# A Wireless Covert Channel Based on Dirty Constellation with Phase Drift
## 4 Evaluation Criteria for Covert Channels  
To evaluate the covert channel efficiency, we may use the following parameters:  
* Covert channel detectability defined by the detection probability,
* Cost understood as the carrier signal distortion,
* Transmission rate and BER in the covert channel. In steganography, the most important parameter is its transparency, understood as the undetectability of the transmission existence by outside users (i.e., third parties). It should be highlighted that an easily detectable covert channel is completely irrelevant, even if it provides a high transmission rate. The limit values of the cost function are usually defined for a given cover transmission standard by an error vector magnitude (EVM). The EVM for a signal with a covert channel is the cumulative result of influencing the transmitter systems and distortions introduced by the covert channel. For example, Table 1 contains the EVMs for quadrature PSK (QPSK) and \(N\)-ary QAM in the 5G systems [48] (Table 6.5.2-1, p. 48). There are no clear criteria defining the channel detectability. The presence of a covert channel can be indicated when an exceedingly high EVM level is observed or the high level is more frequent (i.e., higher than assumed). This was detected in the statistical studies, including signal histograms. Instead of determining the statistical values of the signal at the receiver input by using the classic prisoner problem proposed by [PERSON] [49] we may use the scheme of a moving observer [50] to assess the detection. In this model, [PERSON], [PERSON], and [PERSON] correspond to the steganographic source (SS), observer (Ob), and steganographic receiver (SR), respectively. Figure 6 illustrates the analyzed scenario. \begin{table}
\begin{tabular}{c c} \hline \hline
**Modulation Scheme for Physical Downlink Shared Channel (PDSCH)** & **Required EVM (\%)** \\ \hline QPSK & 17.5 \\
16 QAM & 12.5 \\
64 QAM & 8.0 \\
256 QAM & 3.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Error vector magnitudes (EVMs) in 5G standard. In this model, detecting the covert channel depends on the distance from the SS. As the distance increases, the influence of the radio channel intensifies. However, in the case of postmodulation steganography, there is a situation in which the mobile Ob, being near the SR, is able to detect steganographic emission with a high probability. With the increase in SNR, it is easier to identify the regularity of covert information constellation. By moving away from the SS, noise and other propagation phenomena occurring in the real channel make it difficult to detect the emission, as well as its reception, understood as the reproduction of the bitstream [50]. When considering the detectability of the covert channel as a priority, the proposed solution offers several basic properties:  
* Random \(A_{m}\) and \(\varphi_{x}\), i.e., no fixed constellation points, which provides robustness on statistical steganalysis methods--a major advantage over [30];
* Adaptive choice of \(A_{m}\) allow minimizing the EVM--a major advantage over [32];
* Possible to adaptively adjust the transmission rate by selecting the number \(K\) of phase changes--a major advantage over [30; 31; 32]. In steganographic signals, the lower EVM provides a lower probability of detecting the covert channel. On the other hand, the lack of fixed constellation points makes the histograms more random. Therefore, it is worth carrying out statistical analysis based on histograms and illustrating the covert channel implementation. In this simple example, we assumed that the cover is the 4 QAM signal, for \(M=4\), i.e., \(\varphi_{m}\) takes four values according to Equation (3). Figures 7-11 show the impact of random \(A_{m}\) and \(\varphi_{x}\) on the obtained constellations and histograms. In Figures 7-9, channel interference impact was not considered. On the other hand, we assumed that the transmitter system did not introduce any impairments, i.e., transmitter EVM is equal to 0%.