## 4 SBS Energy Efficiency Management Decisions
### SBS State Admission and Correction Algorithm  
In Section 3, we used a method based on traffic thresholds and traffic forecasts to initially determine the state of the SBS in the period \(t\). However, such decisions are extremely dependent on the setting of traffic load thresholds, which makes the decision results have a large error. Therefore, we need to verify these decision results, accept the correct decisions and correct the incorrect ones, so as to obtain the optimal SBS state. In this paper, we use a heuristic algorithm to confirm the SBS states one by one, and its algorithm complexity is mainly related to the number of SBSs, so we can reduce the complexity by reducing the number of SBSs that need to be verified. In the initial state decision of the SBS, it is assumed that the traffic prediction results are accurate. We set the threshold, \(\varphi_{b}\), to be high relative to the general empirical threshold, and therefore the SBS \(\widetilde{B}_{on}^{t}\) which is determined to be turned on in period \(t\) by the traffic prediction will be directly accepted without further verification. Similarly, we set \(\varphi_{s}\) to be low, so that SBS \(\widetilde{B}_{sleep}^{t}\), which is determined to be sleep at time \(t\) by traffic prediction, will be accepted directly. Therefore, the main issue to be considered is that for the SBSs in \(\widetilde{B}_{stand}^{t}\), some of them need to be On and some need to be in Sleep mode, so we use the system performance objective function to determine the status of the SBSs in \(\widetilde{B}_{stand}^{t}\) in turn. To facilitate reading, the system performance optimization objective function is rewritten as  
\[ \begin{array}{ll}\underset{\boldsymbol{\rho}^{t},\boldsymbol{\Psi}}{\text{ min}}&Q\big{(}\boldsymbol{\rho}^{t},\boldsymbol{b}^{t}\big{)}=D^{t}\big{(} \boldsymbol{\rho}^{t}\big{)}+\alpha\sum\limits_{i\in B_{s}}\left(\boldsymbol{ p}_{i}^{t}+\boldsymbol{P}_{i,h}^{t}\right)\\ \text{s.t.}&b_{i}^{t}=\left\{-1,0,1\right\},\quad\forall i\in B\\ &\boldsymbol{\rho}^{t}\in\boldsymbol{\Omega}^{t}\big{(}B_{on}^{t}\big{)}\\ \end{array}  \tag{33}\]  
Algorithm 2 gives the pseudocode of the joint optimization algorithm for SBS state control and user association to solve (34). ```
Initialization: The initial \(\widetilde{B}_{om}^{t}\), \(\widetilde{B}_{stand}^{t}\), \(\widetilde{B}_{sleep}^{t}\), and \(\widetilde{\mathbf{b}}^{t}\) obtained by LSTM traffic prediction. while\(\widetilde{B}_{stand}^{t}\
eq\varnothing\)  The optimal load \(\widehat{\mathbf{p}}^{t}\) under \(\widetilde{B}_{om}^{t}\) is calculated from Algorithm 1, and the system performance objective function value \(Q\big{(}\widehat{\mathbf{p}}^{t^{*}},\widetilde{\mathbf{b}}^{t}\big{)}\) is calculated by combining the set \(\mathbf{b}^{t-1}\) of base station states in period \(t-1\) and the set \(\widetilde{\mathbf{b}}^{t}\) of predicted states in period \(t\);  Select SBS \(i=\underset{j\in\widetilde{B}_{rand}^{t}}{argmax}T_{j}^{t}\), \(\widetilde{B}_{om}^{t}\leftarrow\widetilde{B}_{om}^{t}\cup\{i\}\), and at the same time adjust \(b_{i}^{t}\) in \(\widetilde{\mathbf{b}}^{t}\) from \(b_{i}^{t}=0\) to \(b_{i}^{t}=1\) to get the new \(\widetilde{b}_{near}^{t}\), \(\widetilde{B}_{stand}^{t}\leftarrow\widetilde{B}_{stand}^{t}-\{i\}\) ;  Run Algorithm 1 to compute the optimal load \(\widehat{\mathbf{p}}_{new}^{t}\) under the current \(\widetilde{B}_{om}^{t}\).