generating Functional property of Poisson Point Process (PPP). Using this result, the secrecy outage probability and the conditional secrecy outage probability of random networks with multiple eavesdroppers are obtained, with basic factors such as the density of eavesdropping nodes, the number of transmit antennas and the fading coefficient all accounted for by explicit parameters. The impact of transmission factors, including number of transmit antennas, fading figure, legitimate node distance and node density are studied and analysed in numerical results.
In this paper, we investigate the secrecy outage probability of random wireless networks from the perspective of the k-th best source, which has still not been well characterized. We consider the artificial noise (AN) transmission strategy at source nodes to confuse the eavesdropper. Furthermore, we use a concept of security-region based on the k-th best source index. This is pragmatic in creating a protected communication zone for the typical destination and also in bounding the number of sources that can cooperate in a Coordinated Multi-point transmission (CoMP) network. We further derive the secrecy outage probability for these CoMP sources based on the security-region. We also provide a closed-form expression for the maximum number of eavesdroppers for a given secrecy outage constraint, which can effect the secure communication. Tractable numerical results are presented under various assumptions of densities, antenna gains, AN transmission factors and path loss exponents.
We investigated the secrecy outage of unicast channels in random networks exposed to unknown numbers of randomly located eavesdroppers, obtaining original expressions which include uncertainty in terms of the location of legitimate nodes relative to eavesdroppers, the number of eavesdroppers, and fading. Under such conditions, we derive the path gain distributions of legitimate and eavesdropper nodes, as well as the corresponding secrecy non-outage. Two interesting conclusions can be drawn from our analysis. The first is that the uncertainty on the number of eavesdropper does not play a significant role in quantifying secrecy outage; and the second is that secret communication at a given rate is possible (albeit subjected to outage), with very low power. Specifically, it is found that the for a given fading figure and network density (which fundamentally determines the secrecy outage) similar secrecy outage is experience by the k-th furthest legitimate node, independent on the source's transmit power.
The wiretap channel model in a wireless scenario is analyzed where there is a transmitter, multiple legitimate receivers, non-colluding and colluding eavesdroppers; each of them is equipped with one antenna. Furthermore, all the channels are mutually independent and experiencing quasi-static Nakagami-m fading. We derive closed-form expressions for the exact secrecy outage probability as well as the average secrecy capacity with both non-colluding and colluding eavesdroppers. Such performance metrics are used to analyze the impacts of the number of receivers and eavesdroppers on the system. Remarkably, our results reveal that, for non-colluding eavesdroppers, increasing the number of users will cause greater secrecy degradation than the number of eavesdroppers, especially when the main channel is far superior to the wiretap channel or the value of the fading parameter is high. And for the colluding case, it turns out to be the opposite.
Physical layer security helps enormously cryptography to improve the confidentiality of communications over wireless networks. Indeed, the secrecy capacity is used at the physical layer to ensure not only the security of communications but also to exploit efficiently the channel capacity. The principle of secrecy capacity is to characterize the maximum data transmission rate, that can be reached while the exchanged information is kept secret from a malicious entity. In this paper, we present a closed-form expression of outage probability and we specify the outage secrecy capacity of a Nakagami-m fading channel in the presence of cooperative correlated eavesdroppers performing the maximal ratio combining which helps the eavesdroppers to tap the maximum of the exchanged information between the transmitter and the legitimate receiver. Simulations results show that a raise in the number of the cooperative eavesdroppers degrades significantly the secrecy capacity of this communication system, moreover the correlation degree between the eavesdroppers has a negative impact on the communication confidentiality especially when it takes small values.
In this paper, we investigate the secrecy outage performance of a typical cooperative downlink non-orthogonal multiple access (NOMA) system over Nakagami-m fading channel, in which the base station transmits a superimposed signal to two users via a relay. First, the secrecy outage behavior of the considered system over Nakagami-mmm fading channel under three wiretapping cases, e.g., one eavesdropper (Eve), non-colluding and colluding eavesdroppers, are studied, and both analytical and asymptotic expressions for the secrecy outage probability are derived. Next, by considering the availability of Eves' channel state information, we adopt the two-stage relay selection (RS) strategy to improve the system's secrecy outage performance. Finally, simulation results are provided to corroborate the accuracy of our derived expressions. The results show that: 1) there exists secrecy performance floor for cooperative NOMA system, and it was determined by the weak user's secrecy requirement and the channel conditions of the Eves; 2) the two-stage RS scheme can increase the secrecy outage performance significantly under three wiretapping cases; 3) the secrecy performance of cooperative NOMA network is superior to that of orthogonal multiple access network on the condition of low and medium signal-to-noise ratio regions.