## 4 Propagation Loss Calculation Using the Improved TWPE Model
### Deep Learning Model Predicts Land-Based Ducting Propagation Using Geomorphology Data  
It was found that the intercity links whose terrains are similar to that of the intercity link analyzed in the previous sections, such as Shanghai-Wuxi or Jiaxing-Wuxi, are prone to the ducting effects caused by meteorological changes, causing remote interference at the antenna height. Since most of the relevant cities and landform data are less available, in this section, we use d1300 randomly generated datasets with different propagation distances, terrains, and land covers to perform physical simulations of over-the-horizon PL distributions under the same radar parameters, duct parameters, and random turbulence as the previous sections. The intercity link maximum distance was randomly generated within 90-100 km. The terrain relief height was randomly generated within 0-20 m. The LC type was randomly generated between 9 and 17 according to the IGBP classification scheme, and the corresponding dielectric parameters are listed in Table 3.  
The simulated 1300 groups of terrain, land cover, and dielectric parameters at different distances and the PL at the corresponding antenna height were used for deep learning modeling. We intended to build a deep learning model to predict the PL on the intercity link with input parameters of terrain and land cover characteristics, and the ducting and radar environment settings remained the same as in previous sections. Before training, because the randomly generated data may have been inconsistent with the actual situation, the obvious errors of the forward-propagation results were eliminated. A total of 56 sets of data were eliminated, and the remaining 1244 sets of data were used for deep learning modeling. After shuffling the order of datasets, the first 900 datasets were used as training sets, and the last 344 sets of data were used to test the training model. The  
Figure 27: The range-dependent PL on four intercity links at antenna heights of (**a**) 60 m and (**b**) 40 m. (**a**) Range-dependent PL from four cities to Wuxi at ANH = 60 m. (**b**) Range-dependent PL from four cities to Wuxi at ANH = 40 m.  
deep multilayer perceptron (DMLP) network was used here for deep learning modeling. We continuously optimized the parameters to obtain the optimal model, and a total of 4000, 2000, 3000, and 999 neural networks were built for training. The schematic diagram of the deep learning forward prediction model is shown in Figure 28.  
One of the results calculated by the TWPE scattering model in the test set was used to compare the prediction result by the deep learning model, as shown in Figure 29a, with the antenna height at 60 m, and Figure 30a with the antenna height at 40 m. Using the mean square error as the loss function, the formula of the specific loss function is as follows:  
\[loss=\frac{\sum_{i=1}^{n}(pred(i)-y(i))^{2}}{n} \tag{20}\]  
where \(pred(i)\) represents the range-dependent PL predicted by the network, \(y(i)\) is the true range-dependent PL calculated by the TWPE model, and \(n\) is the number of groups of training datasets. Using the following definition to give the model prediction accuracy functions to evaluate the quality of the established model  
\[acc=1-\frac{y_{pred}-y_{true}}{y_{true}} \tag{21}\]  
The accuracy of each range step was solved at antenna heights of 60 or 40 m, and the mean value was defined as the predicted accuracy of the sample. Then the predicted accuracy distribution was obtained on each tested sample. The accuracy results of test datasets are shown in Figures 29b and 30b, respectively. When the antenna height was 60 m, the MSE of the DMLP prediction was 118.202749. When the antenna height was 40 m, the MSE was 108.696593. After the optimized deep learning parameters were well trained, they could quickly and efficiently predict (at a certain fixed antenna height, terrain, and landform) whether there would be communication interference problems between cities around 100 km apart with ducting and turbulence.