A Wireless Covert Channel Based on Dirty Constellation with Phase Drift

: Modern telecommunications systems require the use of various transmission techniques, which are either open or hidden. The open transmission system uses various security techniques against its unauthorized reception, and cryptographic solutions ensure the highest security. In the case of hidden transmissions, steganographic techniques are used, which are based on the so-called covert channels. In this case, the transparency and stealth of the transmission ensure its security against being picked up by an unauthorized user. These covert channels can be implemented in multimedia content, network protocols, or physical layer transmissions. This paper focuses on wireless covert channels. We present a novel method of steganographic transmission which is based on phase drift in phase-shift keying or quadrature amplitude modulation (QAM) and is included in the so-called dirty constellation techniques. The proposed approach is based on the drift correction modulation method, which was previously used in the watermarking of audio-signals. The developed solution is characterized by a variable bit rate, which can be adapted to the used modulation type and transmission conditions occurring in radio channels. In the paper, we present the method of generating and receiving hidden information, simulation research, and practical implementation of the proposed solution using the software-deﬁned radio platform for selected QAM.


Introduction
The increase in capacity is one feature of emerging communication systems, including the fifth (5G) and sixth generation (6G) systems. This is due to the use of wider radio channels, their aggregation, or the use of higher frequency bands, i.e., millimeter, terahertz, or optical waves. A wider band of transmitted signals also gives greater possibilities to implement covert data transmission. Hence, the greater interest in searching for new steganographic methods is more evident [1].
Steganography consists in transmitting information to make the act of transmission undetectable. Unlike cryptographic information, whose content is encrypted, the very existence of steganographic information is concealed. Steganographic information, which is also known as covert information, requires a carrier-or, in other words, a cover. The simplest carrier scenario uses photos [2], audio [3] or video signals [4] (multimedia steganography) to hide additional information. One of the important steganography applications includes creating covert channels. The term "covert channel" was coined by Butler W. Lampson as: " . . . any communication channel that can be exploited by a process to transfer information in a manner that violates the systems security policy . . . " [5]. B.W. Lampson focused on the exchange of data between programs. Nowadays, it is assumed that any method of communication used to illegally transmit information, which violates the system security policy, is a covert channel. solutions. In the literature, we can also find steganographic solutions based on spatial multiplexing. P. Cao 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, P. Cao 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 phaseshift 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, Piotrowski 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. 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.
Lastly, the possibility of the practical implementation of the proposed solution has been shown, which gives a premise for its practical use in hidden data layer creation in SDN for the SOFTANET project and in future wireless systems and networks.
The remainder of the paper is as follows. Section 2 describes the idea of dirty constellation based on [30]. Our solution based on phase drift is presented in Section 3. In Section 4, we introduce the evaluation criteria of the covert channels. Using them, we analyze the developed dirty constellation based on the simulation and measurement approaches in Sections 5 and 6, respectively. Section 7 contains the paper summary.

Concept of Dirty Constellation
The main idea for creating covert channels based on the dirty modulation results from the fact that the received signals do not have an ideal constellation. Instead, we see a radio channel and parameter imperfection caused by both the transmitting and receiving devices' influence on blurring (spreading) the received-signal constellations. This effect translates to phase and amplitude distortions and ultimately to an increase in BER.
To increase the bandwidth efficiency, the N-ary PSK or QAM modulations are commonly used in telecommunications together with OFDM access. A time-frequency structure (waveform) of the OFDM signal provides a lot of space and possibilities for creating the covert channel, e.g., [26]. The suggested solutions include the use of the OFDM symbol waveform. When analyzing the QAM signal, the covert channel is provided based on the errors, which are the differences between the theoretical and the real points of the constellation. This results from environmental noise and hardware impairments. The theoretical, finite M number of constellation points corresponding to the N-ary PSK or QAM, in practice, has the form of the finite number of constellation point sets concentrated around the theoretical values without any distortions. Therefore, the channel will remain "hidden" as long as it is perceived as a noisy version of the carrier signal (i.e., the PSK or QAM signal) by the third uninformed party. It is important that after applying the covert information, the carrier remains distorted as little as possible so that the reception of the primary signal should be error-free.
It is the idea of using the dirty constellation proposed in [30]. The bits of covert information are mapped into additional constellation points placed around the base (i.e., carrier) constellation points, which is illustrated in Figure 1. According to the assumption, these additional constellation points are perceived as noise/error by the uninformed user. The value of the covert information symbol is defined in relation to the carrier constellation point.
It is the idea of using the dirty constellation proposed in [30]. The bits of covert information are mapped into additional constellation points placed around the base (i.e., carrier) constellation points, which is illustrated in Figure 1. According to the assumption, these additional constellation points are perceived as noise/error by the uninformed user. The value of the covert information symbol is defined in relation to the carrier constellation point. The carrier constellation is marked with blue circles, while the constellation related to the covert subsymbols (i.e., covert message bits) is marked with red ones. The probability of detection by adversaries is limited by reducing the predistortion radius, r. In addition, r can be changed (e.g., randomly) within a preset range. A. Dutta et al. for masking purposes used the fact that the QAM signal is transmitted by using the OFDM [30]. Therefore, each unused OFDM subcarrier may be a masking element providing more random (noiselike) in relation to the general character of the covert transmission. Additionally, A. Dutta et al. propose inserting angle rotation, θ, for successive OFDM harmonics, to increase the number of the received QAM constellation states for the subcarrier set. However, it does not change the number of constellation points if only one of the OFDM subcarriers is analyzed.

Phase Drift-Based Dirty Constellation
The developed dirty constellation with the phase drift is based on the DCM [33]. The DCM solution was used to create a watermark in audio files. The covert information is represented in monotonic phase changes of the selected signal harmonics. The mth harmonic selected for steganography is expressed by the following formula [33] ( ) ( ) where m A and m f represent amplitude and frequency of the mth signal, respectively, x φ is an initial phase and Δ m χ is the preset phase drift carrying covert information.
In the DCM detector, the signal is subjected to the phase angle scanning procedure, which results in finding the maximum of the virtual fringe module max .
V χ As shown in [33], the DCM demonstrates good steganographic properties.
In our approach, we adopted the DCM for creating the dirty constellation of the steganographic channel. For further considerations, we assume that the QAM signal (without the use of the OFDM) is the carrier (cover) of the hidden transmission. The proposed The carrier constellation is marked with blue circles, while the constellation related to the covert subsymbols (i.e., covert message bits) is marked with red ones. The probability of detection by adversaries is limited by reducing the predistortion radius, r. In addition, r can be changed (e.g., randomly) within a preset range. A. Dutta et al. for masking purposes used the fact that the QAM signal is transmitted by using the OFDM [30]. Therefore, each unused OFDM subcarrier may be a masking element providing more random (noiselike) in relation to the general character of the covert transmission. Additionally, A. Dutta et al. propose inserting angle rotation, θ, for successive OFDM harmonics, to increase the number of the received QAM constellation states for the subcarrier set. However, it does not change the number of constellation points if only one of the OFDM subcarriers is analyzed.

Phase Drift-Based Dirty Constellation
The developed dirty constellation with the phase drift is based on the DCM [33]. The DCM solution was used to create a watermark in audio files. The covert information is represented in monotonic phase changes of the selected signal harmonics. The mth harmonic selected for steganography is expressed by the following formula [33] where A m and f m represent amplitude and frequency of the mth signal, respectively, ϕ x is an initial phase and ∆χ m is the preset phase drift carrying covert information.
In the DCM detector, the signal is subjected to the phase angle scanning procedure, which results in finding the maximum of the virtual fringe module χ Vmax . As shown in [33], the DCM demonstrates good steganographic properties.
In our approach, we adopted the DCM for creating the dirty constellation of the steganographic channel. For further considerations, we assume that the QAM signal (without the use of the OFDM) is the carrier (cover) of the hidden transmission. The proposed method uses a covert symbol represented by the K ≥ 2 phase drifts of the successive cover constellation points. Therefore, the P symbols of the QAM can carry P/K covert symbols.
For the N-ary QAM, the single constellation point is defined in the complex form: x n = A n exp(jϕ n ) for n = 1, 2, . . . , N, where A n and ϕ n are the amplitude and phase of the nth constellation point. A single M-ary covert message adopts the form of a K-component complex vector: where A m and ϕ m = ∆χ m are the centroid distance and phase drift step for the proposed dirty constellation, respectively, and ϕ x is a random initial phase, which does not change when the covert symbol is in progress. Steganographic information is created by combining (adding) two successive K cover symbols with successive covert message symbols (i.e., vectors y k ). An example of creating hidden information for a single covert symbol and K = 3 is presented in Figure 2.
( ) exp j for 1, 2,..., , where n A and n φ are the amplitude and phase of the nth constellation point.
A single M-ary covert message adopts the form of a K-component complex vector: are the centroid distance and phase drift step for the proposed dirty constellation, respectively, and x φ is a random initial phase, which does not change when the covert symbol is in progress. Steganographic information is created by combining (adding) two successive K cover symbols with successive covert message symbols (i.e., vectors k y ). An example of creating hidden information for a single covert symbol and 3 K = is presented in Figure 2. Possible phase increments correspond to the M-ary DCM. As a result, we receive new constellation points in the following form: where l A and l θ mean the amplitude and phase of the new point in the constellation relative to the origin of the IQ coordinate system, respectively, which is depicted in Figure  3. Possible phase increments correspond to the M-ary DCM. As a result, we receive new constellation points in the following form: where A l and θ l mean the amplitude and phase of the new point in the constellation relative to the origin of the IQ coordinate system, respectively, which is depicted in Figure 3.  The parameters l A and l θ are limited by the following relationships: , Equations (5) and (6)   The parameters A l and θ l are limited by the following relationships: Equations (5) and (6)  The proposed approach allows us to better hide the steganographic channel than the method based on the dirty constellation shown in [30]. This is possible thanks to the random initial phase ϕ x , the adaptive selection of the centroid distance A m and the phase drift step ϕ m . In the general case, the parameters A m and ϕ m could also be random within defined ranges. An example of the phase drift-based dirty constellation for long bit strings is presented in Figure 4.
Equations (5) and (6)  The proposed approach allows us to better hide the steganographic channel than the method based on the dirty constellation shown in [30]. This is possible thanks to the random initial phase , x φ the adaptive selection of the centroid distance m A and the phase drift step m φ . In the general case, the parameters m A and m φ could also be random within defined ranges. An example of the phase drift-based dirty constellation for long bit strings is presented in Figure 4. The transceiver (transmitter-receiver) system is shown in Figure 5. This approach is similar to the framework of wireless covert channel proposed in [31] (Figure 4, p. 5). The transceiver (transmitter-receiver) system is shown in Figure 5. This approach is similar to the framework of wireless covert channel proposed in [31] (Figure 4, p. 5). In the transmitter system, the fixed phase drift is added to the cover constellation obtained at the output of the QAM modulator. The DCM mapper is used to assign vector . k y After putting together vector k y with carrier constellation points , n x the transmission adopts the steganographic form. In the receiver system, if necessary, the detection of the overt signal (cover) is performed using a traditional QAM demodulator. By contrast, information from the covert channel is received by using the so-called DCM demapper. In the first instance, this system determines the residual signal, which is the difference between the constellation points of the carrier and the received signal, ˆ. k y In more detail, it is an assigned complex vector k y with error k e caused by the signal transmission through the radio channel In the transmitter system, the fixed phase drift is added to the cover constellation obtained at the output of the QAM modulator. The DCM mapper is used to assign vector y k . After putting together vector y k with carrier constellation points x n , the transmission adopts the steganographic form.
In the receiver system, if necessary, the detection of the overt signal (cover) is performed using a traditional QAM demodulator. By contrast, information from the covert channel is received by using the so-called DCM demapper. In the first instance, this system determines the residual signal, which is the difference between the constellation points of the carrier and the received signal,ŷ k . In more detail, it is an assigned complex vector y k with error e k caused by the signal transmission through the radio channel whereÂ m andφ m are the amplitude and phase of the covert symbols in the received signal. The DCM demodulator performs the phase angle scanning procedure. In this case, based on the knowledge of the possible angle ϕ m values used in the steganographic transmitter, it calculates the U m values for each ϕ m as follows The maximum value of the module U m for a given ϕ m (m = 1, 2, . . . , M) corresponds to the assigned symbol of the covert information. It is worth noting that according to Equation (8), the value K can be treated as the number of averages performed for a single covert symbol. By providing coherent averaging [34] of the hidden subsymbols, we obtain an increase in the detection gain of covert transmissions according to [33]. The multiplexing use of the hidden symbols may increase the effectiveness of its correct detection. In a similar way, the oversampling application of various credit-related datasets significantly improves the performance of a credit default prediction model presented in [47].

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 6.5.2.2-1, 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 Simmons [49] we may use the scheme of a moving observer [50] to assess the detection. In this model, Alice, Wendy, and Bob correspond to the steganographic source (SS), observer (Ob), and steganographic receiver (SR), respectively. Figure 6 illustrates the analyzed scenario.
Instead of determining the statistical values of the signal at the receiver input by using the classic prisoner problem proposed by Simmons [49] we may use the scheme of a moving observer [50] to assess the detection. In this model, Alice, Wendy, and Bob correspond to the steganographic source (SS), observer (Ob), and steganographic receiver (SR), respectively. Figure 6 illustrates the analyzed scenario. 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 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 ϕ 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., ϕ m takes four values according to Equation (3) . Figures 7-11 show the impact of random A m and ϕ 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%. In real conditions, i.e., EVM > 0, masking the steganographic information is increasing. So, we can see that thanks to the random parameters A m and ϕ x , the distributions of the constellation points in the planes of the IQ quadrature components converge to the Gaussian distributions. Additionally, a real radio channel masks the presence of a covert channel, which is well illustrated by Figures 10 and 11. In these cases, we assume that the energy per bit to noise power spectral density ratio, E b /N 0 , for the signal cover is equal to 20 dB. It is worth emphasizing that the initial phase ϕ x has no influence on the resulting bit rate of the covert channel and the obtained BER, but it has a masking function. 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

Simulation Analysis of Dirty Constellations
Based on simulation studies, we compared our solution with the dirty constellation method presented in [30]. In this case, we assumed that the number K of averaging in the DCM modulator corresponds to the number of covert symbols per carrier symbol (SPS) in [30], the cover is the 4 QAM signal, and M = 4. For easier comparison, we additionally assumed that the centroid distance A m and the radius r of covert information dispersion in [30] remain constant. Figure 12 depicts the obtained comparison results of the transmission capabilities of the covert channels and the effect of the covert channels on the carrier QAM signals for EVM = 3%.
The transmission rate obtained for the covert channel is directly related to the number of symbols transmitted by the cover. Assuming the same value of the cover and steganographic information, K-fold averaging or given SPS brings about a K-fold reduction in the number of symbols transmitted over the covert channel. EVM at the level of 3% does not cause any noticeable deterioration of cover properties. In the proposed solution, compared to [30] higher numbers of averages need to be used to obtain similar BER levels for a covert channel.
Introducing random A m reduces the level of energy per symbol of transmitted covert information, which means that it is necessary to increase the number of averages to provide the assumed BER level. An example for such a case (i.e., random A m ) was presented in Figures 13-16. The cover is provided by 4 QAM, and M = 4. In Figure 13, we show BER versus SNR for different K and EVM = 3%. Figure 14 illustrates EVM versus SNR for the carrier signal and covert channel (K = 30), whereas Figures 15 and 16 depict the constellations and histograms for K = 30, EVM = 3%, SNR > 50 dB and SNR = 38 dB, respectively.
The simulation studies carried out showed that the increase in the number K of averages ensures the BER reduction for a given SNR. On the other hand, introducing the covert information using the proposed approach did not significantly increase the EVM. The difference of a few percent is visible only for SNR > 20 dB. However, in this case, EVM < 8%. The obtained constellations and histograms show that for good transmission quality (i.e., SNR = 38 dB and SNR > 50 dB), the randomness of the centroid distance ensures the undetectability of the proposed method using statistical steganalysis.

Simulation Analysis of Dirty Constellations
Based on simulation studies, we compared our solution with the dirty constellation method presented in [30]. In this case, we assumed that the number K of averaging in the DCM modulator corresponds to the number of covert symbols per carrier symbol (SPS) in [30], the cover is the 4 QAM signal, and 4.

M =
For easier comparison, we additionally assumed that the centroid distance m A and the radius r of covert information dispersion in [30] remain constant. Figure 12 depicts the obtained comparison results of the transmission capabilities of the covert channels and the effect of the covert channels on the carrier QAM signals for EVM = 3%. The transmission rate obtained for the covert channel is directly related to the number of symbols transmitted by the cover. Assuming the same value of the cover and steganographic information, K-fold averaging or given SPS brings about a K-fold reduction in the number of symbols transmitted over the covert channel. EVM at the level of 3% does not cause any noticeable deterioration of cover properties. In the proposed solution, compared to [30] higher numbers of averages need to be used to obtain similar BER levels for a covert channel.
Introducing random m A reduces the level of energy per symbol of transmitted covert information, which means that it is necessary to increase the number of averages to

Hardware Implementation
The concept of the phase drift-based dirty constellation was implemented by using the Universal Software Radio Peripheral (USRP) hardware platform manufactured by National Instruments (NI, Austin, TX, USA). In this case, we used the USRP-2920 model. USRP was the essential hardware part for generating a radio signal, while the software part was provided by the LabView software with MATLAB scripts installed on a personal computer (PC). An Ethernet network adapter with a bit rate of 1 Gb/s was used to provide communication between the USRP platforms and PC via a switch. Two USRP-2920 were used to implement a test-bed for detectors in the transmitter-receiver system. The prepared test-bed was placed in an office room. The distance between the transmitter and receiver was 5 m. This configuration is illustrated in Figure 17. The parameters of the carrier signal and covert information are presented in Table 2.
Electronics 2021, 10, x FOR PEER REVIEW 17 of 22 The concept of the phase drift-based dirty constellation was implemented by using the Universal Software Radio Peripheral (USRP) hardware platform manufactured by National Instruments (NI, Austin, TX, USA). In this case, we used the USRP-2920 model. USRP was the essential hardware part for generating a radio signal, while the software part was provided by the LabView software with MATLAB scripts installed on a personal computer (PC). An Ethernet network adapter with a bit rate of 1 Gb/s was used to provide communication between the USRP platforms and PC via a switch. Two USRP-2920 were used to implement a test-bed for detectors in the transmitter-receiver system. The prepared test-bed was placed in an office room. The distance between the transmitter and receiver was 5 m. This configuration is illustrated in Figure 17. The parameters of the carrier signal and covert information are presented in Table 2.  The results of the experimental research are presented in Figures 18 and 19. In this case, we determined a probability density function (PDF) of EVM and BER versus EVM graphs for two considered K values (see Figure 18). The distribution of the EVM was estimated by using a normalized histogram (see Figure 19).  The results of the experimental research are presented in Figures 18 and 19. In this case, we determined a probability density function (PDF) of EVM and BER versus EVM graphs for two considered K values (see Figure 18). The distribution of the EVM was estimated by using a normalized histogram (see Figure 19).
The carrier constellation is subject to distortions caused by propagation phenomena and impairments introduced by the transceiver systems. We may see that the covert signal detectability reduces if the carrier distortion (i.e., EVM) increases. Tests were performed for two average values: K = 10 and K = 25. As expected, increasing the number of averages provides the increase in the covert signal detectability. On the other hand, the transmission rate decreases.  The carrier constellation is subject to distortions caused by propagation phenomena and impairments introduced by the transceiver systems. We may see that the covert signal detectability reduces if the carrier distortion (i.e., EVM) increases. Tests were performed for two average values: 10 K = and 25.

K =
As expected, increasing the number of averages provides the increase in the covert signal detectability. On the other hand, the transmission rate decreases.
Based on the PDF of EVM, we can conclude that for the analyzed 4 QAM and 0.05 , m n A A = ⋅ the average EVM oscillates between 8%-12%. Comparing this value with  The carrier constellation is subject to distortions caused by propagation phenomena and impairments introduced by the transceiver systems. We may see that the covert signal detectability reduces if the carrier distortion (i.e., EVM) increases. Tests were performed for two average values: 10 K = and 25.

K =
As expected, increasing the number of averages provides the increase in the covert signal detectability. On the other hand, the transmission rate decreases.
Based on the PDF of EVM, we can conclude that for the analyzed 4 QAM and 0.05 , m n A A = ⋅ the average EVM oscillates between 8%-12%. Comparing this value with Based on the PDF of EVM, we can conclude that for the analyzed 4 QAM and A m = 0.05 · A n , the average EVM oscillates between 8-12%. Comparing this value with Table 1, we can expect good transmission quality. On the other hand, increasing the distance between the transmitter and receiver will degrade the transmission quality due to the influence of the propagation conditions occurring in the radio channel. Hence, the adaptive selection of the parameters of the developed method depending on the propagation conditions will determine its future usefulness.

Conclusions
In this paper, we presented the novel dirty modulation method based on the phase drift, which is intended to create covert channels in radio transmissions using the N-ary PSK or QAM modulations. The method is based on the DCM approach that was previously used to watermark audio signals. In the proposed solution, a random change of the dirty constellation parameters is possible. It ensures its greater resistance to detection. On the other hand, it is possible to adapt these parameters to the modulation type and propagation conditions in the current radio channel.
In the paper, we described the idea of dirty modulation and developed a solution. Next, we introduced the criteria of the covert channel evaluation. Based on BER and EVM, we analyzed the proposed method using simulation studies and practical implementation, including comparison with other solutions. The obtained results showed that our dirty modulation method could be a valuable supplement to the existing steganographic methods.
In the near future, we want to focus on developing an adaptive method of selecting dirty modulation parameters, including the centroid distance and phase drift step, as well as multiple repetitions, i.e., averaging of secret transmission subsymbols. This will increase the undetectability of the proposed method. We also consider the effectiveness of this method in the case of additional use of the OFDM signal. Additionally, practical implementation of the method in the wireless part of the SDN within the aforementioned SOFTANET project is planned. In the near future, we want to implement ML algorithms (e.g., [39,40,47]) to increase the detection correctness of secret transmissions. These algorithms can be also used for time-variant selection of the developed dirty constellation parameters to improve their undetectability via various steganalysis techniques.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to project restrictions.

Acknowledgments:
The authors would like to express their great appreciation to the Electronics journal editors and anonymous reviewers for their valuable suggestions, which have improved the manuscript quality.

Conflicts of Interest:
The authors declare no conflict of interest.