# Detection of Constellation-Modulated Wireless Covert Channel Based on Adjusted CNN Model

Authors: Shuhua Huang; Weiwei Liu; Guangjie Liu; Yuewei Dai; Huiwen Bai
Journal: Security and Communication Networks
 (2021)

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## Abstract

With the development of wireless communication technology, more and more information leakage is realized through a wireless covert channel, which brings great challenges to the security of wireless communication. Compared with the wireless covert channel on the upper layer, the wireless covert channel based on the physical layer (WCC-P) has better concealment and greater capacity. As the most widely used scheme of WCC-P, the wireless covert channel with the modulation of the constellation point (WCC-MC) has attracted more and more attention. In this paper, a deep learning scheme based on amplitude-phase characteristics is proposed to detect and classify the WCC-MC scheme. We first extract the amplitude and phase characteristic of error vector magnitude (EVM) and constellation points and then map the amplitude and phase characteristic to the grayscale image, respectively. Finally, the generated feature images are trained, detected, and classified with the adjusted convolution neural network. The experimental results show that the detection accuracy of our proposed scheme can reach 98.5%, and the classification accuracy can reach 81.7%.


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## Body

## 1. Introduction

A covert channel is considered a technique for secretly transmitting information from a malicious entity to other entities. In the wireless covert channel communication model, there are one transmitter and one receiver. The transmitter sends a wireless signal embedded with hidden information to the receiver via the broadcast media. The receiver decodes the hidden information by the rule shared with the transmitter. Wireless covert channel (WCC) is more capable of realizing the purpose of covert communication because of its unique broadcasting characteristics. Although there have been recent research efforts on detecting covert timing channels over the Internet [1–5]. Research on the detection of WCC is currently relatively rare, mainly divided into two types, one is the detection for wireless covert channel based on upper layer protocol (WCC-U), and the other is for wireless covert channel based on the physical layer (WCC-P).WCC-U scheme realizes the information leakage mainly through embedded secret information in the redundant position in the wireless protocol; this kind of covert channel can be detected through the analysis of upper layer protocol and firewall. The realization of the WCC-P covert channel is mainly through the modulation of the physical layer signal, such as modulation of the characteristic parameter (WCC-MP) [6, 7], the modification of Orthogonal Frequency Division Multiplexing symbols (WCC-MO) [8–11], and the modulation of the constellation point (WCC-MC) [12, 13]. The correlation of the time domain signal [14] is used to realize the effective detection of the WCC-MP signal [6]. WCC-MO scheme is constrained by Orthogonal Frequency Division Multiplexing (OFDM) structure and can be detected by numerical statistics [9]. There are little researches on WCC-MC detection due to the randomness of the physical layer (such as channel fading and receiver noise) making the WCC-MC scheme more difficult to crack. In [12], the concealment of the WCC-MC signal is measured by using the characteristics of Kolmogorov–Smirnov (K-S) distance, Kullback–Leibler (K-L) Divergence, and regularity of the constellation point. However, there is no quantitative analysis of the detection accuracy, and no effective detection scheme for the WCC-MC signal is proposed. It is increasingly difficult to identify wireless covert channel hiding techniques used constellation modulation in this era of great advancement in technology.With the development of wireless physical layer covert channels, secret information and even confidential information are at risk of leakage. When hiding information on upper layers, only a few changes are possible, and firewalls can easily detect most types of changes. In contrast, WCC-P schemes [15, 16] contain a high amount of noise and random signal variations. These make the wireless covert channel easier to implement, and this covert channel has a low probability of detection (LPD) [17–20]. This paper concerns the problem of detecting the WCC-MC covert channel, which is an important component of the WCC-P covert channel. Such detection scheme can be used to detect information leakage behavior caused by WCC-MC schemes.The detection scheme based on deep learning has achieved good results in many fields. Convolutional Neural Network (CNN), as one of the representative algorithms of deep learning, is widely used in image processing problems. It excels in many aspects such as target recognition, speech recognition, and natural language processing. The CNN has the characteristics of local perception, weight-sharing, and subsampling, which can achieve higher performance at a lower cost. In deep learning, the convolutional neural network (CNN) [21] plays a leading role in dealing with problems related to vision. The modern structure of CNNs was firstly introduced in [22] and refined in [23, 24]. Researchers improved it and designed a multilayer artificial neural network LeNet-5, which has excellent applications for handwritten digit classification [25]. To the best of our knowledge, this model is not used before for the WCC-MC signal detection.The purpose of this paper is to detect and classify WCC-MC signals. We convert the amplitude-phase characteristics of EVM signal and constellation points into the EVM grayscale feature image and constellation feature image. These feature images are used for deep learning model training and detection. Under different channel noise intensities, the adjusted convolutional neural network (CNN-T) is used to train and classify legitimate communication signals and WCC-MC communication signals with different embedding rates, based on the difference between the constellation diagrams of legitimate communication and covert communication. Dutta et al. [13] proposed a WCC-MC scheme with a dirty constellation (WCC-DC) that uses existing modulation schemes of OFDM. The covert messages are hidden within “dirty” constellations that mimic noise commonly imposed by hardware imperfections and channel conditions. In this paper, we use the proposed scheme for detecting and classifying WCC-DC communication signal, which is difficult to detect in the WCC-MC schemes, to verify the effectiveness of the scheme. This paper’s contributions can be summarized as follows:(1)
A detection and classification scheme is proposed for WCC-MC signal based on deep learning, which uses the amplitude and phase characteristics of EVM and constellation points.(2)
The amplitude-phase characteristics of EVM signal and constellation points will be converted into grayscale feature images. The input layer of the CNN-T network is adjusted to train and test the EVM feature image and the constellation feature image at the same time.(3)
In this paper, the legitimate communication signal and covert signal are collected at the platform of software radio, and the proposed scheme is used to effectively detect and classify the WCC-MC signal.The remainder of the paper is structured as follows. Section2 introduces the background and related work for our work. Section 3 describes characteristic extraction, CNN design, and detection process. Section 4 shows the simulation and experiment results of applying our scheme and the advantages of our algorithm compared to other schemes. Section 5 concludes the paper and discusses directions for our future work.


## 2. Background and Related Work

This section first detailed introduces the WCC-DC covert channel to be detected in this paper. Then, we summarize the existing covert channel detection schemes.


### 2.1. Wireless Covert Channel with Dirty Constellation

Wireless covert channels are an existing technology used to hide and leak information through wireless networks [26]. Because the ubiquitous wireless devices and wireless communication signals make the wireless covert communication possible, the wireless covert channel attracts more and more attention. In the WCC-MC communication schemes, the secret message bit can be transmitted as the constellation error of legitimate signal to realize the transmission of secret information. Dutta et al. [13] used a more straightforward technique that uses existing modulation schemes of OFDM.The information is hidden within “dirty” constellations that mimics noise commonly imposed by hardware imperfections and channel conditions. The hidden information is embedded in the covert subcarriers by modifying the position of the constellation points at the transmitter. For the uninformed user, the secret constellation points will be treated as random channel noise. Taking Quadrature Phase Shift Keying (QPSK) modulation as an example, the legitimate constellation modulation is shown in Figure1(a).Figure 1
The constellation points of legitimate and WCC-DC signal. (a) Legitimate signal. (b) WCC-DC signal.
(a)(b)For the covert subcarriers, the mapping sequence bits are checked after the hidden information is modulated by the QPSK constellation. The mapping sequence bits shared between the transmitter and receiver are used to select the appropriate mapping for covert and cover subcarriers. To embed the hidden information, the positions of the constellation points for the covert subcarriers are modified. Figure2(b) corresponds to the upper right quadrant of the constellations of the QPSK constellation shown in Figure 2(a). Firstly, the constellation points are moved from the original position to the red dot according to the hidden information. As shown in Figure 2(b), the dispersion of covert constellation points is limited to a radius of θ, which is a distance equal to that of a 64 Quadrature Amplitude Modulation (64QAM) constellation. The red dot represents the initial covert constellation point and the constellation points are modulated to the blue dot by rotating the axis. The rotation is performed with a monotonically increasing rotation angle θ; the transmitter and receiver both start with θ=0° at the start of the packet and increment θ for each covert subcarrier.Figure 2
The WCC-MC signal detection framework architecture.For the cover subcarriers, the random noise (Meet Gaussian distribution in the in-phase and quadrature (I/Q) vectors) is added to the original constellation points. To make the modulation points of the secret information closer to hardware imperfections and channel conditions and avoid sudden changes in the modulation characteristics.


### 2.2. Wireless Covert Channel Detection Approaches

The purpose of covert channel detection is to distinguish covert communication signals from legitimate communication signals. However, as far as we know, there is no special work to realize the detection of the WCC-MC signal. In the field of signal analysis, the difference between two signals can be measured in the frequency domain and time domain. Kolmogorov–Smirnov (K-S) test [12] and regularization test [2] in the wireless covert channel are proposed to measure the difference between covert and cover signals from the aspect of distribution characteristics. The correlation of the time domain signal [14] is used to realize the effective detection of the WCC-MP signal. The detection of the covert channel is realized mainly by studying the time sequence of communication signal arrival and the temporal correlation of signal. In [2], the author uses a flat metric of a standard deviation metric to determine the existence of a covert timing channel. On the other hand, the author uses entropy as a measure in [27] to detect covert timing channels. Entropy provides important evidence for the existence of patterns within the data, the presence of signals with high probability in covert channels.In general, the detection of covert channels uses statistical tests to differentiate covert traffic from legitimate traffic. These include standard deviation, mean, entropy, regularity, and median. In the current literature, the support vector machine (SVM) [28, 29] has been viewed as an efficient and stable scheme for covert channel classification tasks. SVM attempts to separate different types of data by learning the best decision hyperplane which best separates training samples in the high-dimensional feature space (implemented with different kernel functions). Neural networks (NN), such as multilayer perceptron (MLP) [30, 31] neural networks, have already been investigated for the classification of remote sensing data.


## 2.1. Wireless Covert Channel with Dirty Constellation

Wireless covert channels are an existing technology used to hide and leak information through wireless networks [26]. Because the ubiquitous wireless devices and wireless communication signals make the wireless covert communication possible, the wireless covert channel attracts more and more attention. In the WCC-MC communication schemes, the secret message bit can be transmitted as the constellation error of legitimate signal to realize the transmission of secret information. Dutta et al. [13] used a more straightforward technique that uses existing modulation schemes of OFDM.The information is hidden within “dirty” constellations that mimics noise commonly imposed by hardware imperfections and channel conditions. The hidden information is embedded in the covert subcarriers by modifying the position of the constellation points at the transmitter. For the uninformed user, the secret constellation points will be treated as random channel noise. Taking Quadrature Phase Shift Keying (QPSK) modulation as an example, the legitimate constellation modulation is shown in Figure1(a).Figure 1
The constellation points of legitimate and WCC-DC signal. (a) Legitimate signal. (b) WCC-DC signal.
(a)(b)For the covert subcarriers, the mapping sequence bits are checked after the hidden information is modulated by the QPSK constellation. The mapping sequence bits shared between the transmitter and receiver are used to select the appropriate mapping for covert and cover subcarriers. To embed the hidden information, the positions of the constellation points for the covert subcarriers are modified. Figure2(b) corresponds to the upper right quadrant of the constellations of the QPSK constellation shown in Figure 2(a). Firstly, the constellation points are moved from the original position to the red dot according to the hidden information. As shown in Figure 2(b), the dispersion of covert constellation points is limited to a radius of θ, which is a distance equal to that of a 64 Quadrature Amplitude Modulation (64QAM) constellation. The red dot represents the initial covert constellation point and the constellation points are modulated to the blue dot by rotating the axis. The rotation is performed with a monotonically increasing rotation angle θ; the transmitter and receiver both start with θ=0° at the start of the packet and increment θ for each covert subcarrier.Figure 2
The WCC-MC signal detection framework architecture.For the cover subcarriers, the random noise (Meet Gaussian distribution in the in-phase and quadrature (I/Q) vectors) is added to the original constellation points. To make the modulation points of the secret information closer to hardware imperfections and channel conditions and avoid sudden changes in the modulation characteristics.


## 2.2. Wireless Covert Channel Detection Approaches

The purpose of covert channel detection is to distinguish covert communication signals from legitimate communication signals. However, as far as we know, there is no special work to realize the detection of the WCC-MC signal. In the field of signal analysis, the difference between two signals can be measured in the frequency domain and time domain. Kolmogorov–Smirnov (K-S) test [12] and regularization test [2] in the wireless covert channel are proposed to measure the difference between covert and cover signals from the aspect of distribution characteristics. The correlation of the time domain signal [14] is used to realize the effective detection of the WCC-MP signal. The detection of the covert channel is realized mainly by studying the time sequence of communication signal arrival and the temporal correlation of signal. In [2], the author uses a flat metric of a standard deviation metric to determine the existence of a covert timing channel. On the other hand, the author uses entropy as a measure in [27] to detect covert timing channels. Entropy provides important evidence for the existence of patterns within the data, the presence of signals with high probability in covert channels.In general, the detection of covert channels uses statistical tests to differentiate covert traffic from legitimate traffic. These include standard deviation, mean, entropy, regularity, and median. In the current literature, the support vector machine (SVM) [28, 29] has been viewed as an efficient and stable scheme for covert channel classification tasks. SVM attempts to separate different types of data by learning the best decision hyperplane which best separates training samples in the high-dimensional feature space (implemented with different kernel functions). Neural networks (NN), such as multilayer perceptron (MLP) [30, 31] neural networks, have already been investigated for the classification of remote sensing data.


## 3. Methodology

This section describes the details of the designed framework as well as the methods used aiming at detecting and classifying the WCC-MC signal.


### 3.1. Framework Architecture

The proposed framework is shown in Figure2. We propose a three-stage approach to detect and classify the WCC-P signal based on the amplitude-phase feature images and adjusted CNN. The first block is traffic preprocessing, including the EVM generation and SNR estimate. Without further processing, the generated EVM data is fed to the next block for amplitude-phase feature image generation. During feature image generation, the EVM amplitude-phase feature image and constellation amplitude-phase feature image are generated with the EVM signal. Then these feature images will be subject to statistical computations which will be fed to the final block (deep neural network) for training/testing purposes and eventually WCC-MC signal classification (detection). In the rest of this section, we describe in detail the process for WCC-MC detection.


### 3.2. WCC-MC Signal Detection Process

This process starts with the collection of a large number of data streams between the transmitter and receiver entities. Following the step, a flow set is created based on different channel noise intensity, which contains legitimate communication signals and covert communication signals under different embedding rates. Each flow is then divided into small subflows; each one hasN constellation points. The constellation points are converted into EVM amplitude-phase feature image and adjusted constellation amplitude-phase feature image. Finally, the feature images are fed to the deep neural network which trains the model and tests the performance of that model.


### 3.3. Traffic Preprocessing

In this paper, we assume that the detector can demodulate the cover message. As shown in Figure3, The EVM signal can be expressed as(1)EVM=RI+j⋅RQ−DI+j⋅DQ=EI+j⋅EQ,where RI+j⋅RQ is the received constellation points and DI+j⋅DQ is the QPSK demodulation result of the communication signal.Figure 3
Schematic diagram of receiving constellation diagram converted to EVM constellation diagram.Besides, considering the received constellation points, there will be a small number of constellation points with large deviation; we will exclude these points in EVM statistics of constellation points. We select the circular region as shown in Figure4, so that the constellation points that fall in the box account for 99% of the total constellation points and discard the other 1% possible error signals.Figure 4
Selection of constellation points for EVM computing.Due to the different signal-to-noise ratios (SNRs), the EVM signals received by the detector are significantly different, which leads to the amplitude-phase characteristic difference of the constellation points generated under different SNR conditions even for the legitimate communication signals. Therefore, we need to train the samples under different SNR conditions in the CNN training process. We can estimate the signal-to-noise ratio of EVM signal by the following equation:(2)psnr=round10∗lgN∑i=1NEVMi2,where N is the number of EVM data. round⋅ is the nearest integer function. A small error of SNR has little influence on the feature images. To facilitate statistics, we do a rounding operation when estimating SNR.


### 3.4. Gray Scale Image Generation

For the scheme of wireless covert communication based on constellation modulation, there is a difference between the amplitude-phase characteristic of covert communication and that of legitimate communication due to the regular change of constellation points in the process of modulation. For the WCC-MC scheme, the secret messages are embedded by moving the legitimate constellation points regularly, so that there are constellation points with certain distribution around the legitimate constellation points. In this paper, we use a certain distribution to implement WCC-MC detection through a deep learning network, although these distributions will be weakened in the process of wireless signal transmission. The difference between legitimate communication and WCC-MC communication is mainly reflected in the amplitude and phase of constellation points. To extract the distribution characteristics of the constellation diagram, we convert the received constellation diagram into the EVM constellation diagram and the adjusted constellation diagram to generate amplitude-phase feature images, respectively.


#### 3.4.1. EVM Constellation Diagram Amplitude-Phase Characteristic Extraction

For the amplitude characteristics, the EVM signal can be defined as the difference between the actual observed constellation point and the ideal constellation point in the process of wireless communication. The dispersion degree of the EVM signal in the covert constellation is different from that in the legitimate constellation due to the movement of constellation points with the WCC-MC scheme. The amplitude and phase values of the EVM signal are extracted with(3)ri=|realevmi|2+|imagevmi|2,(4)φi=arctanimagevmirealevmi,where real⋅ represents the real value extractor; imag⋅ represents the imaginary value extractor; ri is the amplitude value of constellation point, and φi is the phase value of constellation point. We use the phase as abscissa and the amplitude as ordinate to establish a phase-amplitude coordinate system. As shown in Figure 5, the EVM constellation points in the rectangular coordinate system are transferred to the phase-amplitude coordinate system.Figure 5
The amplitude and phase values extraction of EVM signal.In this paper, QPSK modulation is taken as an example to extract EVM signal, which is the same as that of other modulation schemes. The phase-amplitude coordinate in the range is divided into32×32 small areas, the size of each small area is maxΦ/32×maxR/32. The number of constellation coordinates in each region is counted and normalized to obtain a characteristic matrix N. nij=eij/maxE∈N is the element of the characteristic matrix, where i,j=1,2,…,32 and eij∈E is the number of constellation points in the small area in row i and column j.


#### 3.4.2. Adjusted Constellation Diagram Amplitude-Phase Characteristic Extraction

In this section, we analyze the amplitude and phase characteristics of the adjusted constellation points. As shown in Figure6, we add a fixed signal 2/2+j⋅2/2 to the EVM signal; it is equivalent to transferring the received constellation diagram to the first quadrant. The amplitude and phase values of adjusted constellation points are extracted with (5)di=|realevmi+22|2+|imagevmi+22|2,(6)θi=arctanimagevmi+2/2realevmi+2/2.Figure 6
The amplitude and phase values extraction of adjusted constellation points.Similar to the amplitude and phase values extraction of EVM signal, the adjusted constellation points in the rectangular coordinate system are transferred to the phase-amplitude coordinate system. The phase-amplitude coordinate in the range is divided into32×32 small areas (the size of each small area is maxΘ/32×maxD/32) to get the normalized characteristic matrix M. mij=aij/maxA is the element of the characteristic matrix M, where i,j=1,2,…,32 and aij∈A is the number of constellation points in the small area in row i and column j.


#### 3.4.3. Amplitude-Phase Feature Image Generation

As shown in Figure7, the two different grayscale image samples formed by gray-scale mapping of the wireless signal of the physical layer are obtained, and the two grayscale images are used for training and testing of the network model.Figure 7
The amplitude and phase values extraction of adjusted constellation points.
(a)(b)To classify wireless signals using constellation characteristics, we transform the constellation characteristics into32×32 pixel gray images according to the image format. We deal with each element in the characteristic matrix corresponding to a normalized gray pixel value in the image.


### 3.5. Detection and Classification with Adjusted CNN

CNN was originally used for image classification and recognition because its structure is very suitable for extracting pixel-level characteristics from 2D images. Therefore, CNN can extract complex characteristics automatically by the convolution layer containing multiple filters. The CNN-T used in this paper is shown in Figure8.Figure 8
The architecture of the proposed CNN-T classifier.The input layer is the data front end of the whole neural network, that is, the image to be trained. The input layer images are processed to a size of32×32; the preprocessed images are shown in Section 3.4 which includes the EVM feature image and adjusted constellation feature image. The number of each type of image in each input layer can be adjusted, and the adjustment parameter is called batch size. In our experiment, we set the batch size to 128; that is, 128 EVM feature image and 128 adjusted constellation feature image are input each time for training, mainly for two reasons: (1) the memory of the machine can be used reasonably; (2) the algorithm converges within the set number of iterations. Besides, the time complexity is optimal [32, 33].The convolution layer is the local perception characteristic of the image, which is the characteristic perception of each part of the image, and then carries out a higher-level comprehensive operation to obtain the global information. The purpose of this operation, as shown in (7), is to reduce the calculation parameters of the model:(7)zi,jl,t=∑i=1m∑j=1nxi:i+p,j:j+qt⊙kl,1≤l≤L2,∑i=1m∑j=1nyi:i+p,j:j+qt⊙kl,L2<l≤L,where t=1,2,…,T, T represents the batch size; l=1,2,…,L, L represents the number of the filter; zi,jl,t is the (i, j) element of the l-th feature map with the size of m×n for the t-th group feature maps; kl is the convolution kernel coefficient of the l-th filter with the size of p×q; x represents the grayscale value of the EVM feature image; and y represents the grayscale value of the adjusted constellation feature image.The pooling layer is mainly used for feature dimension reduction, compressing the number of data and parameters, reducing overfitting, and improving the fault tolerance of the model. The algorithm is shown as(8)Du,vl,t=du−1∗g+1,v−1∗h+1l,t⋯du−1∗g+1,v∗hl,t⋮⋱⋮du∗g,v−1∗h+1l,t⋯du∗g,v∗hl,t,(9)pu,vl,t=averageDu,vl,twhere dl,t=σzl,t is the input of pooling layer, pl,t is the output, and g×h is the size of pooling size.The full connection and softmax layer play the role of “Classifier” in the whole convolutional neural network. Each node of the full connection layer is connected with each node of the upper layer, which integrates the output characteristics of the previous layer. The algorithm for this step is(10)o1,1⋯o1,T⋮⋱⋮on,1⋯on,T=W11⋯W1m⋮⋱⋮Wn1⋯Wnm∗h1,1⋯h1,T⋮⋱⋮hm,1⋯hm,T+b1⋮bn,(11)a1,1⋯a1,T⋮⋱⋮an,1⋯an,T=expo1,1∑i=1nexpoi,1⋯expo1,T∑i=1nexpoi,T⋮⋱⋮expon,1∑i=1nexpoi,1⋯expon,T∑i=1nexpoi,T,where h is the input of the full connection layer, a is the output of the softmax layer and W and b represent the weight value and bias value.The backpropagation algorithm [34] can be divided into two parts: error calculation and parameter gradient calculation. For the feature map generated by each layer, we calculate an error to show the difference between the result calculated by this layer and the correct result it should give. For the feature map generated by each layer, we calculate an error to show the difference between the result calculated by each layer and the desired result it should give. The errors of all layers are as follows:(12)ΔSp,q=ap,q−yp,q,(13)ΔPu,vl,t=resampleWT∗ΔS,(14)ΔKi,jl,t=upsampleΔP⊙σ′zi,jl,t,where ΔS is the error of softmax layer, ΔP is pooling layer, and ΔK is convolution layer.The parameter gradients of all layers are as follows:(15)Wd_grad=1TΔS∗hT,(16)bd_grad=1T∑q=1TΔSp,q,(17)Wc_gradl=1T∑t=1Tx⊗ROT180ΔKi,jl,t,1≤l≤L2,1T∑t=1Ty⊗ROT180ΔKi,jl,t,L2<l≤L,(18)bc_gradl=1T∑t=1T∑i,jΔKi,jl,t,where Wd_grad and bd_grad are the gradients of weight and bias for full connection layer and Wc_grad and bc_grad are the gradients of weight and bias for convolution layer.


## 3.1. Framework Architecture

The proposed framework is shown in Figure2. We propose a three-stage approach to detect and classify the WCC-P signal based on the amplitude-phase feature images and adjusted CNN. The first block is traffic preprocessing, including the EVM generation and SNR estimate. Without further processing, the generated EVM data is fed to the next block for amplitude-phase feature image generation. During feature image generation, the EVM amplitude-phase feature image and constellation amplitude-phase feature image are generated with the EVM signal. Then these feature images will be subject to statistical computations which will be fed to the final block (deep neural network) for training/testing purposes and eventually WCC-MC signal classification (detection). In the rest of this section, we describe in detail the process for WCC-MC detection.


## 3.2. WCC-MC Signal Detection Process

This process starts with the collection of a large number of data streams between the transmitter and receiver entities. Following the step, a flow set is created based on different channel noise intensity, which contains legitimate communication signals and covert communication signals under different embedding rates. Each flow is then divided into small subflows; each one hasN constellation points. The constellation points are converted into EVM amplitude-phase feature image and adjusted constellation amplitude-phase feature image. Finally, the feature images are fed to the deep neural network which trains the model and tests the performance of that model.


## 3.3. Traffic Preprocessing

In this paper, we assume that the detector can demodulate the cover message. As shown in Figure3, The EVM signal can be expressed as(1)EVM=RI+j⋅RQ−DI+j⋅DQ=EI+j⋅EQ,where RI+j⋅RQ is the received constellation points and DI+j⋅DQ is the QPSK demodulation result of the communication signal.Figure 3
Schematic diagram of receiving constellation diagram converted to EVM constellation diagram.Besides, considering the received constellation points, there will be a small number of constellation points with large deviation; we will exclude these points in EVM statistics of constellation points. We select the circular region as shown in Figure4, so that the constellation points that fall in the box account for 99% of the total constellation points and discard the other 1% possible error signals.Figure 4
Selection of constellation points for EVM computing.Due to the different signal-to-noise ratios (SNRs), the EVM signals received by the detector are significantly different, which leads to the amplitude-phase characteristic difference of the constellation points generated under different SNR conditions even for the legitimate communication signals. Therefore, we need to train the samples under different SNR conditions in the CNN training process. We can estimate the signal-to-noise ratio of EVM signal by the following equation:(2)psnr=round10∗lgN∑i=1NEVMi2,where N is the number of EVM data. round⋅ is the nearest integer function. A small error of SNR has little influence on the feature images. To facilitate statistics, we do a rounding operation when estimating SNR.


## 3.4. Gray Scale Image Generation

For the scheme of wireless covert communication based on constellation modulation, there is a difference between the amplitude-phase characteristic of covert communication and that of legitimate communication due to the regular change of constellation points in the process of modulation. For the WCC-MC scheme, the secret messages are embedded by moving the legitimate constellation points regularly, so that there are constellation points with certain distribution around the legitimate constellation points. In this paper, we use a certain distribution to implement WCC-MC detection through a deep learning network, although these distributions will be weakened in the process of wireless signal transmission. The difference between legitimate communication and WCC-MC communication is mainly reflected in the amplitude and phase of constellation points. To extract the distribution characteristics of the constellation diagram, we convert the received constellation diagram into the EVM constellation diagram and the adjusted constellation diagram to generate amplitude-phase feature images, respectively.


### 3.4.1. EVM Constellation Diagram Amplitude-Phase Characteristic Extraction

For the amplitude characteristics, the EVM signal can be defined as the difference between the actual observed constellation point and the ideal constellation point in the process of wireless communication. The dispersion degree of the EVM signal in the covert constellation is different from that in the legitimate constellation due to the movement of constellation points with the WCC-MC scheme. The amplitude and phase values of the EVM signal are extracted with(3)ri=|realevmi|2+|imagevmi|2,(4)φi=arctanimagevmirealevmi,where real⋅ represents the real value extractor; imag⋅ represents the imaginary value extractor; ri is the amplitude value of constellation point, and φi is the phase value of constellation point. We use the phase as abscissa and the amplitude as ordinate to establish a phase-amplitude coordinate system. As shown in Figure 5, the EVM constellation points in the rectangular coordinate system are transferred to the phase-amplitude coordinate system.Figure 5
The amplitude and phase values extraction of EVM signal.In this paper, QPSK modulation is taken as an example to extract EVM signal, which is the same as that of other modulation schemes. The phase-amplitude coordinate in the range is divided into32×32 small areas, the size of each small area is maxΦ/32×maxR/32. The number of constellation coordinates in each region is counted and normalized to obtain a characteristic matrix N. nij=eij/maxE∈N is the element of the characteristic matrix, where i,j=1,2,…,32 and eij∈E is the number of constellation points in the small area in row i and column j.


### 3.4.2. Adjusted Constellation Diagram Amplitude-Phase Characteristic Extraction

In this section, we analyze the amplitude and phase characteristics of the adjusted constellation points. As shown in Figure6, we add a fixed signal 2/2+j⋅2/2 to the EVM signal; it is equivalent to transferring the received constellation diagram to the first quadrant. The amplitude and phase values of adjusted constellation points are extracted with (5)di=|realevmi+22|2+|imagevmi+22|2,(6)θi=arctanimagevmi+2/2realevmi+2/2.Figure 6
The amplitude and phase values extraction of adjusted constellation points.Similar to the amplitude and phase values extraction of EVM signal, the adjusted constellation points in the rectangular coordinate system are transferred to the phase-amplitude coordinate system. The phase-amplitude coordinate in the range is divided into32×32 small areas (the size of each small area is maxΘ/32×maxD/32) to get the normalized characteristic matrix M. mij=aij/maxA is the element of the characteristic matrix M, where i,j=1,2,…,32 and aij∈A is the number of constellation points in the small area in row i and column j.


### 3.4.3. Amplitude-Phase Feature Image Generation

As shown in Figure7, the two different grayscale image samples formed by gray-scale mapping of the wireless signal of the physical layer are obtained, and the two grayscale images are used for training and testing of the network model.Figure 7
The amplitude and phase values extraction of adjusted constellation points.
(a)(b)To classify wireless signals using constellation characteristics, we transform the constellation characteristics into32×32 pixel gray images according to the image format. We deal with each element in the characteristic matrix corresponding to a normalized gray pixel value in the image.


## 3.4.1. EVM Constellation Diagram Amplitude-Phase Characteristic Extraction

For the amplitude characteristics, the EVM signal can be defined as the difference between the actual observed constellation point and the ideal constellation point in the process of wireless communication. The dispersion degree of the EVM signal in the covert constellation is different from that in the legitimate constellation due to the movement of constellation points with the WCC-MC scheme. The amplitude and phase values of the EVM signal are extracted with(3)ri=|realevmi|2+|imagevmi|2,(4)φi=arctanimagevmirealevmi,where real⋅ represents the real value extractor; imag⋅ represents the imaginary value extractor; ri is the amplitude value of constellation point, and φi is the phase value of constellation point. We use the phase as abscissa and the amplitude as ordinate to establish a phase-amplitude coordinate system. As shown in Figure 5, the EVM constellation points in the rectangular coordinate system are transferred to the phase-amplitude coordinate system.Figure 5
The amplitude and phase values extraction of EVM signal.In this paper, QPSK modulation is taken as an example to extract EVM signal, which is the same as that of other modulation schemes. The phase-amplitude coordinate in the range is divided into32×32 small areas, the size of each small area is maxΦ/32×maxR/32. The number of constellation coordinates in each region is counted and normalized to obtain a characteristic matrix N. nij=eij/maxE∈N is the element of the characteristic matrix, where i,j=1,2,…,32 and eij∈E is the number of constellation points in the small area in row i and column j.


## 3.4.2. Adjusted Constellation Diagram Amplitude-Phase Characteristic Extraction

In this section, we analyze the amplitude and phase characteristics of the adjusted constellation points. As shown in Figure6, we add a fixed signal 2/2+j⋅2/2 to the EVM signal; it is equivalent to transferring the received constellation diagram to the first quadrant. The amplitude and phase values of adjusted constellation points are extracted with (5)di=|realevmi+22|2+|imagevmi+22|2,(6)θi=arctanimagevmi+2/2realevmi+2/2.Figure 6
The amplitude and phase values extraction of adjusted constellation points.Similar to the amplitude and phase values extraction of EVM signal, the adjusted constellation points in the rectangular coordinate system are transferred to the phase-amplitude coordinate system. The phase-amplitude coordinate in the range is divided into32×32 small areas (the size of each small area is maxΘ/32×maxD/32) to get the normalized characteristic matrix M. mij=aij/maxA is the element of the characteristic matrix M, where i,j=1,2,…,32 and aij∈A is the number of constellation points in the small area in row i and column j.


## 3.4.3. Amplitude-Phase Feature Image Generation

As shown in Figure7, the two different grayscale image samples formed by gray-scale mapping of the wireless signal of the physical layer are obtained, and the two grayscale images are used for training and testing of the network model.Figure 7
The amplitude and phase values extraction of adjusted constellation points.
(a)(b)To classify wireless signals using constellation characteristics, we transform the constellation characteristics into32×32 pixel gray images according to the image format. We deal with each element in the characteristic matrix corresponding to a normalized gray pixel value in the image.


## 3.5. Detection and Classification with Adjusted CNN

CNN was originally used for image classification and recognition because its structure is very suitable for extracting pixel-level characteristics from 2D images. Therefore, CNN can extract complex characteristics automatically by the convolution layer containing multiple filters. The CNN-T used in this paper is shown in Figure8.Figure 8
The architecture of the proposed CNN-T classifier.The input layer is the data front end of the whole neural network, that is, the image to be trained. The input layer images are processed to a size of32×32; the preprocessed images are shown in Section 3.4 which includes the EVM feature image and adjusted constellation feature image. The number of each type of image in each input layer can be adjusted, and the adjustment parameter is called batch size. In our experiment, we set the batch size to 128; that is, 128 EVM feature image and 128 adjusted constellation feature image are input each time for training, mainly for two reasons: (1) the memory of the machine can be used reasonably; (2) the algorithm converges within the set number of iterations. Besides, the time complexity is optimal [32, 33].The convolution layer is the local perception characteristic of the image, which is the characteristic perception of each part of the image, and then carries out a higher-level comprehensive operation to obtain the global information. The purpose of this operation, as shown in (7), is to reduce the calculation parameters of the model:(7)zi,jl,t=∑i=1m∑j=1nxi:i+p,j:j+qt⊙kl,1≤l≤L2,∑i=1m∑j=1nyi:i+p,j:j+qt⊙kl,L2<l≤L,where t=1,2,…,T, T represents the batch size; l=1,2,…,L, L represents the number of the filter; zi,jl,t is the (i, j) element of the l-th feature map with the size of m×n for the t-th group feature maps; kl is the convolution kernel coefficient of the l-th filter with the size of p×q; x represents the grayscale value of the EVM feature image; and y represents the grayscale value of the adjusted constellation feature image.The pooling layer is mainly used for feature dimension reduction, compressing the number of data and parameters, reducing overfitting, and improving the fault tolerance of the model. The algorithm is shown as(8)Du,vl,t=du−1∗g+1,v−1∗h+1l,t⋯du−1∗g+1,v∗hl,t⋮⋱⋮du∗g,v−1∗h+1l,t⋯du∗g,v∗hl,t,(9)pu,vl,t=averageDu,vl,twhere dl,t=σzl,t is the input of pooling layer, pl,t is the output, and g×h is the size of pooling size.The full connection and softmax layer play the role of “Classifier” in the whole convolutional neural network. Each node of the full connection layer is connected with each node of the upper layer, which integrates the output characteristics of the previous layer. The algorithm for this step is(10)o1,1⋯o1,T⋮⋱⋮on,1⋯on,T=W11⋯W1m⋮⋱⋮Wn1⋯Wnm∗h1,1⋯h1,T⋮⋱⋮hm,1⋯hm,T+b1⋮bn,(11)a1,1⋯a1,T⋮⋱⋮an,1⋯an,T=expo1,1∑i=1nexpoi,1⋯expo1,T∑i=1nexpoi,T⋮⋱⋮expon,1∑i=1nexpoi,1⋯expon,T∑i=1nexpoi,T,where h is the input of the full connection layer, a is the output of the softmax layer and W and b represent the weight value and bias value.The backpropagation algorithm [34] can be divided into two parts: error calculation and parameter gradient calculation. For the feature map generated by each layer, we calculate an error to show the difference between the result calculated by this layer and the correct result it should give. For the feature map generated by each layer, we calculate an error to show the difference between the result calculated by each layer and the desired result it should give. The errors of all layers are as follows:(12)ΔSp,q=ap,q−yp,q,(13)ΔPu,vl,t=resampleWT∗ΔS,(14)ΔKi,jl,t=upsampleΔP⊙σ′zi,jl,t,where ΔS is the error of softmax layer, ΔP is pooling layer, and ΔK is convolution layer.The parameter gradients of all layers are as follows:(15)Wd_grad=1TΔS∗hT,(16)bd_grad=1T∑q=1TΔSp,q,(17)Wc_gradl=1T∑t=1Tx⊗ROT180ΔKi,jl,t,1≤l≤L2,1T∑t=1Ty⊗ROT180ΔKi,jl,t,L2<l≤L,(18)bc_gradl=1T∑t=1T∑i,jΔKi,jl,t,where Wd_grad and bd_grad are the gradients of weight and bias for full connection layer and Wc_grad and bc_grad are the gradients of weight and bias for convolution layer.


## 4. Experiment and Simulation

In this section, we validate the effectiveness of our proposed approach through a series of simulations and experiments. All trainable parameters in our CNN-T are initialized to random values between −0.05 and 0.05. The effectiveness of the proposed scheme for detecting WCC-MC signals is verified by detecting and classifying WCC-DC (the classic scheme of WCC-MC) signals. The test in this paper is divided into two steps: WCC-DC signal detection and WCC-DC signal classification under different embedding rates and SNRs. The purpose of the detection test is to distinguish WCC-DC traffic from legitimate traffic. The classification test is to classify WCC-DC signals with different embedding rates.To evaluate the detection effectiveness of the proposed scheme, the following terms are used for determining the quality of the classification models:(1)
True positive (TP), the number of WCC-DC samples correctly classified to the covert class(2)
True negative (TN), the number of legitimate samples correctly classified to the legitimate class(3)
False positive (FP), the number of legitimate samples wrongly classified to the covert class(4)
False negative (FN), the number of WCC-DC samples wrongly classified to the legitimate classBased on the aforementioned terms, the following most commonly used evaluation metrics are considered.Accuracy estimates the ratio of the correctly recognized wireless communication samples to the entire test dataset:(19)accuracy=TP+TNTP+TN+FP+FN.Precision estimates the ratio of the correctly identified WCC-DC samples to the total number of samples classified to covert class. It is denoted as(20)precision=TPTP+FP.Recall estimates the ratio of the correctly identified WCC-DC samples to the number of all WCC-DC samples. It is denoted as(21)recall=TPTP+FN.F1-Score is the harmonic mean of Precision and Recall. It is denoted as(22)F1−score=2×precision×recallprecision+recall.


### 4.1. Simulation Analysis

#### 4.1.1. Establishment of Simulation Database

Due to the influence of channel noise on the generated feature image, the accuracy of detection results will be affected. Therefore, we set up data samples under different SNRs. We can estimate the SNR with the EVM signal by (2).As shown in Figure9, for each SNR, we generate a positive sample set Ps (legitimate communication sample) and a negative sample set Ns (WCC-DC communication sample), where Ps is the set of positive samples when the SNR is s. Ps=Pstr∪Pste, Pstr is the set of positive samples for training; Pste is the set of positive samples for test. Ns is the set of negative samples when the SNR is s. Ns=Nstr∪Nste, Nstr is the negative sample set used for training; Nste is the set of negative samples for test. The training set with SNR of s is TRs=Pstr∪Nstr; the test set is TEs=Pste∪Nste.Figure 9
Establishment of the simulation database.


#### 4.1.2. Simulation Setup

We use MATLAB software to verify our proposed scheme, and the wireless communication is set on the 802.11a/g physical layer. There are 48 subcarriers in the symbols being transmitted. In the simulation experiment, the high throughput group (TGn) channel model and the Gaussian noise (AWGN) channel model were selected as the wireless channel model [21]. The TGn channel models B selected for the simulation experiment on the 802.11a/g PHY layer is universal, and the receivers of the transmitter and the informer remain static. Therefore, the Doppler shift of wireless communication can be ignored.Different channel noise intensity will have a great impact on the characteristic picture, so in the simulation, we mainly study the influence of channel noise (SNR) on the detection and classification effect. Under each group of different SNRs, the simulation samples possessed include the following sets:(1) Samples of Covert Communication Signals. 10000 sets of WCC-DC signal samples with the embedding rate of 10%; 10000 sets of WCC-DC signal samples with the embedding rate of 20%; 10000 sets of WCC-DC signal samples with the embedding rate of 30%.(2) Sample of Legitimate Communication Signal. 10000 sets of legitimate communication samples with OFDM modulation.Among the 10000 sets of samples of various types, 7000 sets of samples are used as training samples, and the remaining 3000 sets are used for detection and classification. Each sample contains 2080 constellation points.


#### 4.1.3. Simulation Result

In the following chapters, simulation experiments are used to verify the detection and classification effects of the proposed scheme on WCC-DC communication signals under AWGN and TGn-B channels.(1) Detection Result under AWGN Channel. To verify the effectiveness of the proposed scheme, we implement the detection of WCC-DC signals with different embedding rates in the AWGN channel model. As shown in Figure 10, it is apparent that the reliability of the proposed scheme is influenced by the SNR and the embedding rate. With the improvement of SNR, the proposed scheme has more accurate detection results and our scheme has a higher detection rate for WCC-DC signals with a higher embedding rate.Figure 10
Detection result for the WCC-DC signal under AWGN channel: (a) Accuracy, (b) Precision, (c) Recall, and (d) F1-Score.
(a)(b)(c)(d)(2) Detection Result under TGn-B Channel. Similar to the simulation test in the AWGN channel, we detect the wireless communication signal under the TGn-B channel with the proposed scheme. Figure 11 shows the detection results of the proposed scheme for WCC-DC signals with different embedding rates under different SNRs. It is consistent with the simulation results in the AWGN channel, with the improvement of SNR and embedding rate, the proposed scheme can achieve a higher detection rate. However, the detection accuracy is lower than that in the AWGN channel due to the complexity of the TGn-B channel.Figure 11
Detection result for the WCC-DC signal under TGn-B channel: (a) Accuracy, (b) Precision, (c) Recall, and (d) F1-Score.
(a)(b)(c)(d)(3) Classification Result. In this section, we use the proposed scheme to classify WCC-DC signals with different embedding rates. Figure 12 shows the classification results of the proposed scheme for WCC-DC signals under different channel models and SNRs. The horizontal axis denotes the SNR and the vertical axis denotes the corresponding classification accuracy. As shown in Figure 12, the classification accuracy of the proposed scheme can achieve 80% when SNR = 23 dB for both types of channel models.Figure 12
Classification result for the WCC-DC signal under AWGN and TGn-B channel.


### 4.2. Experiment Analysis

#### 4.2.1. Experimental Setup

The experiment data set used in this paper is based on the Long-Term Evolution (LTE) communication system for physical layer wireless covert channel construction and wireless signal acquisition. The whole wireless communication system is divided into transmitting and receiving sides. Both sides use Universal Software Radio Peripheral (USRP) b210 as the LTE base station, and the two LTE workstations are connected to a PC, respectively. The PC is equipped with Linux Ubuntu 16.04 and the CPU processor is Intel Core i7. The operating frequency is 2.685 GHz, the bandwidth is 5 MHz, and the modulation mode is set to QPSK. The samples possessed include the following sets:(1) Samples of Covert Communication Signals. 13000 sets of WCC-DC signal samples with the embedding rate of 10%, 13000 sets of WCC-DC signal samples with the embedding rate of 20%, and 13000 sets of WCC-DC signal samples with the embedding rate of 30%.(2) Sample of Legitimate Communication Signal. 13000 sets of legitimate communication samples with OFDM modulation.Among the 13000 sets of samples of various types, 10000 sets of samples are used as training samples, and the remaining 3000 sets are used for detection and classification. Each sample contains 2080 constellation points.


#### 4.2.2. Experimental Result

In the following chapters, we use the data received by the radio platform to verify the detection and classification performance of the proposed scheme on WCC-DC communication signals.(1) Detection Result. The detailed description of detection performance indexes of different detection schemes is shown in Table 1. CNN-T represents the proposed scheme in this paper; K-S-A-P represents the K-S test with the amplitude-phase characteristic; K-S-A represents the K-S test with the amplitude characteristic; K-S-P represents the K-S test with the phase characteristic. Label 0-1 represents the detection for the WCC-DC signal with the embedding rate of 10%. Label 0-2 is the detection for the WCC-DC signal with the embedding rate of 20%. Label 0-3 is the detection for the WCC-DC signal with the embedding rate of 30%. In the K-S test, we measured the K-S distance between the tested sample and the legitimate sample. Thus, if the test score is small, it indicates that the sample under test is close to legitimate behavior. However, if the sample does not fit well into the legitimate behavior, the test score will be large, indicating the possible presence of WCC-P communication signals.Table 1
Detection performance of different detection schemes.
Label 0–1Label 0–2Label 0–3CNN-TAccuracy0.98590.99370.9968Precision0.98980.99540.9969Recall0.98200.99210.9968F1-score0.98590.99370.9968K-S-A-PAccuracy0.94530.96230.9877Precision0.95320.97270.9900Recall0.93670.95130.9853F1-score0.94490.96190.9876K-S-AAccuracy0.94000.96130.9867Precision0.94960.97140.9899Recall0.92930.95070.9833F1-score0.93920.96090.9866K-S-PAccuracy0.52500.56000.6837Precision0.53280.57770.7033Recall0.40670.44600.6353F1-score0.46130.50340.6676As shown in Table1, the proposed scheme (CNN-T) has the highest detection performance among all detection schemes. The detection accuracy for the WCC-DC signal with the 10% embedding rate is more than 98.5%, while the accuracy of the K-S test (K-S-A-P, K-S-A, K-S-P) can only reach 94.53%.(2) Classification Result. In this section, we use the WCC-DC signals with different embedding rates received by the radio platform to verify the reliability of our proposed scheme for WCC-DC signal classification and compare it with other classification schemes. Label 1-2-3 represents the classification for the WCC-DC signal with the embedding rates of 10%, 20%, and 30%. As shown in Table 2, the proposed scheme has the best classification result, which has over 81.7% classification accuracy for Label 1-2-3. In contrast, the K-S test (K-S-A-P, K-S-A, K-S-P) has only 65.2% classification accuracy.Table 2
Classification performance of different classification schemes.
CNN-TK-S-A-PK-S-AK-S-PLabel 1-2-30.817360.6520.64890.4649


## 4.1. Simulation Analysis

### 4.1.1. Establishment of Simulation Database

Due to the influence of channel noise on the generated feature image, the accuracy of detection results will be affected. Therefore, we set up data samples under different SNRs. We can estimate the SNR with the EVM signal by (2).As shown in Figure9, for each SNR, we generate a positive sample set Ps (legitimate communication sample) and a negative sample set Ns (WCC-DC communication sample), where Ps is the set of positive samples when the SNR is s. Ps=Pstr∪Pste, Pstr is the set of positive samples for training; Pste is the set of positive samples for test. Ns is the set of negative samples when the SNR is s. Ns=Nstr∪Nste, Nstr is the negative sample set used for training; Nste is the set of negative samples for test. The training set with SNR of s is TRs=Pstr∪Nstr; the test set is TEs=Pste∪Nste.Figure 9
Establishment of the simulation database.


### 4.1.2. Simulation Setup

We use MATLAB software to verify our proposed scheme, and the wireless communication is set on the 802.11a/g physical layer. There are 48 subcarriers in the symbols being transmitted. In the simulation experiment, the high throughput group (TGn) channel model and the Gaussian noise (AWGN) channel model were selected as the wireless channel model [21]. The TGn channel models B selected for the simulation experiment on the 802.11a/g PHY layer is universal, and the receivers of the transmitter and the informer remain static. Therefore, the Doppler shift of wireless communication can be ignored.Different channel noise intensity will have a great impact on the characteristic picture, so in the simulation, we mainly study the influence of channel noise (SNR) on the detection and classification effect. Under each group of different SNRs, the simulation samples possessed include the following sets:(1) Samples of Covert Communication Signals. 10000 sets of WCC-DC signal samples with the embedding rate of 10%; 10000 sets of WCC-DC signal samples with the embedding rate of 20%; 10000 sets of WCC-DC signal samples with the embedding rate of 30%.(2) Sample of Legitimate Communication Signal. 10000 sets of legitimate communication samples with OFDM modulation.Among the 10000 sets of samples of various types, 7000 sets of samples are used as training samples, and the remaining 3000 sets are used for detection and classification. Each sample contains 2080 constellation points.


### 4.1.3. Simulation Result

In the following chapters, simulation experiments are used to verify the detection and classification effects of the proposed scheme on WCC-DC communication signals under AWGN and TGn-B channels.(1) Detection Result under AWGN Channel. To verify the effectiveness of the proposed scheme, we implement the detection of WCC-DC signals with different embedding rates in the AWGN channel model. As shown in Figure 10, it is apparent that the reliability of the proposed scheme is influenced by the SNR and the embedding rate. With the improvement of SNR, the proposed scheme has more accurate detection results and our scheme has a higher detection rate for WCC-DC signals with a higher embedding rate.Figure 10
Detection result for the WCC-DC signal under AWGN channel: (a) Accuracy, (b) Precision, (c) Recall, and (d) F1-Score.
(a)(b)(c)(d)(2) Detection Result under TGn-B Channel. Similar to the simulation test in the AWGN channel, we detect the wireless communication signal under the TGn-B channel with the proposed scheme. Figure 11 shows the detection results of the proposed scheme for WCC-DC signals with different embedding rates under different SNRs. It is consistent with the simulation results in the AWGN channel, with the improvement of SNR and embedding rate, the proposed scheme can achieve a higher detection rate. However, the detection accuracy is lower than that in the AWGN channel due to the complexity of the TGn-B channel.Figure 11
Detection result for the WCC-DC signal under TGn-B channel: (a) Accuracy, (b) Precision, (c) Recall, and (d) F1-Score.
(a)(b)(c)(d)(3) Classification Result. In this section, we use the proposed scheme to classify WCC-DC signals with different embedding rates. Figure 12 shows the classification results of the proposed scheme for WCC-DC signals under different channel models and SNRs. The horizontal axis denotes the SNR and the vertical axis denotes the corresponding classification accuracy. As shown in Figure 12, the classification accuracy of the proposed scheme can achieve 80% when SNR = 23 dB for both types of channel models.Figure 12
Classification result for the WCC-DC signal under AWGN and TGn-B channel.


## 4.1.1. Establishment of Simulation Database

Due to the influence of channel noise on the generated feature image, the accuracy of detection results will be affected. Therefore, we set up data samples under different SNRs. We can estimate the SNR with the EVM signal by (2).As shown in Figure9, for each SNR, we generate a positive sample set Ps (legitimate communication sample) and a negative sample set Ns (WCC-DC communication sample), where Ps is the set of positive samples when the SNR is s. Ps=Pstr∪Pste, Pstr is the set of positive samples for training; Pste is the set of positive samples for test. Ns is the set of negative samples when the SNR is s. Ns=Nstr∪Nste, Nstr is the negative sample set used for training; Nste is the set of negative samples for test. The training set with SNR of s is TRs=Pstr∪Nstr; the test set is TEs=Pste∪Nste.Figure 9
Establishment of the simulation database.


## 4.1.2. Simulation Setup

We use MATLAB software to verify our proposed scheme, and the wireless communication is set on the 802.11a/g physical layer. There are 48 subcarriers in the symbols being transmitted. In the simulation experiment, the high throughput group (TGn) channel model and the Gaussian noise (AWGN) channel model were selected as the wireless channel model [21]. The TGn channel models B selected for the simulation experiment on the 802.11a/g PHY layer is universal, and the receivers of the transmitter and the informer remain static. Therefore, the Doppler shift of wireless communication can be ignored.Different channel noise intensity will have a great impact on the characteristic picture, so in the simulation, we mainly study the influence of channel noise (SNR) on the detection and classification effect. Under each group of different SNRs, the simulation samples possessed include the following sets:(1) Samples of Covert Communication Signals. 10000 sets of WCC-DC signal samples with the embedding rate of 10%; 10000 sets of WCC-DC signal samples with the embedding rate of 20%; 10000 sets of WCC-DC signal samples with the embedding rate of 30%.(2) Sample of Legitimate Communication Signal. 10000 sets of legitimate communication samples with OFDM modulation.Among the 10000 sets of samples of various types, 7000 sets of samples are used as training samples, and the remaining 3000 sets are used for detection and classification. Each sample contains 2080 constellation points.


## 4.1.3. Simulation Result

In the following chapters, simulation experiments are used to verify the detection and classification effects of the proposed scheme on WCC-DC communication signals under AWGN and TGn-B channels.(1) Detection Result under AWGN Channel. To verify the effectiveness of the proposed scheme, we implement the detection of WCC-DC signals with different embedding rates in the AWGN channel model. As shown in Figure 10, it is apparent that the reliability of the proposed scheme is influenced by the SNR and the embedding rate. With the improvement of SNR, the proposed scheme has more accurate detection results and our scheme has a higher detection rate for WCC-DC signals with a higher embedding rate.Figure 10
Detection result for the WCC-DC signal under AWGN channel: (a) Accuracy, (b) Precision, (c) Recall, and (d) F1-Score.
(a)(b)(c)(d)(2) Detection Result under TGn-B Channel. Similar to the simulation test in the AWGN channel, we detect the wireless communication signal under the TGn-B channel with the proposed scheme. Figure 11 shows the detection results of the proposed scheme for WCC-DC signals with different embedding rates under different SNRs. It is consistent with the simulation results in the AWGN channel, with the improvement of SNR and embedding rate, the proposed scheme can achieve a higher detection rate. However, the detection accuracy is lower than that in the AWGN channel due to the complexity of the TGn-B channel.Figure 11
Detection result for the WCC-DC signal under TGn-B channel: (a) Accuracy, (b) Precision, (c) Recall, and (d) F1-Score.
(a)(b)(c)(d)(3) Classification Result. In this section, we use the proposed scheme to classify WCC-DC signals with different embedding rates. Figure 12 shows the classification results of the proposed scheme for WCC-DC signals under different channel models and SNRs. The horizontal axis denotes the SNR and the vertical axis denotes the corresponding classification accuracy. As shown in Figure 12, the classification accuracy of the proposed scheme can achieve 80% when SNR = 23 dB for both types of channel models.Figure 12
Classification result for the WCC-DC signal under AWGN and TGn-B channel.


## 4.2. Experiment Analysis

### 4.2.1. Experimental Setup

The experiment data set used in this paper is based on the Long-Term Evolution (LTE) communication system for physical layer wireless covert channel construction and wireless signal acquisition. The whole wireless communication system is divided into transmitting and receiving sides. Both sides use Universal Software Radio Peripheral (USRP) b210 as the LTE base station, and the two LTE workstations are connected to a PC, respectively. The PC is equipped with Linux Ubuntu 16.04 and the CPU processor is Intel Core i7. The operating frequency is 2.685 GHz, the bandwidth is 5 MHz, and the modulation mode is set to QPSK. The samples possessed include the following sets:(1) Samples of Covert Communication Signals. 13000 sets of WCC-DC signal samples with the embedding rate of 10%, 13000 sets of WCC-DC signal samples with the embedding rate of 20%, and 13000 sets of WCC-DC signal samples with the embedding rate of 30%.(2) Sample of Legitimate Communication Signal. 13000 sets of legitimate communication samples with OFDM modulation.Among the 13000 sets of samples of various types, 10000 sets of samples are used as training samples, and the remaining 3000 sets are used for detection and classification. Each sample contains 2080 constellation points.


### 4.2.2. Experimental Result

In the following chapters, we use the data received by the radio platform to verify the detection and classification performance of the proposed scheme on WCC-DC communication signals.(1) Detection Result. The detailed description of detection performance indexes of different detection schemes is shown in Table 1. CNN-T represents the proposed scheme in this paper; K-S-A-P represents the K-S test with the amplitude-phase characteristic; K-S-A represents the K-S test with the amplitude characteristic; K-S-P represents the K-S test with the phase characteristic. Label 0-1 represents the detection for the WCC-DC signal with the embedding rate of 10%. Label 0-2 is the detection for the WCC-DC signal with the embedding rate of 20%. Label 0-3 is the detection for the WCC-DC signal with the embedding rate of 30%. In the K-S test, we measured the K-S distance between the tested sample and the legitimate sample. Thus, if the test score is small, it indicates that the sample under test is close to legitimate behavior. However, if the sample does not fit well into the legitimate behavior, the test score will be large, indicating the possible presence of WCC-P communication signals.Table 1
Detection performance of different detection schemes.
Label 0–1Label 0–2Label 0–3CNN-TAccuracy0.98590.99370.9968Precision0.98980.99540.9969Recall0.98200.99210.9968F1-score0.98590.99370.9968K-S-A-PAccuracy0.94530.96230.9877Precision0.95320.97270.9900Recall0.93670.95130.9853F1-score0.94490.96190.9876K-S-AAccuracy0.94000.96130.9867Precision0.94960.97140.9899Recall0.92930.95070.9833F1-score0.93920.96090.9866K-S-PAccuracy0.52500.56000.6837Precision0.53280.57770.7033Recall0.40670.44600.6353F1-score0.46130.50340.6676As shown in Table1, the proposed scheme (CNN-T) has the highest detection performance among all detection schemes. The detection accuracy for the WCC-DC signal with the 10% embedding rate is more than 98.5%, while the accuracy of the K-S test (K-S-A-P, K-S-A, K-S-P) can only reach 94.53%.(2) Classification Result. In this section, we use the WCC-DC signals with different embedding rates received by the radio platform to verify the reliability of our proposed scheme for WCC-DC signal classification and compare it with other classification schemes. Label 1-2-3 represents the classification for the WCC-DC signal with the embedding rates of 10%, 20%, and 30%. As shown in Table 2, the proposed scheme has the best classification result, which has over 81.7% classification accuracy for Label 1-2-3. In contrast, the K-S test (K-S-A-P, K-S-A, K-S-P) has only 65.2% classification accuracy.Table 2
Classification performance of different classification schemes.
CNN-TK-S-A-PK-S-AK-S-PLabel 1-2-30.817360.6520.64890.4649


## 4.2.1. Experimental Setup

The experiment data set used in this paper is based on the Long-Term Evolution (LTE) communication system for physical layer wireless covert channel construction and wireless signal acquisition. The whole wireless communication system is divided into transmitting and receiving sides. Both sides use Universal Software Radio Peripheral (USRP) b210 as the LTE base station, and the two LTE workstations are connected to a PC, respectively. The PC is equipped with Linux Ubuntu 16.04 and the CPU processor is Intel Core i7. The operating frequency is 2.685 GHz, the bandwidth is 5 MHz, and the modulation mode is set to QPSK. The samples possessed include the following sets:(1) Samples of Covert Communication Signals. 13000 sets of WCC-DC signal samples with the embedding rate of 10%, 13000 sets of WCC-DC signal samples with the embedding rate of 20%, and 13000 sets of WCC-DC signal samples with the embedding rate of 30%.(2) Sample of Legitimate Communication Signal. 13000 sets of legitimate communication samples with OFDM modulation.Among the 13000 sets of samples of various types, 10000 sets of samples are used as training samples, and the remaining 3000 sets are used for detection and classification. Each sample contains 2080 constellation points.


## 4.2.2. Experimental Result

In the following chapters, we use the data received by the radio platform to verify the detection and classification performance of the proposed scheme on WCC-DC communication signals.(1) Detection Result. The detailed description of detection performance indexes of different detection schemes is shown in Table 1. CNN-T represents the proposed scheme in this paper; K-S-A-P represents the K-S test with the amplitude-phase characteristic; K-S-A represents the K-S test with the amplitude characteristic; K-S-P represents the K-S test with the phase characteristic. Label 0-1 represents the detection for the WCC-DC signal with the embedding rate of 10%. Label 0-2 is the detection for the WCC-DC signal with the embedding rate of 20%. Label 0-3 is the detection for the WCC-DC signal with the embedding rate of 30%. In the K-S test, we measured the K-S distance between the tested sample and the legitimate sample. Thus, if the test score is small, it indicates that the sample under test is close to legitimate behavior. However, if the sample does not fit well into the legitimate behavior, the test score will be large, indicating the possible presence of WCC-P communication signals.Table 1
Detection performance of different detection schemes.
Label 0–1Label 0–2Label 0–3CNN-TAccuracy0.98590.99370.9968Precision0.98980.99540.9969Recall0.98200.99210.9968F1-score0.98590.99370.9968K-S-A-PAccuracy0.94530.96230.9877Precision0.95320.97270.9900Recall0.93670.95130.9853F1-score0.94490.96190.9876K-S-AAccuracy0.94000.96130.9867Precision0.94960.97140.9899Recall0.92930.95070.9833F1-score0.93920.96090.9866K-S-PAccuracy0.52500.56000.6837Precision0.53280.57770.7033Recall0.40670.44600.6353F1-score0.46130.50340.6676As shown in Table1, the proposed scheme (CNN-T) has the highest detection performance among all detection schemes. The detection accuracy for the WCC-DC signal with the 10% embedding rate is more than 98.5%, while the accuracy of the K-S test (K-S-A-P, K-S-A, K-S-P) can only reach 94.53%.(2) Classification Result. In this section, we use the WCC-DC signals with different embedding rates received by the radio platform to verify the reliability of our proposed scheme for WCC-DC signal classification and compare it with other classification schemes. Label 1-2-3 represents the classification for the WCC-DC signal with the embedding rates of 10%, 20%, and 30%. As shown in Table 2, the proposed scheme has the best classification result, which has over 81.7% classification accuracy for Label 1-2-3. In contrast, the K-S test (K-S-A-P, K-S-A, K-S-P) has only 65.2% classification accuracy.Table 2
Classification performance of different classification schemes.
CNN-TK-S-A-PK-S-AK-S-PLabel 1-2-30.817360.6520.64890.4649


## 5. Conclusions

In this paper, we have proposed a detection scheme based on a convolutional neural network for the wireless covert channel with the modulation of the constellation points (WCC-MC). We use the difference of amplitude and phase characteristics between the WCC-MC scheme and legitimate communication constellation points to realize the detection and classification of the WCC-MC signal. By extracting the amplitude and phase characteristics of the EVM signal and constellation points, we transform them into grayscale images and use the adjusted CNN network (CNN-T) to realize the detection and classification of the WCC-MC signal. Through simulation and radio experiments, we prove the effectiveness of the scheme for WCC-MC covert channel detection and classification. In the radio experiment, we get more than 98.5% detection accuracy rate for WCC-DC signal with the 10% embedding rate and more than 81.7% classification accuracy rate for WCC-DC with different embedding rates (10%, 20%, and 30%). Although the proposed scheme has been shown to be effective in detecting the WCC-MC communication signal, however, there are areas of our study that can be further improved. The problem of capturing radio signals, including the choice of listening frequencies and capturing radio signals by adding listening devices, is not described in our scheme. This problem will be studied in future work.



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*Source: 5569745-2021-06-07.xml*