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 conventional radio frequency (RF) counterpart. We assume that the transmitter Alice employs one of its antenna arrays to form a directive beam for transmission to Bob. The other antenna array is used by Alice to generate another beam toward Willie as a jamming signal with its transmit power changing independently from a transmission block to another block. We characterize Willie's detection performance with the optimal detector and the closed-form of its expected value from Alice's perspective. We further derive the closed-form expression for the outage probability of the Alice-Bob link, which enables characterizing the optimal covert rate that can be achieved using the proposed setup. Our results demonstrate the superiority of mmWave covert communication, in terms of covertness and rate, compared to the RF counterpart.
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…
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…
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 legitima…
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.…
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…
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）
Covert communication prevents legitimate transmission from being detected by a warden while maintaining certain covert rate at the intended user. Prior works have considered the design of covert communication over conventional low-frequency bands, but few works so far have explored the higher-frequency millimeter-wave (mmWave) spectrum. The directional nature of mmWave communication makes it attractive for covert transmission. However, how to establish such directional link in a covert manner in the first place remains as a significant challenge. In this paper, we consider a covert mmWave comm…
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…
In this paper, we investigate covert communication over millimeter-wave (mmWave) frequencies. In particular, a mmWave transmitter, referred to as Alice, attempts to reliably communicate to a receiver, referred to as Bob, while hiding the existence of communication from a warden, referred to as Willie. In this regard, operating over the 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 conve…
Rate Splitting Multiple Access (RSMA) has recently emerged as a promising technique to enhance the transmission rate for multiple access networks. Unlike conventional multiple access schemes, RSMA requires splitting and transmitting messages at different rates. The joint optimization of the power allocation and rate control at the transmitter is challenging given the uncertainty and dynamics of the environment. Furthermore, securing transmissions in RSMA networks is a crucial problem because the messages transmitted can be easily exposed to adversaries. This work first proposes a stochastic op…
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…
In this work, for the first time, we tackle channel estimation design with pilots in the context of covert wireless communication. Specifically, we consider Rayleigh fading for the communication channel from a transmitter to a receiver and additive white Gaussian noise (AWGN) for the detection channel from the transmitter to a warden. Before transmitting information signals, the transmitter has to send pilots to enable channel estimation at the receiver. Using a lower bound on the detection error probability, we first prove that transmitting pilot and information signals with equal power can m…
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…
We consider the situation in which a transmitter attempts to communicate reliably over a discrete memoryless channel while simultaneously ensuring covertness (low probability of detection) with respect to a warden, who observes the signals through another discrete memoryless channel. We develop a coding scheme based on the principle of channel resolvability, which generalizes and extends prior work in several directions. First, it shows that, irrespective of the quality of the channels, it is possible to communicate on the order of $\sqrt{n}$ reliable and covert bits over $n$ channel uses if t…
Consider a channel where authorized transmitter Jack sends packets to authorized receiver Steve according to a Poisson process with rate $λ$ packets per second for a time period $T$. Suppose that covert transmitter Alice wishes to communicate information to covert receiver Bob on the same channel without being detected by a watchful adversary Willie. We consider two scenarios. In the first scenario, we assume that warden Willie cannot look at packet contents but rather can only observe packet timings, and Alice must send information by inserting her own packets into the channel. We show that t…
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…
This paper explores a new secure wireless communication paradigm where the physical layer security technology is applied to counteract both the detection and eavesdropping attacks, such that the critical covertness and secrecy properties of the communication are jointly guaranteed. We first provide theoretical modeling for covertness outage probability (COP), secrecy outage probability (SOP) and transmission probability (TP) to depict the covertness, secrecy and transmission performances of the paradigm. To understand the fundamental security performance under the new paradigm, we then define …
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…
Fundamental limits of covert communication have been studied in literature for different models of scalar channels. It was shown that, over $n$ independent channel uses, $\mathcal{O}(\sqrt{n})$ bits can transmitted reliably over a public channel while achieving an arbitrarily low probability of detection (LPD) by other stations. This result is well known as square-root law and even to achieve this diminishing rate of covert communication, some form of shared secret is needed between the transmitter and the receiver. In this paper, we establish the limits of LPD communication over the MIMO AWGN…
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…
Emerging wireless communication systems will be characterized by a tight coupling between communication and positioning. This is particularly apparent in millimeter-wave (mm-wave) communications, where devices use a large number of antennas and the propagation is well described by geometric channel models. For mm-wave communications, initial access, consisting in the beam selection and alignment of two devices, is challenging and time-consuming in the absence of location information. Conversely, accurate positioning relies on high-quality communication links with proper beam alignment. This pa…
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…
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…
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…
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 develops a stochastic geometry-based approach for the modeling and analysis of finite millimeter wave (mmWave) wireless networks where a random number of transmitters and receivers are randomly located inside a finite region. We consider a selection strategy to serve a reference receiver by the transmitter providing the maximum average received power among all transmitters. Considering the unique features of mmWave communications such as directional transmit and receive beamforming and having different channels for line-of-sight (LOS) and non-line-of-sight (NLOS) links according to …
Covert communication, also known as low probability of detection (LPD) communication, prevents the adversary from knowing that a communication is taking place. Recent work has demonstrated that, in a three-party scenario with a transmitter (Alice), intended recipient (Bob), and adversary (Warden Willie), the maximum number of bits that can be transmitted reliably from Alice to Bob without detection by Willie, when additive white Gaussian noise (AWGN) channels exist between all parties, is on the order of the square root of the number of channel uses. In this paper, we begin consideration of ne…
We consider covert communication using a queuing timing channel in the presence of a warden. The covert message is encoded using the inter-arrival times of the packets, and the legitimate receiver and the warden observe the inter-departure times of the packets from their respective queues. The transmitter and the legitimate receiver also share a secret key to facilitate covert communication. We propose achievable schemes that obtain non-zero covert rate for both exponential and general queues when a sufficiently high rate secret key is available. This is in contrast to other channel models suc…
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…
We consider a covert communication scenario where a transmitter wishes to communicate simultaneously to two legitimate receivers while ensuring that the communication is not detected by an adversary, the warden. The legitimate receivers and the adversary observe the transmission from the transmitter via a three-user discrete or Gaussian memoryless broadcast channel. We focus on the case where the "no-input" symbol is not redundant, i.e., the output distribution at the warden induced by the no-input symbol is not a mixture of the output distributions induced by other input symbols, so that 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…
Covert communication is necessary when revealing the mere existence of a message leaks sensitive information to an attacker. Consider a network link where an authorized transmitter Jack sends packets to an authorized receiver Steve, and the packets visit Alice, Willie, and Bob, respectively, before they reach Steve. Covert transmitter Alice wishes to alter the packet stream in some way to send information to covert receiver Bob without watchful and capable adversary Willie being able to detect the presence of the message. In our previous works, we addressed two techniques for such covert trans…
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…
Covert communication is to achieve a reliable transmission from a transmitter to a receiver while guaranteeing an arbitrarily small probability of this transmission being detected by a warden. In this work, we study the covert communication in AWGN channels with finite blocklength, in which the number of channel uses is finite. Specifically, we analytically prove that the entire block (all available channel uses) should be utilized to maximize the effective throughput of the transmission subject to a predetermined covert requirement. This is a nontrivial result because more channel uses result…
Suppose that a transmitter Alice potentially wishes to communicate with a receiver Bob over an adversarially jammed binary channel. An active adversary James eavesdrops on their communication over a binary symmetric channel (BSC(q)), and may maliciously flip (up to) a certain fraction p of their transmitted bits based on his observations. We consider a setting where the communication must be simultaneously covert as well as reliable, i.e., James should be unable to accurately distinguish whether or not Alice is communicating, while Bob should be able to correctly recover Alice's message with h…
This paper presents a 3-D statistical channel model of the impulse response with small-scale spatially correlated random coefficients for multi-element transmitter and receiver antenna arrays, derived using the physically-based time cluster - spatial lobe (TCSL) clustering scheme. The small-scale properties of multipath amplitudes are modeled based on 28 GHz outdoor millimeter-wave small-scale local area channel measurements. The wideband channel capacity is evaluated by considering measurement-based Rician-distributed voltage amplitudes, and the spatial autocorrelation of multipath amplitudes…
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 …
This paper presents 73 GHz human blockage measurements for a point-to-point link with a 5 m transmitter-receiver separation distance in an indoor environment, with a human that walked at a speed of approximately 1 m/s at a perpendicular orientation to the line between the transmitter and receiver, at various distances between them. The experiment measures the shadowing effect of a moving human body when using directional antennas at the transmitter and receiver for millimeter-wave radio communications. The measurements were conducted using a 500 Megachips-per-second wideband correlator channel…
Millimeter wave (mmWave) systems will likely employ large antenna arrays at both the transmitters and receivers. A natural application of antenna arrays is simultaneous transmission to multiple users, which requires multi-user precoding at the transmitter. Hardware constraints, however, make it difficult to apply conventional lower frequency MIMO precoding techniques at mmWave. This paper proposes and analyzes a low complexity hybrid analog/digital beamforming algorithm for downlink multi-user mmWave systems. Hybrid precoding involves a combination of analog and digital processing that is moti…
This work examines the performance gain achieved by deploying an intelligent reflecting surface (IRS) in covert communications. To this end, we formulate the joint design of the transmit power and the IRS reflection coefficients by taking into account the communication covertness for the cases with global channel state information (CSI) and without a warden's instantaneous CSI. For the case of global CSI, we first prove that perfect covertness is achievable with the aid of the IRS even for a single-antenna transmitter, which is impossible without an IRS. Then, we develop a penalty successive c…
In this paper, we study two novel massive multiple-input multiple-output (MIMO) transmitter architectures for millimeter wave (mmWave) communications which comprise few active antennas, each equipped with a dedicated radio frequency (RF) chain, that illuminate a nearby large intelligent reflecting/transmitting surface (IRS/ITS). The IRS (ITS) consists of a large number of low-cost and energy-efficient passive antenna elements which are able to reflect (transmit) a phase-shifted version of the incident electromagnetic field. Similar to lens array (LA) antennas, IRS/ITS-aided antenna architectur…
