We consider the problem of covert communication over a state-dependent channel when the channel state is available either non-causally, causally, or strictly causally, either at the transmitter alone or at both transmitter and receiver. Covert communication with respect to an adversary, called "warden," is one in which, despite communication over the channel, the warden's observation remains indistinguishable from an output induced by innocent channel-input symbols. Covert communication involves fooling an adversary in part by a proliferation of codebooks; for reliable decoding at the legitimate receiver, the codebook uncertainty is typically removed via a shared secret key that is unavailable to the warden. In contrast to previous work, we do not assume the availability of a shared key at the transmitter and legitimate receiver. Instead, shared randomness is extracted from the channel state in a manner that keeps it secret from the warden, despite the influence of the channel state on the warden's output. When channel state is available at the transmitter and receiver, we derive the covert capacity region. When channel state is only available at the transmitter, we derive inner and outer bounds on the covert capacity. We provide examples for which the covert capacity is positive with knowledge of channel state information but is zero without it.
Full quantum capability devices can provide secure communications, but they are challenging to make portable given the current technology. Besides, classical portable devices are unable to construct communication channels resistant to quantum computers. Hence, communication security on portable devices cannot be guaranteed. Semi-Quantum Communication (SQC) attempts to break the quandary by lowering the receiver's required quantum capability so that secure communications can be implemented on a portable device. However, all SQC protocols have low qubit efficiency and complex hardware implementa…
A covert communication system under block fading channels is considered where users experience uncertainty about their channel knowledge. The transmitter seeks to hide the covert communication to a private user by exploiting a legitimate public communication link while the warden tries to detect this covert communication by using a radiometer. We derive the exact expression for the radiometers optimal threshold which determines the performance limit of the wardens detector. Furthermore for given transmission outage constraints the achievable rates for legitimate and covert users are analyzed w…
Covert communication hides the transmission of a message from a watchful adversary while ensuring reliable information decoding at the receiver, providing enhanced security in wireless communications. In this letter, covert communication in the presence of a multi-antenna adversary and under delay constraints is considered. Under the assumption of quasi-static wireless fading channels, we analyze the effect of increasing the number of antennas employed at the adversary on the achievable throughput of covert communication. It is shown that in contrast to a single-antenna adversary, a slight inc…
We analyze a two-receiver binary-input discrete memoryless broadcast channel, in which the transmitter communicates a common message simultaneously to both receivers and a covert message to only one of them. The unintended recipient of the covert message is treated as an adversary who attempts to detect the covert transmission. This model captures the problem of embedding covert messages in an innocent codebook and generalizes previous covert communication models in which the innocent behavior corresponds to the absence of communication between legitimate users. We identify the exact asymptoti…
Prior studies on covert communication with noise uncertainty adopted a worst-case approach from the warden's perspective. That is, the worst-case detection performance of the warden is used to assess covertness, which is overly optimistic. Instead of simply considering the worst limit, in this work, we take the distribution of noise uncertainty into account to evaluate the overall covertness in a statistical sense. Specifically, we define new metrics for measuring the covertness, which are then adopted to analyze the maximum achievable rate for a given covertness requirement under both bounded…
We develop a low-complexity coding scheme to achieve covert communications over binary-input discrete memoryless channels (BI-DMCs). We circumvent the impossibility of covert communication with linear codes by introducing non-linearity through the use of pulse position modulation (PPM) and multilevel coding (MLC). We show that the MLC-PPM scheme exhibits many appealing properties; in particular, the channel at a given index level remains stationary as the number of level increases, which allows one to use families of channel capacity- and channel resolvability-achieving codes to concretely ins…
Covert communication aims to shield the very existence of wireless transmissions in order to guarantee a strong security in wireless networks. In this work, for the first time we examine the possibility and achievable performance of covert communication in one-way relay networks. Specifically, the relay opportunistically transmits its own information to the destination covertly on top of forwarding the source's message, while the source tries to detect this covert transmission to discover the illegitimate usage of the recourse (e.g., power, spectrum) allocated only for the purpose of forwardin…
In this paper, we investigate covert communication in an intelligent reflecting surface (IRS)-assisted non-orthogonal multiple access (NOMA) system, where a legitimate transmitter (Alice) applies NOMA for downlink and uplink transmissions with a covert user (Bob) and a public user (Roy) aided by an IRS. Specifically, we propose new IRS-assisted downlink and uplink NOMA schemes to hide the existence of Bob's covert transmission from a warden (Willie), which cost-effectively exploit the phase-shift uncertainty of the IRS and the non-orthogonal signal transmission of Roy as the cover medium witho…
In this paper, we consider the issue of covert communications with random access protocol. We consider that the legitimate user Bob has no priori knowledge about packet arrival time and thus employs data-aided frame detection based on reference sequence. The warden user Willie tries to detect this covert communication by using a radiometer. The detection performance analysis is provided for both Bob and Willie under Rayleigh fading channel. It is demonstrated that the covert performance can benefit from the increase of the frame length or the number of receive antennas from frame detection per…
Widely-deployed encryption-based security prevents unauthorized decoding, but does not ensure undetectability of communication. However, covert, or low probability of detection/intercept (LPD/LPI) communication is crucial in many scenarios ranging from covert military operations and the organization of social unrest, to privacy protection for users of wireless networks. In addition, encrypted data or even just the transmission of a signal can arouse suspicion, and even the most theoretically robust encryption can often be defeated by a determined adversary using non-computational methods such …
In this paper, we investigate the optimal design of a wireless-powered covert communication (WP-CC) system, in which a probabilistic accumulate-then-transmit (ATT) protocol is proposed to maximize the communication covertness subject to a quality-of-service (QoS) requirement on communication. Specifically, in the considered WP-CC system, a full-duplex (FD) receiver transmits artificial noise (AN) to simultaneously charge an energy-constrained transmitter and to confuse a warden's detection on the transmitter's communication activity. With the probabilistic ATT protocol, the transmitter sends i…
This paper studies multi-antenna-aided covert communications coexisting with randomly located wardens and interferers, considering both centralized and distributed antenna systems (CAS/DAS). The throughput performance of the covert communication is analyzed and optimized under a stochastic geometry framework, where the joint impact of the small-scale channel fading and the large-scale path loss is examined. To be specific, two probabilistic metrics, namely, the covert outage probability and the connectivity probability, are adopted to characterize the covertness and reliability of the transmis…
We study the first- and second-order asymptotics of covert communication over binary-input DMC for three different covertness metrics and under maximum probability of error constraint. When covertness is measured in terms of the relative entropy between the channel output distributions induced with and without communication, we characterize the exact first- and second-order asymptotics of the number of bits that can be reliably transmitted with a maximum probability of error less than $ε$ and a relative entropy less than $δ$. When covertness is measured in terms of the variational distance bet…
In this paper, we study covert communications between {a pair of} legitimate transmitter-receiver against a watchful warden over slow fading channels. There coexist multiple friendly helper nodes who are willing to protect the covert communication from being detected by the warden. We propose an uncoordinated jammer selection scheme where those helpers whose instantaneous channel gains to the legitimate receiver fall below a pre-established selection threshold will be chosen as jammers radiating jamming signals to defeat the warden. By doing so, the detection accuracy of the warden is expected…
This paper investigates covert communication over an additive white Gaussian noise (AWGN) channel in finite block length regime on the assumption of Gaussian codebooks. We first review some achievability and converse bounds on the throughput under maximal power constraint. From these bounds and the analysis of TVD at the adversary, the first and second asymptotics of covert communication are investigated by the help of some divergences inequalities. Furthermore, the analytic solution of TVD, and approximation expansions which can be easily evaluated with given snr (signal noise ratio) are pres…
We consider the problem of covert communication over a state-dependent channel, where the transmitter has causal or noncausal knowledge of the channel states. Here, "covert" means that a warden on the channel should observe similar statistics when the transmitter is sending a message and when it is not. When a sufficiently long secret key is shared between the transmitter and the receiver, we derive closed-form formulas for the maximum achievable covert communication rate ("covert capacity") for discrete memoryless channels and, when the transmitter's channel-state information (CSI) is noncaus…
We consider the problem of covert communication over continuous-time additive white Gaussian noise (AWGN) channels under spectral mask constraints, wherein two legitimate parties attempt to communicate reliably in the presence of an eavesdropper that should be unable to estimate if communication takes place. The spectral mask constraint is imposed to restrict excessive radiation beyond the bandwidth of interest. We develop a communication scheme with theoretical reliability and covertness guarantees based on pulse amplitude modulation (PAM) with Binary Phase Shift Keying (BPSK) and root raised…
In this paper, we study covert communication in wireless networks consisting of a transmitter, Alice, an intended receiver, Bob, a warden, Willie, and a Poisson field of interferers. Bob and Willie are subject to uncertain shot noise due to the ambient signals from interferers in the network. With the aid of stochastic geometry, we analyze the throughput of the covert communication between Alice and Bob subject to given requirements on the covertness against Willie and the reliability of decoding at Bob. We consider non-fading and fading channels. We analytically obtain interesting findings on…
In this work, we propose a covert communication scheme where the transmitter attempts to hide its transmission to a full-duplex receiver, from a warden that is to detect this covert transmission using a radiometer. Specifically, we first derive the detection error rate at the warden, based on which the optimal detection threshold for its radiometer is analytically determined and its expected detection error rate over wireless fading channels is achieved in a closed-form expression. Our analysis indicates that the artificial noise deliberately produced by the receiver with a random transmit pow…
This work considers covert communications in the context of unmanned aerial vehicle (UAV) networks, aiming to hide a UAV for transmitting critical information out of a scenario that is monitored and where communication is not allowed. Specifically, the UAV as a transmitter intends to transmit information to a legitimate receiver (Bob) covertly in order to avoid being detected by a warden (Willie) with location uncertainties at Bob and/or Willie. In order to enhance the considered covert communication performance, we prefer to jointly optimize the UAV's trajectory and transmit power in terms of…
This paper considers the problem of covert communication with mismatched decoding, in which a sender wishes to reliably communicate with a receiver whose decoder is fixed and possibly sub-optimal, and simultaneously to ensure that the communication is covert with respect to a warden. We present single-letter lower and upper bounds on the information-theoretically optimal throughput as a function of the given decoding metric, channel laws, and the desired level of covertness. These bounds match for a variety of scenarios of interest, such as (i) when the channel between the sender and receiver …
In this paper, we design the first computationally efficient codes for simultaneously reliable and covert communication over Binary Symmetric Channels (BSCs). Our setting is as follows: a transmitter Alice wishes to potentially reliably transmit a message to a receiver Bob, while ensuring that the transmission taking place is covert with respect to an eavesdropper Willie (who hears Alice's transmission over a noisier BSC). Prior works show that Alice can reliably and covertly transmit O(\sqrt{n}) bits over n channel uses without any shared secret between Alice and Bob. One drawback of prior wo…
We investigate the fundamental limit of quantum-secure covert communication over the lossy thermal noise bosonic channel, the quantum-mechanical model underlying many practical channels. We assume that the adversary has unlimited quantum information processing capabilities as well as access to all transmitted photons that do not reach the legitimate receiver. Given existence of noise that is uncontrolled by the adversary, the square root law (SRL) governs covert communication: up to c*sqrt{n} covert bits can be transmitted reliably in n channel uses. Attempting to surpass this limit results in…
Covert communications hide the transmission of a message from a watchful adversary while ensuring a certain decoding performance at the receiver. In this work, a wireless communication system under fading channels is considered where covertness is achieved by using a full-duplex (FD) receiver. More precisely, the receiver of covert information generates artificial noise with a varying power causing uncertainty at the adversary, Willie, regarding the statistics of the received signals. Given that Willie's optimal detector is a threshold test on the received power, we derive a closed-form expres…
Second-Order Asymptotics for Covert Communication over Quasi-Static Multiple-Antenna Fading Channels
Beihang University（北京航空航天大学）；School of Automation and Intelligent Manufacturing, Southern University of Science and Technology（南方科技大学自动化与智能制造学院）；Shanghai AI Laboratory（上海人工智能实验室）
We extend previous results on covert communication over the additive white Gaussian noise channel to two other types of additive noise channels. The first is the Gaussian channel with memory, where the noise sequence is a Gaussian vector with an arbitrary invertible covariance matrix. We show that the fundamental limit for covert communication over such a channel is the same as over the channel with white, i.e., memoryless, Gaussian noise. The second type of channel we consider is one with memoryless generalized Gaussian noise. For such a channel we prove a general upper bound on the dominant …
In this letter, we analyze the performance of covert communications under faster-than-Nyquist (FTN) signaling in the Rayleigh block fading channel. Both Bayesian criterion- and Kullback-Leibler (KL) divergence-based covertness constraints are considered. Especially, for KL divergence-based one, we prove that both the maximum transmit power and covert rate under FTN signaling are higher than those under Nyquist signaling. Numerical results coincide with our analysis and validate the advantages of FTN signaling to realize covert data transmission.
This paper investigates the covert communications via cooperative jamming and relay selection in a wireless relay system, where a source intends to transmit a message to its destination with the help of a selected relay, and a warden attempts to detect the existence of wireless transmissions from both the source and relay, while friendly jammers send jamming signals to prevent warden from detecting the transmission process. To this end, we first propose two relay selection schemes, namely random relay selection (RRS) and max-min relay selection (MMRS), as well as their corresponding cooperativ…
We study the covert communication over K-user discrete memoryless interference channels (DM-ICs) with a warden. It is assumed that the warden's channel output distribution induced by K "off" input symbols, which are sent when no communication occurs, is not a convex combination of those induced by any other combination of input symbols (otherwise, the square-root law does not hold). We derive the exact covert capacity region and show that a simple point-to-point based scheme with treating interference as noise is optimal. In addition, we analyze the secret key length required for the reliable …
We consider a scenario in which $K$ transmitters attempt to communicate covert messages reliably to a legitimate receiver over a discrete memoryless MAC while simultaneously escaping detection from an adversary who observes their communication through another discrete memoryless MAC. We assume that each transmitter may use a secret key that is shared only between itself and the legitimate receiver. We show that each of the $K$ transmitters can transmit on the order of $\sqrt{n}$ reliable and covert bits per $n$ channel uses, exceeding which, the warden will be able to detect the communication.…
Covert communications enable a transmitter to send information reliably in the presence of an adversary, who looks to detect whether the transmission took place or not. We consider covert communications over quasi-static block fading channels, where users suffer from channel uncertainty. We investigate the adversary Willie's optimal detection performance in two extreme cases, i.e., the case of perfect channel state information (CSI) and the case of channel distribution information (CDI) only. It is shown that in the large detection error regime, Willie's detection performances of these two cas…
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 computation…
In this paper, we investigate covert communication over millimeter-wave (mmWave) frequencies. In particular, a dual-beam mmWave transmitter, comprised of two independent antenna arrays, attempts to reliably communicate to a receiver Bob when hiding the existence of transmission from a warden Willie. In this regard, operating over mmWave bands not only increases the covertness thanks to directional beams, but also increases the transmission data rates given much more available bandwidths and enables ultra-low form factor transceivers due to the lower wavelengths used compared to the conventiona…
In this paper, we consider fundamental communication limits over a compound channel. Covert communication in the information-theoretic context has been primarily concerned with fundamental limits when the transmitter wishes to communicate to legitimate receiver(s) while ensuring that the communication is not detected by an adversary. This paper, however, considers an alternative, and no less important, setting in which the object to be masked is the state of the compound channel. Such a communication model has applications in the prevention of malicious parties seeking to jam the communication…
In this work, we adopt channel inversion power control (CIPC) to achieve covert communications aided by a full-duplex receiver. Specifically, the transmitter varies the power and phase of transmitted signals as per the channel to the receiver, such that the receiver can decode these signals without knowing the channel state information. This eliminates the required feedback from the transmitter to the receiver, which aids hiding the transmitter from a warden. The truncated CIPC and conventional CIPC schemes are proposed and examined, where for truncated CIPC covert transmission ceases when the…
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 $\mathcal{O}(\sqrt{n})$ bits in $n$ 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 $n$, thus conveying $\mathcal{O}(n)$ bits…
In this letter, we consider the requirement of information freshness in covert communications for the first time. With artificial noise (AN) generated from a full-duplex (FD) receiver, we formulate a covertness maximization problem under the average age of information (AoI) constraint to optimize the transmit probability of information signal. In particular, the transmit probability not only represents the generation rate of information signal but also represents the prior probability of the alternative hypothesis in covert communications, which builds up a bridge between information freshness…
We consider that a transmitter covertly communicates with multiple receivers under the help of a friendly jammer. The messages intended for different receivers are transmitted in mutually orthogonal frequency bands. An adversary observes all these frequency bands aiming at detecting whether or not communication occurs, while the friendly jammer broadcasts jamming signals to degrade the detection performance of the adversary. We consider a block Rayleigh fading channel model and evaluate the performance of covert communication in two situations: 1) the wireless channels vary slowly such that th…
We study a backscatter communication protocol over a AWGN channel, where a transmitter illuminates a tag with a directional multi-antenna. The tag performs load modulation on the signal while hiding its physical presence from a warden. We show that, if the transmitter-to-tag channel is inaccessible to the warden, then $Θ(n)$ reliable and covert bits can be transmitted over $n$ channel usages. This overcomes the square-root law for covert communication. This paper provides the first evidence for practical implementation of covert backscatter communication, with potential applications in IoT sec…
Fundamental Scaling Laws of Covert Communication in the Presence of Block Fading
Manning College of Information and Computer Sciences, University of Massachusetts at Amherst（马萨诸塞大学阿默斯特分校曼宁信息与计算机科学学院）；Department of Electrical and Computer Engineering, University of Massachusetts at Amherst（马萨诸塞大学阿默斯特分校电气与计算机工程系）
Exploiting UAV Attitude for Covert Communications: Dynamics-Consistent Trajectory-Attitude Co-Design
The Hong Kong University of Science and Technology（香港科技大学）；Southern University of Science and Technology（南方科技大学）；Chongqing University of Posts and Telecommunications（重庆邮电大学）；Beihang University（北京航空航天大学）
We study the effect of node mobility on the throughput scaling of the covert communication over a wireless adhoc network. It is assumed that $n$ mobile nodes want to communicate each other in a unit disk while keeping the presence of the communication secret from each of $Θ(n^s)$ non-colluding wardens ($s>0$). Our results show that the node mobility greatly improves the throughput scaling, compared to the case of fixed node location. In particular, for $0<s<1$, the aggregate throughput scaling is shown to be linear in $n$ when the number of channel uses that each warden uses to judge the prese…
