# NN-Based 8 FSK Demodulator for the Covert Channel
## 2 Model of the Cover Transmission
### The System Model for Cover Communication  
Figure 3 shows in a detail the system model (compatible with Figure 1b) used to describe principles of a covert channel, based on the superposition of signals. The cover and covert signals are transmitted simultaneously (in our case, not necessarily synchronously). To increase the BER performance, and for better analysis of our proposed solutions, we assumed channel coding before covert data transmission. The coding was not carried out for cover bits. Next, the superimposed signals with different power levels were transmitted via a wireless channel. In the receiver, SIC operation (successive interference cancellation) was performed to recover the covert signal. SIC, in short, means subtraction operation, where the minuend represents the received combined signal (superposition of cover and covert modulated signals), and the subtrahend is the recovered signal of the cover (after remodulation). Figure 3: Transmitter/receiver structure for covert channel. Figure 2: BER curve vs. \(E_{b}/N_{0}\) for FSK, PSK, and QAM modulation. The transmitter signal is shown in Equation (1) [14]. \[s(t)=s_{1}(t)+s_{2}(t), \tag{1}\]  
where \(s_{1}(t)\) is the signal of the cover (with the variance \(\sigma_{1}^{2}\)), and \(s_{2}(t)\) is the covert signal (with the variance \(\sigma_{2}^{2}\)). To ensure the secrecy of communication, the variance of the signals should satisfy the inequality \(\sigma_{2}^{2}<<\sigma_{1}^{2}\). If the receiver (user) is aware that additional information is embedded, it is able to decode (demodulate) the covert message. This is achieved by removing the cover signal from the received signal. An uninformed user treats signal \(s(t)\) as a noised version of \(s_{1}(t)\). The received signal is given as Equation (2) [15]:  
\[y(t)=h\cdot s(t)+n=\sum_{i=1}^{2}h_{i}\cdot s_{i}(t)+n. \tag{2}\]  
In this model, \(h\) represents the channel gain (e.g., Rayleigh fading channel) between the transmitter and receiver, and it is represented by a circularly-symmetric, complex Gaussian random variable. The symbol \(n\) represents Gaussian noise. Perfect SIC operation means that the recovery and re-modulation of the signal \(s_{1}(t)\) are achieved without any errors, which means [15], as shown in Equation (3):  
\[s_{2}(t)=y(t)-s_{1}(t)=y(t)-s_{1}(t)=s_{2}(t). \tag{3}\]  
Assumed that a perfect SIC operation can be performed, the simulation was conducted for the following parameters. Different numbers of samples per symbol for different covert modulation (Table 1) were adopted to achieve the same covert data rate. The results of the simulation are depicted in Figure 4, where the value \(E_{b}/N_{0}\) refers only to the cover signal (16 QAM). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Modulation** & **Variance** & **Number Samples Per Symbol** \\ \hline
16 QAM (cover) & \(\sigma_{1}^{2}\) & 1 \\ BPSK (covert) & \(0.05\cdot\sigma_{1}^{2}\) & 8 \\
2 FSK (covert) & \(0.05\cdot\sigma_{1}^{2}\) & 8 \\
8 FSK (covert) & \(0.05\cdot\sigma_{1}^{1}\) & 24 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the simulation. Figure 4: The comparative simulation of the covert data transmission in AWGN channel. The covert signal causes additional distortions and degrades the system performance that can be measured by EVM. For this case, the results of the simulation are depicted in Figures 5 and 6. From the results depicted above, we can conclude that FSK, 8 FSK, and BPSK have the same impact on the cover signal. Slightly worse transmission parameters of 8 FSK in relation to BPSK (Figure 4) may be treated as a cost of the non-coherent demodulation. There remains the question of the steganalysis mentioned in the previous section. It is usually based on histograms. It is achieved by carrying out the I/Q analysis of the received signal s(t) and examining its histograms. The example of histogram-based steganalysis is presented in Figure 7. For a clearer graphical presentation, we assumed QAM as the cover. We compare 8 FSK IQ histograms with covert modulation 4 PSK.