# Coordination of Macro Base Stations for 5G Network with User Clustering
## 2 Energy Management Model of 5G Macro Base Station Network
### Optimization Step 1: Energy Management of the 5G Communication Equipment  
The proposed model assumes that the distribution of users and their traffic loads are known. The objective is to minimize the energy consumption of all AAUs and BBUs in the network during time period \(t\), which is expressed as  
\[\min F_{1}^{t}=\min\sum_{m\in M}P_{com}^{m,t}\Delta t \tag{6}\]where \(P_{com}^{m,t}\) is the power consumption of the communication equipment (i.e., AAU and BBU); \(\mathbf{M}\) denotes the set of all 5G macro BSs in the network; and \(\Delta t\) is the time step of one time period and is assumed to be equal to 15 min in this study. BS sleeping and user allocation are adopted to reduce the energy consumption of 5G communication equipment in the network. During the periods of valley traffic load, some of the BSs could be switched to sleep mode, and the users served by these BSs could be transferred to adjacent BSs for service. According to Equation (1), although the transmitting power \(P_{tr}^{m,t}\) needed by users would increase after transfer, the constant power parts \(P_{AAU,Ac}^{m,t}\) and \(P_{BBU,Ac}^{m,t}\) of these BSs are saved so that the total energy consumption of the communication equipment can be reduced. The operation of communications equipment needs to meet the following constraints. 1. Power consumption constraints of communications equipment: \[P_{com}^{m,t}=P_{AAU}^{m,t}+P_{BBU}^{m,t}\] (7) \[P_{AAU}^{m,t}=\left\{ \begin{array}{l}\dfrac{1}{\delta_{PA}^{m}}P_{tr}^{m,t }+P_{AAU,Ac}^{m,t},\;U_{bs}^{m,t}=1\\ P_{AAU,Sl}^{m,t},\;U_{bs}^{m,t}=0\end{array} \right.\] (8) \[P_{BBU}^{m,t}=\left\{ \begin{array}{l}P_{BBU,Ac}^{m,c},\;U_{bs}^{m,t}=1\\ P_{BBU,Sl}^{m,c},\;U_{bs}^{m,t}=0\end{array} \right.\] (9) \[U_{bs}^{m,t}\in\{0,1\}\] (10) where \(P_{com}^{m,t}\) denotes the power of communication equipment in BS \(m\); \(P_{AAU}^{m,t}\) and \(P_{BBU}^{m,t}\) are the power consumptions of the AAU and BBU in BS \(m\), respectively; \(U_{bs}^{m,t}\) represents the working status of BS \(m\); BS \(m\) is in sleep mode when \(U_{bs}^{m,t}=0\) and active mode when \(U_{bs}^{m,t}=1\); \(\delta_{PA}^{m}\) is the PA efficiency of the AAU in BS \(m\); \(Pm\),\(c\)\(AAU\), \(Ac\) and \(Pm\),\(c\)\(AAU\), \(Sl\) denote the constant parts of the power of AAU in BS \(m\) in the active and sleep modes, respectively; and \(Pm\),\(c\)\(BBU\), \(Ac\) and \(P_{BBU,sl}^{m,c}\) are the constants of the power of BBU in BS \(m\) in the active and sleep modes, respectively. 2. With the BS in sleep mode and the use of the user allocation method, each user in the network could be served by local or adjacent BSs. However, each user can only connect to one BS at a time, and its QoS requirements should be met. The user allocation constraints are as follows: \[a_{t}^{m,u_{t}}\leq U_{bs}^{m,t},m\in\mathbf{N}_{u_{t}}\] (11) \[\sum_{m\in\mathbf{N}_{u_{t}}}a_{t}^{m,u_{t}}=1\] (12) where \(a_{t}^{m,u_{t}}\) denotes the connection relationship between BS \(m\) and user \(u_{t}\); user \(u_{t}\) is not connected with BS \(m\) when \(a_{t}^{m,u_{t}}=0\), while user \(u_{t}\) is connected to BS \(m\) when \(a_{t}^{m,u_{t}}=1\), and \(\mathbf{N}_{u_{t}}\) represents the set of adjacent BSs of user \(u_{t}\). Equation (11) indicates that user \(u_{t}\) can only connect with BSs that are in active mode. Equation (12) indicates that user \(u_{t}\) can only connect with one BS at a time. 3. Maximum data transmission rate constraints of BSs: \[L_{tr}^{m,t}=\sum_{u_{t}\in\mathbf{N}_{m}}a_{t}^{m,u_{t}}L_{te}^{u_{t}}\] (13) \[L_{tr}^{m,t}\leq L_{tr}^{\max,m}\] (14)where \(\mathbf{N}_{m}\) denotes the set of users in cell \(m\) and its adjacent cells; \(L_{tr}^{m,t}\) denotes the total data processing rate of BS \(m\); and \(L_{tr}^{max,m}\) denotes the maximum data processing capacity of BBU in BS \(m\). 4.