This research investigates the feasibility of covert and reliable communication between Alice and Bob in the presence of a vigilant adversary, Willie, employing a jammer in a complex Gaussian channel. Alice strategically manipulates the noise-power ratio along the real and imaginary axes to disrupt Willie’s detection capabilities. Covertness constraints are quantified using KL divergence, and transmission performance is assessed through mutual information. Additionally, an optimization method is introduced to enhance covert communication by fine-tuning the amplitude gain and noise-power ratio. Numerical results confirm the effectiveness and superiority of the proposed method, showcasing its ability to maximize covert transmission rates.
This research investigates the feasibility of covert and reliable communication between Alice and Bob in the presence of a vigilant adversary, Willie, employing a jammer in a complex Gaussian channel. Alice strategically manipulates the noise-power ratio along the real and imaginary axes to disrupt Willie’s detection capabilities. Covertness constraints are quantified using KL divergence, and transmission performance is assessed through mutual information. Additionally, an optimization method is introduced to enhance covert communication by fine-tuning the amplitude gain and noise-power ratio. Numerical results confirm the effectiveness and superiority of the proposed method, showcasing its ability to maximize covert transmission rates.
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.
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 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 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 considers the ability of transmitter Alice to communicate reliably to receiver Bob without being detected by warden Willie. Previous work has generally considered a discrete-time model, and, in the standard Alice-Bob-Willie scenario, it has been shown that a discrete-time model captures the salient aspects of the underlying continuous-time covert communications system. However, in the presence of a jammer assisting Alice, where it has been shown in previous work that Alice can achieve a positive covert rate on a discrete-time model, we demonstrate here that a straightforward extension of the discrete-time construction to the continuous-time system does not guarantee a positive covert rate, hence indicating that the discrete-time model does not capture the salient aspects of the continuous-time system in such a scenario. This is because Willie is able to exploit excess bandwidth for co-channel interference suppression, as we demonstrate with an interference cancellation receiver. Hence, for the case when Alice is assisted by an uninformed jammer, we consider the continuous-time channel directly and study whether efficient covert communication can still be achieved against any possible receiver that Willie might employ. By presenting and characterizing an approach much different than that suggested by previous work for discrete-time systems in such a scenario, we establish thatO(WT)information bits can be transmitted covertly and reliably on a continuous-time channel of asymptotic bandwidthWinTseconds, regardless of the receiver that Willie employs. This is done for two separate scenarios: 1) when there is perfect frame synchronization between Alice and the jammer’s signals; 2) when there is no frame synchronization between Alice and the jammer’s signals. Numerical results are provided to validate the theory.
Recent work has established that when transmitter Alice wishes to communicate reliably to recipient Bob without detection by warden Willie, with additive white Gaussian noise (AWGN) channels between all parties, communication is limited to O(√n) bits in n channel uses. However, this assumes that Willie has an accurate statistical characterization of the channel. When Willie has uncertainty about such and his receiver is limited to a threshold test on the received power, Alice can transmit covertly with a power that does not decrease with n, thus conveying O(n) bits covertly and reliably in n uses of an AWGN channel. Here, we consider covert communication of O(n) bits in n channel uses while generalizing the environment and removing any restrictions on Willie's receiver. We assume that an uninformed “jammer” is present to help Alice, and we consider AWGN and block fading channels. In some scenarios, Willie's optimal detector is a threshold test on the received power. When the channel between the jammer and Willie has multiple fading blocks per codeword, a threshold test on the received power is not optimal. However, we establish that Alice can remain covert with a transmit power that does not decrease with n even when Willie employs an optimal detector.