# Game Algorithm for Resource Allocation Based on Intelligent Gradient in HetNet
## 4 Simulation Results and Analyze  
In this part, we conduct simulation analysis of the above algorithm performance. For the sake of convenience, we first consider a simple scenario containing one macro base station and one femtocell. Then we consider the complex network environment, where the system contains \(N\) femtocells whose distribution conforms to Poisson Point Process. The rest of the simulation parameters are shown in Table 1.  
Figure 3 presents the simulation analysis of the Nash equilibrium strategy under different adjustment factors with the use of a linear gradient iteration algorithm and one that uses the intelligent \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Macrocell** & **Femtocell** \\ \hline System bandwidth \(W\) & 20 MHz & 20 MHz \\ User density & \(100/\text{macro}\) & 2–15/femto \\ Cell radius & 500 m & 15 m \\ Max transmit power of base stations \(P_{m}(P_{\bar{f}_{i}})\) & 43 dBm & 20 dBm \\ Fast fading & SCME & SCME \\ Noise level \(N_{0}\) & \(-174\ dBm/\Hz\) & \(-174\ dBm/\Hz\) \\ \(c_{th}\) & 10 dB & 10 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameter. SCME: Spatial Channel Model extension. gradient algorithm proposed in the paper. \(\alpha\) represents the optimal released spectrum ratio, and \(\beta\) refers to the optimal biasing factor of femtocells. It can be seen that selecting adjustment factors plays an important role in the convergence rate of iteration solution of the Nash equilibrium price strategy. When the adjustment factor is small, strategy adjustment has a slow convergence rate; when the adjustment factor is big, fluctuation in using iteration to solve Nash equilibrium strategy is a big influence on the convergence rate. The players' strategy of the proposed gradient algorithm is the same as the strategy of the linear gradient algorithm. Through choosing the fastest changing direction of the system revenue function, we can rapidly obtain the Nash equilibrium strategy. The simulation result in Figure 3 has shown that the algorithm proposed in the paper can get the Nash equilibrium as same as it is obtained through the linear gradient algorithm, and we can rapidly obtain Nash equilibrium strategy. Then we consider the complex network environment, where the system contains one macro base station and nine femtocells whose distribution conforms to Poisson Point Process. Figure 4 presents the simulation analysis of the Nash equilibrium strategy. The red lines show the Nash equilibrium of femtocells that act as the followers, and the blue line shows the Nash equilibrium of the macro base station that acts as the leader. It can be seen that the Nash equilibrium strategy can be obtained through the proposed algorithm and the iteration period is short. Figure 4: Nash equilibrium strategy under the proposed algorithm in the paper. Figure 3: Nash equilibrium strategy under different adjustment factors and the proposed algorithm in the paper. Figure 5 presents the error performance analysis of the Nash equilibrium strategy obtained between the proposed intelligent gradient iteration algorithm and linear iteration algorithm, from which we can see that when adjustment factor is small, the price strategy error of linear iteration algorithm becomes small as well; with increase of adjustment factor, the error between linear iteration algorithm and intelligent gradient iteration algorithm proposed in the paper is close. Figures 6 and 7 show the performance of the proposed scheme and the existing scheme. The existing scheme is the one introduced by the reference [29]. Figure 6 shows the femto users' (FUEs') cumulative distribution function (CDF) of the SINR. It obviously shows that the femto users' SINR performance is better. It is because the existing scheme made improvements by defining the utility function as average throughput capacity of the macro base station and standard distortion rate of femtocells, respectively.