# Covert Anti-Jamming Communication Based on Gaussian Coded Modulation
###### Abstract
In this paper, we consider wireless communications under a jammer and eavesdropper scenario, for example, the electronic warfare scenario depicted in Figure 1. The proposed system transmits information messages on a coded Gaussian signal through a wireless channel that is attacked by an eavesdropper, called [PERSON] in this paper, and a jammer. We consider two types of jammers. The first type is a blind jammer, which radiates a partial-band or pulse jamming signal without knowing when or where a target communication signal exists. The second type is a follower jammer, which detects an ongoing communication signal and then radiates a jamming signal to interfere with this ongoing signal. We assume that [PERSON] is not aware of the exact codebook and time-frequency band of the target system. Suppose that there is no secret information shared between the transmitter and the receiver. Then the achievability of covert communication depends entirely on the channel quality difference between the receiver and [PERSON], which is difficult for communicators to control. Thus, many studies assume that the transmitter and the receiver share some secret information, such as a codebook [2; 12] or spreading sequence [13; 14]. This secret information is often time-varying to prevent information leakage [15]. One practical example is a frequency-hopping radio that exploits the exact time-frequency band of a signal as secret information. In this paper, we propose a novel covert anti-jamming communication system based on a noise-like Gaussian-coded time-frequency modulation, as illustrated in Figure 2. To provide covertness to a communication signal, we propose a time-frequency modulation scheme. It is difficult to distinguish a signal generated using the proposed scheme from Gaussian noise. To provide robust anti-jamming performance, we propose two receiver algorithms that estimate and remove the jamming signal from the received signal by exploiting the sparse nature of the jamming signal. The main contributions of this paper are as follows:  
* We propose a covert anti-jamming communication system based on Gaussian-coded time-frequency modulation. We consider the communication system that is exposed to the threat of the jammer and Eve. Previous studies on analog coding [5; 6; 7; 9; 10; 11] have not considered the threat of jammers and eavesdroppers simultaneously. We designed a coding and modulation method for a transmitter to achieve anti-jamming and covert communication simultaneously. For a receiver, to estimate and remove jamming, we propose two novel sparse jamming estimation (SJE) algorithms, i.e., greedy SJE (GSJE) and Bayesian SJE (BSJE), which are described as Algorithm 1 and Algorithm 2, respectively. * For the proposed Gaussian coding scheme, we aimed to develop a real-valued coding scheme in which a coding gain is provided. Previous studies on analog coding [5; 7] have considered analog messages. In this paper, we show that the coding method cannot provide a coding gain for finite-field messages. As a countermeasure, we introduce two methods to achieve coding gain even when the finite-field messages are encoded. The first method is a two-stage coding approach, applying finite-field coding and linear Gaussian coding sequentially. In this method, the overall coding gain is equivalent to that of the finite-field coding used in the first stage. Another coding method is a codebook method that uses a pregenerated codebook rather than a linear operation on message vectors. We demonstrate the existence of a coding gain through numerical results that compare the bit error rate (BER) performance of the proposed system under jamming and the uncoded direct-sequence spread spectrum (DSSS) without jamming. * We show the undetectability of the signal transmitted from the proposed system. The signal of the proposed system is compared to that of a conventional binary phase-shift keying (BPSK)-DSSS scheme.