In this paper, we utilize frequency hopping spread spectrum (FHSS) to help enhance covert performance in frequency diverse array (FDA) covert system. Compared to conventional FDA covert communication, FHSS signals can hide in different channels by rapidly switching the transmission frequency to avoid being detected. Therefore, FHSS-aided FDA covert system can effectively counter the warden with strong detection ability and enhance covert performance. We focus on maximizing the covert capacity during the entire transmission by jointly optimizing the beamfoming vector and antenna frequency vector at the transmitter. Based on the system equipment constraints, two different optimization schemes, i.e., instantaneous optimization scheme (IOS) and robust optimization scheme (ROS), are proposed to solve the problem. Moreover, to evaluate the covert performance provided by FHSS-aided FDA covert communication, we introduce three benchmark schemes, i.e., phased array (PA) and logarithmic distribution FDA (Log-FDA) and non-FHSS. Simulation results demonstrate that FHSS combined with IOS can significantly improve covert performance compared to other benchmark schemes. In contrast, FHSS combined with ROS can effectively enhance covert performance when transmitting signals over a wide bandwidth.

The beam focusing characteristic of frequency diverse array (FDA) in direction-distance dimension has been widely applied in covert communication. To reduce the covert performance loss caused by time-varying FDA channels, the instantaneous optimization of antenna beamforming vector (ABV) and antenna frequency vector (AFV) is required for FDA. However, due to the difficulty in acquiring instantaneous channel state information (CSI) and the limitations of transmit device, instantaneous optimization scheme (IOS) may not be feasible in practical communication scenarios. Moreover, the existing robust schemes only adopt some simple and fixed AFVs without optimizing AFV. This paper investigates robust optimization scheme (ROS) in FDA-aided covert system, where the optimization frequency of the ABV and AFV at the transmitter can be adaptively adjusted based on the acquired CSIs. We maximize the average covert rate during the transmission by jointly optimizing ABV and AFV, and modify the conventional block successive upper-bound minimization (BSUM) method to solve the optimization problem. Furthermore, both perfect CSI and partial CSI at the warden are considered. Numerical results demonstrate that our proposed ROS outperforms the existing robust schemes, especially in the cases of highly correlated channels and partial CSI. Although ROS is indeed inferior to IOS, enhancing the channel decoupling capability of FDA and deteriorating the detection capability of the warden can effectively narrow the covert performance gap between ROS and IOS. Moreover, the beampattern generated by the optimal ABV and AFV at each time slot ensures that the beamfoming gain is maximized at the legitimate receiver and minimized at the warden simultaneously.

Frequency diverse array (FDA) is a promising antenna technology to achieve physical layer security by varying the frequency of each antenna at the transmitter. However, when the channels of the legitimate user and eavesdropper are highly correlated, FDA is limited by the frequency constraint and cannot provide satisfactory security performance. In this paper, we propose a novel movable FDA (MFDA) antenna technology where the positions of antennas can be dynamically adjusted in a given finite region. Specifically, we aim to maximize the secrecy capacity by jointly optimizing the antenna beamforming vector, antenna frequency vector and antenna position vector. To solve this non-convex optimization problem with coupled variables, we develop a two-stage alternating optimization (AO) algorithm based on block successive upper-bound minimization (BSUM) method. Moreover, to evaluate the security performance provided by MFDA, we introduce two benchmark schemes, i.e., phased array (PA) and FDA. Simulation results demonstrate that MFDA can significantly enhance security performance compared to PA and FDA. In particular, when the frequency constraint is strict, MFDA can further increase the secrecy capacity by adjusting the positions of antennas instead of the frequencies.

The frequency diverse array (FDA) is highly promising for improving covert communication performance by adjusting the frequency of each antenna at the transmitter. However, when faced with the cases of multiple wardens and highly correlated channels, FDA is limited by the frequency constraint and cannot provide satisfactory covert performance. In this paper, we propose a novel movable FDA (MFDA) antenna technology where positions of the antennas can be dynamically adjusted in a given finite region. Specifically, we aim to maximize the covert rate by jointly optimizing the antenna beamforming vector, antenna frequency vector and antenna position vector. To solve this non-convex optimization problem with coupled variables, we develop a two-stage alternating optimization (AO) algorithm based on the block successive upper-bound minimization (BSUM) method. Moreover, considering the challenge of obtaining perfect channel state information (CSI) at multiple wardens, we study the case of imperfect CSI. Simulation results demonstrate that MFDA can significantly enhance covert performance compared to the conventional FDA. In particular, when the frequency constraint is strict, MFDA can further increase the covert rate by adjusting the positions of antennas instead of the frequencies.

We propose a joint covert beamforming design and jamming strategy to protect the communication process between Alice and Bob from being discovered by Willie with the help of another pair of neutral nodes. Specifically, with the help of irrelevant communication parties that commonly exist in practical communication scenarios, Jammer increases his transmission power by interfering with the neutral receiver, thus indirectly increasing the interference to Willie, which can be viewed as leveraging the force to make a big impact with a small effect. In our designed beamformer, we jointly optimize the beam power allocation factor, Alice’s transmission power, and Jammer’s transmission power when Alice transmits, to maximize the covert rate, which also maximizes Alice’s transmission power. In the perfect channel state information (CSI) scenario, the transformed optimization problem is solved via a one-dimensional search method and CVX solver. Due to the solution’s high complexity, we further propose a method to determine the optimal power allocation factor. For the imperfect Willie’s CSI scenario, three cases are investigated: Alice to Willie imperfect CSI, Transmitter to Willie imperfect CSI, and Jammer to Willie imperfect CSI. We utilize the S-procedure to tackle the optimization problem. Simulation results demonstrate the effectiveness of our proposed strategy.

Surveillance performance is studied for a wireless eavesdropping system, where a full-duplex legitimate monitor eavesdrops a suspicious user's link with artificial noise (AN) assistance. Different from the existing works, the suspicious receiver is assumed to be capable of detecting the presence of AN. Once such receiver detects the AN, the suspicious user will stop transmission, which can therefore degrade the surveillance performance. Hence, to improve the surveillance performance, AN should be transmitted covertly with a low detection probability. Under these assumptions, an optimization problem is formulated to maximize the surveillance performance under a covert constraint. Then, based on the detection ability at the suspicious receiver, a novel scheme is proposed to solve the optimization problem using an iterative search. Moreover, we investigate the impact of both the suspicious-transmitter-to-suspicious-receiver and the monitor-to-suspicious-receiver links uncertainties on the covert surveillance performance. Simulations are performed to verify the analyses. We show that the uncertainty in the suspicious user's link can enhance the surveillance performance, while the uncertainty in the monitor-to-suspicious-receiver link can degrade the surveillance performance.

Secrecy transmission is investigated for a cooperative jamming scheme, where a multi-antenna jammer generates artificial noise (AN) to confuse eavesdroppers. Two kinds of eavesdroppers are considered: passive eavesdroppers who only overhear the legitimate information, and active eavesdroppers who not only overhear the legitimate information but also jam the legitimate signal. Existing works only treat the passive and active eavesdroppers separately. Different from the existing works, we investigate the achievable secrecy rate in presence of both active and passive eavesdroppers. For the considered system model, we assume that the instantaneous channel state information (CSI) of the active eavesdroppers is available at the jammer, while only partial CSI of the passive eavesdroppers is available at the jammer. A new zero-forcing beamforming scheme is proposed in the presence of both active and passive eavesdroppers. For both the perfect and imperfect CSI cases, the total transmission power allocation between the information and AN signals is optimized to maximize the achievable secrecy rate. Numerical results show that imperfect CSI between the jammer and the legitimate receiver will do more harm to the achievable secrecy rate than imperfect CSI between the jammer and the active eavesdropper.

A cooperative jamming and beamforming scheme is proposed for secrecy transmission. Different from the existing works, an internal eavesdropper (Eve) and multiple external Eves coexist in the system, where a multi-antenna jammer is deployed to confuse Eves by using artificial noise. Specifically, the jammer can obtain the instantaneous channel state information (CSI) of the internal Eve, but only has the partial CSI of the external Eves. Upon setting up, the transmission outage requirement at Bob and secrecy outage constraint at the Eves, the transmit power is optimized to derive the maximum secrecy rate for the transmission. Moreover, we investigate the optimal power allocation scheme by characterizing the beamforming vectors under considering both perfect and imperfect CSI cases for the internal Eve. Numerical results show that the proposed scheme can improve the secrecy rate significantly by making full use of instantaneous CSI between the jammer and the internal Eve.

In this paper, when transmit antenna selection (TAS) and maximal ratio combining (MRC) schemes are deployed for secrecy enhancement, the impact of channel correlation on secrecy performance is investigated over Rayleigh fading channels. Specially, both the exact and asymptotic secrecy outage probability (SOP) for TAS/MRC are derived based on a novel correlation model, where the correlated legitimate channels and eavesdropper channels are modeled as a set of conditional independent channel gains. Moreover, the lower bound of SOP is obtained in high signal-to-noise ratio (SNR) region. Finally, simulation results verify our analysis, and show that the channel correlation between the legitimate receiver and the eavesdropper is beneficial to the SOP at high SNR.