# Adversarial Sample Generation Method Based on Frequency Domain Transformation and Channel Awareness
## 4 Channel Estimation Method Based on Deep Learning
### Residual Channel Estimation Framework for Super-Resolution Denoising Based on Deep Learning
#### 4.1.2 Model Integration  
In the task of channel estimation, the time-frequency domain characteristics of the channel are complex and changeable, and are vulnerable to noise interference, resulting in limited estimation accuracy. In the field of image processing, super-resolution technology can restore high-resolution details from low-resolution data, and denoising technology can effectively remove noise from images. Since the signal data structure in channel estimation is similar to the image data in features such as multi-channel and two-dimensional distribution, drawing on the SRCNN and DNCNN networks in image processing, the two are integrated and applied to channel estimation. By taking advantage of their abilities to extract details and reduce noise, the accuracy and reliability of channel estimation are improved.  
The purpose of SRCNN is to improve the spatial resolution of images. The core idea of SRCNN is to learn the mapping from low-resolution images to high-resolution images through convolutional neural networks. SRCNN consists of three convolutional layers:  
\[Y_{srcm}=f_{3}(w_{3}\times f_{2}(w_{2}\times f_{1}(w_{1}\times X))) \tag{22}\]  
where \(X\) is the input signal, \(Y_{srcm}\) is the output signal, \(w_{i}\) represents the convolutional kernel of layer \(i\), \(f_{i}\) represents the activation function.  
SRCNN achieves super-resolution through three layers of convolution. Feature extraction layer \(f_{1}\): Map the low-resolution input to the high-dimensional feature space to capture the macroscopic characteristics of the channel response. Nonlinear mapping layer \(f_{2}\): Enhance the feature expression ability and restore the high-frequency details lost due to the multipath effect. Reconstruction layer \(f_{3}\): Synthesize high-resolution output, whose output dimension matches the input dimension of DNCNN.  
The purpose of DNCNN is to remove noise from images, and its core idea is to reduce noise through residual learning. DNCNN consists of multiple convolutional layers and batch normalization layers:  
\[Y_{dncnn}=X-\mathcal{F}(X;\Theta) \tag{23}\]  
where \(X\) is the input signal, \(Y_{dncnn}\) is the output signal, \(\mathcal{F}(X;\Theta)\) is the convolutional network part of DNCNN, which is capable of extracting the mapping relationship of noise.  
In order to integrate these two networks and apply them to channel estimation, this paper designs a model (SDNet) that combines the advantages of both. First, the real and imaginary parts of the complex signal are regarded as two channels of the image, respectively, to construct the input data. Next, the input data is sent to SRCNN to improve the resolution of the signal and obtain the preliminary estimated signal. Finally, the estimated signal output by SRCNN is sent to DNCNN to further remove the noise in the signal and obtain the final accurate channel estimation result. Channel estimation requires restoring the frequency domain details (super-resolution) first and then suppressing the noise (denoising), which is consistent with the image processing flow. The real and imaginary parts of the complex signal are used as dual-channel inputs, retaining the joint phase-amplitude information and enabling the image processing method to be transferred to channel estimation. The key to model fusion lies in the reasonable connection of the two networks, so that the output of the former network can be seamlessly used as the input of the latter network.