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International Wireless Communications and Mobile Computing Conference (IWCMC)

A tight estimation of the security gap over the fast fading wiretap channel

Marco Baldi, Marco Bianchi, Nicola Maturo, Franco Chiaraluce

Published Jul 1, 2013• 3 citations
Publisher

Abstract

In this paper, we provide a tight estimation of the security gap for the wiretap channel with fast Rayleigh fading. The error rate has already been used as a practical physical layer security metric, and the security gap has been defined to exploit such a metric over the wiretap channel with additive white Gaussian noise. We study two different approaches for estimating the security gap also over a fast fading wiretap channel. The first approach is quite conservative, and tends to overestimate the security gap. The second approach instead allows to perform a more realistic evaluation, and to highlight the gain achievable through information scrambling and coding, even when both the legitimate receiver and the eavesdropper channels are known only in statistical terms.

DOI
10.1109/iwcmc.2013.6583549

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In this paper, we provide a tight estimation of the security gap for the wiretap channel with fast Rayleigh fading. The error rate has already been used as a practical physical layer security metric, and the security gap has been defined to exploit such a metric over the wiretap channel with additive white Gaussian noise. We study two different approaches for estimating the security gap also over a fast fading wiretap channel. The first approach is quite conservative, and tends to overestimate the security gap. The second approach instead allows to perform a more realistic evaluation, and to highlight the gain achievable through information scrambling and coding, even when both the legitimate receiver and the eavesdropper channels are known only in statistical terms.
Using the error rate as a metric is useful for assessing the performance of actual transmission schemes from the physical layer security viewpoint. The security gap concept has been used over the additive white Gaussian noise channel as a practical measure for combined reliability and security. In this paper, the definition of security gap is extended to a wire-tap channel with fast fading. Our aim is to show that by introducing scrambling and error correction coding can significantly reduce the required quality difference between the channel of the authorized user and that of the unauthorized one.
We study the secrecy capacity of fast fading channels under imperfect main channel (between the transmitter and the legitimate receiver) estimation at the transmitter. Lower and upper bounds on the ergodic secrecy capacity are derived for a class of independent identically distributed (i.i.d.) fading channels. The achievable rate follows from a standard wiretap code in which a simple on-off power control is employed along with a Gaussian input. The upper bound is obtained using an appropriate correlation scheme of the main and eavesdropper channels and is the best known upper bound so far. The upper and lower bounds coincide with recently derived ones in case of perfect main CSI. Furthermore, the upper bound is tight in case of no main CSI, where the secrecy capacity is equal to zero. Asymptotic analysis at high and low signal-to-noise ratio (SNR) is also given. At high SNR, we show that the capacity is bounded by providing upper and lower bounds that depend on the channel estimation error. At low SNR, however, we prove that the secrecy capacity is asymptotically equal to the capacity of the main channel as if there were no secrecy constraint. Numerical results are provided for i.i.d. Rayleigh fading channels.
We consider a secure integrated sensing and communication (ISAC) scenario, where a signal is transmitted through a state-dependent wiretap channel with one legitimate receiver with which the transmitter communicates and one honest-but-curious target that the transmitter wants to sense. The secure ISAC channel is modeled as two state-dependent fast-fading channels with correlated Rayleigh fading coefficients and independent additive Gaussian noise components. Delayed channel outputs are fed back to the transmitter to improve the communication performance and to estimate the channel state sequence. We establish and illustrate an achievable secrecy-distortion region for degraded secure ISAC channels under correlated Rayleigh fading, for which we show that the signal-to-interference-plus-noise is not a sufficient statistic. We also evaluate the inner bound for a large set of parameters to derive practical design insights. The presented results include parameter ranges for which the secrecy capacity of a classical wiretap channel setup is surpassed and for which the channel capacity is approached. Thus, we illustrate for correlated Rayleigh fading cases that our secure ISAC methods can (i) eliminate the need for the legitimate receiver to have a statistical advantage over the eavesdropper and (ii) provide communication security with minimal rate penalty.
We consider a secure integrated sensing and communication (ISAC) scenario, in which a signal is transmitted through a state-dependent wiretap channel with one legitimate receiver with which the transmitter communicates and one honest-but-curious target that the transmitter wants to sense. The secure ISAC channel is modeled as two state-dependent fast-fading channels with correlated Rayleigh fading coefficients and independent additive Gaussian noise components. Delayed channel outputs are fed back to the transmitter to improve the communication performance and to estimate the channel state sequence. We establish and illustrate an achievable secrecy-distortion region for degraded secure ISAC channels under correlated Rayleigh fading. We also evaluate the inner bound for a large set of parameters to derive practical design insights for secure ISAC methods. The presented results include in particular parameter ranges for which the secrecy capacity of a classical wiretap channel setup is surpassed and for which the channel capacity is approached.
A (layered) broadcast approach is studied for fading wiretap channels. The basic idea is to employ superposition coding to encode information into a number of layers and use stochastic encoding for each layer to keep the corresponding information secret from an eavesdropper. The legitimate receiver successively decodes information one layer after another by canceling the interference caused by the layers that the receiver has already decoded. The advantage of this approach is that the transmitter does not need to know the channel states to the legitimate receiver and the eavesdropper, but can still securely transmit certain layers of information to the legitimate receiver. The layers that can be securely transmitted are determined by the channel states to the legitimate receiver and the eavesdropper. The Gaussian wiretap channel with fixed channel gains is first studied to illustrate the idea of the broadcast approach. Three cases of block fading wiretap channels with a stringent delay constraint are then studied, in which either the legitimate receiver's channel, the eavesdropper's channel, or both channels are fading. For each case, the secrecy rate that can be achieved by using the broadcast approach is obtained, and the optimal power allocation over the layers (or the conditions on the optimal power allocation) is also derived.
We consider a wiretap channel consisting of a source with multiple antennas, a legitimate receiver and an eavesdropper with a single antenna each. The channels between the source and the receivers undergo fast fading. We assume that the transmitter, in addition to the statistics of both channels, is only aware of a noisy version of the CSI to the legitimate receiver referred to as main channel. The legitimate receiver is aware of both its instantaneous channel gain and the transmitter's estimate of the main channel. On the other hand, the eavesdropper's receiver, in addition to its instantaneous channel realization, is aware of the actual main CSI and the transmitter's estimate as well. While the capacity of this channel is still open even with perfect CSI at the transmitter, we provide in this paper upper and lower bounds on the secrecy capacity. The upper bound is tighter than the one corresponding to perfect main CSI and the gap between the two upper bounds is characterized in function of the channel estimation error variance, at high-SNR. Furthermore, we show that our upper and lower bounds coincide in the case of no main CSI providing a trivial secrecy capacity.