Data-and-Knowledge Dual-Driven Automatic Modulation Recognition for Wireless Communication Networks

The modulation classification can be identified as a $K$-class hypothesis test, where $K$ denotes the number of modulations. The received signal under the $k$th modulation hypothesis ${H}_{k}$ is given as

where ${s}_{k}(n)$ and ${x}_{k}(n)$ are the transmitted signal and the received signal, respectively. $N$ is the number of signal symbols. ${{\omega}_{k}}(n)$ is the additive white Gaussian noise with mean being zero and variance being ${{\sigma}^{2}}$.

The in-phase and quadrature (I/Q) parts of the received signal are both utilized. These two parts usually obey an identical independent distribution, which can be input into the neural network without normalization [15]. The I/Q signal samples can be expressed as a vector by turning the received signal ${x}_{k}(n)$ into the vector $\mathbf{x}_{k}$, given as

where $\mathbf{I}_{k}$ and $\mathbf{Q}_{k}$ represent the in-phase part and the quadrature part of the received signal, respectively, and $j=\sqrt{-1}$. $\Re(\cdot)$ and $\Im(\cdot)$ represent the operators of the real and imaginary parts of the signal, respectively. The raw data $\mathbf{x}_{k}$ can be specifically expressed as the form of matrix, given as

The DL-based schemes such as CNN and RNN are utilized to extract features from the raw data. Then, a fully connected (FC) layer is utilized to integrate the information and carry out the conversion of feature dimension. The feature learning can be expressed as a process that the raw data $\mathbf{x}_{k}\in{\mathbb{R}^{N\times 2}}$ is mapped into a $L$-dimensional vector $\mathbf{y}$, given as

where mapping function $f$ represents the feature learning model with the fully connected layer, and $\mathbf{y}$ represents the feature vector output from the FC layer.

Finally, the learned feature vectors are classified by another FC layer with the $softmax$ classifier. The number of neurons in the last layer is equal to the number of modulation formats. Thus, each output neuron corresponds to a modulation format. $Softmax$ is used to convert the output into the probability that the input signal belongs to each candidate modulation format. The cross-entropy loss function is utilized to measure the gap between the model output and the true label. It can be given as

where $K$ represents the number of classes, $N$ represents the number of samples. ${p}_{j,k}$ is the output of $softmax$, which represents the probability when data sample $j$ belongs to class $k$. ${q}_{j,k}$ is a indicative variable, which is given as

However, the pure data-driven AMC method requires a large number of samples to complete the training of deep networks. Moreover, the classification accuracy of traditional methods is poor in the practical complex and dynamic scenarios, especially in the low SNRs. Fortunately, the exploitation of expert knowledge is promising to tackle those problems [16]. However, to our best knowledge, few investigations have studied it. Therefore, we propose a novel data and knowledge dual-driven AMC method.

Fig. 2 illustrates the framework of the visual model. The multi-scale convolutional network (MSNet) is employed as the visual model. The MSNet consists of several multiscale (MS) modules, global average-pooling (GAP), FC layers and the $softmax$ classifier. MS modules are used to capture the multi-level feature information by using a $3\times 1$ convolution layer with stride = 2 to reduce the feature dimension at the top layer of the module. Then, several parallel convolutions with different kernel sizes are utilized to capture multi-level features. Features from different convolutional layers are consolidated together by using the concat operation. After the concat operation, the FC layer of the traditional CNN is replaced by the GAP for aggregating information from the MS modules to average each feature output from the four corresponding channels. Compared with the traditional FC layer, the over-fitting problem is avoided since there is no parameter required to be optimized in GAP. Moreover, another FC layer with rectified linear units (ReLU) is utilized to reduce the feature dimensionality. ReLU function can be expressed as

where $\max(\cdot)$ represents the operator for obtaining the maximum value.

The values of several neurons are set to be zero, which results in the sparsity of the network and reduces the interdependence among parameters. Therefore, the occurrence of over-fitting problems can be alleviated. Moreover, different from $sigmoid$ and $tanh$ activation function, ReLU function dose not have the saturation zone. Thus, the gradient vanishing problem can be avoided. The specific architecture of the visual model is shown in Table I.

The core goal of AMC is to recognize the category of different modulations. Each modulation has its unique characteristics. Thus, modulation can be identified based on the high-level description that is phrased in terms of semantic attributes. Different classes are usually different in the high dimensional feature space. In this case, it is promising to combine semantic attributes and visual features to achieve a higher classification accuracy.

An adaptation of residual network was exploited to learn the attribute representation of different modulations. The residual unit is shown in Fig. 3(a). Two 2D convolution operations with kernel size $3\times 3$ are performed in the residual unit. Different from ResNet in [15], the batch normalization layer is used to standardize the data in the intermediate layers to avoid the gradient disappearance caused by the saturation of the partial derivative of the intermediate variable. Alongside, ReLU activation is used after the first convolution and after the skip connection to introduce non-linear operations as shown in Fig. 3(a). The residual stack, as shown in Fig. 3(b) consists of a convolution operation with a kernel size of $1\times 1$ followed by two residual units. The maxpool layer is used to compress features. Moreover, the GAP is used to average the outputs of different channels. Therefore, the parameters are reduced greatly compared with FC in ResNet proposed in [15]. The specific architecture of the attribute learning network is shown in Fig. 3(c). The number of residual stack is decreased from 6 to 3 to reduce the complexity of the model. The kernel size and output dimensions corresponding to different layers of the attribute learning model are shown in Table II.

Since the learning of each attribute transcends the specific classification task, the attribute learning model can be pre-learned independently [16]. In this way, we can perform attribute learning through bigger datasets that are not limited to AMC datasets.

The visual-attribute embedding model has two branches. One branch is the visual encoding branch adapted from the MSNet in Fig. 1, and the $softmax$ classification layer is removed. The visual encoding branch can output the visual feature vector. It takes the raw data of the signal samples $\mathbf{I}_{{i}}$ as the input. Then, the MS module is used to extract multi-dimensional features. The GAP is used to flatten multi-channel features. Finally, the FC layer outputs a $D$-dimensional feature vector $\phi_{1}({\mathbf{I}_{i}})\in{\mathbb{R}^{D\times 1}}$.

The semantic embedding is achieved by the other branch which is a attribute learning subnet as illustrated in III-B. The subnet outputs a $L$-dimensional feature vector $\phi_{2}({\mathbf{I}_{i}})\in{\mathbb{R}^{L\times 1}}$. Moreover, a joint embedding space is learned where both the attribute vectors and the visual feature vectors can be projected. The authors in [16] has proved that the visual feature space is the most appropriate embedding space, which can alleviate the hubness problem [16]. Therefore, a transformation subnet is designed to convert attribute vectors into vectors in the same dimensional space as the visual feature vectors. Specifically, it takes the $L$-dimensional attribute representation vector $\phi_{2}({\mathbf{I}_{i}})\in{\mathbb{R}^{L\times 1}}$ of the attribute learning subnet as input, and after going through two FC layers and the ReLU activation outputs a D-dimensional semantic embedding vector ${{\phi}_{3}}({{\phi}_{2}}({\mathbf{I}_{i}}))\in{\mathbb{R}^{D\times 1}}$. In order to show the process of the transformation subnet in detail, the output can be expressed as

where $\mathbf{W}_{1}\in{\mathbb{R}^{L\times M}}$ and $\mathbf{W}_{2}\in{\mathbb{R}^{M\times D}}$ are the weights to be learned in the first FC layer and the second FC layer. The rectified linear units $f(\cdot)$ is used as the activation function to introduce non-linearity into the network.

Each of the FC layer has a ${l}_{2}$ parameter regularization loss. The two branches are linked together by a least square embedding loss which aims to minimise the discrepancy between the visual feature vector $\phi_{1}({\mathbf{I}_{i}})\in{\mathbb{R}^{D\times 1}}$ and its class representation embedding vector in the visual feature space. The loss function is given as

where $N$ is the number of training samples and $\lambda$ is the hyper-parameter weighting the strengths of the two parameter regularization losses against the embedding loss.

As is shown in Fig. 3, different from the traditional pure data-driven architecture, our proposed scheme constructs a embedding space where both visual features and attribute features can be projected. The integration of attribute features can improve the performance of the model in low SNRs. Meanwhile, the existence of two pre-trained models makes end-to-end training only be required for the transformation model. Therefore, the training speed of our proposed scheme can be extremely high. Moreover, due to the introduction of attribute knowledge, we can reduce the requirements for visual model data. Lastly, different from abstract visual features, the attribute features labels are composed of deterministic binary variables which have clear physical implications.