## 3 Fast Channel Information Prediction Based Random Forest
### Random Forest Prediction SINR
When the depth of the tree is less than the maximum depth of the tree d, the optimal branch characteristics and split points are computed, and the node sample is branched into two nodes in the next level;
9 End while
10 End for
11 calculate the mean of the evaluation indexes of K-1 test sets as the evaluation indexes of the prediction model;
12 Calculate the evaluation index of the predicted data as with the remaining one-fold data;
13 Input the test set data to each tree to receive the regression results of each tree and use the average value to obtain the prediction results of the model. ```  
**Algorithm 1**Random forest prediction channel SINR  
The flowchart of Algorithm 1 (random forest prediction) is shown in Figure 1.  
Figure 1: The flow chart of Algorithm 1 (random forest prediction). Energy-Efficient Resource Optimization Allocation Algorithm Based on Channel Information Prediction  
The mathematical model of energy-efficient optimization established according to Section 2 P1 and its constraints, P1 is a mixed integer nonlinear programming (MINLP) problem. In order to obtain accurate channel information, we use the proposed random forest prediction channel SINR for obtaining real-time CQI and MCS and design the optimal energy-efficient resource allocation scheme on this basis. Define the CQI index set allocated on the available RB as \(\mathbb{J}_{\mathrm{m}}=\left\{\mathrm{j}|C_{\mathrm{n},\mathrm{m},\mathrm{k}} \geq\mathrm{j},\forall\mathrm{j},\forall\mathrm{k}\right\}\). In order to obtain the optimal energy-efficient resource allocation scheme, according to the mathematical model of energy-efficient optimization P1 and its constraints, redefine the expressions of the total user rate and total power consumption, which are, respectively, Formulas (11) and (12):  
\[\mathrm{R}a,b,p=\sum_{\mathrm{k}=1}^{\mathrm{K}}\sum_{\mathrm{n}=1}^{\mathrm{N }}\sum_{\mathrm{m}=1}^{\mathrm{M}}\sum_{\mathrm{j}\in\mathbb{J}_{\mathrm{m}}} \chi_{\mathrm{n}}^{\mathrm{kj}}\eta_{\mathrm{n},\mathrm{m}}^{\mathrm{kj}}B_{ \mathrm{RB}}\log_{2}\left(1+p_{\mathrm{n},\mathrm{m}}^{\mathrm{kj}}\gamma_{ \mathrm{n},\mathrm{m}}^{\mathrm{k}}\right) \tag{11}\]  
\[P(a,b,p)=\zeta\sum_{\mathrm{k}=1}^{\mathrm{K}}\sum_{\mathrm{n}=1}^{\mathrm{N }}\sum_{\mathrm{m}=1}^{\mathrm{M}}\sum_{\mathrm{j}\in\mathbb{J}_{\mathrm{m}}} \chi_{\mathrm{n}}^{\mathrm{kj}}\eta_{\mathrm{n},\mathrm{m}}^{\mathrm{kj}}p_{ \mathrm{n},\mathrm{m}}^{\mathrm{kj}}+P_{C} \tag{12}\]  
where \(a,b,p\) represents the CC allocation scheme, the RB allocation scheme, and the power allocation scheme, respectively. Therefore, the energy-efficient optimization mathematical model P1 is simplified to P2:  
\[P_{2}:\max R(a,b,p)/R(a,b,p) \tag{13}\]  
\[\sum_{\mathrm{k}=1}^{\mathrm{K}}\sum_{\mathrm{j}\in\mathbb{J}_{\mathrm{m}}} \eta_{\mathrm{n},\mathrm{m}}^{\mathrm{kj}}\leq 1,\forall\mathrm{n}\in C_{ \mathrm{k}},\forall\mathrm{m} \tag{13a}\]  
\[\sum_{\mathrm{n}=1}^{\mathrm{N}}\sum_{\mathrm{j}\in\mathbb{J}_{\mathrm{m}}} \chi_{\mathrm{n}}^{\mathrm{kj}}\leq C_{\mathrm{k}},\forall\mathrm{k} \tag{13b}\]  
\[\sum_{\mathrm{j}\in\mathbb{J}_{\mathrm{m}}}\chi_{\mathrm{n}}^{\mathrm{kj}}\leq 1,\forall\mathrm{n},\forall\mathrm{k} \tag{13c}\]  
\[\sum_{\mathrm{k}=1}^{\mathrm{K}}\sum_{\mathrm{n}=1}^{\mathrm{N}}\sum_{\mathrm{ m}=1}^{\mathrm{M}}\sum_{\mathrm{j}\in\mathbb{J}_{\mathrm{m}}}\chi_{\mathrm{n}}^{ \mathrm{kj}}\eta_{\mathrm{n},\mathrm{m}}^{\mathrm{kj}}p_{\mathrm{n},\mathrm{m }}^{\mathrm{kj}}\leq P_{\mathrm{T}} \tag{13d}\]  
Figure 1.0