Covert communication is crucial in privacy protection for users of wireless networks, and efforts have been made to improve the system throughput subject to a constraint on a warden's detection error probability. However, most existing research is based on an unclear relation between system throughput and covertness, due to the use of the Kullback-Leibler divergence. To solve this problem, in this paper, we explore the exact throughput-covertness relation by investigating the likelihood variation distance. An algorithm is established to find the minimum channel uses required for the transmission of a given amount of information and a certain covertness constraint. The rigorous proof of the convergence of the algorithm is also given. Our results show that an overly strict constraint on covertness would lead to a large sacrifice of system throughput, and it is not cost-effective to increase the number of channel uses to improve covertness if only a small amount of information is to be transmitted. These results could be very helpful for system designers in achieving a desirable tradeoff between system throughput and covertness.
Covert communication is crucial in privacy protection for users of wireless networks, and efforts have been made to improve the system throughput subject to a constraint on a warden's detection error probability. However, most existing research is based on an unclear relation between system throughput and covertness, due to the use of the Kullback-Leibler divergence. To solve this problem, in this paper, we explore the exact throughput-covertness relation by investigating the likelihood variation distance. An algorithm is established to find the minimum channel uses required for the transmission of a given amount of information and a certain covertness constraint. The rigorous proof of the convergence of the algorithm is also given. Our results show that an overly strict constraint on covertness would lead to a large sacrifice of system throughput, and it is not cost-effective to increase the number of channel uses to improve covertness if only a small amount of information is to be transmitted. These results could be very helpful for system designers in achieving a desirable tradeoff between system throughput and covertness.
Covert communication guarantees the security of wireless communications via hiding the existence of the transmission. This paper focuses on the first and second order asymptotics of covert communication in the AWGN channels. The covertness is measured by the total variation distance between the channel output distributions induced with and without the transmission. We provide the exact expressions of the maximum amount of information that can be transmitted with the maximum error probability and the total variation less than any small numbers. The energy detection and the random coding are employed to prove our results. We further compare our results with those under relative entropy. The results show how many additional amounts of information can be transmitted covertly when changing the covertness constraint to total variation.
This work tackles the asymptotics of the maximal throughput of covert communications over AWGN channels when the covert metric is Kullback-Leibler divergence (KL divergence). It is shown that the first and second order asymptotics of the maximal throughput arenδlogeand (2)21(nδ)41(loge)43⋅Q−1(ϵ), respectively bynchannel uses, whereδandϵare constraints imposed on covertness and channel decoding error probabilities, respectively. The technique we use in the achievability is quasi-ε-neighborhood notion from information geometry. For finite blocklengthn, the generating distributions are chosen to be a family of truncated Gaussian distributions with decreasing variances. The law of decreasing is carefully designed so that it maximizes the throughput at the main channel in the asymptotic sense under the condition that the output distributions satisfy the covert constraint. For the converse, the optimality of Gaussian distribution for minimizing KL divergence under second order moment constraint is extended from dimension 1 to dimensionn, which further leads to the direct converse bound in terms of covert metric.
Covert communication enforces the transmitted signal to be indistinguishable from other signals under wireless environment, making it difficult for an eavesdropper to detect and intercept the message. The most common approach within covert systems is the augmentation of artificial noise (AN), ensuring reliable transmission. However, this strategy becomes problematic when the eavesdropper's position is uncertain, as continuous amplification of interference power can precipitate a substantial decline in covert communication capacity. In this paper, we investigate the covert communication between legitimate transmitter (i.e., Alice) and full duplex receiver (i.e., Bob) in the presence of the location uncertainties of the eavesdropper (i.e., Willie). We first derive the sufficient condition for achieving covert communication through robustness analysis. Then, we derive the effective throughput to measure the covert communication capacity. Afterward, by using joint optimization technology, the optimal AN power of Bob and the number of antennas for Alice are jointly designed to maximize the effective throughput subject to a covertness constraint. Theoretical analysis indicates that reducing the AN power while increasing the number of antennas helps to improve the system capacity, the effective throughput between Alice and Bob is inversely proportional to the distance between them. Finally, the validity of our analytical approach is corroborated by simulation results.
The fundamental limits of covert communication, where a message is sent from transmitter Alice to intended recipient Bob without detection by an attentive adversary warden Willie, has been considered extensively in recent years at the physical layer. The covert throughput depends critically on the warden's understanding of the characteristics of the radio environment and the type of receiver that he employs, and, as expected, the throughput increases when the warden has some uncertainty about the environment or some non-idealities in his receiver. In this paper, we consider the covert throughput when the adversary is only able to observe the medium access control (MAC) layer in a wireless communication system. In particular, given that the system has a rate ofλpackets per slot transmitted overnchannels by allowable system users, we study the allowable rateλaby covert users while maintaining covertness from an attentive warden observing the channel status in a slotted ALOHA system. We characterize performance for wardens with different abilities to discern the number of packets on a given channel, ranging from simple receivers that detect only whether there was a packet present to complicated receivers that can determine the number of packets involved in any collision, and also consider intended recipients Bob with varying abilities to perform multi-packet reception. In contrast to prior work in covert communications, the application considered motivates the consideration of results for finite (often small) observation vector lengthsnat the adversary. Numerical results are provided both to illustrate the tightness of our achievability regions for the packet transmission rate of the covert transmitters and to demonstrate the covert throughput of the system as a function ofλandn.
We study the second-order asymptotics of optimal codes for covert communication over quasi-static multi-antenna fading channels, under the covertness metric of Kullback--Leibler (KL) divergence. In particular, we study all four cases regarding the availability of channel state information (CSI) for the legitimate transmitter and receiver, assume that the warden knows perfect CSI for the channel from the legitimate transmitter to itself, whereas the legitimate transmitter knows only that the warden's channel matrix belongs to a bounded deterministic uncertainty set. Specifically, we show that, when the blocklength is n, the first-order covert rate satisfies the square root law, scaling as Θ(n−21) with the coefficient determined by the traces of the channel matrices of the legitimate users and the warden, and the second-order rate vanishes. We also show that the availability of CSI at the transmitter enables optimal covert power allocation across the spatial sub-channels, which can increase the covert rate, relatively to equal power allocation, without changing the square root law. Furthermore, we reveal the significant spatial diversity gain provided by multiple-antenna systems for covert communication and demonstrate the critical role of the number of antennas to achieve high throughput covert communication. For the covertness analysis, we extend the quasi-η-neighborhood framework to quasi-static fading channels. For the reliability analysis, due to the vanishing power imposed by the covertness constraint, we refine the non-covert analysis by Yang et al. (TIT, 2014), by carefully controlling higher-order terms and exploiting the properties of covert outage probability.
This paper investigates the covert communication in the scenario of counter detection. In traditional covert communication design where the uncertainty of the position of the Warden Willie typically reduces covert performance. To overcome this limitation, we leverage the sensing ability of the ISAC system in a new way to reduce the channel uncertainty between Alice and Willie, thereby enabling less conservative power allocation and significantly improving the achievable covert throughput. In the first stage, the dual functional sensing and communication (DFRC) base station Bob sends joint signals to estimate the azimuth of Willie and transmits information to Alice at the same time. In the second stage, Alice uses the obtained azimuth information of Willie to adjust transmit power while meeting the covert constraints. We build a mathematical model of azimuth angle estimation error and connect it with the Cramér-Rao Bound (CRB) to change it into distance error. This connects sensing accuracy with channel state information (CSI) uncertainty in a linear way, allowing Alice to adopt a higher transmit power while still satisfying the covert constraint, and thus improving the achievable covert throughput. To increase the covert throughput of the user, we use a layered solving strategy to decouple the original problem. First, we use S-procedure to change the constraint on possible distance error into a linear matrix inequality (LMI) constraint and then find the upper limit of transmit power on the user side. Second, we combine it with the uplink communication link rate constraint to find the closed form expression of the resource allocation strategy in vector space. Finally, we use one dimensional search to find the optimal time slot allocation strategy. Simulation results show that the proposed two-stage protocol effectively improves the achievable covert throughput by reducing position uncertainty through sensing.