Automatic Modulation Classification Based on In-Phase Quadrature Diagram Constellation Combined with a Deep Learning Model

Objectives: This study aims to present a framework for Automatic Modulation recognition using Deep learning without feature extraction. Methods: We study seven modulations using the In-Phase Quadrature constellation polluted by Additive White Gaussian Noise. We apply the K-means algorithm to normalize data transmitted and polluted by noise; the new diagram obtained is considered as an image and coded in pixel before entering in a Deep Neural Network where we apply 20% dropout on hidden layers to avoid overfitting. The simulation is carried out in Matlab. Findings: Experiment performed on selected modulations following the proposed framework gives a good percentage of recognition equal to 96.12%. Our algorithm Deep Neural Network imaGe gives the best performance results at epoch equal to 2,000,000. Applications: The outcome will be beneficial for researchers in Software-Defined Radio for civilian and military applications like electronic attacks and electronic protection.


Introduction
Modulation recognition has many commercial applications in areas such as space communications and cellular telecommunications where it is used as a Software-Defined Radio. Software-Defined Radios use a blind modulation recognition system to reduce system overhead and increase system accuracy.
The advantage of using machine learning in Automatic Modulation Classification is that system that uses a decision tree for this purpose with several detection levels is not an easy thing [1]. In [2] used a Neural Network to improve the percentage of modulation recognition during classification. In [3] used fuzzy c-means combined with Neural Networks to classify different types of modulations, but the proposed technique required features extractions before entering in the Neural Network. In [4] proposed a classification method using the combination of two clustering methods, namely the k-means and the k-center for the modulation classification, one used to initialize the data and the other one come up in support for decision-making using as a basis of the I-Q constellation diagram.
In [5] used the K-nearest neighbor method which is a learning method that uses two phases, the learning phase and the classification phase [6] for the classification of modulations. In most of the methods proposed in many papers [3][4][5][6][7], authors combine two methods to solve the classification problem. In [8] proposes a new model that combines extraction and classification as a single entity with a deep learning model.
In this study, we propose an approach based on the use of the Gaussian noise polluted I-Q diagram as basic information for use in modulation recognition problem-solving. We propose to use the k-means algorithm to normalize the noise-polluted diagram and then enter the new modified diagram into a hidden multi-layered Neural Network and apply an adequate dropout on our Neural Network to prevent overfitting.

Literature Survey
In this section, we will present the algorithms and models known in the literature.

k-means Algorithm
The principle of k-means is to minimize the distortions that are call cost.
where x i is a number of clusters C k and µ k is the centroid of each cluster C k. .
The fundamental purpose of the clustering method is to assign observations into a cluster.

Neural Network
Neural Networks are derived from biology and are today one of the most explored areas of artificial intelligence due to its applications in several fields [9]. Figure 1 shows us a typical Neural Network.
In the application of Neural Networks in problem-solving, one of the major problems is overfitting. To overcome the problem of overfitting, we use dropout techniques [10]. This has been applied by [11] to Recurrent Neural Networks (RNNs) to ward off the problem of random selection of certain nodes and the deactivation of unselected nodes.
The principle is illustrated in Figure 2 (a) and (b).

Model of [3]
In [3] proposed a model for automatic modulation classification. This is illustrated in Figure 3. In this model, the modulated signal during transmission is polluted by Gaussian noise which can cause an improbable demodulation. At first, they apply a clustering algorithm that is fuzzy c-means to try to normalize the data polluted by the noise. After extracting    some parameters, these parameters are introduced into a Neural Network to recognize the modulation.

Classification Model Proposed by [8]
Traditional models used in the literature [2][3]7] used to extract certain parameters which will then be used to feed the Neural Network. The problem occurs because it was necessary to choose good parameters at the risk of feeding the Neural Network with bad parameters which were crucial because a wrong choice will lead to erroneous results due to the parameters received. In [8] proposed a model that combines extraction and classification phases into a single block to classify modulations used in unmanned aerial vehicles. This model is shown in Figure 4 (a) and (b).

Proposed Model for Classification
Our model proposed in this study is a combination of approaches proposed by [3] and that of [8]. This is illustrated in Figure 5.

Signal Model
In this study, used signals are in Intermediate Frequency (IF) and are corrupted by Additive White Gaussian Noise (AWGN). The signals used are the same type as those proposed by [12]. The transmitted signal r(t) is as follows: where m A , n a , s T , c f , m f , 0 ϕ , m ϕ are the modulation amplitude, symbol sequence, symbol period, carrier frequency at IF, modulation frequency, initial phase, and modulation phase, respectively. g(t) is the gate function

Application of the k-means Algorithm
We know that the purpose of clustering is to assign observations to a cluster. In [13] suggested that the receiver could use the geometry of the constellation of the modulated signal to deduct the modulation. To have this result, they propose to consider the matrix X where N represents a set of points and where jI x is the component In Phase and jQ x is the component in Quadrature. When the modulation used is 16 QAM with N = 10000 and S / N = 4 dB, Figure 6 shows the representation of 16 QAM modulated signal constellation.
The received signal polluted by the noise gives the following representation in Figure 7.
The application of the k-means algorithm gives us the result of Figure 8.

The Aspect of Our Neural Network
To solve our problem of classification, we consider a Deep Neural Network with three hidden layers. Each hidden layer consists of 40 nodes. Neural network has 49 nodes of entry and 7 output corresponding to 7 classes corresponding also to our 7 modulations chosen which are the most used in many papers [3][4][5]7,13]. As each modulation constellation can be set on a matrix 7x7, we set 49 input nodes. Our three hidden layers represent the deep model of the Neural Network proposed by [14] which has a single hidden layer. Figure 11 shows the architecture of our neural network. W1, W2, W3, W4, respectively, represent the weights of the matrices of the input nodes-hidden1 layer, hidden1 layer-hidden2 layer, hidden2 layer-hidden3 layer, hidden3 layer-output layer. The activation function for neural network is softmax function.

Proposed Algorithm
Our algorithm has been named Deep Neural Network imaGe (DNNG) because it uses I-Q constellation diagrams as a pixel-coded image to feed the neural network. A normality test [4] is performed on the signal to know whether we are dealing with a single carrier signal or multiple carrier signal type. In this article, we will deal with the case of single carrier signal.
After applying the k-means clustering algorithm, this information is entered into the Deep Neural Network for modulation recognition.
To avoid overfitting, we drop out 20% of each hidden node. Proposed algorithm is presented in Figure 12.

Results and Discussion
For the learning phase of our Neural Network, we set the learning rate for the proper functioning at α = 0.01 ( 0 1 α ≤  ); a bad choice of this parameter will lead to a slow convergence of the neural network [15].
Our simulation has been done with these parameters:

Application of dropout
In several papers [3][4][5]7,13,16] dealing with the automatic classification of modulations, the weak classification results generally occur when there are low values of S/N.
That is why we used to test our model at S/N = 4 dB. Table 1 shows the order of entrance of our seven modulations chosen in the Deep Neural Network. Table 2 shows all the modulation recognition percentages of the Neural Network starting from an epoch value equal to 10,000.
The curve in Figure 13 shows that our Neural Network converges well, but after the value of epoch equals 2,000,000, it enters in overfitting.
It is at this value that our Neural Network gives the best results, with a general recognition percentage of our seven modulations equaling 96.12%.

Comparisons with Other Results
To compare our results with those which exist in the literature, we will do it with four modulations because it is these modulations that several authors have used [3][4][5]14]. But the comparison with other results of the literature is difficult as was mentioned in papers [7,13] because there are no standard databases of modulations that everyone should use to facilitate comparison and the parameters of experiments differ from one author to another. Table 3 presents the main results of some methods proposed in the literature. Table 3 summarizes results obtained and shows an improved performance in terms of modulation recognition of our DNNG method. We have especially compared it to our first  We have a significant improvement in the level of the iterations because with the ANNG, it was necessary to go to value of epoch equal to 4 000000 before having good results, but with the DNNG at 2,000,000, its gives better results. DNNG brings a gain in CPU resource consumption compared to ANNG.
The curve in Figure 14 shows the evolution of the ratio of the percentage of recognition of the seven modulations used in our DNNG model concerning the signal-to-noise ratio (S/N).

Conclusion
In this study, we presented a model for Automatic Modulation Classification that we named DNNG which is a model of deep learning from another model that we proposed