## 3 System Model and Assumptions
\begin{table}
\begin{tabular}{l l} \hline \hline
**Symbol** & **Meaning** \\ \hline \(M\) & A macrocell \\ \(Fl\) & A femtocell \(l\) \\ \(L\) & Set of femtocells \\ \(I\) & Set of MUEs \\ \(J\) & Set of FUEs \\ \(K\) & Set of RBs \\ \(k\) & A RB \(k\) \\ \(MUE_{i}\) & A macrocell user \(i\) \\ \(FUE_{j}\) & A femtocell user \(j\) \\ \(N_{0}\) & Power of the additive White Gaussian noise \\ \(SINR_{M,MUE_{i}}^{k}\) & SINR of a given \(MUE_{i}\) associated with MBS \(M\) on RB \(k\) \\ \(C_{M,MUE_{i}}^{k}\) & Channel fast fading gain between \(M\) and \(MUE_{i}\) on RB \(k\) \\ \(C_{F_{I},MUE_{i}}^{k}\) & Channel fast fading gain between \(MUE_{i}\) and the neighboring \(F_{I}\) on RB \(k\) \\ \(Z_{i,k}^{k}\) & Set of all interfering FBSs on user \(MUE_{i}\) on RB \(k\) \\ \(P_{M,MUE_{i}}^{k}\) & Transmit power allocated on RB \(k\) by the serving cell \(M\) \\ \(RSS_{M,MUE_{i}}^{k}\) & Received signal strength by \(MUE_{i}\) from MBS \(M\) on RB \(k\) \\ \(RSS_{F_{I},MUE_{i}}^{k}\) & Received signal strength by \(MUE_{i}\) from FBS \(F_{I}\) on RB \(k\) \\ \(P_{F_{I}}^{k}\) & Transmit power allocated on RB \(k\) by the serving femtocell \(F_{I}\) \\ \(P_{F_{I}}^{k}\) & New value of transmission power of femtocell \(F_{I}\) on RB \(k\) \\ \(CLS_{y}\) & Clusters \\ \(y\) & Index of the cluster \\ \(PT_{F_{I}}\) & Geographical position of the femtocell \\ \(RP_{PT_{i}}\) & Repeated position \\ \(T_{MUE}\) & Total number of MUE \\ \(\mu_{i}\) & Average traffic rate for video connection \(i\) \\ \(Q\) & Operational mode set of the video encoder \\ \(L(d_{T,R})\) & Path loss exponent with the distance \(d_{T,R}\) between \(T\) and \(R\) \\ \(S(d_{T,R})\) & Shadowing component \\ \(F(v)\) & Fast fading component \\ \(X\) & Total number of MUEs and FUEs \\ \(\mu_{c}\) & Average traffic rate for video connection \\ \(u_{k}\) & Average data rate for the RB \(k\) \\ \(X\) & Total number of MUEs and FUEs \\ \(RELs\) & Rate of enhancement layer \\ \(RBL\) & Rate of base layer \\ \hline \hline \end{tabular}
\end{table} 
Table 2: List of variables. \[SINR^{k}_{M,MUE_{i}}=\frac{P^{k}_{M,MUE_{i}}|G^{k}_{M,MUE_{i}}|^{2}}{N_{0}+\sum_{ F_{1}\in Z_{i,k}}P^{k}_{F_{i},MUE_{i}}|G^{k}_{F_{i},MUE_{i}}|^{2}}, \tag{1}\]  
where \(P^{k}_{M,MUE_{i}}\) is the present transmit power allocated on RB k by the serving cell M, and \(|G^{k}_{M,MUE_{i}}|^{2}\) is the channel gain between \(MUE_{i}\) and its macrocell M on RB \(k\). In the same way, \(P^{k}_{F_{1},MUE_{i}}\) is the transmit power of neighboring femtocell \(F_{l}\) on RB \(k\). \(N_{0}\) is the white noise power spectral density and \(Z_{i,k}\) represents the set of all interfering FBSs on \(MUE_{i}\) on RB \(k\). \(|G^{k}_{F_{1},MUE_{i}}|^{2}\) is the channel gain between the \(MUE_{i}\) and the neighboring \(F_{l}\) on RB \(k\). In general, the average channel \(|G_{T,R}|^{2}\) between the transmitter (T) represented by \(M/Fs\) and the receiver (R) represented by \(MUE_{i}/FUE_{j}\) is formulated as follows:  
\[|G_{T,R}|^{2}=L(d_{T,R})\cdot S(d_{T,R})\cdot F(\upsilon), \tag{2}\]  
where \(L(d_{T,R})\) is the path loss exponent with the distance \(d_{T,R}\) between T and R, \(S(d_{T,R})\) and \(F(\upsilon)\) are the shadowing and fast fading components, respectively, and \(\upsilon\) is a factor related to speed of users. Using preambles in several RBs by the MUEs assist in knowing the average \(RSS_{M,MUE_{i}}\) by the serving cell M and all neighboring Fs. This means that Fs can capture this information according to \(RSS_{M,MUE_{i}}\) report sent back by the MUEs during uplink transmission. We suppose that M knows the \(RSS^{k}_{M,MUE_{i}}\) on each RBs \(k\), as well as the \(RSS^{k}_{F_{1},MUE_{i}}\) from an \(F_{l}\) according to some conditions detailed in the following sections. Consequently, the Fs can detect also a \(MUE_{i}\) whether it is in the neighborhood or not by receiving the \(MUE_{i}\)'s report, which includes the \(RSS^{k}_{F_{1},MUE_{i}}\) from the UL transmission.