## 5 Performance Evaluation
### Simulation Setup
#### 5.1.4 Estimation Model  
The estimation model is responsible for processing the information in the environment and predicting the satellite-to-ground channel state. In experiments, we set the satellite-to-ground channel state as SNR. Accurate prediction of SNR with as little introduced noise as possible becomes the keynote of the estimation model network design. In the experiments, we set the LSTM network to contain 100 neurons in 1 layer and set the fully connected layer behind the LSTM layer to also contain 100 neurons as the LSTM network itself is powerful enough. The neurons responsible for processing weather information and distance information in the embedding layer are \(n_{W}\) and \(n_{D}\), respectively. Their influences on prediction accuracy are discussed in the following text. The number of passing moments considered by the LSTM network \(n\) is also significant. An excessively small \(n\) leads the network not fully to consider past information, while an excessively large \(n\) will cause the network to consider too much noise, and the training speed and convergence speed will be slow. Thus, we need to strike a balance between the two. In summary, the network structure of the estimation model from front to back is an embedding layer consisting of \(n_{W}\) and \(n_{D}\) neurons, an LSTM layer containing 100 neurons, a complete connection layer contains 100 neurons, and an output layer contains one neuron. In the experiment, the learning rate is 0.01, all data are trained at 400 epochs, and the learning rate is reduced at 100 and 200 epochs such that the initial learning rate is multiplied by 0.1. The sequence length is \(n\), which means that \(n\) pieces of data enter the network each time. Therefore, the batch size that we select is 128. We divided the overall dataset into a training set, test set, and validation set according to the ratio of 70%, 20%, and 10%. We used STK to collect data from Starlink on 8 December 2020 and the weather data of that day for training, with a total data volume of 600 MB. Mean absolute error (MAE) is served as the criterion of loss. The above parameters are summarized in Table 3.  
We have chosen the following methods as the estimation methods for comparison:  
* Linear Smoothing [17]: The historical data are assigned weights, and the sum of these weights is 1. We define all weights as \(\frac{1}{n}\), where \(n\) is the number of past moments we need to consider. \[SNR_{t}=\sum_{\tau=t-n}^{t-1}\frac{1}{n}SNR_{\tau}\] (18)* Exponential Smoothing [17]: Compared to linear smoothing, the importance of the historical data is measured by exponential weights, which focus more on the data at the nearer moments. The sum of the weights is equal to \(1\). \[S\dot{N}R_{t}=\sum_{\tau=t-n}^{t-1}a(1-a)^{t-\tau}SNR_{\tau}\] (19) where \(a\) is the weighting factor, and a higher value of \(a\) indicates a greater appreciation of historical information. To balance historical and new information, we set \(a\) as \(0.6\). * SVR [18; 19]: SVR borrows ideas from SVM and applies them to the field of time-series prediction. Samples that are linearly indistinguishable in low-dimensional space can be linearly distinguishable after mapping to higher dimensions. Kernel function avoids computing the parameters of the nonlinear transformation function and avoids dimensional catastrophe [44]. SVR also adopted this method [45], and the objective function is set as \[f(x)=\sum_{i=0}^{t-1}(\widehat{\alpha}_{i}-\alpha_{i})\kappa\left(x_{i}^{T}x \right)+b,\] (20) where \(\widehat{\alpha}\) and \(\alpha\) is the Lagrange multiplier, \(b\) is the bias term, and \(\kappa(\cdot)\) is the kernel function. We adopt the radial basis function [46] as the kernel function. As the above estimation methods for comparison has a different ability to process information, we provide the linear smoothing and exponential smoothing method with the sequence of past SNRs as input.