In this paper, we investigate a covert communication system based on a hybrid active and passive reconfigurable intelligent surface (HAPRIS), where each RIS element can be dynamically configured to operate in either active or passive mode. By dynamically configuring the operational mode of each element, the system can effectively harness the high-gain benefits of the active RIS while simultaneously preserving the low power consumption and enhanced covertness properties offered by the passive RIS. Then, we formulate an energy efficiency maximization problem by jointly optimizing the active/passive mode selection vector, transmit beamforming vector and reflect coefficient matrix subject to the power, covertness and hardware constraints. To evaluate the detection performance of the warden, we further derive a tractable expression of the covertness constraint for the multi-antenna warden. To solve the mixed-integer non-convex problem, we propose a penalty dual decomposition (PDD) scheme utilizing the block coordinate descent method to decompose the original problem into several sub-problems, which are subsequently solved via the Lagrangian multiplier method and the interior-point method. In addition, we investigate a comparative scenario considering the position error of warden. Specifically, we first derive an expression for the estimation error of channel state information (CSI) based on the position error. We then propose a successive convex approximation method to obtain an upper bound on the CSI error, enabling us to formulate a worst-case covertness constraint. Finally, we extend the proposed PDD scheme to such a scenario with the CSI error. Simulation results demonstrate the effectiveness of the proposed schemes.

We investigate hybrid beamforming design for covert millimeter wave multiple-input multiple-output systems with finite-resolution digital-to-analog converters (DACs), which impose practical hardware constraints not yet considered by the existing works and have negative impact on the covertness. Based on the additive quantization noise model, we derive the detection error probability of the warden considering finite-resolution DACs. Aiming at maximizing the sum covert rate (SCR) between the transmitter and legitimate users, we design hybrid beamformers subject to power and covertness constraints. To solve this nonconvex joint optimization problem, we propose an alternating optimization (AO) scheme based on fractional programming, quadratic transformation, and inner majorization-minimization methods to iteratively optimize the analog and digital beamformers. To reduce the computational complexity of the AO scheme, we propose a vector-space based heuristic (VSH) scheme to design the hybrid beamformer. We prove that as the number of antennas grows to be infinity, the SCR in the VSH scheme can approach the channel mutual information. Simulation results show that the AO and VSH schemes outperform the existing schemes and the VSH scheme can be used to obtain an initialization for the AO scheme to speed up its convergence.

We investigate hybrid beamforming design for covert multiple-input multiple-output communications with finite-resolution digital-to-analog converters (DACs), which im-pose practical hardware constraints not yet considered by the existing works and have negative impact on the covertness. Based on the additive quantization noise model, we derive the detection error probability of the warden considering finite-resolution DACs. Aiming at maximizing the sum covert rate (SCR) between the transmitter and legitimate users, we design hybrid beamformers subject to the power and covertness constraints. To solve this nonconvex joint optimization problem, we propose an alternating optimization (AO) scheme based on fractional programming, quadratic transformation, and inner majorization-minimization methods to iteratively optimize the analog and digital beamformers. Simulation results verify the performance gain provided by the proposed AO scheme.

Rather than considering only one legitimate user as in the existing works, we investigate multiple legitimate users served by Alice using multicast millimeter wave communications in this paper. Hybrid beamformers for the max-min fairness problem are designed to maximize the minimum covert rate between Alice and the legitimate users subject to the power constraint for confidential signal (CS) and the covertness constraint. In particular, the fully-digital beamformers for the CS and jamming signal are designed by temporarily neglecting the hardware constraints from the constant envelop for phase shifters and the limited number of RF chains, where a semi-definite programming-based method and a successive convex approximation (SCA)-based method are proposed. To approach the fully-digital beamformers, hybrid beamformers are designed subject to the hardware constraints, where an alternating minimization method is proposed to iteratively optimize the analog and digital beamformers. Simulation results show that the proposed methods can achieve better covert communication performance than the existing methods.