# Joint Cell Association and User Scheduling in Carrier Aggregated Heterogeneous Networks
## 4 Numerical Analysis
### Numerical Results  
Numerical results are demonstrated in this section under pre-discussed network layout and system parameters under different carrier deployments. Figure 2 shows the sum-rate performance of the proposed joint cell association schemes for multi-flow CA when the total number of users within the HetNets are changing under different carrier bands deployments. The proposed multi-flow solution (MF) is compared with the Max-SINR (SINR) association scheme under different network density, where \(K=20\) and \(K=40\) state the total BS number in the network layout. It can be seen that, under different carrier deployment conditions, the proposed joint scheme is proved to have much better performance in terms of network capacity. Compared with the previous work [37], under the same condition of carrier deployment, the proposed joint scheme is also better than the stochastic single flow scheme due to the user diversity gain. The relaxation of the user association factor \(\psi_{k,m}^{n}\) makes the users capable of associating with multiple BSs on multiple carriers in the same time and in the mean time, the global solution is achieved. When carrier deployment changes among the two-layer HetNets, Figures 3-5 show the performance on network capacity against the transmit power lever of both Macro BS and Femto BSs. In general, the proposed joint solution gives the best performance as expected. According to different carrier deployment conditions, the performance differences are summarized below in detail. Figure 3 indicates the situation in which the first layer of the HetNets is employed with both high and low frequency bands while the second layer is left with a single carrier band. In Figure 3a, as the growth of the transmit power of Macro BS, the proposed joint solution achieves better performance due to its designed multiple data flow cell association scheme. For the other two schemes, the users scheduled in the second layer suffered severely from the growing interference level, which blocks the whole network performances from improving. From Figure 3b, it could be seen that the proposed joint scheme is more sensitive to the transmit power level of the Femto BS compared to the other two \begin{table}
\begin{tabular}{c c} \hline \hline
**Macrocell Transmit Power** & 46 dBm \\ \hline
**Femtocell Transmit Power** & 20 dBm \\ \hline
**Macrocell coverage Radius** & 500 m \\ \hline
**Femtocell coverage Radius** & 50 m \\ \hline
**AWGN \(N_{0}\)** & \(-174\) dBm/Hz \\ \hline
**Total Users Number** & M = 200 \\ \hline
**Carrier Frequency of \(C^{1}\)** & 2.5 GHz \\ \hline
**Carrier Frequency of \(C^{2}\)** & 800 MHz \\ \hline
**Bandwidth \(B^{1}\) of \(C^{1}\)** & 10 MHz \\ \hline
**Bandwidth \(B^{2}\) of \(C^{2}\)** & 10 MHz \\ \hline
**Wavelength \(\lambda_{1}\) of \(C^{1}\)** & 0.125 m \\ \hline
**Wavelength \(\lambda_{2}\) of \(C^{2}\)** & 0.375 m \\ \hline
**Path Loss Exponent \(\gamma^{1}\) of Macrocell** & 4 \\ \hline
**Path Loss Exponent \(\gamma^{2}\) of Femtocell** & 3 \\ \hline
**Reference distance \(d_{0}\) in Macrocell** & 10 m \\ \hline
**Reference distance \(d_{0}\) in Femtocell** & 1 m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation Parameter Statements. scheme. As the transmit power grows, the users are offloaded from the Macro BS, which causes the network utility improving. However, as the power level continues to grow, the cross layer interference has become a threat to the HetNets, which causes the performance drop. This precisely proves the effectiveness and flexibility and effectiveness of the proposed joint scheme. Under different circumstances in Figure 4, the proposed solution along with the two benchmark schemes have shown their own characteristics when cross layer interferences exists([1 1;1 1], [0 1;1 1], [1 0;1 1]). In Figure 3(a), the proposed joint multi-flow solution achieves the best performance under full carrier deployment across different network layers ([1 1;1 1]).