## 3 Simulation Results  
Here, we simulate the proposed PSO-based ANC system (single channel) with switching filter selection in MATLAB to demonstrate its effectiveness in terms of convergence properties. Specifically, we develop a set of simulation experiments under the following conditions:  
1. We model the primary and secondary paths as finite impulse response (FIR) filters using 256 and 128 coefficients [33], respectively. 2. The MSE was evaluated at error microphones. 3. We consider a white Gaussian noise signal with a zero mean as input signal \(x(n)\). 4. Table 1 shows the selected acceleration coefficients and inertia weights to produce the best convergence properties. As is well known, acceleration coefficients are static. Therefore, the optimal values need to be found empirically. In general, the use of low values for \(c_{1}\) and \(c_{2}\) produces smooth particle trajectories [34]. Here, the proper selection of these values have allowed the particles to roam close from good regions which produces more acceleration. Based on [34], we select of the inertia weights (\(\phi_{max}\)) and values for \(c_{1}\) and \(c_{2}\), as follows: \[\phi_{max}>\frac{1}{2}(c_{1}+c_{2})-1\] (16)According to previous equation, if the condition is not satisfied, the PSO algorithm may diverge or could present cyclic behavior. To validate the performance of the proposed algorithm, we made a comparison between this bio-inspired algorithm and the conventional FXLMS algorithm. In addition, we carried out several experiments by varying the filter's order, number of particles and changing the secondary/primary path during the filtering process to validate the performance of the proposed PSO-based ANC system. * _Comparison between the proposed algorithm and the FXLMS algorithm_. To evaluate the MSE level, we use a population of 100 particles. To verify the tracking capabilities of the algorithms, we induce an abrupt change in the middle of the generations (1500) by multiplying the secondary path by \(-1\). The FXLMS step-size was adjusted by trial and error; the value producing the fastest convergence speed was selected.As can be observed from Figure 5, the proposed algorithm exhibits higher convergence speed when compared to the conventional FXLMS. Besides, the FXLMS requires an estimation of the secondary path to avoid instability and low accuracy. In contrast, this estimation is not required when the PSO algorithm is used. * _Effect of changing the order of adaptive filter_. To evaluate the MSE level, we use a population of 100 particles and different adaptive filter's length (\(N\) from 20 to 50), as shown in Figure 6. To verify the tracking capabilities of the proposed PSO-based ANC system, we induce an abrupt change in the middle of the generations (1500) by multiplying the secondary path by \(-1\). As can be observed from Figure 6, the MSE level is high when low number of coefficients are used. Otherwise, the use of large number of coefficients improves the MSE level by paying a penalty in terms of convergence speed. In addition, the use of high order adaptive filters demands a high computational cost by improving significantly the MSE level, where this parameter is crucial in practical ANC systems since it determines the level of noise reduction. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(c_{1}\) & \(c_{2}\) & \(c_{3}\) & \(c_{4}\) & \(\phi_{1_{max}}\) & \(\phi_{1_{min}}\) & \(\phi_{2_{max}}\) & \(\phi_{2_{min}}\) \\ \hline
1.0599 & 1.0599 & 1.0993 & 1.0993 & 0.79 & 0.0009 & 0.9449 & 0.01649 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Acceleration coefficients and inertia weights used in all experiments. Figure 5: Learning curves of the proposed PSO-based ANC algorithm and the FXLMS algorithm. * _Effect of changing the number of particles of the PSO algorithm._ According to previous results, we obtained the higher level reduction when 50 filter coefficients are used. When selecting a number higher than 50, the performance of the algorithm does not change and remains the same.