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International Conference on Communications

Secrecy outage of Nakagami-m MISO channels with randomly located receivers

Satyanarayana Vuppala, Weigang Liu, Giuseppe Thadeu Freitas de Abreu, Tharmalingam Ratnarajah

Published Jun 1, 2015• 2 citations
Publisher

Abstract

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.

DOI
10.1109/icc.2015.7249327

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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.
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 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.
Correlation between the legitimate receiver and the eavesdropper has been seldom considered in the literature when evaluating secrecy metrics in stochastic wireless networks. In practice, however, poor scattering conditions may lead to spatially correlated channels, which can be exploited by eavesdroppers. In this paper we investigate the connection outage and secrecy outage in Poisson-distributed random networks under Nakagami-m fading and mutually correlated legitimate and eavesdropping channels. Numerical results show that correlated fading has an important effect on security, which may be either beneficial or harmful, depending on the secrecy outage constraints.
This paper considers transmit antenna selection (TAS) and receive generalized selection combining (GSC) for secure communication in MIMO wiretap channel, where confidential messages transmitted from an NA-antenna transmitter to an NB-antenna legitimate receiver are overheard by an NE-antenna eavesdropper. We assume that the main channel and the eavesdropper's channel undergo Nakagami-m fading with fading parameters mBand mE, respectively. In an effort to assess the secrecy performance, we present a closed-form expression for the secrecy outage probability. We then derive closed-form expressions for the secrecy outage probability at high signal-to-noise ratio (SNR) for two realistic scenarios: 1) the legitimate receiver is located close to the transmitter, and 2) the legitimate receiver and the eavesdropper are located close to the transmitter. In the first scenario, we confirm that the secrecy diversity order is mBNBNA. In the second scenario, we confirm that the secrecy diversity order collapses to zero. While this may appear discouraging at a first glance, we show that low secrecy outage probability can still be achieved.
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.
In this paper, for the conventional MISO wiretap channel, we take into account the locations' random nature regarding those eavesdroppers and the ambient interferers in the wireless networks. For the convenience of mathematical analysis, these location distributions are modeled as Poisson point processes (PPPs). We assume that the transmitter Alice has no channel state information (CSI) about the other nodes except that it knows the statistical CSI of links about the legitimate user Bob and those eavesdroppers. In order to improve the security of Bob, we further set up a protected zone (PZ) to prevent excessive eavesdroppers from overhearing confidential signals. We investigate the probabilities of connection outage and secrecy outage to derive the closed form expression of secrecy transmission rate. Afterwards, we formulate an secrecy rate maximization problem and solve it to determine the optimized beamforming vector. The numerical results reveal the superiority of the proposed beamforming optimization over the relevant eigen beamforming design in [1].