## 3 Learning Model
### Model to Predict the Beam Quality by Deep Learning  
In this paper, in order to reduce the training cost, the pilot signal is propagated only once in the coherence time of one channel. By contrast, past pilot signals predict the acquired power of the current narrow beam. With this, the training time will be halved. The architecture of the model that was used for prediction is shown in Figure 4. It can be seen that the basic architecture of this model inheritance comes from the estimation model, which means that the convolutional layers of this, as represented in Table 1, have exactly the same parameters and construction. The most fundamental difference between the estimation and the forecasting of models is the tracking of the differences in the time domain by using LSTMs for forecasting models, as Figure 5 shows. The convolution-based LSTM network was used in the prediction model. Both the spatial features that are extracted by the convolution, and the temporal features that are extracted by the LSTM, can be captured at the same time by the convolutional LSTM. A list of pixels is the input to the convolutional LSTM. In this method, in order to capture the variation in the beam quality in the time domain, the L-shaped low-resolution image is input into the prediction model.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Layer Type** & **Filters** & **Filter Size** & **FC Neurons** \\ \hline Conv 2D & 4 & (3,3) & - \\ \hline Sub-pixel Conv 2D [18] & - & - & - \\ \hline Upsampling 2D [19] & - & (2,2) & - \\ \hline Conv 2D & 40 & (3,3) & - \\ \hline Flatten & - & - & - \\ \hline Dense & - & - & 128 \\  & & & 64 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Architecture of the estimation model.  
Figure 4: The estimated model of this paper.  
LSTM is a kind of dynamic neural network that solves the problem that the traditional neural network cannot, which is to adaptively use the past data. LSTM is a special RNN with the ability to learn long-term dependency, and its structure is shown in Figure 6.  
The repeating module in an LSTM cell contains four interacting layers: a forgetting gate layer (\(f_{t}\)), an input gate layer (\(i_{t}\)), an output gate layer (\(o_{t}\)), and a new candidate layer (\(C_{t}\)). In the LSTM net structure, the gate is realized by a sigmoid function, and the forward propagation mathematical model of the LSTM neural network is as follows:  
\[\begin{array}{c}f_{t}=\sigma\Big{(}W_{f}\cdot[h_{t-1},x_{t}]+b_{f}\Big{)},\\ i_{t}=\sigma(W_{i}\cdot[h_{t-1},x_{t}]+b_{i}),\\ \widetilde{C}_{t}=tanh(W_{c}\cdot[h_{t-1},x_{t}]+b_{c}),\\ C_{t}=f_{t}\ast C_{t-1}+i_{t}\ast\widetilde{C}_{t},\\ o_{t}=\sigma(W_{o}\cdot[h_{t-1},x_{t}]+b_{o}),\\ h_{t}=o_{t}\ast tanh(C_{t})\end{array} \tag{7}\]  
where \(\sigma\) represents the sigmoid function:  
\[\sigma(x)=1/\big{(}1+e^{-x}\big{)} \tag{8}\]  
In the LSTM estimation model, the LSTM layer contains 256 neurons. To enrich this article, the deconvolution layer is used instead of the FC layer in the last part of the network. It is worth noting that the performance of the deconvolution super-resolution architecture is almost the same as that of the FC-layer super-resolution architecture in the case of input of different amounts of training data (namely, pixel sequences). However, in the case of deconvolution, the time cost of the training parameters is expensive, and so the training speed of each epoch element is slightly slower.  
Figure 5: The LSTM estimation model of this paper.  
Figure 6: The LSTM net structure.