Gaussian signalling for covert communications

Shihao Yan, Yirui Cong, Stephen V. Hanly, Xiangyun Zhou

Research output: Contribution to journalArticleResearchpeer-review

Abstract

In this paper, we examine the optimality of Gaussian signalling for covert communications with an upper bound on D(p1||p0) or D(p0||p1) as the covertness constraint, where D(p1||p0) and D(p0||p1) are different due to the asymmetry of Kullback-Leibler divergence, p0(y) and p1(y) are the likelihood functions of the observation y at the warden under the null hypothesis (no covert transmission) and alternative hypothesis (a covert transmission occurs), respectively. Considering additive white Gaussian noise at both the receiver and the warden, we prove that the Gaussian signalling is optimal in terms of maximizing the mutual information of transmitted and received signals for covert communications with an upper bound on D(p1||p0) as the constraint. More interestingly, we also prove that the Gaussian signalling is not optimal for covert communications with an upper bound on D(p0||p1) as the constraint, for which as we explicitly show skew-normal signalling can outperform the Gaussian signalling in terms of achieving higher mutual information. Finally, we prove that, for Gaussian signalling, an upper bound on D(p1||p0) is a tighter covertness constraint in that it leads to lower mutual information than the same upper bound on D(p0||p1) , by proving D(p0||p1) ≤ D(p1||p0).

LanguageEnglish
Pages3542-3553
Number of pages12
JournalIEEE Transactions on Wireless Communications
Volume18
Issue number7
DOIs
Publication statusPublished - Jul 2019

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Upper bound
Communication
Mutual Information
Kullback-Leibler Divergence
Gaussian White Noise
Likelihood Function
Null hypothesis
Skew
Asymmetry
Optimality
Receiver
Alternatives

Cite this

Yan, Shihao ; Cong, Yirui ; Hanly, Stephen V. ; Zhou, Xiangyun. / Gaussian signalling for covert communications. In: IEEE Transactions on Wireless Communications. 2019 ; Vol. 18, No. 7. pp. 3542-3553.
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Gaussian signalling for covert communications. / Yan, Shihao; Cong, Yirui; Hanly, Stephen V.; Zhou, Xiangyun.

In: IEEE Transactions on Wireless Communications, Vol. 18, No. 7, 07.2019, p. 3542-3553.

Research output: Contribution to journalArticleResearchpeer-review

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