# Laboratory Test of a Vehicle Active Noise-Control System Based on an Adaptive Step Size Algorithm
## 3 Simulation Analysis
However, the FxLMS algorithm became unstable when it encountered a large impact. The MNFxLMS algorithm is stable, but the convergence speed is slow. The convergence speed and stability of the NASFSxLMS algorithm and NASFSxLMSPSO algorithm both demonstrated good performance. However, the performance of the proposed AASFxLMS algorithm had significant advantages; the convergence speed of the proposed algorithm after particle swarm optimization was further improved, and the noise reduction effect of 20 dB was reached when the number of iterations reached 4000 times. Table 2 shows the key parameters of the simulation process. \begin{table}
\begin{tabular}{c c} \hline \hline FxLMS & u = 0.00005 \\ \hline MNFxLMS & \(p\) = 1.59, \(\mu\) = 2.0 \(\times\) 10\({}^{-3}\) \\ NASFSxLMS & \(\rho\) = 0.3, \(\gamma\) = 1.2 \\ NASFSxLMSPSO & \(\rho\) = 0.4524, \(\gamma\) = 1.1458, \(\omega\) = 0.6, \(C_{1}\) = 2, \(C_{2}\) = 2, \(p\)=50, \(m\) = 10, \(G\) = 100 \\ AASFxLMS & \(a\) = 0.0005, \(c\) = 0.05 \\ AASFxLMSPSO & \(a_{\text{limit}}\) = [0.0001, 0.001], \(c_{\text{limit}}\) = [0.02, 0.06], \(K\) = 1000, \(\omega\) = 0.6, \(m_{1}\) = 2, \(m_{2}\) = 2, \(p\)=5, \(r\) = 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The key parameters of each algorithm in the MATLAB simulation of Example 2. \begin{table}
\begin{tabular}{c c} \hline \hline FxLMS & u = 0.00005 \\ \hline MNFxLMS & \(p\) = 1.59, \(\mu\) = 2.0 \(\times\) 10\({}^{-3}\) \\ NASFSxLMS & \(\rho\) = 0.3, \(\gamma\) = 1.2 \\ NASFSxLMSPSO & \(\rho\) = 0.4524, \(\gamma\) = 1.1458, \(\omega\) = 0.6, \(C_{1}\) = 2, \(C_{2}\) = 2, \(p\)=50, \(m\) = 10, \(G\) = 100 \\ AASFxLMSPSO & \(a\) = 0.0005, \(c\) = 0.05 \\ AASFxLMSPSO & \(a_{\text{limit}}\) = [0.0001, 0.001], \(c_{\text{limit}}\) = [0.02, 0.06], \(K\) = 1000, \(\omega\) = 0.6, \(m_{1}\) = 2, \(m_{2}\) = 2, \(p\)=5, \(r\) = 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The key parameters of each algorithm in the MATLAB simulation of Example 1. Figure 7: The noise reduction effect of the S\(\alpha\)S distributed pulse noise, where \(\alpha\) = 1.7. Example 3: So\(\alpha\)S pulse noise with \(\alpha=1.3\) is used as the reference signal. The noise reduction effect is shown in Figure 9. With the further increase of impact amplitude, the FxLMS algorithm becomes extremely unstable and diverges when the reference signal suddenly increases. The MNFxLMS algorithm is stable when the signal suddenly increases, but the convergence rate is slow. NASFSxLMS algorithm convergence speed is slow, NASFSxLMSPSO algorithm convergence speed is relatively fast. The proposed AASFxLMS algorithm has a fast convergence speed and remains stable in the face of the sudden increase of reference signal noise reduction performance. After particle swarm optimization, the convergence speed and stability of AASFxLMSPSO are further improved. Table 3 shows the key parameters of the simulation process. By comparing the simulated S\(\alpha\)S pulse noise of three different characteristic indices, the proposed algorithms all showed better noise reduction performance under different impact amplitudes, which verifies the performance of the proposed algorithms.