# Marginal Contribution-Based Distributed Subchannel Allocation in Small Cell Networks
## 5 Simulation Results  
In this section, we simulate and compare performance of the proposed MCBR algorithm with information feedback from the neighborhood, denoted as MCBR (Neighborhood Information), for different performance metrics. The simulations are performed in MATLAB version R2017b (9.3.0.713579).  
We consider deployment of SBSs that belong to several operators in a cluster [36]. The small cell cluster consists of SBSs uniformly deployed in a circular area of radius \(R\) meters. MSs are uniformly distributed around circular coverage of radius \(r_{n}\) meters of SBSs. For simulations, we choose \(R=100\) m and \(r_{n}=30\) m. The propagation model considered is the 3 GPP Model 1 (Table A.2.1.1.2-3) in [37]. The channel gains include path-loss, lognormal shadowing, and multipath Rayleigh fading. The lists of parameters used for simulation are shown in Table 2.  
We evaluate performance of the proposed algorithm in three different radio resource scenarios, namely: sparse, moderate, and dense scenarios, where the numbers of SBSs and MSs, \((N,M)\), are set to \((10,15),(10,55)\), and \((10,100)\), respectively. The reason for considering the three radio resource scenarios is to show the effectiveness of our proposed scheme in different types of scenarios. For the sparse scenario, the evaluated performance metrics include effects of varying the number of subchannels, convergence analysis, and efficiency comparison with other schemes. One reason for considering the sparse scenario to show the efficiency comparison is that the search for global optimum using an exhaustive search can be performed, while it is intolerably time consuming in the other two scenarios. Finally, for all the three scenarios, we compare the performance of MCBR (Neighborhood  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Values** \\ \hline Carrier frequency & 2 GHz \\ \hline Channel bandwidth (\(B\)) & 1.4 MHz \\ \hline Number of subchannels (\(K\)) & [6; 9; 12; 15; 18] \\ \hline SBS max. transmit power (\(P_{\text{max}}\)) & 20 dBm \\ \hline Noise power density & \(-174\) dBm/Hz \\ \hline Neighborhood distance & 30 m \\ \hline Path-loss: & \\ Between SBS and MS link & \(127+30 log_{10}(D)\) \\ Between other links & \(128.1+37.6 log_{10}(D)\) \\  & where \(D\) is link distance in km. \\ \hline Standard deviation of lognormal shadowing &
\begin{tabular}{l} 10 dB (between SBS and MS link) \\ 8 dB (between other links) \\ \end{tabular} \\ \hline Multipath Rayleigh fading & Exponential random variable with unit mean \\ \hline Penetration loss & 0 dB (between SBS and MS link) \\  & 20 dB (between other links) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation parameters.  
Information) with other schemes in terms of Jain's fairness index, average system capacity, average interference, and information feedback requirements from an average number of links.  
For comparison, we consider the BR strategy with utility in Equation (2) for two different schemes, namely, BR (Simultaneous) and BR (Sequential) [31]. In the simultaneous scheme, all links update their strategies simultaneously, without knowing the strategies that have been chosen by other links. Hence, they are making a simultaneous move. In the sequential scheme, each link take turns to update their strategies for selecting a subchannel that maximizes their utility. We also compare the performance of the MCBR algorithm for the utility function described in Equation (10), i.e, with complete information feedback from all other links using a particular subchannel in the SCN, denoted as MCBR (Complete Information).