# DMCNet-Pro: A Model-Driven Multi-Pilot Convolution Neural Network for MIMO-OFDM Receivers
## 4 The Structure of DMCNet-Pro  
_Model-Driven Receiver Network Structure_  
In Section 3, a data-driven scheme is adopted to treat the whole receiver as a black box for end-to-end model training. In some previous work, such as [13], a model-driven scheme was used to solve the problem of a single-antenna OFDM signal receiver. Based on the research results in Section 3, a model-driven receiver design is also used in this paper. DMCNet, designed in Section 3, includes several network components to process different input data and perform end-to-end model training. This section attempts to split and improve it, and design a model-driven deep learning receiver scheme. The model-driven network model is shown in Figure 5, which is named DMCNet-pro in this paper. The model-driven network DMCNet-pro includes signal denoising, a channel estimation network, and a signal detection network. In Section 3, it was shown that the model is also divided into several modules; however, in the training process, as a whole, an end-to-end training method is adopted. The final output result of the receiver and the transmitted signal are used to calculate the loss function, and then the optimizer uses this loss function to adjust the parameters of the entire network to reduce the loss of the next iteration, and the process is repeated to guide the specified training cycle. In the model-driven scheme, the loss function is calculated and trained in stages by using some known information. In DMCNet, a signal denoising network is added to initially remove the noise of the received signal passing through the channel. In DMCNet-pro, a signal denoising module is also added to denoise the pilot frequency and data, respectively. The difference is that the denoising network needs to be trained separately at this time. The input signal of the signal denoising module is the received signal, the label is the result after the same input passes through the noiseless channel, and the loss function is the mean square error loss between the actual received signal \(y\) and the result \(\hat{y}\) after the same signal passes through the noiseless channel, which can be expressed as:  
\[loss=\frac{1}{n}\sum_{i=1}^{n}\left(y_{i}-\hat{y_{i}}\right)^{2} \tag{4}\]  
where \(n\) represents the length of signal \(y\). This loss function is passed to the Adam optimizer, which adjusts the model parameters. The second step is required to train the channel estimation network. As mentioned above, the pilot frequency can actually be understood as a known sequence, which experiences the same channel propagation path as the actual data sequence to be sent; that is, it undergoes the same channel operation, and then obtains a string of output sequences. Through the output sequence and the known pilot sequence, the distribution of the channel can be estimated and the data can be received. Therefore, the received data and the known transmit pilot sequence can be used for channel estimation, and the least-squares (LS) channel estimation algorithm is used for initialization, that is:  
\[\widehat{H}_{LS}=\frac{y_{p}}{x_{p}} \tag{5}\] \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline  & **Module Type** & **Output Shape (8 Pilots)** & **Output Shape (32 Pilots)** \\ \hline Convolution layer 2 & \(1\times 9\) & [1, 256, 4] & [1, 256, 4] \\ \hline Sigmoid & – & [1, 256, 4] & [1, 256, 4] \\ \hline Bit decision & Threshold function & [1, 1024] & [1, 1024] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._where \(y_{p}\) represents the pilot part of the received signal and \(x_{p}\) represents the pilot sequence known at both ends of the transceiver. The initialized channel estimate \(\hat{H}_{LS}\) serves as the input to the channel estimate network. After initialization by the LS algorithm, the size of \(\hat{H}_{LS}\) is a vector with a length of 256, and the input channel estimation network is further purified.