# Efficient Support Vector Regression for Wideband DOA Estimation Using a Genetic Algorithm
## 1 Introduction  
Direction of arrival (DOA) estimation is a crucial part of array signal processing that is widely used in radar, sonar, navigation, communication, and various other applications [1, 2, 3]. The main goals of DOA estimation are to improve the estimation precision and reduce computational complexity simultaneously. After a long period of development, researchers have proposed many DOA estimation methods, such as conventional beamforming (CBF) [4, 5, 6], multiple signal classification (MUSIC) [7, 8, 9, 10], maximum likelihood estimation (ML) [11, 12, 13, 14], and estimation of signal parameters via rotational invariance techniques (ESPRIT) [15, 16, 17]. The performance of these methods significantly degrades with a low signal-to-noise ratio (SNR) or a small number of snapshots. Later, many researchers applied sparse representation (SR) [18, 19, 20] to DOA estimation and achieved good estimation accuracy. However, DOA estimations based on SR rely on prior information about the signals. Additionally, all of the above approaches belong to the category of model-driven approaches and require the establishment of a parametric model betweenthe angle information of incident signals and array outputs. In practical applications, it is difficult to establish a complete and accurate parametric model due to the presence of element errors and mutual coupling effects. Meanwhile, the challenges in achieving high-precision calibration make traditional DOA estimation poorly adaptable to complex electromagnetic environments and reduce the estimation performance. With the expansion of the field of DOA estimation, more requirements have been imposed for its effectiveness and real-time performance, compelling researchers to continuously seek new technological approaches. Machine learning is a data-driven approach used to learn signal features from massive amounts of data and can transcend model constraints to overcome the limitations of traditional approaches [21]. Now, machine learning theory has been widely applied in DOA estimation. It can be adapted to complex and changing environments through real-time learning and adaptive adjustment [22], thus improving response speed and accuracy to track signal and environmental changes. Furthermore, by integrating modern hardware and optimization strategies during online testing, machine learning approaches can fully harness parallel computing advantages, thereby improving computational efficiency and satisfying real-time performance demands following offline training. The latest research achievements in DOA estimation have provided new ideas for increasing accuracy, robustness, and processing efficiency. One option is to incorporate the You Only Look Once version 3 (YOLOv3) [23] neural network structure into DOA estimation. By framing the problem as a target detection task, this method avoids the typical spectral peak search step, allowing for end-to-end estimation. Another significant research direction is the construction of an iterative neural network based on deconvolved beamforming [24]. This technique reduces the training burden and the need for large-scale datasets. In addition, it has a strong ability to suppress sidelobes and false peaks, especially under low-SNR conditions. As a result, the robustness and accuracy of DOA estimation have greatly improved. Particle swarm optimization (PSO) is employed to fine-tune the weights and thresholds of a backpropagation (BP) neural network [25], thereby enhancing the accuracy and real-time performance of the DOA estimation and improving its adaptability to dynamic environments. To enhance the accuracy of DOA estimation under low-SNR conditions, [PERSON] et al. [26] proposed a DOA estimation method based on support vector regression (SVR) optimized by a genetic algorithm (GA). Leveraging the GA to optimize the SVR parameters during training significantly enhances the model's generalization capability.