## 2 An Optimized Handover Based on Context Information
### An Optimized Handover Scheme
A high speed UE moves from small cell 1 to small cell 2 but it is not handed over to small cell BS2 but to a macro cell BS, and thus small cell BS2 can be turned off to save power. As shown in Figures 5 and 6, the proposed handover scheme can turn off more BSs. Figure 5: An example of CAC-based handover. In this paper, the main objective of the proposed optimal handover is either to reduce the number of handovers or the total energy consumption of BSs. To this end, we develop optimization problems with either the minimization of the number of handovers or the minimization of energy consumption of BSs as the objective function of the optimization problem. To check service availability of a BS, the state of a macro cell and a small cell is classified as on and off, as in Equations (2) and (3):  
\[\mathrm{w_{Mm}}= \begin{cases}1,&\text{if $\mathrm{B_{Mm}}$ is ON state}\\ 0,&\text{otherwise}\end{cases}  \tag{2}\]  
\[\mathrm{w_{Ss}}= \begin{cases}1,&\text{if $\mathrm{B_{Ss}}$ is ON state}\\ 0,&\text{otherwise}\end{cases}  \tag{3}\]  
Also, the service state of UE k in a macro cell and a small cell are defined as in Equations (4) and (5):  
\[\mathrm{a_{Mm,k}}= \begin{cases}1,&\text{if $\mathrm{u_{k}}$ is served by $\mathrm{B_{Mm}}$}\\ 0,&\text{otherwise}\end{cases}  \tag{4}\]  
\[\mathrm{a_{Ss,k}}= \begin{cases}1,&\text{if $\mathrm{u_{k}}$ is served by $\mathrm{B_{Ss}}$}\\ 0,&\text{otherwise}\end{cases}  \tag{5}\]  
The existence of data service request by UE k, the data type of UE k, and the speed of UE k are defined as in Equations (6)-(8):  
\[\mathrm{d_{k}}= \begin{cases}1,&\text{if $\mathrm{u_{k}}$ requires data services}\\ 0,&\text{otherwise}\end{cases}  \tag{6}\]  
Figure 6: An example of proposed handover. \[\mathrm{r_{k}}= \begin{cases}1,&\text{if $\mathrm{u_{k}}$ requires high rate data services}\\ 0,&\text{if $\mathrm{u_{k}}$ requires low rate data services}\end{cases}  \tag{7}\]  
\[\mathrm{v_{k}}= \begin{cases}1,&\text{if $\mathrm{u_{k}}$ has high speed velocity }>\ \mathrm{V_{-threshold}}\\ 0,&\text{if $\mathrm{u_{k}}$ has low speed velocity }\leq\ \mathrm{V_{-threshold}}\end{cases}  \tag{8}\]  
The traffic load of a macro cell and a small cell are defined as in Equation (9):  
\[\mathrm{D\_Cell_{load\_B_{target\_BS,\_k}}}= \begin{cases}1,&\text{if a traffic of $\mathrm{B_{target\_BS,k}}$ is the highest level}\\ 0,&\text{otherwise}\end{cases}  \tag{9}\]  
In order to consider the RSRP of BSs, A2 and A3 events [35; 3  
Then, the total energy consumption of BSs in the considered network is obtained using Equation (17):  
\[\mathrm{P_{Total}}=\mathrm{P_{Macro\_total}}+\sum_{k=1}^{Num\_SBSs in on state}\mathrm{P_{Small\_total,\ k}} \tag{17}\]  
Finally the optimization problem of the proposed scheme to minimize the number of handovers is formulated as in Equation (18):  
\[ \begin{array}{ll}\min&\mathrm{HO_{total}}\\ \mathrm{s.t.}&\mathrm{a_{m,k}\leq w_{Mm}}\\ &\mathrm{a_{n,k}\leq w_{Ss}}\\ &\mathrm{r_{k}\leq d_{k}}\\ &\sum_{n=1}^{Num\_SBSs}\mathrm{a_{n,k}\leq 1}\\ &\mathrm{w_{Mm},\ w_{Ss}\leq 1}\\ &1\leq k\leq Num\_UEs,\quad 1\leq n\leq Num\_SBSs}\end{array}  \tag{18}\]  
The optimization problem of the proposed scheme to minimize the energy consumption of BSs is formulated as in Equations (19)-(22). Considering all the previous equations, the possible power consumption of a small cell is defined as in Equation (19):  
\[ \begin{array}{ll}\mathrm{P(Ss)_{small}}=\mathrm{w_{Ss}}\times\left(\mathrm{ P_{small}^{static}+P_{Small\_linear}}\right.\\ \qquad\qquad\qquad\qquad\times\sum_{k=1}^{Num\_UEs}\left(d_{k}\times\mathrm{a _{Ss,k}}\times\left(1-A2_{B_{aver,BS,\ k}}\right)\times A3_{B_{target,BS,\ k}} \times\left(1-\mathrm{v_{k}}\right)\right.\\ \qquad\qquad\qquad\times\mathrm{C_{B_{target,BS,\ k}}\times D\_Cell load\_BS_{target,BS,\ k}}\\ \qquad\qquad\qquad\times\left.\frac{\left(\mathrm{r_{k}\times C_{req,high}}+ \left(1-\mathrm{r_{k}}\right)\times C_{req,low}\right)}{C_{small}^{static}} \right)\right)\end{array}  \tag{19}\]  
Also, possible power consumption of a macro cell is defined as in Equation (20):  
\[