# Channel Estimation for UAV Communication Systems Using Deep Neural Networks
## 2 System Model and Problem Formulation
### Problem Formulation
#### 2.1.2 Enhanced Gradient
Of this test information, the outcomes are more stable, the variance among the consequent RBMs is smaller than the results obtained with the learning rate regardless of the initial learning rate, and all RBMs were trained efficiently. These results have revealed that the adaptive learning rate performs better, leading to ameliorated results. However, it was slightly better to use a continuous learning rate of 0.001 in both pre-training and training stages. Figure 7 shows the adaptive learning rate performance during learning. The process found suitable learning rate values when the enhanced gradient was used. Specifically, one will find six GBRBM blocks for the pre-training stages and five network layers to the training in the autoencoder. The neuron numbers for hidden layers of multi-block GBRBM are 64, 56, 48, 32, and 16, respectively. The epoch amounts of the pre-training and coaching phases are set to 250 and 500, respectively. The learning speeds of the two phases are equally set to 0.001, as shown in Table 2.

The GBRBM-AE parameters were set as training and pre-training algorithms to compare the results for 50 independent trails to obtain the mean, best, and worst values, as shown in Table 3.

Figures 9 and 10 depict the best results obtained from the SVM algorithm, and similarly, Figures 11 and 12 present the best results of the ANN method. Specifically, Figure 9 presents the value of the received signal obtained by the best SVM compared to the measurement the UAV took. The red dots represent the measurement values, while the blue line represents the SVM output. Although the SVM predicted value was close to the experimental value, it does not consider adequately near optimum values. Furthermore, Figure 10 depicts the histogram of the difference between the real and estimated values. Therefore, we may conclude that the SVM is well modeled but insufficient, as it has accentuated large errors. Table 4 indicates the best results obtained from GBRBM-AE, ANN, and SVM, and the indicators used are the mean absolute error (MAE), mean absolute percent error (MAPE), and the root mean squared error (RMSE). Figure 10: Statistical distribution of the difference in the RSS value of estimated (SVM) and real RSS values (dB). Figure 9: Difference in the RSS value of estimated (SVM) and real RSS values (dB). In contrast, the results of ANN show a better performance, as can be seen in Figures 11 and 12. ANN performs better than SVM and adequately modeled the received signal power with better prediction accuracy. In addition, the best results were obtained with GBRBM-AE, as presented in Figures 13 and 14. Clearly, the values of the GBRBM-AE method are the best results compared to the previously considered algorithms. The green line represents the GBRBM-AE output, while the red dots depict real UAV measurements. In addition, we noticed that the predicted values are adequately close to the measurement values. The accuracy result of the proposed model is shown by the time-complexity analysis, which also shows how long it takes to train and validate the model in Figure 5:0

Figure 5:1 Difference in the RSS value of estimated (ANN) and real RSS values (dB). Figure 5:2 Statistical distribution of the difference in the RSS value of estimated (ANN) and real RSS values (dB). Figure 5:3 Statistical distribution of the difference in RSS value of estimated (GBRBM-AE) and real RSS values (dB). Figure 5:4 Difference in the RSS value of estimated (GBRBM-AE) and real RSS values (dB). \begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Time Cost (ms)** \\ \hline GBRBM-AE & 2.1 \\ ANN & 7 \\ SVM & 68 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Time Cost. ## 5 Conclusions

This paper proposed a framework based on GBRBMs integrated with an autoencoder-based DNN to estimate the received signal power at a UAV flying in a range of altitudes and connected to a cellular network. Real UAV signal power measurements are used for system training and validation.