Limits of Covert Communication on Two-Hop AWGN Channels

Wu, Huihui; Liao, Xuening; Dang, Yongchao; Shen, Yulong; Jiang, Xiaohong

doi:10.1109/nana.2017.55

Cited by 21 publications

(9 citation statements)

References 11 publications

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“…where p(x, z) is the joint probability function of x and z, p(z) is the marginal probability distribution of z, Z is the set of z, and X is the set of [32,Theorem 8.6.5]. This is the main reason why Gaussian signaling is widely adopted in the literature of covert communications (e.g., [3], [10]). Noting that the elements of x are i.i.d.…”

Section: Mutual Informationmentioning

confidence: 99%

“…However, the achieved covertness by spread spectrum has never been proven theoretically, because there is no fundamental understanding on when or how often spread spectrum fails to hide wireless transmissions. As such, recent cutting-edge research on wireless communication security has focused on the fundamental limits of covert communications (e.g., [3], [8]- [10]). In covert communications, a transmitter (Alice) desires to transmit information to a legitimate receiver (Bob) without being detected by a warden (Willie), who is collecting observations to detect this transmission.…”

Section: Introductionmentioning

confidence: 99%

“…For example, with the aid of D(p 0 ||p 1 ) to bound the detection error probability in part of the considered covertness constraint, the authors of [3] established the square root limit on the amount of information that can be transmitted from Alice to Willie reliably for any ǫ > 0. With the same constraint, the work [10] extended this square root law into a two-hop wireless system, where the source intends to communicate with the destination covertly via a Decode-and-Forward relay node and the conducted analysis shows that this square root law can be extended into a multi-hop system. Meanwhile, using D(p 1 ||p 0 ) ≤ 2ǫ 2 as the covertness constraint, the authors of [9] proved that the square-root law holds for a broad class of discrete memoryless channels (DMCs), in which the scaling constant of the amount of information with respect to the square root of the blocklength has been determined for DMCs and AWGN channels.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Gaussian Signalling for Covert Communications

Yan

Cong

Hanly

et al. 2019

IEEE Trans. Wireless Commun.

144

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In this work, we examine the optimality of Gaussian signalling for covert communications with an upper bound on D(p 1 ||p 0 ) or D(p 0 ||p 1 ) as the covertness constraint, where D(p 1 ||p 0 ) and D(p 0 ||p 1 ) are different due to the asymmetry of Kullback-Leibler divergence, p 0 (y) and p 1 (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 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(p 1 ||p 0 ) as the constraint. More interestingly, we also prove that Gaussian signalling is not optimal for covert communications with an upper bound on D(p 0 ||p 1 ) as the constraint, for which as we explicitly show skew-normal signalling can outperform Gaussian signalling in terms of achieving higher mutual information. Finally, we prove that, for Gaussian signalling, an upper bound on D(p 1 ||p 0 ) is a tighter covertness constraint in terms of leading to lower mutual information than the same upper bound on D(p 0 ||p 1 ), by proving D(p 0 ||p 1 ) ≤ D(p 1 ||p 0 ).

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Section: Mutual Informationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Gaussian Signalling for Covert Communications

Yan

Cong

Hanly

et al. 2019

IEEE Trans. Wireless Commun.

144

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show abstract

“…The achievability of the square root law (SRL) was established in [5] where in order to achieve covert communication over the additive white Gaussian noise (AWGN) channel, Alice can only transmit no more than O ( √ n) bits to Bob in n channel uses. Moreover, the SRL results have been verified in discrete memoryless channels (DMCs) [7], [8], two-hop systems [9], multiple access channels [10] and broadcast channels [11]. In short, these results imply that the average number of covert bits per channel use asymptotically approaches zero despite the noiseless transmission, i.e., lim n→∞ O ( √ n)/n = 0.…”

Section: Introductionmentioning

confidence: 86%

Robust Beamforming Design for Covert Communications

Al-Dhahir³

et al. 2021

Preprint

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In this paper, we consider a common unicast beamforming network where Alice utilizes the communication to Carol as a cover and covertly transmits a message to Bob without being recognized by Willie. We investigate the beamformer design of Alice to maximize the covert rate to Bob when Alice has either perfect or imperfect knowledge about Willie's channel state information (WCSI). For the perfect WCSI case, the problem is formulated under the perfect covert constraint, and we develop a covert beamformer by applying semidefinite relaxation and the bisection method. Then, to reduce the computational complexity, we further propose a zero-forcing beamformer design with a single iteration processing. For the case of the imperfect WCSI, the robust beamformer is developed based on a relaxation and restriction approach by utilizing the property of Kullback-Leibler divergence. Furthermore, we derive the optimal decision threshold of Willie, and analyze the false alarm and the missed detection probabilities in this case. Finally, the performance of the proposed beamformer designs is evaluated through numerical experiments.

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“…The work [6] proposed that achieving covert communications by adopted channel inversion power control with Rayleigh fading channels. Some recent works [14,16,17] considered the two-hop scenario and analyzed its effects on the covert communication performance in terms of detection error probability of warden and covert capacity. Note that these works on the performance of covert communication mainly focus on the two scenarios of one hop or two-hop with the help of a single relay.…”

Section: Introductionmentioning

confidence: 99%

Covert Communication in Relaying Sensor Systems

Gao

Yang

Jiang

et al. 2020

Proceedings of the 1st International Workshop on Physical-Layer Augmented Security for Sensor Systems

Self Cite

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Sensor systems are paramount importance for data transmission in the Internet of Things (IoT) applications. However, lots of unauthorized attacking from the adversary makes such systems to face security challenges due to the broadcast and openness natures of wireless channels. This paper studies the performance of covert communication in a relaying sensor system. We first propose random relay selection scheme and based on this scheme, we derive the expressions of covert performances in terms of transmission outage probability, detection error probability and covert capacity. We further optimize the covert transmit power of source to maximize the covert capacity with the covert requirement. Finally, numerical results are provided to illustrate our theoretical achievements and the impact of some parameters on the performances of such system. CCS CONCEPTS • Security and privacy → Mobile and wireless security.

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Limits of Covert Communication on Two-Hop AWGN Channels

Cited by 21 publications

References 11 publications

Gaussian Signalling for Covert Communications

Gaussian Signalling for Covert Communications

Robust Beamforming Design for Covert Communications

Covert Communication in Relaying Sensor Systems

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