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International Conference on Communications

Achieving positive rate with undetectable communication over AWGN and Rayleigh channels

Seonwoo Lee, Robert J. Baxley

Published Jun 1, 2014• 40 citations
Publisher

Abstract

In this paper we consider the problem of achieving a positive error-free communications rate without being detected by an eavesdropper - we coin this the privacy rate. Specifically, we present the privacy rate over Additive White Gaussian Noise (AWGN) and Rayleigh channels when an eavesdropper employs a radiometer detector and has uncertainty about her noise variance. Leveraging recent results on the phenomenon of an Signal to Noise Ratio (SNR) wall when there is eavesdropper noise power measurement uncertainty, we show that a non-zero privacy rate is possible. We also find the SNR wall under Rayleigh fading. We conclude by presenting realizable privacy rates for several practical scenarios.

DOI
10.1109/icc.2014.6883414

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In this paper we consider the problem of achieving a positive error-free communications rate without being detected by an eavesdropper - we coin this the privacy rate. Specifically, we present the privacy rate over Additive White Gaussian Noise (AWGN) and Rayleigh channels when an eavesdropper employs a radiometer detector and has uncertainty about her noise variance. Leveraging recent results on the phenomenon of an Signal to Noise Ratio (SNR) wall when there is eavesdropper noise power measurement uncertainty, we show that a non-zero privacy rate is possible. We also find the SNR wall under Rayleigh fading. We conclude by presenting realizable privacy rates for several practical scenarios.
In this paper we consider the problem of achieving a positive error-free communications rate without being detected by an eavesdropper-we coin this the privacy rate. Specifically, we analyze the privacy rate over additive white Gaussian Noise (AWGN) channels with finite and infinite number of samples and Rayleigh single input-single (SISO) and multiple input-multiple output (MIMO) channels with infinite samples when an eavesdropper employs a radiometer detector and has uncertainty about his noise variance. Leveraging recent results on the phenomenon of a signal-to-noise ratio (SNR) wall when there is eavesdropper noise power measurement uncertainty, we show that a nonzero privacy rate is possible. We also show that in this scenario, the detector should not necessarily take as many samples as possible.
We investigate the achievable secrecy rate with Gaussian random codes when the main channel is an AWGN channel, while the eavesdropper's channel is Rayleigh fading with additive Gaussian noise. Several transmission strategies according to the main channel's relative channel gain are proposed and evaluated. We show that even if the main channel channel gain is arbitrarily worse than the eavesdropper's average channel gain, positive secrecy rate can still be achieved with artificial noise injection and a burst signaling strategy.
We consider a secret communication scenario where Alice wants to transmit secretly to Bob in presence of a passive eavesdropper Eve. The Alice-Bob channel is a fixed-SNR AWGN channel, while the Alice-Eve channel is a fast Rayleigh fading channel, with the channel states only known to Eve. Alice knows the statistics of Alice-Eve channel, but not the exact realizations. We investigate the achievable secrecy rates for this channel model with Gaussian signaling and discrete signaling. For Gaussian signaling, several transmission strategies according to the main channel's relative channel gain are proposed and evaluated. For discrete signaling, achievable secrecy rates with Quadrature Amplitude Modulation (QAM) are evaluated. When Bob's channel is much better than Eve's channel, simple Gaussian signaling can perform close to the upper bound, and is better than the rate achieved with M-QAM. When Bob's channel gain is on average worse than the eavesdropper's average channel gain, positive secrecy rate can still be achieved for Gaussian signaling with artificial noise injection and a burst signaling strategy. Moreover, M-QAM can outperform Gaussian signaling. The key factor that enables secret communication in this case is that both M-QAM and artificial noise limit the leakage of information when Eve's channel is unusually good.
We consider a secret communication scenario where Alice wants to transmit secretly to Bob in presence of a passive eavesdropper Eve. The Alice-Bob channel is a fixed-SNR AWGN channel, while the Alice-Eve channel is a fast Rayleigh fading channel, with the channel states only known to Eve. Alice knows the statistics of Alice-Eve channel, but not the exact realizations. We investigate the achievable secrecy rates for this channel model with Gaussian signaling and discrete signaling. For Gaussian signaling, several transmission strategies according to the main channel's relative channel gain are proposed and evaluated. For discrete signaling, achievable secrecy rates with Quadrature Am- plitude Modulation (QAM) are evaluated. When Bob's channel is much better than Eve's channel, simple Gaussian signaling can perform close to the upper bound, and is better than the rate achieved with M-QAM. When Bob's channel gain is on average worse than the eavesdropper's average channel gain, positive secrecy rate can still be achieved for Gaussian signaling with artificial noise injection and a burst signaling strategy. Moreover, M-QAM can outperform Gaussian signaling. The key factor that enables secret communication in this case is that both M-QAM and artificial noise limit the leakage of information when Eve's channel is unusually good.
Covert or low probability of detection communication is crucial to protect user privacy and provide a strong security. We analyze the joint impact of imperfect knowledge of the channel gain (channel uncertainty) and noise power (noise uncertainty) on the average probability of detection error at the eavesdropper and the covert throughput in Rayleigh fading channel. We characterize the covert throughput gain provided by the channel uncertainty as well as the covert throughput loss caused by the channel fading as a function of the noise uncertainty. Our result shows that the channel fading is essential to hiding the signal transmission, particularly when the noise uncertainty is below a threshold and/or the receive SNR is above a threshold. The impact of the channel uncertainty on the average probability of detection error and covert throughput is more significant when the noise uncertainty is larger.
Uncertainty about noise variance is unavoidable. Many existing works exploited the noise uncertainty for covert communication and meanwhile assumed that the adversary third party Willie adopts a radiometer detector, in which case a positive covert and reliable rate O(N) bits/N channel uses is achievable. Nonetheless, the radiometer is not optimal in general. The limit covert and reliable rate based on noise uncertainty against the optimal detector remains unknown. To shed light on this problem, this letter proves that when Willie suffers from noise uncertainty but has two or more antennas for detection, the limit covert and reliable rate over additive white Gaussian noise channels is O(N) bits/N channel uses. This rate is the same as the limit rate without the noise uncertainty, which means that the covert performance gain stemming from the noise uncertainty is indeed fragile. The key of the proof is the proposed correlation detector for Willie, which is easy to deploy and does not require any knowledge about channel coefficients or transmitter’s codebook.