# Channel Estimation for UAV Communication Systems Using Deep Neural Networks
## 2 System Model and Problem Formulation
### Problem Formulation
#### 2.1.2 Enhanced Gradient
```
Input:Epoch number, \(v\), \(K\), GBRBM number, \(L\) Output:\(\
abla_{o}w_{ij}\), \(\
abla_{o}c_{j}\)
1 Initialize \(\
abla w_{ij}\), \(\
abla b_{i}\), \(\
abla c_{j}\) randomly, \(\mathbf{v}_{dm}^{1}\leftarrow\mathbf{v}\)
2 whilefor each epochdo
3 while\(m\leq M\)do
4 Calculate \(h_{dm}^{m}\) from (5)
5 Calculate \(v_{dm}^{m}\) from (6)
6 Update the value of \(\
abla w_{ij}\), \(\
abla b_{i}\), \(\
abla c_{j}\) using (16)
7 end while
8 Repeat until the convergence is met
9 end while
```  
**Algorithm 1**Pre-training the GBRBM blocks (Unsupervised learning)  
```
Input:Epoch number, \(v\), \(K\), GBRBM number, \(L\) Output:\(\
abla_{o}w_{ij}\), \(\
abla_{o}c_{j}\)
1 Initialize \(\
abla_{e}w_{ij}\leftarrow\
abla w_{ij}\), \(\
abla_{e}b_{i}\leftarrow\
abla b_{i}\), \(\
abla_{e}c_{j}\leftarrow\
abla c_{j}\)
2 whilefor each epochdo
3 while\(m\leq M\)do
4 Estimate the decoded output using (18)
5 end while
6 Estimate the MSE using (10)
7 Fine tune \(\
abla_{e}w_{ij}\), \(\
abla_{e}b_{i}\), \(\
abla_{e}c_{j}\) using backpropagation
8 Repeat until the convergence is met
9 end
```  
**Algorithm 2**Fine tuning of autoencoder (Unsupervised Learning)  
```
Input:Epoch number, \(v\), \(K\), GBRBM number, \(L\) Output:\(\
abla_{o}w_{ij}\), \(\
abla_{o}c_{j}\)
1 Initialize \(\
abla_{o}w\leftarrow\
abla_{e}w^{m}\), \(\
abla_{o}b\leftarrow\
abla_{e}b^{m}\), \(\
abla_{o}c\leftarrow\
abla_{e}c^{m}\)
2 whilefor each epochdo
3 Use backpropagation to estimate the fine tuning \(\
abla_{o}c\), \(\
abla_{o}w\)
4 Repeat until the convergence is met
5 end
```  
**Algorithm 3**Fine tuning of the data labels (Supervised Learning)  
```
Input:Epoch number, \(v\), \(K\), GBRBM number, \(L\) Output:\(\
abla_{o}w_{ij}\), \(\
abla_{o}c_{j}\)
1 Initialize \(\
abla_{o}w\leftarrow\
abla_{e}w^{m}\), \(\
abla_{o}b\leftarrow\
abla_{e}b^{m}\), \(\
abla_{o}c\leftarrow\
abla_{e}c^{m}\)
2 whilefor each epochdo
3 Use backpropagation to estimate the fine tuning \(\
abla_{o}c\), \(\
abla_{o}w\)
4 Repeat until the



## 3 UAV Measurements

In this section, simulation results are provided to evaluate the performance of the proposed CSI prediction scheme for air-ground links in UAV communication systems. For UAV communications, mmWave bands hold a lot of promise to meet the data rate requirements of high-throughput mobile applications. Particularly, by hovering at a preferable place, UAVs can keep line-of-sight (LOS) connection (or at least an acceptable NLOS) link with a desired user. Ray tracing offers a deterministic method of characterizing the mmWave channel under various conditions. Since studying the behavior of Air-to-Ground channels at mmWave bands using UAVs might be difficult, ray tracing provides a useful alternative. Here, we utilize the Remcom Wireless InSite ray tracing program to simulate the UAV's real-time movements along a specified trajectory. The simulation parameters were set up as follows: the area's dimensions are 10 km by 10 km in size as shown in \[+ \langle v_{i}\rangle_{dm}\
abla_{c_{j}}+\langle h_{j}\rangle_{dm} \
abla_{h_{i}},\]3 In all situations, the UAVs are flying at a speed of 15 m per second from altitudes of 200 m (resembling a land vehicle); the flight trajectory of the UAV is around 2 km in length. Both the transmitter and receiver employ vertically polarized half-wave dipole antennas. The channel at 28 GHz has a sinusoid to sound the channel at the center of the frequency. The power level is set at 30 dBm for transmission [22]. Considering mmWave frequencies of 28 GHz, we present the cumulative distribution functions (CDFs) of the RMS-DS of the multipath channel between the GS transmitter and the UAV in Figure 5 for four different scenarios. The major reason for this behavior is that at higher UAV altitudes, the UAV moves above tall structures and is able to observe signals that are scattered from a majority of surrounding buildings. In contrast, findings in rural and suburban settings demonstrate that unlike in urban settings, the RMS-DS actually declines as the number of buildings increases.