# Amplitude and Phase Information Interaction for Speech Enhancement Method
## 3 The Proposed Method Architecture  
The objective of this paper is to enhance noisy speech in the short-time Fourier transform (STFT) domain and attenuate background noise and reverberation to obtain clean speech. To accomplish this task, a model architecture named FullSubNet-pMix is proposed, as shown in Figure 1. This method utilizes the magnitude spectrum and phase spectrum of the speech in the frequency domain. It consists of three main components: an information interaction module, a full-band module, and a sub-band module. The sub-band module takes the information from the full-band module as part of its input. Figure 1: Structure of FullSubNet-pMix. The pMix block implements the interaction of magnitude and phase information. The unfold block partitions the magnitude spectrum into sub-bands. The full-band block obtains the features of the full-band. The concatenate operation concatenates the sub-bands’ features with the full-band’s features. The sub-band block obtains the features of all sub-bands. The model takes the magnitude spectrum \(X_{m(F\times T)}\) and the phase spectrum \(X_{p(F\times T)}\) as input, where \(F\) represents the temporal length of the speech and \(T\) represents the number of frequencies obtained after performing STFT on the speech. After the magnitude spectrum and phase spectrum are input into the model, the pMix module is first utilized to extract the temporal correlation of the phase spectrum and facilitate information interaction between the magnitude and phase spectra. The output of this module, denoted as \(X_{mp}\), is then fed into the subsequent full-band module to extract features and obtain the full-band feature \(F_{mp}\), which contains both the phase spectrum and magnitude spectrum information. By contrast, the initial input magnitude spectrum is divided into multiple sub-band units \(F_{sub}\), using the unfold module, where each unit corresponds to a specific frequency range. The full-band spectrum feature \(F_{np}\) and the sub-band units \(F_{sub}\) are concatenated to form the complete sub-band information. This information is then fed into the sub-band module to extract information and generate the predicted target CIRM using deep learning. The following sections provide a detailed description of these modules. The structure of the PMix module is illustrated in Figure 2. This unit takes the magnitude spectrum and phase spectrum as inputs and pads them with zeros, where the number of zeros is determined by the Lookahead value. PMix consists of four consecutive Magphase units. In each Magphase unit, a single 2D convolutional layer is used to process the input phase spectrum feature, followed by the information interaction between the phase and magnitude spectra. The corresponding formula is as follows:  
\[X_{0}^{P_{0}}=X^{P} \tag{1}\]  
\[X_{1}^{P_{i}}=conv^{P_{i}}(X_{0}^{P_{i}})(i=0,1,2) \tag{2}\]  
\[X_{2}^{P_{i}}=f_{m2P}\Big{(}X_{1}^{P_{i}},X^{m_{i}}\Big{)} \tag{3}\]  
\[X_{0}^{P_{i+1}}=X_{2}^{P_{i}}(i=0,1,2) \tag{4}\]  
where \(conv^{P_{i}}\) represents the output features of the i-th phase spectrum passed through the convolutional layer in Magphase. \(X_{0}^{P_{i}}\) and \(X_{1}^{P_{i}}\) represent the input and output information, respectively. The convolutional layer utilizes a kernel of size \(15\times 1\), aiming to capture the temporal correlation of the phase spectrum within a certain time range. There is no normalization layer or activation function following this convolutional layer. The addition of phase features in the input helps improve the training results of speech enhancement, and the interaction between phase and magnitude features also contributes  
Figure 2: Structure of pMix. The term ‘lookahead’ refers to zero-padding applied after the input features. The structure inside the dashed box is called the Magphase unit, and four connected Magphase units form the pMix block. to the prediction of the target result [19].