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China Communications

Covert rate characterization under multi-antenna detection: A study on warden's CSI availability and noise uncertainty

Yuchen Zhang, Sa Xiao, Wang Jianquan, Boyu Ning, Yuan Xiaojun, Wanbin Tang

Published Feb 1, 2025• 1 citation
Publisher

Abstract

In this paper, we investigate covert communications under multi-antenna detection, and explore the impacts of the warden's channel state information (CSI) availability and the noise uncertainty on system covert capability. The detection performance at warden is analyzed in two cases under the perfect and statistical CSI at warden, respectively. In particular, for the former one, the warden utilizes the likelihood ratio (LR) detector, while for the latter one, the generalized likelihood ratio (GLR) detector is adopted. We first consider the scenario where the blocklength is finite, and demonstrate that the covert rate under both cases asymptotically goes to zero as the blocklength goes to infinity. Subsequently, we take the noise uncertainty at the warden into account which leads to positive covert rate, and characterize the covert rate for infinite blocklength. Specially, we derive the optimal transmit power for the legitimate transmitter that maximizes the covert rate. Besides, the rate gap under two cases, with different CSI availability at the warden, can be presented in closed form. Finally, numerical results validate the effectiveness of our theoretical analysis and also demonstrate the impacts of the factors studied on the system covertness.

DOI
10.23919/jcc.ja.2023-0004

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In this paper, we investigate covert communications under multi-antenna detection, and explore the impacts of the warden's channel state information (CSI) availability and the noise uncertainty on system covert capability. The detection performance at warden is analyzed in two cases under the perfect and statistical CSI at warden, respectively. In particular, for the former one, the warden utilizes the likelihood ratio (LR) detector, while for the latter one, the generalized likelihood ratio (GLR) detector is adopted. We first consider the scenario where the blocklength is finite, and demonstrate that the covert rate under both cases asymptotically goes to zero as the blocklength goes to infinity. Subsequently, we take the noise uncertainty at the warden into account which leads to positive covert rate, and characterize the covert rate for infinite blocklength. Specially, we derive the optimal transmit power for the legitimate transmitter that maximizes the covert rate. Besides, the rate gap under two cases, with different CSI availability at the warden, can be presented in closed form. Finally, numerical results validate the effectiveness of our theoretical analysis and also demonstrate the impacts of the factors studied on the system covertness.
In this paper, we investigate covert communications under multiple-antenna eavesdropping, and explore the impact of the channel state information (CSI) at the adversary on the covertness of the system with noise uncertainty. We first analyze the detection performance of the adversary without the CSI of the eavesdropping channel. Specially, the generalized likelihood ratio (GLR) detection is adopted to handle this scenario. Then, a more practical scenario with the uncertain noise power at the adversary is considered, and the covertness of the system is analyzed. In addition, the optimal transmit power at the legitimate transmitter is derived theoretically to maximize the covert throughput. Finally, we present numerical results to compare the covert throughputs when the adversary knows or doesn't know the CSI. The results demonstrate the significance of unknown CSI at the adversary when considering the covert throughput of the system.
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 nnn, the first-order covert rate satisfies the square root law, scaling as Θ(n−12)Θ(n^{-\frac{1}{2}})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-ηηη-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.
In this paper, we investigate a covert communications system that consists of a source node communicating with a disguised full-duplex (FD) destination node. Supposedly receive-only, the destination node covertly transmits confidential messages to a hidden receiver while avoiding the surveillance of a warden node. Our specific focus is on the impact of the channel uncertainty of the warden node from the perspective of the destination node on covert communications. We take the expected minimum detection error probability (DEP) at the warden node into consideration and obtain the optimal public data rate and transmit power to maximize the covert rate. Numerical results verify that the covert rate increases as the availability of the channel state information (CSI) improves and highlight the importance of optimization regardless of the level of CSI based on comparisons with baseline schemes.
In this paper, we consider a covert communication system with a multi-antenna full-duplex (FD) receiver to enhance covert performance. More precisely, the receiver Bob (i.e., multiple antennas) selects the best antenna to receive the covert message, and then it sends artificial noise (AN) to the warden Willie causing uncertainty by utilizing an antenna among the remaining antennas. In order to take full advantage of multi-antenna technology, we consider two cases: (1) Willie does not know which antenna Bob chooses to send AN, and Willie knows only part of the channel information. (2) Willie knows which antenna Bob chooses to send AN, and Willie knows all the channel information. Based on the analysis of the optimal detection threshold, we derive the minimum detection error probability of the two cases. Furthermore, given the pre-determined convert constraints, the closed-form expression of the maximum effective convert rate is derived. When the power of AN sent by Bob is greater than that of covert message sent by the sender Alice, surprised research results are shown: (1) the detection error rate of case 1 is higher than that of case 2. (2) the effective covert rate of case 1 is always lower than that of case 2. The simulation results show that the proposed scheme is more conducive to sending covert messages for Alice; in addition, the numerical results imply that the maximum effective covert rate of the system using the multi-antenna FD receiver is significantly higher than that of the traditional dual-antenna FD receiver system.
Covert communication has recently been recognized as a highly promising security technology that enables a transmitter Alice to reliably and covertly communicate with a receiver Bob without being detected by a malicious warden. Available works on covert communication mainly focus on scenarios with only one warden, while the fundamental limits of covert communication in more practical multi-warden scenarios remain largely unknown. This paper therefore investigates the fundamental limits of covert communication over an additive white Gaussian noise (AWGN) channel in the presence of multiple wardens. We first consider a scenario with two wardens and derive the maximum number of bits Alice can transmit to Bob over n channel uses while ensuring a negligible detection probability at wardens. We then generalize this result to the multi-warden case and find that the minimal power of wardens has impacts on the scaling law of the performance limits of covert communication over AWGN channels.
Covert communications can hide confidential signals in environmental noise to avoid being detected and provide comprehensive security for wireless transmissions. However, there still exist significant risks in wireless transmission once being detected. In this letter, we propose a more secure covert scheme, where a multiple antennas transmitter, assisted by a multi-antenna UAV jammer, maximizes the covert secrecy rate under the scenarios of both correct and incorrect detection by a warden with both error detection probability and eavesdropping rate limitations satisfied. The transmitter and jammer adopt maximum ratio transmission (MRT) and zero-forcing, respectively, to maximize the transmission rate and minimize the interference at the legitimate receiver. First, we analyze the monotonicity of error detection probability to determine the optimal power detection threshold and the corresponding smallest error detection probability. Then, under this worst case, we jointly optimize the transmit and jamming power to maximize the covert secrecy rate while guaranteeing the covert and eavesdropping limits meet their requirements, respectively. Finally, simulation results are presented to prove the correctness of the theoretical conclusion and evaluate the effectiveness of our proposed scheme.