# A Multi-Source Separation Approach Based on DOA Cue and DNN
## 1 Introduction  
Sound source separation is a regular research field in audio signal processing, which has been studied dating back to the middle of the twentieth century. Sound source separation plays an important role in many areas, such as automatic speech recognition (ASR) [1, 2] and speech coding [3]. In the early years, researchers mainly focused on the sound source methods based on a statistical method. The hidden Markov model (HMM) can describe the short-time stationary characteristics of a speech signal which is generally used in speech separation [4]. The relationship between the mixed signal and the sound source signal is modeled by multiple independent HMMs, and then the model parameters are calculated to estimate the separated signals [5]. Subsequently, the separation method based on computational auditory scene analysis (CASA) was proposed in [6]. Firstly, auditory peripheral analysis is performed on mixed signals, and acoustic features such as the amplitude spectrum of the signal are obtained. The features are segmented to obtain the intermediate feature. Then, the sound source signal is separated by acoustic recombination. However, it is difficult for an auditory scene model to fully describe the real acoustic scene, so the CASA-based separation algorithm is limited in a complex environment. Later, the sound source separation method based on beamforming, which is divided into a fixed beamforming algorithm [7] and an adaptive beamforming algorithm, became popular [8]. The main idea of this method is to obtain the separation matrix. Recently, the improved beamforming method has been proposed. 'Single source zone' detection is introduced into linearly constrained minimum variance beamforming to achieve multi-source separation [9]. However, the performance ofthis method is poor in a high-reverberation environment. At the same time, researchers also pay attention to the sound source separation method based on independent component analysis (ICA), which assumes that the observed signals are statistically independent [10]. As an observed signal, the mixed signal is decomposed into the linear sum of statistically independent components through a series of linear transformations aiming to obtain the separated signals. The separation approach based on ICA is suitable for the case of low-reverberation conditions. Nevertheless, when the number of sound sources is more than that of microphones, it is difficult to obtain the separated signal with a high quality. In the last few years, approaches have been proposed based on the sparsity of a speech signal. First, the W-disjoint orthogonality (W-DO) hypothesis was proposed in [11], which means that there is at most one sound source dominant in some TF points when there are two or more sound sources. The core of the W-DO-based source separation is to find these TF points dominated by only one sound source, which can be achieved using different methods. For example, the direction of arrival (DOA) of a sound source provides guidance for finding these TF points in sound source separation [12]. Compared with some previous methods, the separation method based on the W-DO hypothesis has lower computational complexity [13]. However, with an increasing number of sound sources, the W-DO characteristic becomes weakened so that the performance of the W-DO-based approach decreases. Subsequently, improved methods have been proposed, which focus on both TF components dominated by one sound source (i.e., sparse components) and the other remaining TF components (i.e., non-sparse components). The separation method proposed in [14] uses a clustering algorithm with a dynamic threshold for the sparse component separation. Then, the non-sparse component is recovered by using the \"local-zone stationarity\" assumption. In recent years, deep neural networks (DNNs) have been introduced into sound source separation [15; 16], which have dramatically improved separation performance [17].