## 3 Fast Channel Information Prediction Based Random Forest
### Random Forest Prediction SINR  
The CART in a random forest is composed of a bagging algorithm and random subspace method (RSM). Among them, CART is a dichotomous recursive segmentation technique proposed by [PERSON] et al. in 1984. At each node (except the leaf node), the current sample set is divided into two subsets. For the regression problem, the minimum mean square error is used to partition the data set. For any partition feature T, two sides of the corresponding partition point s are divided into the left data set DI and the right data set Dr [32]. The expression is:  
\[\min_{\text{T},s}\left[\sum_{\text{x}_{\text{i}}\in\text{D}_{\text{T},\text{ s}}}\left(\text{y}_{\text{i}}-\text{c}_{\text{i}}\right)^{2}+\sum_{\text{x}_{ \text{i}}\in\text{D}_{\text{T}},\text{S}}\left(\text{y}_{\text{i}}-\text{c}_ {\text{i}}\right)^{2}\right] \tag{10}\]  
where c1 and c2 are the output mean values of the data sets DI and Dr. This principle is used to divide continuously at each branch node until the set threshold is reached. Bagging (bootstrap aggregating) is an ensemble learning algorithm. In random forest, Bagging specifically expresses that multiple samples are randomly selected with replacement from the original training sample set to generate a new training sample set. Then, multiple decision trees are constructed to form the random forest. Finally, the random forest averages the output of each decision tree to determine the final result. Additionally, then, the remaining samples that have not been drawn are called out-of-bag samples (out of bag, OOB), these OOB samples can be used as verification samples for the internal evaluation of the model and the final model prediction results are determined by \"voting\". In this paper, the average result of each CART model is used as the prediction results of the random forest regression model. In the fields of statistical analysis and machine learning, K-fold cross validation is commonly used to evaluate the generalization ability of the model. The K-fold cross validation means that the training set is divided into K disjoint subsets, in which K-1 subsets data are used for training and the remaining one is used for validation to obtain the accuracy results. Train K times in this way and use the average value of each training as the final result of cross validation model. The grid search algorithm is an exhaustive search parameter adjustment method, which obtains the optimal parameters by looping through the range of candidate parameters and using the cross-validation results as indicators. This method has generality and is simple and efficient. In order to facilitate model comparison, this method is used as a model parameter selection method. Select historical CQI, MCS, and SINR as input variables to predict the SINR of the current channel. According to the principle of random forest, the algorithm process for building an SINR model of random forest prediction channel is Algorithm 1. The specific steps are as follows:  
```
1 Input: Pre-treatment the original data. Select historical CQI, MCS, and SINR Output: the prediction results
2 Output: current channel SINR;
3 Divide the sample set into test set and training set and divide the training set into K parts;
4 Set the grid search range for the number of decision regression trees as n, the maximum eigenvalue as m, and the maximum tree depth as D;
5 Select a set of parameters for the grid search range and use the selected K-1 fold subsets data as the sample of the single decision tree;
6 For i = 1, i! k, i++;
7 While j!= n do
8 Select m features from the feature set using the selection method in the grid search parameters.