# Efficient Support Vector Regression for Wideband DOA Estimation Using a Genetic Algorithm
## 1 Introduction
Convolutional neural networks (CNNs) [39] are widely used for DOA estimation of broadband signals due to their powerful nonlinear mapping capabilities, which enable excellent accuracy. In addition, deep-learning-based approaches [40; 41] offer superior robustness and adaptability in wideband DOA estimation, ensuring reliable performance across diverse and challenging environments. These methods are extremely demanding in terms of training data and may be limited in their ability to generalize to unseen scenarios. To address the complexity of wideband signals, a method based on coherent wideband SVR (CWSVR) [42] has been proposed. This method performs well in processing wideband signals. However, as the number of sub-bands grows, the input dimension of the network increases significantly, resulting in a substantial rise in training time. This limits the applicability of the method to large-scale datasets. To address this issue, a novel multiband joint direction-finding SVR model is proposed. The model employs a processed and optimized array covariance matrix as input features, while its parameters are fine-tuned using a genetic algorithm. Then, an effective framework is constructed and applied to DOA estimation. This approach not only improves estimation performance through joint estimation across frequency bands but also effectively reduces model training time. The method proposed in this paper is mainly aimed at the DOA estimation of wideband signals, but it can also be applied to ultra-wideband signals. It is worth noting that broadband signals are defined as signals with a relative bandwidth greater than 10% of the carrier frequency. Ultra-wideband(UWB) signals have a relative bandwidth greater than 20% of the carrier frequency. The contributions of our work are summarized as follows:  
* An efficient SVR architecture for wideband DOA estimation via a GA is proposed. It exhibits superior estimation and resolution capabilities, along with strong generalization performance. The results of experiments confirm the superior performance and efficiency of the proposed network compared to typical existing algorithms such as RSS-MUSIC, L1-SVD, and CWSVR. * We have employed a coherent focusing operation to initially extract the features from the covariance matrix and ensure the preservation of essential signal features. Multiband data are projected onto a designated reference frequency point, which substantially lowers the dimensionality of the input signals to the network. In particular, the dimensionality of the input features does not scale with the number of sub-bands, making the method well suited for broadband and ultra-broadband signals. This not only substantially reduces the model training time and system storage requirements but also makes the method especially beneficial in resource-limited environments. * The performance of SVR models is highly sensitive to parameter selection, particularly the regularization and kernel function parameters. Here, we employ a GA to optimize the model parameters due to its notable advantages, including global optimization capability, strong adaptability, and effectiveness in mitigating overfitting. The optimized SVR model exhibits improved fitting and generalization performance on the training data, leading to a significant improvement in DOA estimation. The remainder of this paper is organized as follows. In Section 2, we introduce the mathematical model and theoretical foundations for wideband array signal processing. In Section 3, we present our methodology, including the data preprocessing, parameter optimization, and model construction. In Section 4, the effectiveness of the algorithm is verified through simulation and compared with existing methods. Finally, conclusions are drawn in Section 5.