# Denoising Generalization Performance of Channel Estimation in Multipath Time-Varying OFDM Systems
## 4 NDR-Net Assisted Channel Estimation
### NLE Module  
To solve the problem of insufficient performance of DnCNN under unknown noise level, a convolutional and fully connected noise level estimation network is proposed in this paper. The network is used as a feedforward network of DnCNN to achieve adaptive noise by taking the noise level of NLE output as a known condition of DnCNN. When SNR does not match, \(\hat{\sigma}\) represents the estimated SNR value of the current environment. When the channel model does not match, \(\hat{\sigma}\) represents the root mean square delay spread of the current model. When the moving speed does not match, represents the corresponding Doppler shift value.  
The specific structure of NLE is shown in Figure 4, with 10 layers. The first layer is a convolutional layer using 32 different filters of size \(3\times 3\times 1\), followed by a ReLU function. The middle five layers are convolutional layers, which serve the same purpose as the hidden layers of DnCNN, except that the filter size is changed to 32. A pooling layer of size \(2\times 2\) is also added after each layer to reduce the network parameters. The last four layers are fully connected layers, which gradually synthesize the features extracted from the previous layer. The number of connection points is 2000, 200, 50, 1, respectively. Each fully connected layer is followed by a ReLU function for nonlinear operations.  
Selection of Pooling Layers  
Pooling includes Maxpooling and Averagepooling. In NLE, in order to determine the final pooling choice, the noisy channel is modeled as an image input to NLE, SNR is used as a label, and NLE is considered as a regression problem for the experiment. SNR was chosen as the label because the changes of channel model and moving speed are based on SNR.  
Figure 4: The network structure of the NLE.  
Figure 3: The framework of NDR-Net.  
Therefore, ensuring the accuracy of SNR estimation is also a prerequisite for improving the generalization performance in other aspects. By employing these two pooling methods separately, the estimates of NLE at different SNRs were recorded. Root Mean Squared Error (RMSE) was used to measure the accuracy of the prediction results. The calculation formula is as follows:  
\[\text{RMSE}(\sigma)=\sqrt{\frac{1}{N}\sum_{i=1}^{N}(\hat{\sigma}-\sigma)^{2}} \tag{12}\]  
where \(N\) indicates the size of the data sample in each SNR group, \(\sigma\) denotes the true SNR value, and \(\hat{\sigma}\) denotes the predicted SNR result.Tables 2 and 3 list the predicted \(\hat{\sigma}\) and the corresponding RMSE values for 500 sets of data when \(\sigma\) is equal to 5, 10, 15, 20, 25, 30, 35, respectively. As can be seen from Table 3, the error predicted by using average pooling is smaller than that predicted by maximum pooling at any SNR. The reason for this result is that the network model is not deep in layers, and the use of maximum pooling can easily filter out the useful signals by judging them as noisy signals, which leads to a poorer estimation performance than the average pooling. Therefore, the Averagepooling method is used in the subsequent experiments.