# Robust DOA Estimation Using Multi-Scale Fusion Network with Attention Mask
## 1 Introduction  
Direction-of-arrival (DOA) estimation plays a crucial role in various applications such as speech enhancement, speech separation, and speech recognition [1; 2; 3; 4; 5; 6]. Accurate DOA estimation enables robust audio signal processing in reverberant and noise environments. Traditional DOA estimation methods, including beamforming and multiple signal classification (MUSIC) [7; 8; 9; 10], have shown limitations in complex acoustic scenarios due to their sensitivity to reverberation and noise. To address these challenges, recent research has explored deep neural networks for DOA estimation tasks [11; 12; 13; 14; 15; 16]. Eigenmike32 is one of the most widely used microphone arrays in acoustic signal processing [17]. It is a compact sensor array with 32 electret microphones embedded in a rigid sphere with a diameter of 84 mm, which has a great advantage in sound source localization. The sound field can be decomposed into a set of spherical harmonic functions [18]; therefore, signals can be processed in the spherical harmonic domain. In recent years, many deep learning-based DOA methods have been proposed in the spherical harmonic domain. Most of them are based on real-valued neural networks (RVNNs). However, speech signals after short-time Fourier transform (STFT) are inherently complex-valued. Conventional neural networks typically concatenate the magnitude and phase components or the real and imaginary components, then use them as real-valued inputs. These kinds of convolutional neural networks (CNNs) limit their ability to effectively model the complex-valued nature of acoustic signals, leading to suboptimal performance, particularly in reverberant and noisy environments. In contrast, complex-valued neural network (CVNN) has the ability to capture both magnitude and phase information inherent in audio signals, offering a more comprehensive representation of theunderlying data. In the realm of speech processing, CVNN has demonstrated promising performance in tasks [19; 20; 21; 22; 23]. For example, in speech recognition tasks, CVNNs have shown improved robustness to background noise and reverberation, leading to higher recognition accuracy, especially in adverse acoustic conditions [24]. Similarly, in emotion recognition tasks, CVNNs achieved better performance, even when dealing with variations in speaking styles and environmental conditions [25]. By explicitly modeling the phase information inherent in speech signals, CVNNs can learn more robust representations that are less sensitive to reverberation and noise than RVNN, ultimately leading to improved performance in various speech processing tasks. It may be well suited for DOA estimation in challenging acoustic environments. Moreover, CVNNs have been shown to exhibit faster convergence and better generalization capabilities compared to their real-valued counterparts. This is attributed to the fact that complex-valued representations can capture richer information about the underlying data distribution, leading to more efficient learning and improved generalization to unseen data. To solve the problem of the nature of complex-valued features and the computational cost, we propose a new CVNN-based DOA estimation method. The main contributions of this work are summarized as follows:  
1. A robust multi-scale fusion network with attention mask (MF-AMnet) is proposed based on CVNN. By directly handling complex-valued inputs in the spherical harmonic domain, the proposed method preserves the rich information of the original signal, meanwhile minimizing data redundancy caused by data concatenation. 2. A low-complexity multi-scale fusion block (MF) is designed to efficiently capture the inherent spatial patterns of the input feature maps by stacking complex-valued convolutional layers with small kernels. The module complexity is effectively reduced by a special branching operation while promoting information flow. Additionally, we adopt an attention mask (AM) module to dynamically assign varying weights to the input features.