# NN-Based 8 FSK Demodulator for the Covert Channel
## 1 Introduction  
The first use of the term \"covert channel\" occurred in research study [1]. It focused on the exchange of data between programs. It defined the covert channel as a communication channel that is not at all designed or intended for the transmission of information. Nowadays, it is assumed that any manner of communication that violates the system security policy is a covert channel. In the physical layer of wireless communication, there were proposed solutions [2, 3, 4, 5], based on the so-called post-modulation [6] method, which embeds the hidden data stream after the modulation stage. In this method, the covert modulated signal is superposed on the cover (unhidden) signal. The hidden signal must be much weaker than the cover signal to avoid detection (in the sense of the low probability of detection). Moreover, additional phase shift mechanisms [2] can be implemented to decrease detection through statistical analysis. The previous studies on covert channels consider only selected, coherent types of modulation for hidden signals. Generally, it was assumed that the separation of the superimposed signals (SIC operation) can be performed in a perfect way, which means that the receiver has perfect information about the cover signal. It is far from practice and reality. In this paper, we analyze an 8 FSK modulation superimposed onto a QAM signal (cover). For the so-defined covert channel, an NN-based demodulator was proposed. To support the examinations, we compared the presented demodulator with a traditional FSK correlator-based demodulator. Our results indicate that the NN-based demodulator outperforms 8 FSK correlator-based demodulator for imperfect SIC measured by channel gain estimator error. In this paper, we present a strictly defined problem connected with a covert channel that combines several topics, such as steganography, FSK demodulation, impartments in the receiver, soft/hard metrics, and neural networks, as well as their applications. So, it needs to be analysed and merged with the use of several literature references to enhance the physical secrecy and quality of the transmission. The idea of the use of a neural network in the demodulation process and, generally, in the physical layer of wireless communication [7] is not quite new. A NN-based BPSK demodulation is a subject of the article [8]. A fully convolutional neural network with variable input and output length, called DemodNet, to demodulate BPSK and QAM modulation was presented in [9]. DemodNet provides, under the AWGN channel, results that are very close to the traditional methods. What is important in this approach is the soft and hard demodulation realized by NN. To reduce the overall computational complexity of the soft-decision, a trainable universal neural network-based demodulator architecture was introduced in [10] for QAM signals  
In the literature, much less attention has been devoted to FSK demodulators, when it comes to soft demodulation and neural networks, in general. A soft-decision Viterbi decoder for FSK demodulation was presented in [11]. However, it deals with frequency discriminator for FSK demodulation. Soft-decision metrics for FSK signalling, in the presence of Cauchy and Gaussian noise, are derived in [12]. The authors proposed utilizing correlators in the detection process, which is useful for dealing with non-coherent demodulation. A neural network, as a technique for BFSK demodulation, was presented in [13]. The authors simulated the demodulation process over the AWGN Rayleigh fading channel, but the NN works in a hard-decision manner. The problem of the imperfect SIC operation (caused by channel gain estimation error) and superposition of signals are closely related to NOMA, specifically P-NOMA (power non-orthogonal multiple access) systems. In the case of NOMA, SIC errors have less impact on the system performance. There are some positions in the subject literature [14; 15].