# A Wireless Covert Channel Based on Dirty Constellation with Phase Drift
## 1 Introduction
The modulation choice has a significant impact on the number of points (i.e., transmitted symbols) in its constellation, which translates into the distances of neighboring points on it. The influence of the transmission conditions, i.e., a signal-to-noise ratio (SNR), translates into a detection interference of the symbols and hidden subsymbols in the received signal. During the transmission, the received symbols (i.e., constellation points) change. Hence, phase drift detection, and thus steganalysis of the developed method, is more difficult than other dirty modulations. This is due to the fact that we do not set constant points in the constellation as the place of reading the subsymbol of covert transmission, but we hide the information in the drift step, i.e., the phase difference of the consecutive constellation points. This proves the originality of the proposed solution in comparison with other dirty modulation or wireless postmodulation steganography methods available in the literature. In the paper, we present a methodology for generating and receiving the covert channels based on the dirty constellation with the phase drift and compare it with [30] as others have done. We want to emphasize that in addition to the simulation analysis typical for this kind of paper, we also present the first lab tests. In this practical implementation, we conducted tests using hardware and covert transmission over a real radio channel. To increase the SNR of the covert signal, multiple repetitions of the hidden subsymbols on the transmitting side and coherent averaging [34] of the successive drift phase differences on the receiving side shall be applied. This reduces the resulting bit rate of the covert transmission in the proposed method. However, this approach allows adaptation to the transmission conditions occurring in the radio channel. The proposed method will be used in future radio communication systems, including 5G networks dedicated to military applications. We plan to use it in the upcoming European Defense Agency (EDA) project, codenamed SOFTANET, for the hidden data layer in the wireless part of a software-defined network (SDN) [35; 36; 37]. It is in line with the trend, visible in the literature, of using steganography in 5G systems and networks, e.g., [21; 38]. Analyzing the security system trends, including those based on cryptography and steganography, we see numerous threats to the existing techniques. They result from the increasing use of artificial intelligence (AI) algorithms [39; 40] and quantum technologies [41; 42] in security breach systems. On the other hand, these technologies may also be potential development directions of the security systems. Currently, the literature offers numerous solutions, including steganographic ones, which are based on modern AI (such as machine learning (ML) [43; 44]) and quantum technologies [45; 46] increasing the robust ness, undetectability, and efficiency of emerging security and data transmission systems. In the case of the developed method, in the near future we want to use these ML techniques for a time-varying selection of the DCM parameters, which may increase its robustness, transparency, and the bitrate of the covert transmission. Based on an approach presented in [47], we want to summarize the contribution of this paper. This research possesses various contributions in the domain of wireless steganography, watermarking, and wide-sense security of future wireless systems. 1. First, a DCM-based novel dirty constellation has been proposed, which can be used in \(N\)-ary PSK and QAM signals. The previous DCM solution [33] was dedicated to watermarking audio signals using the OFDM. 2. Second, based on simulation studies, the impact of the parameter variability of the developed method on its detection possibility using statistical analysis techniques has been shown. 3. Third, the efficiency of the developed method and its comparison with another dirty constellation technique [30] have been presented. 4.