# A Wireless Covert Channel Based on Dirty Constellation with Phase Drift
## 1 Introduction
For orthogonal frequency-division multiplexing (OFDM) signals, different methods may be used, e.g., virtual carriers [25], the modification of training sequences, the covert-data-dependent shift of the signal carrier frequency, or using changes in the cyclic prefix [26]. The disadvantage of all these solutions is the low bit rates obtained. In contrast, theoretical approaches for the direct sequence spread spectrum (DSSS) and frequency-hopping spread spectrum (FHSS) techniques are shown in [27]. The DSSS and FHSS techniques are used primarily in military communication systems due to the low probability of detection/intercept (LPD/LPI) [28]. However, in [27], [PERSON] et al. do not show the practical implementation of the proposed solutions. In the literature, we can also find steganographic solutions based on spatial multiplexing. [PERSON] et al. propose to use multiple-input multiple-output (MIMO) technologies to create covert channels [29]. In this case, artificial noise modulated from secret messages is distributed as Gaussian channel noise, which increases the undetectability of a hidden transmission. Additionally, to improve its transparency, [PERSON] et al. propose to modify the channel state information (CSI) parameters to reduce their correlation [29]. For modulations with constant points in their constellations, such as \(N\)-ary phase-shift keying (PSK) or quadrature amplitude modulation (QAM), dedicated steganography techniques are applicable. These methods are based on hiding information around the core points of the modulation constellation, and they seem more practical and convenient. For example, [30] describes the embedding of points in a constellation offset from the original points and adopts the term \"dirty constellation\". A similar solution defined as \"constellation shaping modulation\" is proposed in [31], although it focuses more on increasing covertness. In comparison to [30], the approach of [31] improves nondetectability at the expense of reliability degradation measured by bit error rate (BER). Creating a covert channel by superimposing pseudonoise asymmetric shift keying (PN-ASK) modulation was proposed in [32]. In this case, covert symbols are mapped by shifting the amplitude of primary symbols to a high order amplitude-phase modulation on a carrier constellation. The main drawback of this solution is limitations to the only phase-modulated cover signals. Moreover, multilevel amplitude modulation of the covert signal causes decreasing security (increasing detectability). Considering the high concentration of radio emissions in the available radio spectrum and the ever-growing number of used transceiver devices, this type of steganographic technique seems to be worth attention, research, and development. Considering the fact that [31] and [32] basically made a comparative analysis of [30], in this paper, we similarly focused on developing a novel idea of dirty modulation. In this paper, we present a novel dirty modulation that is based on a phase drift and dedicated to the \(N\)-ary PSK or QAM signals. A similar solution, but based on the frequency drift in the \(N\)-ary FSK signals, is presented in [24]. The idea of hiding information in the drift of radio signal parameters is based on the drift correction modulation (DCM) method [33], which was used to hide information in audio signals. In this case, Z, [PERSON] also used the phase drift in the OFDM signal, which was then psychoacoustic corrected and added to the audio cover [33]. In the developed solution, we hide the information in a determined phase drift around the current constellation point of the transmitted radio signal. The phase difference constituting the drift step and the centroid distance from the constellation points are the parameters of the developed method. These parameters may be selected adaptive to the modulation type or transmission conditions.