## 5 Proposed Active Power Control Technique  
Figure 1 shows the ICI scenario between the elements of the primary and the secondary system. The downlink transmission power of femtocell causes interference to the MUE that existing in its coverage area. In such condition, MUE starts the handover or cell re-selection process. Since the femtocell is working in closed access mode, the macro user cannot subscribe to the services of the femtocell. In order to deal with such a scenario, the MUE measures the interference level from the HeNB and sends an interference message (IM) to the femtocell based on the Interference Indication Function (IDF) [37]. The IDF determines whether the interference experienced by the macro user is higher or lower than the threshold interference level. The IDF can be expressed as. \[I_{i}=P_{i}^{i}\psi_{i}(R_{i})^{-\beta} \tag{9}\]  
\[x_{i}= \begin{cases}0,&I_{i}\leqslant I_{Threshold}\\ 1,&Otherwise\end{cases}  \tag{10}\]  
In (9), \(P_{i}^{i}\) is the transmit power of the femtocell \(F_{i}\). \(\psi\) represents log-normal shadowing, whereas the path loss is given as \((R)^{\beta}\). The range from the interfered FBS to UE is denoted as \(R\), whereas the path loss component for the indoor transmission is \(\beta\). In (10), \(I_{Threshold}\) is the interference threshold set for the macro user. The IDF determines whether the interference experienced by the macro user is higher than the threshold interference to maintain the desired QoS of the MUE or the interference is lower than the threshold level. Based on the IDF, the macro user decides to send the interference message (IM) including HeNB information to eNB. When the femtocell receives the IM from the macro user via eNB backhaul, it understands that the non-CSG user is getting interference from its downlink transmission. In the first stage of the active power control technique, we introduced different power levels and time levels to tune the downlink power of the HeNB. The power levels (\(P_{x}\), \(P_{y}\) and \(P_{z}\)) and time levels (\(TL_{1}\) and \(TL_{2}\)) were used to reduce and enhance transmission power based on received IM. The APC technique activates when the femtocell receives an IM from the MUE, The femtocell then takes necessary measures to tune its downlink transmission power from \(P_{x}\) to \(P_{y}\) ( reduces \(\Delta_{down}\)). The time levels play an important role in the smooth tuning of HeNB transmission power. If the femtocell receives a new IM from the nearby MUE, it would not reduces its transmission power to \(P_{z}\) level until the time level (\(TL_{1}\)) expires. Similarly, when HeNIB has no IM and \(TL_{1}\) expires, then the time level \(TL_{2}\) starts and the transmission power level of the femtocell increases from \(P_{z}\) to \(P_{y}\) (\(\Delta_{up}\)). The same procedure of reducing and increasing transmission power will be carried out based the HeNIB receiving a new interference message. Figure 2 show the femtocell adjusts its transmission power to respond to the IM from the MUE under the active power control technique. The femtocell updates it downlink transmission power based on IM using following formulas  
\[P_{t} =P_{x} No\ Interference\ Message \tag{11}\] \[P_{t} =P_{y} =P_{x}-\Delta_{down} Interference\ Message\ \&\ TL_{1}\ starts\] (12) \[P_{t} =P_{z} =P_{y}-\Delta_{down} New\ Interference\ Message\ \&\ TL_{1}\ running\] (13) \[P_{t} =P_{y} =P_{z}+\Delta_{up} No\ Interference\ Message\ \&\ TL_{2}\ starts\] (14) \[P_{t} =P_{x} =P_{y}+\Delta_{up} No\ Interference\ Message\ \&\ TL_{2}\ running \tag{15}\]  
The IDF only focuses on the interference level of MUE. In order to maintain the necessary QoS of the FUE, we used the QoS Indication Function (\(\xi\)) in the second step, which indicates the minimum required QoS of FUE. The QoS Indication Function can be expressed as follows:  
\[\xi=\frac{P_{ref}\ \Gamma_{FUE}}{minRSRP_{j}} \tag{16}\]  
In (16), \(\Gamma_{FUE}\) is the minimum required SINR for FUE. \(P_{ref}\) is the downlink reference signal transmit power of the HeNIB.