# Path Loss Prediction Based on Machine Learning: Principle, Method, and Data Expansion
## 3 Methods for Path Loss Prediction
### Comparison of Different Models  
The BPNN-based model can fully approximate the complicated nonlinear relationship, whereas many parameters need to be selected. In addition, it is difficult to explain the learning process and predicted results. The SVR-based model is flexible because we can get different models by choosing different kernel functions and different parameters. This flexibility theoretically ensures that the model has strong generalization ability. Besides, the complexity of the model does not depend on the dimension of the input features, avoiding the curse of dimensionality. The main weaknesses of the SVR-based method are the kernel definition and its computational complexity. The meaning of the decision tree is easy to understand and explain. As an example, RF-based algorithm can provide a natural ranking of features in the model. This advantage is good for the feature selection. Nevertheless, the decision tree often ignores the correlation between the features. In order to evaluate the performance of these machine learning models, a measurement campaign was carried out in an urban macrocell scenario in Beijing, China. Figure 3 shows the top view of the measurement routes. The considered scenario mostly consists of buildings lower than ten stories. There were also large pedestrian bridges and road signs sparsely distributed, and an average tree density of roughly 6 m high along both sides of the roads. The received signals from a TD-SCDMA BS at the operating frequency of 2021.4 MHz in this area were considered. The antenna height of the TD-SCDMA BS was about 40 m over the ground. The measurements were made with cars driving on roads in this urban area. An omni-directional receive antenna was mounted on the top of the car roof and connected to a drive-test equipment. The drive-test equipment can record the received signal power and the location information through an external GPS module. Then, the path loss values can be calculated in the offline post-processing and mapped to locations. More details of the equipment can be found in [28]. The measurement routes and the position of the TD-SCDMA BS are illustrated in Figure 3. The car moved from the south (sample index 1) to the north (sample index 517), and then turned to the west direction. The total number of collected samples through the two routes was 1483. Each sample included a path loss record and an antenna-separation distance which was calculated according to the GPS information. The antenna-separation distance was used as a single feature. We randomly selected 80% of samples as the training dataset and the remaining 20% as the test dataset. Three aforementioned models, including BPNN, SVR, and RF, were used to predict the path loss values in the test dataset. For BPNN, rectified linear unit function was selected as the activation function. A three-layer feed-forward structure was employed and the optimal number of neurons in  
Figure 3: Top view of the measurement routes and TD-SCDMA BS in the urban scenario. the hidden layer was 15. The Gaussian radial basis function was used as the kernel in the SVR-based model. Regularization coefficient, insensitive loss, and the kernel function parameter are set to 451, 91, and 0.25. As the hyperparameters used in RF-based model, the maximum tree depth was 5 and the number of ensemble members was 150. The log-distance model was also considered for comparison. Figure 4 illustrates the measured data and the predicted results of different models. The x-axis represents the index of test samples, which is corresponding to the positions in the route along the driving direction as shown in Figure 3. As can be observed, the path loss values of Route 1 were higher than those of Route 2. The reason may be that in Route 1, the receive antenna was mainly under non-line-of-sight conditions due to the obstructions of buildings and trees. In contrast, the line-of-sight path played a dominant role in Route 2. The path loss values at all positions in the test dataset were predicted by using different models.