# A Dual-Channel End-to-End Speech Enhancement Method Using Complex Operations in the Time Domain
## 1 Introduction  
Speech enhancement refers to a set of signal processing techniques aimed at improving the quality and intelligibility of speech signals by suppressing interference signals, such as background noise and reverberation. External noise and environmental reverberation can negatively impact speech signals received by microphones, resulting in a low signal-to-noise ratio (SNR) that impairs human hearing and the accuracy of systems used in human-computer interactions, such as speech recognition and speech wake-up applications [1]. Therefore, the study of speech enhancement techniques is critical to enhancing speech signals and improving overall system performance. Traditional single-channel speech enhancement algorithms rely on signal processing techniques such as time-domain, frequency-domain, spatial-domain, and high-order statistics. However, it is challenging to adapt these methods to changing acoustic scenarios [2]. Over the past decade, deep learning-based algorithms have achieved significant success in speech enhancement. In particular, several methods that exploit time-frequency-domain feature mapping have made marked progress in noise reduction, as demonstrated in [3, 4, 5]. Nevertheless, these approaches typically ignore the modeling of speech signal phase information. Unlike time-frequency-domain-based methods that only focus onmagnitude regression using the short-time Fourier transform (STFT), some recent methods [6; 7] reconstruct the speech signal by directly processing the time-domain waveform. Deep Complex Convolution Recurrent Network for Phase-Aware Speech Enhancement (DCCRN) [8] innovatively proposes complex number-domain features as input features to neural networks and demonstrates great potential in noise reduction. The DCCRN design simulates complex value operations using a complex number network. In DCCRN, the input of the network is both the real and imaginary (RI) information of the complex STFT. By concurrently considering the amplitude and phase of the STFT, DCCRN significantly improves the performance of speech enhancement models. In addition, multichannel speech enhancement generally outperforms single-channel speech enhancement due to additional spatial information provided by the number of available microphones [9]. There are two main types of multichannel approaches: time-domain and frequency-domain approaches. Classic signal processing-based techniques such as beamforming have been used, including minimum variance distortionless response (MVDR) [10] and generalized sidelobe canceller (GSC) formulation [11], where the energy of the signal at the output is minimized, while the energy in the target direction is maintained. A beamformer requires a target steering vector [12], and in most cases, the method for estimating the steering vector is based on direction of arrival (DOA) estimation [13]. However, the estimation is not error-free and can significantly impact the performance of the beamforming technique. Recently, time-domain convolutional denoising autoencoders (TCDAEs) [9] have been designed; they exploit the delay between multichannel signals to directly extract the characteristics of time-domain signals using an encoder-decoder network. Although TCDAEs exhibit better performance than single-channel DAEs [14], they use limited noise types, which results in suboptimal performance. [PERSON] et al., proposed a complex spectral mapping approach combined with minimum variance distortionless response (MVDR) beamforming, which produces beamforming filter coefficients based on the covariance matrix of the signal and noise [15]. Alternatively, [PERSON] et al. [16] proposed neural network adaptive beamforming (NAB), which learns beamforming filters without estimating the direction of arrival (DOA) or computing the covariance matrix. NAB outperforms conventional beamforming methods but is applied to an adaptive neural network in the time-frequency domains.