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Asilomar Conference on Signals, Systems and Computers (ACSSC)

Unicasting on the S-Graph

Satyanaranaya Vuppala, Giuseppe Thadeu Freitas de Abreu

Published Nov 1, 2012• 1 citation
Publisher

Abstract

We consider the secrecy capacity of unicast channels of ad hoc networks exposed to randomly located eavesdroppers, as modeled by S-Graphs. Expressions that quantify the impact of fading and of the density of legitimate nodes relative to that of eavesdroppers are obtained, in terms of the probability that secrecy capacities of unicast channels are non-zero. The results indicate that depending on the relative density of eavesdroppers and the fading intensity, the secrecy capacity of unicast channels subject to fading may be higher that under AWGN.

DOI
10.1109/acssc.2012.6489366

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We consider the secrecy capacity of unicast channels of ad hoc networks exposed to randomly located eavesdroppers, as modeled by S-Graphs. Expressions that quantify the impact of fading and of the density of legitimate nodes relative to that of eavesdroppers are obtained, in terms of the probability that secrecy capacities of unicast channels are non-zero. The results indicate that depending on the relative density of eavesdroppers and the fading intensity, the secrecy capacity of unicast channels subject to fading may be higher that under AWGN.
We consider the secrecy capacity of unicast channels of ad hoc networks exposed to randomly located eavesdroppers, as modeled by S-Graphs. Expressions that quantify the impact of fading and of the density of legitimate nodes relative to that of eavesdroppers are obtained, in terms of the probability that secrecy capacities of unicast channels are nonzero. The results indicate that depending on the relative density of eavesdroppers and the fading intensity, the secrecy capacity of unicast channels subject to fading may be higher than under additive white Gaussian noise (AWGN).
We analyze the effect of fading onto the probability of non-zero secrecy capacity, denoted Pr{Cs:i> 0}, in stochastic wireless random networks modeled as Secrecy-Graphs. Specifically, we derive expressions to characterize the probability that the secrecy capacity of a unicast channel to a legitimate node is non-zero, in the case when the channel is affected by Nakagami-m fading, and in the presence of a random (unknown) number of eavesdroppers. The results show that fading can increase the probability of finding information-theoretic secure channels in such conditions, depending on the relative density of legitimate nodes and eavesdroppers.
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.
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 study the secrecy broadcast transmission capacity of a broadcast wireless ad hoc network of legitimate nodes coexisted with a correlated network of eavesdroppers. We define the secrecy broadcast transmission capacity as the product among the spatial density of broadcast transmissions without secrecy outage, the average number of neighbors of a broadcasting node, and the secrecy rate. By modeling the correlation between the legitimate nodes and the eavesdroppers as a spatial bivariate Poisson process, we derive the average number of eavesdropping neighbors that can cause secrecy outage and characterize the secrecy broadcast transmission capacity over general fading and Rayleigh fading channels. Numerical results show that in comparison to the case that without correlation, the correlation between the legitimate nodes and the eavesdroppers degrades the secrecy broadcast transmission capacity.
This letter deals with the secrecy capacity of the radio channel in interference-limited regime. We assume that interferers are uniformly scattered over the network area according to a Point Poisson Process and the channel model consists of path-loss, log-normal shadowing and Nakagami-m fading. Both the probability of non-zero secrecy capacity and the secrecy outage probability are then derived in closed-form expressions using tools of stochastic geometry and higher-order statistics. Our numerical results show how the secrecy metrics are affected by the disposition of the desired receiver, the eavesdropper and the legitimate transmitter.