# Path Loss Prediction Based on Machine Learning: Principle, Method, and Data Expansion
## 4 Data Expansion: How to Get Enough Data?
### Data Transferring  
One direct way is to utilize the existing data acquired at other frequencies or in other scenarios. Data collected from a similar environment can be adopted for the training purpose. If the generalization capability of the machine-learning-based model is good enough, data from other environments can also be involved.  
Nowadays, new frequency bands are continually exploited in wireless communication systems. In empirical models like the path loss model used in WINNER II [29], a frequency-dependent component is added to make the path loss model suitable for a given frequency range. Machine-learning-based models provide another solution, which can involve the frequency as one input feature. Then, the measured data at a known frequency can also be used for training. It should be noted that the frequency difference cannot be too large. Otherwise, the different mechanisms of electromagnetic wave propagation may affect the model performance.  
The feasibility of this data transferring method has been verified by measured data from different frequencies and different scenarios. Besides the aforementioned TD-SCDMA BS, we considered two more BSs, including an IS-95 BS and a WCDMA BS. These three BSs were at different positions within a 6 km diameter. The measured routes were different from those in Figure 3, but all the route were selected in similar urban scenarios. The operating frequencies of the IS-95 and WCDMA BSs were 877.26 MHz and 2127.6 MHz, respectively. The same equipment was used to collect received power values and locating information.  
We collected 659 samples from the IS-95 BS and 416 samples from the WCDMA BS. All these samples were used as training data. Meanwhile, only 20% samples from TD-SCDMA BS were used for training purpose and the remaining ones were put into the test dataset. After hyperparameter optimization, a three-layer BPNN with 20 neurons in the hidden layer was built. In the SVR-based model, the Gaussian radial basis function was selected as the kernel. Regularization coefficient, insensitive loss, and the kernel function parameter are 491, 21, and 0.25. In the RF-based model, we finally set the maximum tree depth to 7, the number of ensemble members to 14, and maximum 2 features for each split. For comparison, a frequency-dependent component was added to the log-distance model in the same way as [29].  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Metric** & **BPNN** & **SVR** & **RF** & **Log-Distance** \\ \hline RMSE [dB] & 4.65 & 4.21 & 3.93 & 5.28 \\ MAPE [\%] & 5.44 & 4.94 & 4.58 & 6.53 \\ MAE [dB] & 0.81 & 0.11 & 0.10 & 0.24 \\ MaxPE [dB] & 13.97 & 12.18 & 12.06 & 19.50 \\ ESD [dB] & 4.59 & 4.22 & 3.94 & 5.29 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of Prediction Accuracy of Different Predictors on the 20% Test Samples from TD-SCDMA BS.  
The predicted results of different models on the test dataset are illustrated in Figure 5, and the measured path loss values are also shown for comparison. Again, different metrics are employed to evaluate the prediction error. As illustrated in Table 2, the RMSEs of BPNN, SVR, RF, and log-distance models are 4.74 dB, 4.54 dB, 4.19 dB, and 5.10 dB. With most of the training data from other environments and frequencies, machine-learning-based models can still get satisfactory performance at a new frequency and within different routes.  
It should be noticed that limited to the restriction of measured data, only antenna-separation distance and frequency are used as input features. Both of them are important parameters in the path loss modelling and are included in many standardized models, e.g., WINNER I [30], WINNER II [29], WINNER+ [31], and IMT-Advanced (IMT-A) [32] channel models. With these features, our simulation results have already shown that these machine-learning-based models agree well with measured data.