# Adversarial Sample Generation Method Based on Frequency Domain Transformation and Channel Awareness
## 4 Channel Estimation Method Based on Deep Learning
### The Super-Resolution Denoising Residual Network Model Based on OMP Algorithm  
In order to further improve the accuracy of channel estimation, a channel estimation framework was developed. This framework integrates the residual network (Resnet) module based on SDNet and is denoted as SDRNet. Here, the ResNet module is integrated into the channel estimation framework. Adding residual connections in the part after three convolutions can help the network better learn the residuals to solve the problem of vanishing gradients and thereby improve the denoising performance. The improved channel estimation framework OMP-SDRNet also includes two stages: (1) offline training and (2) online estimation. The entire workflow is shown in Figure 6. Similar to the SDNet framework, the training data generation method of SDRNet is the same, but their network architectures are different. The ResBlock component of the super-resolution denoising residual network (SDRNet) is a key architectural innovation. This section focuses on the design, functions, and impacts of ResBlocks, which are integrated to solve the vanishing gradient problem in deep networks and enhance the channel estimation performance in OFDM systems. The ResBlock in Figure 6 consists of a skip connection and two convolutional sub-layers, aiming to facilitate deep learning by enabling the network to learn residual mappings rather than direct input-output relationships. The detailed structure is as follows. Convolutional layer: Two consecutive \(3\times 3\) convolutional layers, filled to maintain the dimension of the feature map. After each convolutional layer, there is batch normalization (BN) to standardize activation and accelerate training, and there is also a ReLU activation function to introduce nonlinearity. Skip the connection: Directly connect the input of the block to the output of the convolutional layer, allowing the network to learn the residual between the input and the expected output. This design ensures that the network can learn incremental improvements (residuals) instead of reconstructing the entire signal from scratch, reducing gradient vanishing. In Figure 6, after the initial feature extraction layer based on srcnn, multiple Resblocks are cascaded in the denoising module of SDRNet. The workflow is as follows. Feature extraction: The SRCNN module (the first few layers) processes the OFDM pilot signal to restore the high-resolution channel features. Residual denoising: Cascades ResBlocks receive features from SRCNN and gradually suppress noise by learning residuals (i.e., the difference between noisy features and clean channel responses). Channel reconstruction: The output of ResBlocks is fed into the final convolutional layer to generate an estimated channel matrix, leveraging denoising and enhanced features. The skip connections in ResBlocks bypass the deep convolutional layers, ensuring that the gradients propagate effectively through the network. Compared with the non-residual SDNet that lacks such connections, this allows SDRNet to train deeper architectures. Noise suppression: By focusing on residual learning, SDRNet more effectively separates noise from the effective channel features. For instance, in low signal-to-noise ratio scenarios, ResBlocks can distinguish between multipath fading (expected signal) and Gaussian noise (residual), thereby generating clearer estimates. At this time, the output result can be expressed as:  
\[x^{(j)}=\mathcal{F}_{conv}\Big{[}x^{(i)}\Big{(}w^{(i)}\Big{)}\Big{]} \tag{32}\]  
The improved channel estimation framework OMP-SDRNet also includes two phases: (1) offline training and (2) online estimation. The whole workflow is shown in Figure 4. where \(\mathcal{F}_{conv}(\cdot)\) represents the convolution operation; \(x^{(i)}\) indicates the input training data; \(w^{(i)}\) represents the set of parameters of the three convolutions operation processes. Next, the results after three convolutions and linear activation are used as the input of the first Residual block.