# Channel Estimation for UAV Communication Systems Using Deep Neural Networks
## 2 System Model and Problem Formulation
### Problem Formulation
#### 2.1.2 Enhanced Gradient
Buildings in rural and suburban areas tend to be smaller and less densely populated than those in cities. These various multipath channel behaviors imply that the environmental variables and UAV height may have a big impact on the channel behavior and consequently the receiver design. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Scenario** & **Building Heights (m)** & **Number of Buildings** \\ \hline Urban & 100–120 & 100 \\ Suburban & 20–30 & 25 \\ Rural & 5–10 & 10 \\ Overseas & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 5: CDF of RMS-DS for different scenarios at 28 GHz. ## 4 Performance Evaluation

In this section, we implement the proposed GBRBM-based DNN in addition to other machine learning algorithms, i.e., backpropagation ANN and SVM. The considered simulation parameters include the GBRBM block, the number of neurons and layers of the network, and the value of the adaptive learning rate and number of the epoch. The total number of training vectors is 710, while the number of test vectors is 177, with 201 unknown variables with 100 iterations. ### GBRBM Blocks

Figure 6 shows the difference error between the measurements and the estimated values by using different numbers of GBRBM-based DNN. Different numbers of GBRBM are considered starting from 2 to 7, while the differences error between the estimated and measured RSS varies from \(-5\) to 15. It can be readily seen that the best results are obtained when six blocks of GBRBM-based DNN in the pre-training stage are used. The performance accuracies are 85.1%, 87.3%, 90.1%, 92.8%, 94.1%, and 93.7%, respectively. Since a proper epoch number can shorten the training period and the search space of solutions, the best epoch number is important to both the pre-training and training phases. Therefore, the perfect epoch number could be selected based on the value of this reduction function. For example, Figure 7 presents the difference error versus the number of epochs. Clearly, the difference error is stable when we reached around the 500 th epoch. Hence, the epoch number of the pre-training stage is set to 250, and the epoch number of the training stage is set to 500 epochs. After the GBRBM blocks and epoch number are determined, the neuron number must be set for every layer. The optimization process is quite tedious because the tuning assortment of the neuron number in every layer is arbitrary. Thus, we empirically set the neuron amounts and then run experiments to maximize the neuron amount of the sixth layer depending on the operation of both GBRBM-based DNN. In the pre-training stage, the difference in the RSS value between the estimated measure and the real measure decreases as the epoch number increases and is set to the 250 th epoch, as depicted in Figure 8.

Figure 6: GBRBM-based DNN in the pre-training stage versus the accuracy. ### Adaptive Learning Rate

The learning rate is similar to the step size of the gradient descent process. The precision will be greatly affected if it is set too big or too small. In particular, if the learning rate is too small, the training period grows, and a local optimal solution is likely to be trapped. Since there are pre-training and training stages, we must discover an individual optimum learning rate for all of them. We trained the traditional gradient with five learning rates (1, 0.1, 0.01, 0.001, 0.0001) to demonstrate how the learning speed can greatly affect training results. The resulting RBMs have enormous variance determined by the learning rate selection. When the learning rate was large, the result models completely failed, whereas better

Figure 8: The average difference between the estimated and real RSS values in the pre-training stage. Figure 7: Accuracy versus adaptive learning rate. results were obtained when the learning rate was too low. To test the suggested adaptive learning rate, we trained RBMs of the hidden neurons with the traditional gradient and the same five values (1, 0.1, 0.01, 0.001, 0.0001) to initialize the learning rate.