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Globecom

Strategies in Covert Communication with Imperfect Channel State Information

Xi Peng, Jianquan Wang, Sa Xiao, Wanbin Tang

Published Dec 1, 2021• 18 citations
Publisher

Abstract

This paper considers the problem of covert communication over a multiple-input single-output channel (MISO) in the case of the imperfect channel state information. The transmitter wants to communication with the receiver while the eavesdropper detects the existence of the transmission. We first study the scenario that the accurate channel state information (CSI) is known and show that the condition achieving the positive rate by the beamforming vector. However, because of the non-cooperation between the transmitter and the eavesdropper, we consider the CSI is imperfect. There are estimation errors for the transmitter. When the positive rate can not be achieved, the objective is to maximize the communication rate. We discuss the deterministic bounded CSI errors for the covert communication. Robust beamforming and the transmitter power is investigated, which can be transformed as a second order cone programming (SCOP) problem. We consider the line-of-sight (LoS) channel and the linear array antenna model. Comparing with the perfect CSI, the results show that the strategy of the transmitter is more conservative under the imperfect CSI. The capacity declines by the estimation errors.

DOI
10.1109/globecom46510.2021.9685518

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This paper considers the problem of covert communication over a multiple-input single-output channel (MISO) in the case of the imperfect channel state information. The transmitter wants to communication with the receiver while the eavesdropper detects the existence of the transmission. We first study the scenario that the accurate channel state information (CSI) is known and show that the condition achieving the positive rate by the beamforming vector. However, because of the non-cooperation between the transmitter and the eavesdropper, we consider the CSI is imperfect. There are estimation errors for the transmitter. When the positive rate can not be achieved, the objective is to maximize the communication rate. We discuss the deterministic bounded CSI errors for the covert communication. Robust beamforming and the transmitter power is investigated, which can be transformed as a second order cone programming (SCOP) problem. We consider the line-of-sight (LoS) channel and the linear array antenna model. Comparing with the perfect CSI, the results show that the strategy of the transmitter is more conservative under the imperfect CSI. The capacity declines by the estimation errors.
This paper proposes a physical-layer secrecy transmission based on artificial noise (AN) for a multi-input single-output (MISO) channel overheard by one single-antenna eavesdropper. Legitimate receiver transmits AN using beamforming to improve the secret capacity. The AN is designed for two cases assuming that legitimate receiver has perfect or imperfect knowledge of eavesdropper's channel state information (CSI). The optimization problem of AN design in both cases are not convex. A one-dimensional line search on a sequence of semidefinite programs (SDP) is proposed to solve the problem in perfect CSI case through reformulation. In the case with imperfect CSI, the beamforming and AN vectors are designed for achieving quality of service discrimination. The problem is approximated to be a convex SDP problem by relaxing some restrictions. Furthermore, the optimal covariance is shown to be of rank one. Simulation results verify that our methods precede the existed AN aided scheme.
In recent years there has been growing interest in study of multi-antenna transmit designs for providing secure communication over the physical layer. This paper considers the scenario of an intended multi-input single-output channel overheard by multiple multi-antenna eavesdroppers. Specifically, we address the transmit covariance optimization for secrecy-rate maximization (SRM) of that scenario. The challenge of this problem is that it is a nonconvex optimization problem. This paper shows that the SRM problem can actually be solved in a convex and tractable fashion, by recasting the SRM problem as a semidefinite program (SDP). The SRM problem we solve is under the premise of perfect channel state information (CSI). This paper also deals with the imperfect CSI case. We consider a worst-case robust SRM formulation under spherical CSI uncertainties, and we develop an optimal solution to it, again via SDP. Moreover, our analysis reveals that transmit beamforming is generally the optimal transmit strategy for SRM of the considered scenario, for both the perfect and imperfect CSI cases. Simulation results are provided to illustrate the secrecy-rate performance gains of the proposed SDP solutions compared to some suboptimal transmit designs.
A Gaussian multiple-input single-output (MISO) secrecy channel is considered, where a transmitter is equipped with multiple antennas, and an intended receiver and an eavesdropper each equipped with a single antenna. This paper studies the robust beamforming design in the presence of uncertainty of channel state information (CSI) on the eavesdropper channel. Under the assumption that all possible states of the eavesdropper channel are in a given set, the problem of optimizing the transmit covariance for the worst-case secrecy capacity which is the maximum transmission rate at which the eavesdropper is unable to decode under any channel realization in the set, is cast as a max-min optimization problem. We propose to transfer the max-min problem into a convex optimization problem that can be solved efficiently. The optimal secrecy rate and transmit covariance are expressed in the form of the generalized eigenvalue and eigenvector, the same form as the conventional case of the perfect eavesdropper's CSI, which indicates our results is the generalization of the conventional case.
This paper studies the robust beamforming design problem for a multiple-input single-output (MISO) secrecy channel with a single-antenna eavesdropper. Due to the illegal nature, the eavesdropper may try to hide itself from being caught; thus, it could be difficult for the secrecy transmitter (S-Tx) to obtain accurate channel state information (CSI) of the eavesdropping link between S-Tx and the eavesdropper. Assuming that the CSI of the eavesdropping link belongs to a known uncertain set, this paper designs the optimal transmit strategy for the secrecy user to maximize the transmit rate under the condition that the eavesdropper cannot decode the secrecy message for all possible channel realizations of the eavesdropping link. This robust design problem is non-convex and cannot be solved by existing algorithms in the literature. By exploiting the relationship between the secrecy MISO channel and the cognitive radio (CR) MISO channel, this problem is transformed into a robust CR beamforming design problem, which can be solved efficiently by the interior point method. Numerical examples are provided to illustrate the effectiveness of the proposed algorithm.
This letter investigates the robust beamforming design for an integrated sensing and covert communications system, where the transmitter (Alice) performs some sensing task and simultaneously communicates with multiple legitimate users (Bobs) covertly, evading detection by the eavesdropper (Willie). Considering the impact of imperfect channel state information (CSI) of Alice-to-Bobs and Alice-to-Willie links, we formulate a robust beamforming optimization problem to minimize the Cramér-Rao bound for sensing parameter while satisfying the total transmit power, the signal-to-interference-plus-noise ratio and covertness constraints for communication. An iterative algorithm, employing semi-definite programming and successive convex approximation, is proposed to address this challenging problem. Numerical results validate the effectiveness of the proposed scheme, highlighting the robustness of the optimized beamforming design under imperfect CSI.
In this paper, we study the achievable secrecy rate of the multiple input single output (MISO) wiretap channel, which consists of a transmitter, a legitimate receiver and multiple eavesdroppers. The transmitter is equipped with multiple antennas, while the receiver and all the eavesdroppers each have a single antenna. We assume that the transmitter has perfect channel state information (CSI) for their links to legitimate receiver, but it has only imperfect CSI for their channels to eavesdroppers. Optimal transmit covariance matrix is obtained based on worst-case secrecy rate maximization, under power constraints. The maximum secrecy rate computation can be formulated as a non-convex optimal problem, which cannot be solved directly. In this paper, we transform non-convex optimal problem into a quasi-convex optimal problem which can be efficiently solved with the bisection method. The simulation result and analysis demonstrate the effectiveness of our methods.