# Underwater-Acoustic-OFDM Channel Estimation Based on Deep Learning and Data Augmentation
## 3 The UWA-OFDM-Channel-Estimation Framework Based on Deep Learning
### DL-Based-Estimated-UWA-OFDM Channel  
We used the CNN-based-network framework to estimate the channel state, before which we needed to solve some necessary problems. First, as an input to the network, the image data are usually represented by the RGB three-channel matrix, but the channel-state information is all complex. Therefore, we wanted to modify the input layer of the network for this case. We first divided each complex matrix into two part-matrices: real and imaginary. To preserve the potential correlation between the real and imaginary parts, we reconstructed the two matrices overlapping as a new two-channel matrix. Moreover, some elements in the channel-state-information matrix usually have negative values, which affects the back propagation in the convolutional network and the correct convergence of  
Figure 4: The CWGAN-CP structure. Figure 5: The generator and discriminator network structures. the network. To do this, we used a Leak-Rectified Linear unit (LReLu) as our activation function after each convolution layer [26]:  
\[\mathrm{LReLu}(x)=\left\{ \begin{array}{cc}x,&x>0\\ b_{i}x,&x\leqslant 0\end{array} \right., \tag{9}\]  
where \(b_{i}\) was the constant parameter between 0 and 1. As the value in the matrix was very close to 0, it was likely to cause gradient vanishing throughout the convolution calculation. In order to solve this problem, we initialized the data before sending them to the network, and we eliminated the influence on the estimated-channel-state-information matrix in the output layer. The proposed channel-estimation-network framework based on the CNN is shown in Figure 6. First, the network input the data \(\hat{H}_{pilot}(k)\) for the preprocessing operation. The input \(\hat{H}_{pilot}(k)\) had to be divided into a real part and a virtual part. Then, we used several convolutional layers acting on the process of upsampling and downsampling, respectively, which were used as features to extract the signal and the transmission of internal information. We used the residual structure between the layers [27], and the output of all the previous layers was the input of the next layer. The output \(\hat{H}(k)\) can be expressed as  
\[\hat{H}(k)=F_{n}(F_{n-1}(\cdots F_{1}(\hat{H}_{pilot}(k)))), \tag{10}\]  
where \(F_{n}(\cdot)\) represents convolution operation. Due to constant underground sampling, the feature information eventually passes through the bottleneck layer, where a lot of detail features may be lost. To alleviate this problem, we adopted a U-Net-like structure, and between upper and downsampling, we used the operation of jump connections, which integrated richer higher convolutional feature layers and lower convolutional features, to further compensate for the lost information of downsampling during the encoding stage. Each of the networks contained three upsampling and downsampling operations. In the first downsampling, 32 filters were used, and for each time of the subsequent downsampling, the number of filters was twice as many as before. The output from each layer in the upsampling remained consistent with the downsampling. After obtaining the features oversampled in the last layer, we did not directly regress the channel information, but we designed a Channel-Attention-Denoising-(CAD) module to further optimize the channel information [28], as shown in Figure 7. Here, our module used the channel-attention mechanism, and we wanted the model to selectively focus on or reinforce the information of a specific underwater-acoustic channel when processing features, reducing the attention to unnecessary information. While reducing the model computational burden, the model was allowed to adaptively learn the weights of frequency features during training, as different environments and underwater-acoustic channels may lead to differences in the signal-frequency spectrum. Specifically, we input the features as follows: \(f\in\mathbb{R}^{C\times H\times W}\).