# Efficient Power Control Framework for Small-Cell Heterogeneous Networks
## 4 Numerical Results  
This section provides numerical results and presents a relevant discussion. We compare the results with two renowned schemes: coordinated beamforming and membership deflation approach. Besides this, the results are compared with the exhaustive search process which is more complex and not scalable for large-scale networks. Unless mentioned otherwise, the values of different simulation parameters are given in Table 1.  
Figure 2 shows the mean power consumption for increasing values of target SINR. It can be noted that an increase in the target SINR results in more power consumption of the small-cell BSs. However, when compared to the conventional coordinated beamforming approach, the proposed solution outperforms significantly. Besides, the proposed algorithm also closely follows the exhaustive search process which indicates the feasibility of the proposed solution. Since the exhaustive search approach does not scale well with an increase in the network size, the proposed solution is a better option among the two.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Simulation Parameters** & **Value** \\ \hline \(p_{l}^{c}\) & 5.6 W \\ \(\lambda_{k}\) & 1 \\ \(\eta_{l}\) & 0.25 \\ \(\epsilon\) & 0.001 \\ Number of small-cell BS & 6 \\ Total multicast groups & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameters and their values.  
Figure 3 shows a number of active small-cell BSs against the increasing values of target SINR. It can be seen from the figure that to match the target SINR values, it becomes important to activate a larger number of small-cell BS. Due to this reason, the active number of small-cell BS increases linearly with an increase in target SINR. However, one can note that the coordinated beamforming approach performs worst among both the proposed solution and the exhaustive search approach. The proposed solution again closely follows the exhaustive search approach for smaller values of SINR but overlaps for larger values for target SINR. This again shows the feasibility of the proposed solution since a smaller number of BSs needs to be activated to meet the quality of service requirements of the UEs.  
Figure 4 illustrates the comparison of the proposed solution against the membership deflation approach in terms of a number of admitted UEs in the network. It can be seen from the figure that to meet the target SINR demands of the UEs, it is important to keep the admitted UEs at a minimum. This is the reason why the total number of admitted UEs decrease with an increase in the values of target SINR. However, our proposed solution tries to maximize the number of admitted UE while meeting the quality of service demands of the UEs. When compared to the proposed solution, the membership deflation approach does not perform well. The membership deflation  
Figure 3: Number of active small-cell base stations (BSs) against target SINR.  
Figure 2: Mean power consumption versus target signal-to-intereference-and-noise ratio (SINR).  
approach allows a limited number of UEs to be admitted to the network against the same value of SINR. By contrast, the proposed solution outperforms the membership deflation approach and closely follows the exhaustive search technique. This clearly indicates the proposed solution is not only good at controlling the power of the network but also improves the overall capacity of the network to accommodate a larger number of UEs.