# Path Loss Prediction Based on Machine Learning: Principle, Method, and Data Expansion
## 4 Data Expansion: How to Get Enough Data?
### Combination with Classical Models  
Classical models are still valuable for path loss prediction, and they can also be combined with machine-learning-based models. In [33; 34], the classical models were employed for the error compensation of machine learning algorithms. Actually, classical models can also be utilized to expand the training dataset. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Metric** & **BPNN** & **SVR** & **RF** & **Log-Distance** \\ \hline RMSE [dB] & 4.74 & 4.54 & 4.19 & 5.10 \\ MAPE [\%] & 5.62 & 5.40 & 4.76 & 6.21 \\ MAE [dB] & 0.29 & -0.26 & 0.26 & 0.01 \\ MaxPE [dB] & 15.27 & 16.70 & 17.94 & 17.27 \\ ESD [dB] & 4.73 & 4.54 & 4.18 & 5.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of Prediction Accuracy of Different Predictors on the 80% Test Samples from TD-SCDMA BS. Figure 5: Prediction performance of different predictors on the test dataset. The samples are from three different BSs, with all samples from IS-95 BS and WCDMA BS and 20% of the samples from TD-SCDMA BS as training dataset and 80% of the samples from TD-SCDMA BS as test dataset. In 5G communication applications, more and more new frequency bands have been introduced. It is very time-consuming and costly to obtain a large amount of measured data at these new frequencies in a short time. It means there would not be no or very limited measured data can be used for modeling. Faced with this challenge, we offer a scheme that employs classical models to generate some training samples. Due to the limitations of accuracy and complexity, it may not be a good choice to directly generate all data samples from classical models and use them for training. The usage of classical models should also be on the basis of the prior information obtained from measured results. The procedure of this scheme is shown in Figure 6. Firstly, at known frequencies, the measured path loss values are compared with those predicted by the classical model. Then, we can find the positions where predicted results fit the measured data well. It means that at these positions the classical model can approximatively characterize the propagation mechanism. If the new frequency point is not far from the old ones, we can generate path loss values at these positions by classical model and insert them into the training dataset together with the measured values at the old frequencies. To show the feasibility of this scheme, we considered an aircraft cabin scenario in which path loss data were collected [35]. Three frequencies including 2.4 GHz, 3.52 GHz, and 5.8 GHz were taken into account. At each frequency we got 110 samples from 5 rows with 22 seats in each row. Each sample included a path loss value and two input features (frequency and antenna-separation distance). Through comparing the log-distance model with the measured data at 2.4 GHz and 3.52 GHz, we chose 30 positions with the smallest fitting errors. Then, path loss values at these positions were estimated by the log-distance model at 5.8 GHz and were added to the training dataset, together with those samples at 2.4 GHz and 3.52 GHz. All measured samples at 5.8 GHz were used for test purpose without participating in the training process. For BPNN, there were 4 neurons in the hidden layer with hyperbolic tangent sigmoid function as active function. In the SVR-based model, the regularization coefficient and parameter in the Gaussian radial basis kernel function are both 1. The insensitive loss is set as 0.125. For RF, the tree depth and the number of ensemble members were set as 6 and 20, respectively. The predicted results for 110 test samples at 5.8 GHz are shown in Figure 7. Although no sample at 5.8 GHz is used for training, these machine-learning-based models are in good agreement with measured data at this frequency. The RMSEs of BPNN, SVR, RF, and log-distance models are 1.61 dB, 2.24 dB, 1.90 dB, and 2.52 dB. The machine-learning-based models still outperform the log-distance model.