# Marginal Contribution-Based Distributed Subchannel Allocation in Small Cell Networks
## 5 Simulation Results
### Performance in Different Radio Resource Scenarios  
In this subsection, we compare performance of MCBR (Neighborhood Information) with other schemes in all the three radio resource scenarios. We average the performance for 200 randomly generated deployments of each scenario, where the number of iterations is fixed to 500. Moreover, we show 95% confidence intervals in the following figures. Note that for all the schemes, the confidence intervals for the sparse scenario are too small to be visible, which is justified by the plots obtained in Figure 5.  
In order to evaluate the fairness in capacities obtained by each link, we use [PERSON]'s fairness index [38], which is expressed as,  
\[\frac{(\sum_{i=1}^{M}C_{i})^{2}}{M\sum_{i=1}^{M}C_{i}^{2}} \tag{13}\]  
This fairness index is widely applied in the literature to evaluate the level of fairness achieved by resource allocation algorithms. Table 3 shows the average fairness index calculated in the three radio resource scenarios. MCBR (Neighborhood Information) is able to provide with satisfying level of fairness as compared to other schemes. BR (Simultaneous) is able to maintain the fairness above 0.9 in all the three radio resource scenarios. However, this performance result comes at an expense in efficiency as shown in Figure 6.  
Figure 5: Average system capacity over 200 random deployments.  
Figure 6: Average system capacity in different radio resource scenarios.  
Figure 6 compares the average system capacity for the three radio resource scenarios. MCBR (Complete Information) provides better average system capacity as compared to other schemes, while considerable performance is obtained from MCBR (Neighborhood Information) in all the scenarios. With increasing number of links, the achievable average system capacity from MCBR (Complete Information) and MCBR (Neighborhood Information) increases more quickly than for the other two schemes. MCBR (Complete Information) and MCBR (Neighborhood Information) are able to provide significant performance improvement even in the dense scenarios. In addition, the accumulated interference for both MCBR schemes compared to other BR strategy schemes is considerably smaller, as seen in Figure 7.  
Next in Table 4, we evaluate the reduction in average number of links from which information feedback are required for MCBR (Neighborhood Information) compared to MCBR (Complete Information) in the three radio resource scenarios. Recall that in both the MCBR schemes, each link requires feedback only from other links that are allocated to the new sensing subchannel and the subchannel allocated in the previous time-slot. Under MCBR (Complete Information), which requires information feedback from all other links in the SCN allocated to the particular sensing subchannel, the average numbers of links for information feedback are 2.65, 12.86, and 46.37 links, respectively. Since MCBR (Neighborhood Information) requires information feedback only of links originating from the neighboring SBSs, the average numbers of links for information feedback drop significantly to 0.94, 4.17, and 12.83 links, respectively, which is a 65-70% reduction in all the three radio resource scenarios. These results show that the computational complexity of MCBR (Neighborhood Information) is low, scalable, and suitable for practical implementation in different radio resource scenarios of SCNs. From these analysis, we can conclude that MCBR (Neighborhood Information) is able to provide efficient and fair subchannel allocation, even with limitations to complete information feedback in the SCN.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Sparse** & **Moderate** & **Dense** \\ \hline BR (Simultaneous) & 0.9705 & 0.9567 & 0.9483 \\ BR (Sequential) & 0.9694 & 0.9309 & 0.8647 \\ MCBR (Complete Information) & 0.9465 & 0.9095 & 0.7743 \\ MCBR (Neighborhood Information) & 0.9582 & 0.9197 & 0.8029 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Fairness comparison.  
Figure 7: Average interference in different radio resource scenarios.