# A Joint Denoising Learning Model for Weight Update Space-Time Diversity Method +
## 4 A Joint Denoising Learning Model for Weight Update STD Method
### The UWA Signal Analysis and Pre-Processing  
The signal transmitted through the UWA channel has the characteristics of a complex-type structure. At the same time, the UWA signal has short-time smoothness, i.e., it can behave as a quasi-steady-state process in a short period. In addition to having the characteristics of an acoustic signal, it can be represented in two dimensions by the time  
Figure 4: Two-stage structure of the proposed method. frequency relationship and has the structural characteristics of an image. Based on the above characteristics, we propose a complex-type orthogonal compression pre-processing structure, the composition of which is shown in Figure 5.  
The pre-processing structure consists of three parts: data collation, complex-type data processing, and orthogonal compression. In the pre-processing stage, \(\mathbf{y}(t)\) and \(\mathbf{\tilde{n}}(t)\) will be separated and compressed into \(\left(\mathbf{TR}_{y},\ \mathbf{TI}_{y}\right)\) and \(\left(\mathbf{TR}_{h},\mathbf{TI}_{h}\right)\) after being processed in the above three steps. \(\left(\mathbf{TR}_{y},\mathbf{TI}_{y}\right)\) and \(\left(\mathbf{TR}_{h},\mathbf{TI}_{h}\right)\) are used as input features for the complex-CGAN, which makes the noise-reduction learning model cope with complex-type data with better performance. The specific pre-processing steps are as follows:  
(1) Data collation. Since the UWA signal has a short-time stable characteristic, we need to crop the UWA data to be within the short-time smooth interval [62]. The UWA signal can show relatively smooth amplitude characteristics at 20-30 ms, suitable for feature extraction. The data can be cropped in frames using windowing, and we set the frame length of each data to 20 ms and the overlap length between frames to 10 ms. A window function was used in the framing to reduce the spectral energy leakage, and the Hamming window was used for the window function [63], which takes the value of 0.53836, and \(N\) is the window length; the window function can be expressed as:  
\[\text{window }(n)=\alpha_{0}-(1-\alpha_{0})\cos\left(\frac{2\pi n}{N-1} \right), \tag{6}\]  
Short-time Fourier transform (STFT) is applied to each frame to obtain the time-frequency two-dimensionalization matrix. For \(\mathbf{y}(t)\) and \(\mathbf{\tilde{n}}(t)\), the corresponding STFT results are \(\mathbf{y}(t)\rightarrow\mathbf{y}(t,f)\) and \(\mathbf{\tilde{n}}(t)\rightarrow\mathbf{\tilde{n}}(t,f)\). The time-frequency two-dimensional form of the received signal \(\mathbf{y}(t)\) is shown in Figure 6a. Figure 6b shows the data framing strategy for the pre-processing stage. (2) Complex processing module. Since the noise-reduction learning model needs to process complex-type data, we designed a complex processing module in the pre-processing stage, which is mainly used to extract complex features. For the received signal \(\mathbf{y}(t)\), \(\mathbf{y}(t)=\mathbf{R}+\mathbf{I}*j\), its real part \(\mathbf{R}\) contains the amplitude information of the signal and the imaginary part \(\mathbf{I}\) contains the phase information. For this purpose, we used multiple complex convolution kernels in the complex processing module to perform feature extraction of complex-type data to obtain features with real and imaginary parts separated. Suppose  
Figure 5: Complex-type orthogonal compression pre-processing structure. Figure 6: Data collation of UWA signals: (**a**) the time–frequency two-dimensional form of the received signal; (**b**) the data framing strategy for the pre-processing stage. the complex vector of a target signal is set as \(\mathbf{h}\). In that case, the complex filter matrix is \(\mathbf{H}\), \(\Re(\mathbf{H}*\mathbf{h})\)denotes the real part of the convolution operation, and \(\Im(\mathbf{H}*\mathbf{h})\) denotes the imaginary part; Figure 7 shows the convolution structure of the complex processing module. (3) Orthogonal compression.