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.
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.
Covert transmission is investigated for a cooperative deception strategy, where a cooperative jammer (Jammer) tries to attract a multi-antenna adversary (Willie) and degrade the adversary's reception ability for the signal from a transmitter (Alice). For this strategy, we formulate an optimization problem to maximize the covert rate when three different types of channel state information (CSI) are available. The total power is optimally allocated between Alice and Jammer subject to Kullback-Leibler (KL) divergence constraint. Different from the existing literature, in our proposed strategy, we also determine the optimal transmission power at the jammer when Alice is silent, while existing works always assume that the jammer's power is fixed. Specifically, we apply the S-procedure to convert infinite constraints into linear-matrix-inequalities (LMI) constraints. When statistical CSI at Willie is available, we convert double integration to single integration using asymptotic approximation and substitution method. In addition, the transmission strategy without jammer deception is studied as a benchmark. Finally, our simulation results show that for the proposed strategy, the covert rate is increased with the number of antennas at Willie. Moreover, compared to the benchmark, our proposed strategy is more robust in face of imperfect CSI.
Covert transmission is investigated for a cooperative deception strategy, where a cooperative jammer (Jammer) tries to attract a multi-antenna adversary (Willie) and degrade the adversary’s reception ability for the signal from a transmitter (Alice). For this strategy, we formulate an optimization problem to maximize the covert rate when three different types of channel state information (CSI) are available. The total power is optimally allocated between Alice and Jammer subject to the Kullback-Leibler (KL) divergence constraint, which can be expressed analytically and be widely used as a covertness measurement. Different from the existing literature, in our proposed strategy, we also determine the optimal transmission power at the jammer when Alice is silent, while existing works always assume that the jammer’s power is fixed. Specifically, we apply the S-procedure to convert infinite constraints into linear-matrix-inequalities (LMI) constraints. When statistical CSI at Willie is available, we convert double integration to single integration using asymptotic approximation and substitution method. Finally, our simulation results show that for the proposed strategy, the covert rate is increased with the number of antennas at Willie. Moreover, compared to the benchmark, our proposed strategy is more robust in the presence of imperfect CSI.
Covert communication conceals transmission of messages between Alice and Bob from an adversary, Willie, who tries to determine if a transmission took place or not. While covert communication in a basic, standard setting where all variables are known to Willie, results in the well-known square-root law, when a jammer is present and assists Alice by creating uncertainty in Willie's decoder, a strictly positive transmission rate is possible. In this work, we analyze the case where the jammer is equipped with multiple antennas. Specifically, we analyze the effect of multiple antennas at the jammer on Alice's transmission power and consequently on the transmission rate. We consider both the case where the channel knowledge of Willie is known as well as the case where it is unknown. We formulate several optimization problems for the transmission strategies of the jammer to maximize his assistance to Alice, in terms of maximizing Bob's received SNR and consequently the covert rate. When the channel information is known to the jammer, we show that under an achievable covertness scheme, the optimal strategy of the jammer is to perform beamforming towards a single direction with all his available power. This direction though, is not trivial, since it reflects a tradeoff point between minimizing the interference at Bob and maximizing the interference at Willie. When the channel knowledge is unknown, we show that the optimal strategy of the jammer is either to transmit isotropically to all directions or to the null-space of Bob, where this choice depends on certain channel conditions. This is in contrast to current schemes in the literature. Furthermore, we extend the optimization problems to the case where Bob is also equipped with multiple antennas, and provide insightful results, shown to be asymptotically optimal, accompanied by simulations.
Covert communication conceals transmission of messages from Alice to Bob out of a watchful adversary, Willie, which tries to determine if a transmission took place or not. While covert communication in a basic, vanilla settings where all variables are known to Willie results in the well known square-root law, when a jammer is present and assists Alice by creating uncertainty in Willie's decoder, this transmission may have a positive rate.In this work, we analyze the case where the jammer is equipped with multiple antennas and obtain the optimal transmission strategy of the jammer in order to maximize his assistance to Alice, in terms of maximizing a ratio between Willie's and Bob's noise variance. We show that the optimal strategy of the jammer is to perform beamforming towards a single direction with all his available power. This direction though, is not trivial, since it reflects an optimal tradeoff point between minimizing the interference at Bob and maximizing the interference at Willie.
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 consider a common unicast beamforming network where Alice utilizes the communication to Carol as a cover and covertly transmits a message to Bob without being recognized by Willie. We investigate the beamformer design of Alice to maximize the covert rate to Bob when Alice has either perfect or imperfect knowledge about Willie's channel state information (WCSI). For the perfect WCSI case, the problem is formulated under the perfect covert constraint, and we develop a covert beamformer by applying semidefinite relaxation and the bisection method. Then, to reduce the computational complexity, we further propose a zero-forcing beamformer design with a single iteration processing. For the case of the imperfect WCSI, the robust beamformer is developed based on a relaxation and restriction approach by utilizing the property of Kullback-Leibler divergence. Furthermore, we derive the optimal decision threshold of Willie, and analyze the false alarm and the missed detection probabilities in this case. Finally, the performance of the proposed beamformer designs is evaluated through numerical experiments.