# Coordination of Macro Base Stations for 5G Network with User Clustering
## 2 Energy Management Model of 5G Macro Base Station Network
### Communication and Power Consumption Model of 5G Macro BS  
The extensively used EARTH model was adopted to describe the power consumption of AAU and BBU [34], as shown in (1). The powers of BBU and AAU in BS \(m\) are a constant and a linear function of the transmitted signal power, respectively, when BS \(m\) is in active mode. The powers of BBU and AAU are two small constants when BS \(m\) is in sleep mode.  
\[\begin{split}& P_{com}^{m}=P_{BBU}^{m}+P_{AAU}^{m}\\ &=\left\{\begin{array}{ll}P_{BBU,Ac}^{m}+P_{AAU,Ac}^{m}&,Active Mode\\ P_{BBU,Li}^{m}+P_{AAU,Sl}^{m}&,SleepMode\end{array}\right.\\ &=\left\{\begin{array}{ll}P_{BBU,Ac}^{m,c}+\frac{1}{P_{RA}^{m}}P_{tr}^{m}+P_ {AAU,Ac}^{m,c}&,ActiveMode\\ P_{BBU,Li}^{m,c}+P_{AAU,Sl}^{m,c}&,SleepMode\end{array}\right.\end{split} \tag{1}\]  
where \(P_{com}^{m}\) denotes the power of communication equipment in BS \(m\); \(P_{BBU}^{m}\) and \(P_{AAU}^{m}\) denote the powers of BBU and AAU in BS \(m\), respectively; \(P_{BBU,Ac}^{m}\) and \(P_{AAU,Ac}^{m}\) denote the powers of BBU and AAU in BS \(m\) when BS \(m\) is in active mode, respectively; \(P_{BBU,SI}^{m}\) and \(P_{AAU,Sl}^{m}\) denote the powers of BBU and AAU in BS \(m\) when BS \(m\) is in sleep mode, respectively; \(P_{BBU,Ac}^{m,c}\) and \(P_{AAU,Ac}^{m,c}\) denote the constant part of the powers of BBU and AAU in BS \(m\) when BS \(m\) is in active mode, respectively; \(\delta^{PA}\) denotes the PA efficiency of the AAU in BS \(m\); \(P_{tr}^{m}\) denotes the total transmit power of AAU in BS \(m\); and \(P_{BBU,SI}^{m,c}\) and \(P_{AAU,SI}^{m,c}\) denote the constant part of the powers of BBU and AAU in BS \(m\) when BS \(m\) is in sleep mode, respectively.  
\[P_{tr}^{m}=\sum_{u\in BSm}P_{tr}^{m,u} \tag{2}\]  
where \(P_{tr}^{m,u}\) denotes the transmit power allocated to user \(u\) by BS \(m\), and \(BSm\) denotes the set of users connected with BS \(m\).  
We now present the downlink transmission model from BS \(m\) to user \(u\). The AAU in BS \(m\) transmits electromagnetic waves to user \(u\) with power \(P_{tr}^{m,u}\), which would attenuate in the air medium. The power of the electromagnetic waves received by user \(u\) is expressed as  
\[P_{re}^{m,u}=P_{tr}^{m,u}\cdot 10^{-\frac{A_{PL}\cdot d^{m,u}+B_{PL}}{10}} \tag{3}\]  
where \(d^{m,u_{t}}\) is the distance between BS \(m\) and user \(u\); \(A_{PL}\) and \(B_{PL}\) are the path loss coefficients; and \(P_{re}^{m,u}\) denotes the power of the electromagnetic waves received by user \(u\) from BS \(m\). The power of the interference signal received by each user was considered constant in this study. According to [PERSON]'s equation, the data rate received by user \(u\) is expressed as  
\[L_{re}^{u}=B\cdot\log_{2}(1+\frac{P_{re}^{m,u}}{N_{0}}) \tag{4}\]  
where \(B\) is the channel bandwidth; \(N_{0}\) denotes the interference signal power received by each user; and \(L_{re}^{u}\) denotes the data rate received by user \(u\). According to (3) and (4), the transmit power of BS \(m\) to user \(u\) is given by (5) when the traffic load of user \(u\) is \(L_{re}^{u}\).  
\[P_{tr}^{m,u}=N_{0}(2^{\frac{1k}{B}}-1)\cdot 10^{\frac{A_{PL}\cdot d^{m,u}+B_{PL}}{10}} \tag{5}\]