# Covert Anti-Jamming Communication Based on Gaussian Coded Modulation
###### Abstract  
In several wireless communication systems, robustness against jammers and covertness against eavesdroppers are required simultaneously. In this paper, we propose a novel covert anti-jamming communication system. The properties of both anti-jamming and covertness are achieved through the Gaussian-coded time-frequency modulation scheme. We propose two receiver algorithms based on the sparse signal recovery framework. The receiver algorithms estimate and remove the jamming signal from the received signal. In addition, it is difficult to distinguish the proposed signal from the actual Gaussian noise in both the time and frequency domains. We compare the covertness of the proposed communication system with that of a conventional digital modulation system in terms of the probability of detection. We numerically evaluated the bit error rate of the proposed system to demonstrate its anti-jamming performance. Keywords:anti-jamming; covert communication; sparse signal recovery; sparse Bayesian learning (SBL); orthogonal frequency-division multiplexing (OFDM); spread spectrum; analog coding +
Footnote †: : 2021: 11, 3759. [[https://doi.org/10.3390/app11093759](https://doi.org/10.3390/app11093759)]([https://doi.org/10.3390/app11093759](https://doi.org/10.3390/app11093759))
scenarios, the presence of wireless communications should not be easily detectable by hostile eavesdroppers. Intentional electromagnetic radiation, also called jamming, is another serious threat to the robustness of WCSs. Jamming attacks can disturb ongoing wireless communications by causing additional errors. Jamming attacks can become more destructive if the jammers cooperate with eavesdroppers. A follower jammer [4] is an example of such cooperation. It first measures the time-frequency band of the target signal and then concentrates its jamming energy onto that band. Covert communication decreases damage by jammers using the eavesdropping-and-jamming strategy by preventing the leakage of system parameters. Thus, to protect the security and robustness of WCSs, covertness and anti-jamming performances are required simultaneously. A spread spectrum (SS) scheme is one common solution for overcoming jamming attacks in the physical layer. Through this scheme, the bandwidth of band-limited jamming becomes much smaller than that of the communication signals. Furthermore, the scheme makes communication difficult to detect by hiding communication signals under the noise level, thus reducing the threat of eavesdroppers and eavesdropper-aided smart jammers such as follower jammers. The coded modulation method using Gaussian-distributed code can be a complement to the SS scheme. If the modulated symbols follow a Gaussian distribution, it is difficult for the eavesdropper to distinguish whether there is a communication signal or not without an exact codebook. Furthermore, the legitimate receiver can use the error-correction property of the coding scheme. The idea of real-valued channel coding has been used, and is known as analog coding [5]. The code can correct sparse errors (e.g., narrowband jamming). Researchers [6] have studied a generalization of this coding scheme: a complex-field coding using orthogonal frequency-division multiplexing (OFDM). [PERSON] and [PERSON] [7] proposed a sparse error-correction method for an arbitrary generator matrix, which is a polynomial-time linear programming method unified within a compressive sensing (CS) recovery framework [8]. Studies motivated by analog coding and many other CS-based anti-jamming approaches have exploited the sparse characteristic of jamming in both the time-frequency [9; 10] and spatial domains [11]. Thus, analog coding can be applied to anti-jamming communication.