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IEEE Transactions on Wireless Communications

Covert Communication in Continuous-Time Systems in the Presence of a Jammer

Ke Li, Tamara V. Sobers, Don Towsley, Dennis Goeckel

Published Dec 16, 2021• 22 citations
Publisher

Abstract

Covert communication considers the ability of transmitter Alice to communicate reliably to receiver Bob without being detected by warden Willie. Previous work has generally considered a discrete-time model, and, in the standard Alice-Bob-Willie scenario, it has been shown that a discrete-time model captures the salient aspects of the underlying continuous-time covert communications system. However, in the presence of a jammer assisting Alice, where it has been shown in previous work that Alice can achieve a positive covert rate on a discrete-time model, we demonstrate here that a straightforward extension of the discrete-time construction to the continuous-time system does not guarantee a positive covert rate, hence indicating that the discrete-time model does not capture the salient aspects of the continuous-time system in such a scenario. This is because Willie is able to exploit excess bandwidth for co-channel interference suppression, as we demonstrate with an interference cancellation receiver. Hence, for the case when Alice is assisted by an uninformed jammer, we consider the continuous-time channel directly and study whether efficient covert communication can still be achieved against any possible receiver that Willie might employ. By presenting and characterizing an approach much different than that suggested by previous work for discrete-time systems in such a scenario, we establish that$\mathcal {O}(WT)$information bits can be transmitted covertly and reliably on a continuous-time channel of asymptotic bandwidth$W$in$T$seconds, regardless of the receiver that Willie employs. This is done for two separate scenarios: 1) when there is perfect frame synchronization between Alice and the jammer’s signals; 2) when there is no frame synchronization between Alice and the jammer’s signals. Numerical results are provided to validate the theory.

DOI
10.1109/twc.2021.3134179

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Covert Communication in Continuous-Time Systems

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Recent works have considered the ability of transmitter Alice to communicate reliably to receiver Bob without being detected by warden Willie. These works generally assume a standard discrete-time model. But the assumption of a discrete-time model in standard communication scenarios is often predicated on its equivalence to a continuous-time model, which has not been established for the covert communications problem. Here, we consider the continuous-time channel directly and study if efficient covert communication can still be achieved. We assume that an uninformed jammer is present to assist Alice, and we consider additive white Gaussian noise (AWGN) channels between all parties. For a channel with approximate bandwidth W, we establish constructions such that O(WT) information bits can be transmitted covertly and reliably from Alice to Bob in T seconds for two separate scenarios: 1) when the path-loss between Alice and Willie is known; and 2) when the path-loss between Alice and Willie is unknown.

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Tamara V. Sobers, Boulat A. Bash, Dennis Goeckel +2 more

Recent work has established that when transmitter Alice wishes to communicate reliably to recipient Bob without detection by warden Willie, with additive white Gaussian noise (AWGN) channels between all parties, communication is limited to O(√n) bits in n channel uses. However, this result is predicated on Willie having an accurate statistical characterization of the background noise. When Willie has uncertainty about his noise characteristics and his receiver is limited to a power detector, O(n) bits can be covertly delivered. Here, we establish covert communication of O(n) bits in n channel uses while: (i) generalizing the environment; and (ii) removing any restrictions on Willie's receiver. We consider the case where an additional node, called the "jammer", is present to help Alice and Bob communicate covertly. This jammer is termed "uninformed", as it does not know the content or timing of Alice's transmission. We consider both AWGN channels and a scenario with a block faded jammer with a single fade per codeword. In these scenarios, we are able to establish the optimality of the power detector for Willie, from which the achievability of reliable and covert communication at a positive rate follows.

Asilomar Conference on Signals, Systems and Computers (ACSSC)•Nov 1, 2015•36 citations
Covert communication considers the ability of transmitter Alice to communicate reliably to receiver Bob without being detected by warden Willie. Previous work has generally considered a discrete-time model, and, in the standard Alice-Bob-Willie scenario, it has been shown that a discrete-time model captures the salient aspects of the underlying continuous-time covert communications system. However, in the presence of a jammer assisting Alice, where it has been shown in previous work that Alice can achieve a positive covert rate on a discrete-time model, we demonstrate here that a straightforward extension of the discrete-time construction to the continuous-time system does not guarantee a positive covert rate, hence indicating that the discrete-time model does not capture the salient aspects of the continuous-time system in such a scenario. This is because Willie is able to exploit excess bandwidth for co-channel interference suppression, as we demonstrate with an interference cancellation receiver. Hence, for the case when Alice is assisted by an uninformed jammer, we consider the continuous-time channel directly and study whether efficient covert communication can still be achieved against any possible receiver that Willie might employ. By presenting and characterizing an approach much different than that suggested by previous work for discrete-time systems in such a scenario, we establish thatO(WT)\mathcal {O}(WT)O(WT)information bits can be transmitted covertly and reliably on a continuous-time channel of asymptotic bandwidthWWWinTTTseconds, regardless of the receiver that Willie employs. This is done for two separate scenarios: 1) when there is perfect frame synchronization between Alice and the jammer’s signals; 2) when there is no frame synchronization between Alice and the jammer’s signals. Numerical results are provided to validate the theory.
Recent works have considered the ability of transmitter Alice to communicate reliably to receiver Bob without being detected by warden Willie. These works generally assume a standard discrete-time model. But the assumption of a discrete-time model in standard communication scenarios is often predicated on its equivalence to a continuous-time model, which has not been established for the covert communications problem. Here, we consider the continuous-time channel directly and study if efficient covert communication can still be achieved. We assume that an uninformed jammer is present to assist Alice, and we consider additive white Gaussian noise (AWGN) channels between all parties. For a channel with approximate bandwidth W, we establish constructions such that O(WT) information bits can be transmitted covertly and reliably from Alice to Bob in T seconds for two separate scenarios: 1) when the path-loss between Alice and Willie is known; and 2) when the path-loss between Alice and Willie is unknown.
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.
This dissertation studies covert wireless communications where a transmitter (Alice) intends to transmit messages to a legitimate receiver (Bob) such that the presence of the message is hidden from an attentive warden (Willie). Here we consider pertinent aspects of covert communications that focus on moving such systems closer to implementation. For example, previous studies use the standard discrete-time communication model when analyzing covert communications, since this is commonly assumed without loss of generality in standard communication theory. However, it is not clear that such a model captures the salient aspects of the continuous-time covert communications problem. A power detector that is optimal for the warden in a discrete-time covert communications scenario may not be optimal on a continuous- time model. Thus, it is of interest to consider this more realistic model for physical channels. After analyzing a power optimization problem using the standard discrete-time model, we move to the key part of system implementation: the instantiation in true continuous-time systems of the discrete-time models studied to this point in the literature. A key goal is to examine Willie’s detection capability on a continuous-time model and study how the limits of covert communications change from the discrete-time case. In particular, we show that detectors for Willie can benefit from the continuous-time setting and outperform detectors based on the discrete-time model; not surprisingly, this has a significant impact on the true covert throughput of the system. Nevertheless, we establish constructions such that efficient covert communications can still be achieved in a continuous-time model, and prove the fundamental limit on the covert communication rate. After considering the continuous-time problem in detail, we then turn to addressing another limitation of previous work - the requirement for an intentional jammer to facilitate efficient covert communication. Instead, we consider how to exploit a pre-existing interference source – a radar - to achieve covert communication. We establish a covert communication scheme in such an environment, and analyze the corresponding covert rate. Finally, we consider the use of a detection technique similar to that in the covert communications problem, in the area of quantized signal detection.
Recent work has established that when transmitter Alice wishes to communicate reliably to recipient Bob without detection by warden Willie, with additive white Gaussian noise (AWGN) channels between all parties, communication is limited to O(√n) bits in n channel uses. However, this assumes that Willie has an accurate statistical characterization of the channel. When Willie has uncertainty about such and his receiver is limited to a threshold test on the received power, Alice can transmit covertly with a power that does not decrease with n, thus conveying O(n) bits covertly and reliably in n uses of an AWGN channel. Here, we consider covert communication of O(n) bits in n channel uses while generalizing the environment and removing any restrictions on Willie's receiver. We assume that an uninformed “jammer” is present to help Alice, and we consider AWGN and block fading channels. In some scenarios, Willie's optimal detector is a threshold test on the received power. When the channel between the jammer and Willie has multiple fading blocks per codeword, a threshold test on the received power is not optimal. However, we establish that Alice can remain covert with a transmit power that does not decrease with n even when Willie employs an optimal detector.
Recent work has established that when transmitter Alice wishes to communicate reliably to recipient Bob without detection by warden Willie, with additive white Gaussian noise (AWGN) channels between all parties, communication is limited to O(n)\mathcal{O}(\sqrt{n})O(n​) bits in nnn channel uses. However, this assumes Willie has an accurate statistical characterization of the channel. When Willie has uncertainty about such and his receiver is limited to a threshold test on the received power, Alice can transmit covertly with a power that does not decrease with nnn, thus conveying O(n)\mathcal{O}(n)O(n) bits covertly and reliably in nnn uses of an AWGN channel. Here, we consider covert communication of O(n)\mathcal{O}(n)O(n) bits in nnn channel uses while generalizing the environment and removing any restrictions on Willie's receiver. We assume an uninformed "jammer" is present to help Alice, and we consider AWGN and block fading channels. In some scenarios, Willie's optimal detector is a threshold test on the received power. When the channel between the jammer and Willie has multiple fading blocks per codeword, a threshold test on the received power is not optimal. However, we establish that Alice can remain covert with a transmit power that does not decrease with nnn even when Willie employs an optimal detector.
Recent work has established that when transmitter Alice wishes to communicate reliably to recipient Bob without detection by warden Willie, with additive white Gaussian noise (AWGN) channels between all parties, communication is limited to O(√n) bits in n channel uses. However, this result is predicated on Willie having an accurate statistical characterization of the background noise. When Willie has uncertainty about his noise characteristics and his receiver is limited to a power detector, O(n) bits can be covertly delivered. Here, we establish covert communication of O(n) bits in n channel uses while: (i) generalizing the environment; and (ii) removing any restrictions on Willie's receiver. We consider the case where an additional node, called the "jammer", is present to help Alice and Bob communicate covertly. This jammer is termed "uninformed", as it does not know the content or timing of Alice's transmission. We consider both AWGN channels and a scenario with a block faded jammer with a single fade per codeword. In these scenarios, we are able to establish the optimality of the power detector for Willie, from which the achievability of reliable and covert communication at a positive rate follows.