# A Method for Underwater Acoustic Target Recognition Based on the Delay-Doppler Joint Feature
## 1 Introduction
In order to solve the problem that it is difficult to recognize more complex targets by using time-frequency feature, this paper analyzes the signal from the perspective of Delay-Doppler domain. The motion characteristics of the target are defined by the Delay-Doppler domain components of the signal. Because of the difference in volume and shape, the velocity of different underwater acoustic targets is quite different. The Delay-Doppler features can represent the difference of targets within a specific range. The coherence integration method of the power spectrum is used to compensate for the Delay-Doppler factor of passive sonar signals, which may significantly enhance the detection efficacy of mobile targets [10]. The underwater acoustic communication receiver has a high bit error rate (BER) since it was constructed using the signal characteristics found in the Delay-Doppler feature [11]. The accuracy of signal features may be increased by using deep learning for the feature extraction of signals in the Delay-Doppler domain as the field develops and advances [12]. The Delay-Doppler features of signals are widely used in underwater acoustic communication. [PERSON] et al. [13] proposed an orthogonal operation based on the Gram-Schmidt method to solve the multi-path sparse Delay-Doppler parameter solution of linear frequency modulated (LFM) signals in shallow water. Compared to the traditional method, it has a lower mean square error. [PERSON] et al. [14] introduced exponential modulation (IM) into the Delay-Doppler feature of the signal, and the system's BER performance was enhanced by using the Hamming distance optimization model. [PERSON] et al. [15] created a generalized approximated message passing (GAMP) algorithm to estimate underwater acoustic channels in a communication system, which can effectively reduce the computational complexity. The signal's Delay-Doppler characteristics can reflect the target's motion characteristics. However, the target's speed varies over time and cannot stably reflect the characteristics of the target. This study combines the temporal and spectral properties of the signal to address the aforementioned problem. By using the Time-Frequency feature and the Delay-Doppler feature together, it is possible to mitigate target identification mistakes that may occur when utilizing these features individually. Instead, it suggests an approach to target feature extraction that is based on both domains. Automatic recognition and classification technology are essential to realize the intelligence and automation of underwater acoustic equipment. The early recognition of underwater targets mainly relies on experienced professionals. With the progress of computers and related algorithms, there have been some target recognition methods based on statistical analysis, such as the Bayesian pattern classification method, cluster analysis method, support vector machine, restricted Boltzmann machine, decision tree, hidden Markov model, and nearest neighbor method [16] using wavelet packet transform to process the signal, extract the wavelet energy spectrum features of the radiated noise signal, and use SVM to identify the signal effectively. [PERSON] et al. [17] used the hidden Markov model to compare the trajectory of underwater fish and realize the trajectory detection of underwater fish. [PERSON] et al. [18] used a restricted Boltzmann machine to examine the normalized spectrum of the signal, obtain the data's deep structural features, and finally classify the data with BP neural network features. With the emergence of artificial intelligence, there is increasingly more research on recognizing underwater acoustic targets using neural networks. Convolutional neural networks (CNNs) are often used for underwater target detection. [PERSON] et al. [19] extracted five characteristic parameters of radiated noise in the frequency, time, and Mel transform domains and established a convolutional neural network to recognize the target. The recognition accuracy was improved by 7.8% compared to the SVM method.