# Laboratory Test of a Vehicle Active Noise-Control System Based on an Adaptive Step Size Algorithm
## 3 Simulation Analysis  
Using the simulated noise signal as the reference signal of the active control algorithm, the proposed algorithm is compared with other known active noise control algorithms to analyze the performance of the proposed active noise reduction algorithm. The primary channel P(\(z\)) and secondary channel \(S(z)\) adopted in this simulation are both from the real physical channel model in the noise suppression laboratory. This offline modeling adopts an FIR (finite impulse response) filter with a length of 128 to establish the primary channel model P(\(z\)) and secondary channel model S(\(z\)). Figure 5 shows the impact response curves of the primary channel and secondary channel. Figure 5: Shock response of the primary channel P(\(z\)) and secondary channel S(\(z\)). Three kinds of analog signals, as adopted by the authors of [20], are used as reference signals, namely, mild impulsive noise (\(\alpha=1.7\)), medium impulsive noise (\(\alpha=1.5\)), and highly impulsive noise (\(\alpha=1.3\)). The average noise reduction (\(ANR\)) can be used to observe the performance of the studied algorithm more intuitively. The average noise reduction [23] is defined as follows:  
\[ANR(n)=20\log_{10}\biggl{(}\frac{A_{e}(n)}{A_{d}(n)}\biggr{)} \tag{20}\]  
\[A_{e}(n)=\lambda A_{e}(n-1)+(1-\lambda)|\mathrm{e}(n)| \tag{21}\]  
\[A_{d}(n)=\lambda A_{d}(n-1)+(1-\lambda)|\mathrm{d}(n)|. \tag{22}\]  
\(\lambda\) is a coefficient with a value range of (0, 1). The closer \(\lambda\) is to 1, the smoother the average noise reduction curve will be. For noise with a large amplitude change, the value of coefficient \(\lambda\) should be as large as possible; in this simulation, \(\lambda\) values are 0.99. Example 1: The standard S\(\alpha\)S distribution pulse noise is used as the reference signal, its characteristic index being \(\alpha=1.7\). For the proposed AASFxLMSPSO algorithm, different particle numbers have a significant impact on the performance and complexity of the algorithm. Given particle movement ranges of \(a_{\mathrm{i}imt}=\) [0.001, 0.01] and \(c_{\mathrm{i}imt}=\) [0.02, 0.1], MATLAB software was used to simulate the noise reduction of the AASFxLMSPSO algorithm with different particle numbers, and the influence of the different particle numbers on the performance of the algorithm was compared. Figure 6 shows the simulation result. It can be seen from the figure that the particle number has little influence on the noise reduction performance when \(p=5\), \(p=20\), and \(p=50\). In the scenario where increasing the number of particles would greatly increase the algorithm complexity, the number of particles was set as \(p=5\) for subsequent analysis. Then, using the \(\alpha=1.7\) pulse noise as a reference signal, several different adaptive algorithms were simulated to verify the performance of the proposed algorithms. As shown in Figure 7, when the reference signal of FxLMS increases, the convergence rate of the FxLMS algorithm will increase over a short time, and the overall convergence rate is very slow. The MNFxLMS algorithm declines steadily, and the convergence rate is slow. The convergence speed and stability of the NASFxLMS algorithm and NASFxLMSPSO algorithm demonstrated a good performance compared with the previous two algorithms. The proposed AASFxLMS algorithm showed better performance in terms of convergence speed and stability. After particle swarm optimization, the noise reduction performance of the AASFxLMSPSO algorithm was further improved, and the noise reduction effect  
Figure 6: Performance of the ASSFxLMSPSO algorithm under different particle numbers. of 20 dB was achieved in about 2000 iterations. Table 1 shows the key parameters of the simulation process. In Example 2, an S\(\alpha\)S pulse noise where \(\alpha\) = 1.5 is used as the reference signal. The noise reduction effect is shown in Figure 8. The FxLMS signal, which originally converged slowly, decreased rapidly when the reference signal increased.