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Asilomar Conference on Signals, Systems and Computers (ACSSC)

Covert Communications Under Environmental Uncertainty on a Continuous-Time Channel

Amna Gillani, Tamara V. Sobers, Don Towsley, Dennis Goeckel

Published Oct 29, 2023• 1 citation
Publisher

Abstract

Covert communication is achieved when a transmitter Al-ice can successfully transmit a message to a receiver Bob without being detected by an attentive and capable adversary Willie. Early results demonstrated the difficulty of the covert communications problem: with AWGN discrete-time channels between all parties, only$O(\sqrt{n})$bits can be sent in$n$channel uses. But it was soon recognized that uncertainty about the environment at Willie, for example, uncertainty in his own noise statistics, could allow for a positive rate:$O(n)$bits can be sent covertly in$n$channel uses. However, most covert communication results, including this promising positive rate result, have been obtained for a discrete-time communications channel. Here, we demonstrate that the assumption of a discrete-time channel is problematic when trying to exploit Willie's noise uncertainty. In particular, we demonstrate that if Alice transmits$\omega(\sqrt{T})$bits in a length$T$interval to Bob on a continuous-time channel, then there exists a detector at Willie that can detect her transmission, as the probability of false alarm and missed detection$P_{MD}+P_{FA}\rightarrow 0$as$T\rightarrow\infty$. In other words, the communication is not covert, unlike the case of a discrete-time channel.

DOI
10.1109/ieeeconf59524.2023.10476936

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Covert communication is achieved when a transmitter Al-ice can successfully transmit a message to a receiver Bob without being detected by an attentive and capable adversary Willie. Early results demonstrated the difficulty of the covert communications problem: with AWGN discrete-time channels between all parties, onlyO(n)O(\sqrt{n})O(n​)bits can be sent innnnchannel uses. But it was soon recognized that uncertainty about the environment at Willie, for example, uncertainty in his own noise statistics, could allow for a positive rate:O(n)O(n)O(n)bits can be sent covertly innnnchannel uses. However, most covert communication results, including this promising positive rate result, have been obtained for a discrete-time communications channel. Here, we demonstrate that the assumption of a discrete-time channel is problematic when trying to exploit Willie's noise uncertainty. In particular, we demonstrate that if Alice transmitsω(T)\omega(\sqrt{T})ω(T​)bits in a lengthTTTinterval to Bob on a continuous-time channel, then there exists a detector at Willie that can detect her transmission, as the probability of false alarm and missed detectionPMD+PFA→0P_{MD}+P_{FA}\rightarrow 0PMD​+PFA​→0asT→∞T\rightarrow\inftyT→∞. In other words, the communication is not covert, unlike the case of a discrete-time channel.
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.
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 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.
Covert communication aims to hide the existence of the transmissions to guarantee the security in wireless communications. In this letter, channel uncertainty is exploited to achieve covert communication in relay networks. The transmitter Alice sends messages to the legitimate receiver Bob with the help of a relay, while the warden Willie wants to detect the existence of the transmission. The channel uncertainty introduces confusions to degrade the performance of Willie's detection. We show that Alice can transmit O{O}O (n{n}n ) bits in n{n}n channel uses covertly with the help of relay and channel uncertainty. Numerical results are shown to illustrate the achievability and the performance of the considered scenario.
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.
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.