# The Optimization of Covert Communication in Asymmetric Jammer - Assist Systems
###### Abstract  
This research investigates the feasibility of covert and reliable communication between [PERSON] and [PERSON] in the presence of a vigilant adversary, [PERSON], employing a jammer in a complex Gaussian channel. [PERSON] strategically manipulates the noise-power ratio along the real and imaginary axes to disrupt [PERSON]'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. c 2024 1483. 11.15.15.15.15.15.15.15.15.15.15.15.15.15.15.15  
of the pre-shared secret's optimal length in [16; 17], the characterization of constants concealed by Big-\(\mathcal{O}\) notation in [17; 18], and the theoretical and experimental exploration of covert communication over quantum channels in [19]. Moreover, this seminal theorem has subsequently been extended to various channel models, including discrete memoryless channels [17; 18; 20], binary symmetric channels [16] and multiuser channels [21; 22; 23; 24; 25], etc. In traditional covert communication theory research, significant attention has been devoted to exploring theoretical boundaries over real Gaussian channels. The work presented in [9] expands the scope of covert communication theoretical research to encompass complex Gaussian channels, substantiating the boundary of covert communication over such channels. Existing works have investigated covert communication with random noise [26] and jammers [14; 27]. Subsequently, jammer-aided covert communication were extended to UAV communication [28] and backscatter communication [29]. However, existing research on the theoretical boundaries of covert communication has been conducted in the context of real Gaussian channels, and for computational simplicity and optimization convenience, Gaussian input has been employed as the channel input. Nevertheless, in practical communication scenarios, the scenario of using Binary Phase Shift Keying (BPSK) as the channel input in a complex Gaussian channel has not been considered. In this work, we consider covert communication over complex Gaussian channels in the presence of an uninformed jammer. It is worth noting that jammer and [PERSON] do not coordinate fully, similar to the scenario in [14]. As shown in Figure 1, the jammer sends asymmetric complex Gaussian noise signals, interfering with [PERSON]'s covert communication detection. [PERSON] can only control the signal allocation ratio of the jammer, i.e., the power ratio of noise on the real and imaginary axes. [PERSON] cannot demodulate the jamming noise, but [PERSON] can know the power ratio of complex Gaussian noise on the real and imaginary axes in the environment. Regarding [PERSON], we consider two scenarios: in one case, [PERSON] can perfectly demodulate the jamming noise from the jammer, thereby eliminating interference. In the other case, [PERSON] cannot fully demodulate the jamming noise from the jammer but can partially mitigate the noise interference introduced by the jammer. Our principal contributions can be succinctly summarized as follows:  
(1) We explore covert communication in a scenario with a partially cooperative jammer within a complex Gaussian channel. KL divergence serves as our metric for covertness, while mutual information quantifies the transmission rate. (2) We adopt BPSK input instead of Gaussian input, enhancing the applicability of our theory in real-world communication systems and bolstering the feasibility of our approach. (3) Employing Taylor series expansion, we approximate KL divergence and mutual information under BPSK input.