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arXiv:2308.04278 · IEEE Transactions on Information Forensics and Security

Achieving Covert Communication With a Probabilistic Jamming Strategy

Xun Chen, Fujun Gao, Min Qiu, Jia Zhang, Feng Shu, Shihao Yan

Published Jan 1, 2024• 29 citations
arXivHTMLPDF

Abstract

In this work, we consider a covert communication scenario, where a transmitter Alice communicates to a receiver Bob with the aid of a probabilistic and uninformed jammer against an adversary warden’s detection. The transmission status and power of the jammer are random and follow some priori probabilities. We first analyze the warden’s detection performance as a function of the jammer’s transmission probability, transmit power distribution, and Alice’s transmit power. We then maximize the covert throughput from Alice to Bob subject to a covertness constraint, by designing the covert communication strategies from three different perspectives: Alice’s perspective, the jammer’s perspective, and the global perspective. Our analysis reveals that the minimum jamming power should not always be zero in the probabilistic jamming strategy, which is different from that in the continuous jamming strategy presented in the literature. In addition, we prove that the minimum jamming power should be the same as Alice’s covert transmit power, depending on the covertness and average jamming power constraints. Furthermore, our results show that the probabilistic jamming can outperform the continuous jamming in terms of achieving a higher covert throughput under the same covertness and average jamming power constraints.

DOI
10.1109/tifs.2024.3402346

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In this work, we consider a covert communication scenario, where a transmitter Alice communicates to a receiver Bob with the aid of a probabilistic and uninformed jammer against an adversary warden’s detection. The transmission status and power of the jammer are random and follow some priori probabilities. We first analyze the warden’s detection performance as a function of the jammer’s transmission probability, transmit power distribution, and Alice’s transmit power. We then maximize the covert throughput from Alice to Bob subject to a covertness constraint, by designing the covert communication strategies from three different perspectives: Alice’s perspective, the jammer’s perspective, and the global perspective. Our analysis reveals that the minimum jamming power should not always be zero in the probabilistic jamming strategy, which is different from that in the continuous jamming strategy presented in the literature. In addition, we prove that the minimum jamming power should be the same as Alice’s covert transmit power, depending on the covertness and average jamming power constraints. Furthermore, our results show that the probabilistic jamming can outperform the continuous jamming in terms of achieving a higher covert throughput under the same covertness and average jamming power constraints.
In this work, the covert communication assisted by a probabilistic jammer is investigated in the finite blocklength regime, in which the jammer emits jamming signals with a certain probability to alleviate its negative effect on legitimate link but still enhance the covertness performance. Specifically, we first derive a tractable expression of covertness constraint based on the average KL divergence. Then, a closed-form expression of average decoding error probability (DEP) involving the effect of probabilistic jamming is presented. Moreover, joint optimization of transmit power and blocklength at the transmitter for maximizing the average effective covert throughput (AECT) is formulated and tackled, which demonstrates the trade-off between the transmit power and blocklength to improve covert communication performance. Our results show that the probabilistic jamming can indeed enhance the covert communication performance, and the jamming probability can be optimized to further improve the AECT.
Covert communication is achieved if the transmitter (Alice) sends messages to a legitimate receiver (Bob) without detection by an attentive warden (Willie). Recently, there has been significant work on establishing the limits of such covert communication, including our work demonstrating that a cooperative jammer can greatly improve the throughput of covert communication systems. However, this previous work has considered a discrete-time model, with the implicit implication that the results will be similar on the true continuous-time model of the physical channel. In this paper, we consider covert communication over the continuous-time channel model to understand the throughput scaling for large blocklengths. For the Alice-Bob-Willie scenario, the results from the discrete-time channel generally follow. However, when a jammer is added to the environment, we demonstrate that timing offsets between Alice's signal and that of the jammer allow for the application of co-channel interference mitigation techniques at Willie's detector, which call into question whether our previous results suggesting an improvement in the covert throughput with the help of the jammer will be obtained in practice. Finally, we consider initial approaches to thwart such a detector and achieve improved throughput scaling in the presence of the jammer.
Covert communication conceals transmission of messages between Alice and Bob from an adversary, Willie, who tries to determine if a transmission took place or not. While covert communication in a basic, standard setting where all variables are known to Willie, results in the well-known square-root law, when a jammer is present and assists Alice by creating uncertainty in Willie's decoder, a strictly positive transmission rate is possible. In this work, we analyze the case where the jammer is equipped with multiple antennas. Specifically, we analyze the effect of multiple antennas at the jammer on Alice's transmission power and consequently on the transmission rate. We consider both the case where the channel knowledge of Willie is known as well as the case where it is unknown. We formulate several optimization problems for the transmission strategies of the jammer to maximize his assistance to Alice, in terms of maximizing Bob's received SNR and consequently the covert rate. When the channel information is known to the jammer, we show that under an achievable covertness scheme, the optimal strategy of the jammer is to perform beamforming towards a single direction with all his available power. This direction though, is not trivial, since it reflects a tradeoff point between minimizing the interference at Bob and maximizing the interference at Willie. When the channel knowledge is unknown, we show that the optimal strategy of the jammer is either to transmit isotropically to all directions or to the null-space of Bob, where this choice depends on certain channel conditions. This is in contrast to current schemes in the literature. Furthermore, we extend the optimization problems to the case where Bob is also equipped with multiple antennas, and provide insightful results, shown to be asymptotically optimal, accompanied by simulations.
Abstract This paper addresses the power allocation problem in a network where joint information-theoretic secrecy and covert communication are required. In this network, a single transmitter (Alice) sends information to two legitimate users (Bob and Carol). There is also an untrusted user who attempts to detect the content of Bob’s message and a warden (Willie) who wants to detect the existence of communication between Alice and the two users. Thus, Carol requires covert transmission, and Bob requires secure and covert communication. The network utilizes a friendly jammer to address these demands and overcome the low transmission rate of covert communication. To achieve covert communication, Alice sends both users’ data simultaneously in selected time slots to hide it from Willie, while the jammer continuously transmits signals in all time slots. The objective is to maximize the average transmission rate over the allocated powers of Bob, Carol, and the jammer while meeting the two users’ requirements. A novel iterative algorithm is proposed to obtain an effective solution. Simulation results indicate that the proposed method can enhance the network’s average rate while satisfying the users’ demands.
This article investigates covert communications in a multirelay Internet of Things (IoT) system with multiple energy harvesting jammers, where a transmitter (Alice) attempts to covertly transmit confidential messages to its destination (Bob) through relay forwarding, while a warden (Willie) detects the existence of Alice’s transmission. Specifically, we employ a harvesting-then-jamming protocol with which the jammers first harvest energy from Alice and then send jamming signals to interfere with Willie’s detection. We propose a relay and jammer selection strategy, namely quality of service (QoS)-aware selection, and use the random selection strategy as a comparison strategy. Under these two selection strategies, we derive the optimal detection threshold and minimum detection error probability at Willie, respectively. We then model the covert throughput performance and obtain the maximum covert throughput by jointly optimizing covert transmit power and jamming transmit power. Extensive numerical results are provided to illustrate the impacts of system parameters on covert throughput performance.
Covert communication is achieved if a transmitter (Alice) sends a message to a legitimate receiver (Bob) without being detected by an attentive warden (Willie). Recent work has taken an outage approach that considers an infinite blocklength and analyzes the probability that channel conditions are such that communication is reliable and/or covert. Power adaptation via truncated channel inversion (TCI) has been examined in previous work in an attempt to minimize outage under the covertness constraint. However, the optimality of TCI was not established, and the associated parameters in the TCI scheme were only found numerically. We provide the exact optimal power adaptation schemes under different covertness constraints and with different channel models: 1) when the channel between Willie and an uninformed jammer is AWGN; and 2) when the channel is a Rayleigh fading channel. We also examine the performance improvement of these schemes over standard approaches. This establishes that TCI is optimal in some, but not all, scenarios of interest.