# A Method for Underwater Acoustic Target Recognition Based on the Delay-Doppler Joint Feature
## 3 Underwater Acoustic Target Recognition Model with Delay-Doppler Joint Feature
### Target Recognition Model with Time-Frequency and Delay-Doppler Features  
This paper establishes a multi-input underwater acoustic target recognition model (TF-DD-CNN) based on Time-Frequency features and Delay-Doppler features of underwater noise emitted by ships. The model consists of a Time-Frequency feature recognition module and a Delay-Doppler domain feature recognition module, and uses a convolutional neural network to construct the target recognition model. The particular arrangement is seen in Figure 11. The model structure mainly comprises the Time-Frequency (TF) feature recognition model and the Delay-Doppler (DD) feature recognition model. Each module consists of nine groups of convolution modules (Conv k, k = 1, 2,..., 9). The feature vector matrix finally obtained by the two modules is fused by the Feature Fusion module, and the high-dimensional and complex signal features are converted into low-dimensional and simple signal features by using two sets of fully connected layers. Finally, the SoftMax layer is used to identify the target, and the network architecture employs cross entropy as the loss function for model training.  
Table 1 displays the comprehensive details of each convolutional layer in the model. In order to add nonlinear conditions to the model, the activation function used to train the model is the Rectified Linear Unit (ReLU), and the pooling layer of each layer is selected as MaxPooling. We take Conv1 as an example to explain the contents in Table 1. The notation \"1 \(\times\) 1-32-ReLu-BN\" indicates that the chosen convolution kernel has a size of \(1\times 1\), the type of convolution kernel is a two-dimensional convolution kernel, 32 represents the number of convolutions, and the selected activation function is the ReLU. Batch Normalization (BN) [27] is a data normalization method. It can accelerate the convergence rate of model training and improve its robustness; \"3 \(\times\) 3-MaxPooling\" indicates that the selected pooling size is 3 \(\times\) 3, and the maximum pooling is selected for processing.  
Figure 11: The structure of the TF-DD-CNN model.  
Figure 10: Principle of target recognition based on joint features.  
The input feature vector passes through nine convolutional layers to obtain the corresponding convolutional feature vector. Finally, we use the Feature Fusion module to merge the two categories of convolutional feature vectors. The process of fusion is referred to as matrix concatenation, and Figure 12 shows the precise fusion process. Assuming that both input vectors are \(m\times n\) matrices, the Feature Fusion module is used to obtain a \(2m\times n\) feature vector at last. Suppose the number of columns of the two feature matrices is inconsistent. In that case, the corresponding column number of the feature matrix with fewer columns will be zeroized and then fused, which will be used as the basis for the final target recognition. The dimensionality of the matrix is reduced using two completely linked layers, and the SoftMax layer is then utilized for identification.