## 4 Results and Discussion
### Scenario 1: Impulsiveness of Noise Sources  
The objective of this case study is to understand the performance of various adaptive algorithms for ANC of various impulsive sources with impulsiveness ranging from severe to mild (a few typical examples of such signals are shown in Figure 5). In this regard, Figure 7 shows detailed simulation results for the MNR performance of various algorithms for a severely impulsive standard SaS process with \(\alpha=1.1\). For clarity of presentation, the performance of individual algorithms is presented in separate sub-figures (the curves for the proposed algorithm are included in all sub-figures). Another objective of such a presentation is to have a clear picture about the variation of the step-size parameters (given in the legend of each sub-figure) for the respective algorithms. Figure 6: Effect of the parameter \(\beta\) on the noise reduction performance of the proposed FSS-MFxRRLS algorithm with \(\mu=0.1\). Figure 7: Detailed simulation results for severely impulsive noise source with \(\alpha=1.1\): **(a)** [PERSON]’s algorithm [24]; **(b)** Th-FxLMS algorithm [25]; **(c)** modified FxLMK algorithm; **(d)** INSS-FxLMS algorithm [26]; **(e)** effect of step-size parameter in the proposed FxRLS-based impulsive ANC algorithms; **(f)** performance comparison between various algorithms: (1) [PERSON]’s algorithm (\(\mu=1\times 10^{-8}\)); (2) Th-FxLMS algorithm (\(\mu=1\times 10^{-6}\)); (3) Th-FxLMS algorithm (\(\mu=5\times 10^{-6}\)); (4) modified FxLMK algorithm (\(\mu=1\times 10^{-4}\)); (5) modified FxLMK algorithm (\(\mu=5\times 10^{-4}\)); (6) INSS-FxLMS algorithm (\(\mu=1\times 10^{-4}\)); (7) INSS-FxLMS algorithm (\(\mu=5\times 10^{-4}\)); (8) previous CCSS-NMFxLMS algorithm (\(\mu_{1}=1.0\), \(\mu_{2}=1\times 10^{-2}\)); (9) FSS-MfxRLS algorithm (\(\mu=0.1\)); (10) FSS-MfxRLS algorithm (\(\mu=0.5\)), (11) Proposed CCSS-MFxRRLS (\(\mu_{1}=1.0\), \(\mu_{2}=0.05\)). Figure 7a shows that [PERSON]'s algorithm is unstable even for a very small-valued step size. The reason lies in the fact that the noise source is of a severely impulsive nature, and the simple thresholding procedure in [PERSON]'s algorithm is unfortunately not able to handle it. Figure 7b-e show MNR results for FSS-based Th-FxLMS, modified FxLMK, INSS-FxLMS, and the proposed FSS-MFxRRLS algorithm, respectively. It is evident that an FSS indeed results in a trade-off situation as discussed earlier: it is almost impossible to realize both fast convergence speed and good steady-state performance. It is in fact noticed that the steady-state performance of these algorithms severely deteriorates for a large-valued step size being selected for a fast convergence speed. Finally, Figure 7f shows performance comparisons between various algorithms where two curves have been selected for each FSS-based algorithm, one for a small step size and one for a large step size. It is observed that the previous CCSS-NMfxLMS and the proposed CCSS-MFxRRLS algorithms achieve fast convergence speed and good steady-state performance, with the proposed CCSS-MFxRRLS algorithm outperforming the rest of the algorithms, the reason being the time-varying step size \(\mu(n)\) as explained below. The experiments for the proposed FSS-MFxRRLS algorithm help in deciding the step-size parameters \(\mu_{1}\) and \(\mu_{2}\) in the proposed CCSS-MFxRRLS algorithm. Note that FSS-MFxRRLS gives the fastest convergence speed for \(\mu=1.0\) and good steady-state performance for \(\mu=0.05\); the CCSS \(\mu(n)\) in the proposed CCSS-MFxRRLS algorithm is computed using \(\mu_{1}=1.0\) and \(\mu_{2}=0.05\). For this choice of step-size parameters and the simulations results presented in Figure 7, the corresponding evolution of various parameters in computing the CCSS is shown in Figure 8. Here, Figure 8a-c plot variations of the adaptive parameters \(b(n)\) (operations (14) and (15) in Table 1), the mixing parameter \(\gamma(n)\) (operation (16) in Table 1), and the time-varying step size \(\mu(n)\) (operation (12) in Table 1), respectively.