## 4 Results and Discussion
### Scenario 1: Impulsiveness of Noise Sources
As described earlier and as shown in Figure 8, the adaptive parameter \(b(n)\) is close to \(+2.49\) at the start-up which ensures \(\gamma(n)\) is close to unity, and as the ANC system converges, the adaptive parameter \(b(n)\) is automatically tuned to \(-2.49\) which makes \(\gamma(n)\to 0\). This ensures fast convergence speed by selecting \(\mu(n)\) close to \(\mu_{1}\) at the start-up, and good steady-state performance by adjusting \(\mu(n)\to\mu_{2}\). The simulation results for the standard S\(\alpha\)S process with \(\alpha=1.4\) (less impulsive as compared with the previous experiment for \(\alpha=1.1\)) are presented in Figure 9. The noise source is strongly impulsive yet, as indicated by the signal shown in Figure 5b which is a typical signal drawn from such process. As in the previous experiment, detailed simulations have been performed to tune the step-size parameters. A similar performance comparison is observed as in the previous experiments: (1) [PERSON]'s algorithm becomes unstable even for a very small step size, (2) FSS-based (Th-FxLMS, modified FxLMK, INSS-FxLMS, and FSS-MFxRRLS) algorithms show slow convergence for a small valued step size, and their performance severely degrades for a large-valued step size, (3) the step size in the FSS-MFxRRLS algorithm can be tuned to give a better performance then the existing algorithms; however, the issue of trade-off situation for performance in transient-state and steady-state remains as it is, (4) both the previous CCSS-NMfxLMS and the proposed CCSS-MFxRRLS algorithms address the trade-off - thanks to being equipped with the CCSS approach, and (5) the proposed CCSS-MFxRRLS algorithm outperforms the rest of the algorithms considered in this simulation study. Figure 8: Evolution various parameters in the proposed CCSS-MFxRRLS for severely impulsive noise source with \(\alpha=1.1\): (**a**) the adaptive parameter \(b(n)\); (**b**) the mixing parameter \(\gamma(n)\); (**c**) the time-varying CCSS \(\mu(n)\). Figure 10 presents the simulation results for various impulsive ANC algorithms for the standard SaS process with \(\alpha=1.6\) (mildly impulsive case). It is noticed that all FSS-based algorithms perform far better than the benchmark [PERSON]'s algorithm--in fact, [PERSON]'s algorithm is convergent only for a very small step size and hence exhibits extremely slow convergence speed. Furthermore, the proposed CCSS-MFxRRLS algorithm does not require any tuning for the parameter values, yet gives the best performance. Figure 9: Detailed simulation results for strongly impulsive noise source with \(\alpha=1.4\): (**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) modified FxLMK algorithm (\(\mu=1\times 10^{-4}\)); (4) INSS-FxLMS algorithm (\(\mu=5\times 10^{-4}\)); (5) previous CCSS-NMFxLMS algorithm (\(\mu_{1}=1.0,\mu_{2}=1\times 10^{-2}\)); (6) FSS-MFxRRLS algorithm (\(\mu=0.1\)); (7) proposed CCSS-MFxRRLS (\(\mu_{1}=1.0,\mu_{2}=0.05\)). Figure 10: Detailed simulation results for a mildly impulsive noise source with \(\alpha=1.6\). **(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 (\(\mu=1\times 10^{-7}\)); (2) Th-FxLMS algorithm (\(\mu=1\times 10^{-5}\)); (3) modified FxLMK algorithm (\(\mu=1\times 10^{-4}\)); (4) INSS-FxLMS algorithm (\(\mu=1\times 10^{-3}\)); (5) previous CCSS-NMfxLMS algorithm (\(\mu_{1}=1.0,\mu_{2}=1\times 10^{-2}\)); (6) FSS-MFxRRLS algorithm (\(\mu=0.1\)); (7) proposed CCSS-MFxRRLS (\(\mu_{1}=1.0,\mu_{2}=0.05\)).