## 4 Results and Discussion
### Scenario 2: Sources with Mixed Stable Distribution  
Consider a mixed stable distribution \(F(x)\) as  
\[F(x)=\tau F_{\alpha_{1}}(x)+(1-\tau)F_{\alpha_{2}}(x), \tag{49}\]  
where \(F_{\alpha_{1}}(x)\) and \(F_{\alpha_{2}}(x)\) denote stable distributions with characteristic exponents \(\alpha_{1}\) and \(\alpha_{2}\), respectively, and \(\tau\) is the mixing parameter selected between \(0\leq\tau\leq 1\). Three situations have been considered. In the first experiment, the values for characteristic exponents have been selected as \(\alpha_{1}=2.0\) and \(\alpha_{2}=1.1\). For \(\alpha\equiv\alpha_{1}=2.0\), the corresponding standard SaS distribution is Gaussian, and for \(\alpha\equiv\alpha_{1}=1.1\) the corresponding distribution is severely impulsive. The mixing parameters has been selected as \(\tau=0.5\), which indicated that 50% of (randomly selected) samples have been generated from the standard SaS distribution with \(\alpha\equiv\alpha_{1}=2.0\) (Gaussian), and the rest of 50% (randomly selected) samples have been drawn from the standard SaS distribution with \(\alpha\equiv\alpha_{1}=1.1\) (severely impulsive). Figure 11a shows one realizations of a typical reference signal obtained from such a mixed distribution (49). It is noticed that the generated signal is indeed severely impulsive with variance being estimated to be \(5.4953\times 10^{3}\). In the second experiment, the parameters in (49) have been selected as \(\tau=0.75\), \(\alpha_{1}=2.0\), and \(\alpha_{2}=1.1\). This choice of parameter values shows that the 75% of (randomly selected) samples have been generated from standard SaS distribution with \(\alpha\equiv\alpha_{1}=2.0\) (Gaussian), and merely 25% (randomly selected) samples are from standard SaS distribution with \(\alpha\equiv\alpha_{1}=1.1\) (severely impulsive). Since majority (75%) of samples have been (randomly) drawn from the Gaussian distribution, this situation would correspond to less impulsive nature as compared with the previous case for \(\tau=0.5\). A typical signal drawn from such a mixed distribution is shown in Figure 11b with the corresponding variance being estimated to be \(0.5527\times 10^{3}\). In the third experiment, the parameters in (49) have been selected \(\tau=0.75\), \(\alpha_{1}=2.0\), and \(\alpha_{2}=1.6\). In this case, the samples from non-Gaussian stable distribution are from a less impulsive source compared with the previous examples. A typical signal drawn from such a mixed distribution is shown in Figure 11c, which has a variance of \(0.0042\times 10^{3}\) and looks more or less a Gaussian signal as impulses are less frequent as compared with the signals shown in Figure 11a,b. The simulation parameters have been adjusted experimentally as in the previous experiments. The simulation results for noise sources having a mixed characteristics stable distribution (49) with \(\tau=0.5\), \(\alpha_{1}=2.0\), and \(\alpha_{2}=1.1\) are presented in Figure 12. It is interesting to compare these results with those presented in Figure 7 which considered 100% samples being drawn from the standard SaS distribution with \(\alpha=1.1\). In the current experiment, though 50% of the samples have been (randomly) drawn from the Gaussian distribution, the performance of the existing algorithms is still very poor compared with that of the proposed algorithm. The sole reason is the severely impulsive nature of the source signals. The proposed CCSS-MFxRRLS algorithm can handle the strongly impulsive source well and demonstrates the best performance among the algorithms considered in this paper. The simulation results for noise sources having a mixed characteristics standard SaS distribution (49) with \(\tau=0.75\), \(\alpha_{1}=2.0\), and \(\alpha_{2}=1.1\) are presented in Figure 13. Though most of the samples (75%) come from Gaussian distribution, it is observed that [PERSON]'s algorithm still fails to show any convergence.