## 5 Simulation Results
For the simulations using an AR(1) sequence as input, the pole was set to 0.95. The four unknown echo paths are real measured acoustic impulse responses, which have been decimated in order to have the desired lengths (indicated in the caption of each figure). Finally, the SNR was experimentally set to 25 dB for all scenarios [4; 5]. In Figure 2, we studied the performance of the proposed algorithm for different values of the DR parameter \(N_{it}\) and for two values of the pre-distortion parameter: (A) \(\alpha_{\mathrm{r}}=0\) (no pre-distortion is applied) and (B) \(\alpha_{\mathrm{r}}=0.33\) ( pre-distortion used for the complex input signal). It can be noted that for every value of \(N_{it}\) the performances corresponding to (B) are considerably superior to their counterparts from case (A). The mitigation of correlation between the real valued input signals associated with the two channels leads to better performance for the adaptive filter. For every value of \(N_{it}>1\), the gain in terms of normalized misalignment is at least 5 dB at steady state. Moreover, as the value of the parameter \(N_{it}\) increases, so does the initial convergence speed of the WL-DR-RLS-DCD. The corresponding compromise is made with the associated extra arithmetic workload and a reduction in accuracy of the adaptive algorithm when steady state is reached. Finally, it can also be observed that with higher values of \(N_{it}\), the progress in terms of convergence speed becomes smaller, such that the corresponding gain tends to become capped. In Figure 3, we compare the performance of the WL-RLS-DCD for different values of \(\alpha_{\mathrm{r}}\) with the WL-DR-RLS-DCD having \(N_{it}>1\). We increased the pre-distortion parameter above the recommended limit in order to analyze the possibility of compensating a high number of DR iterations and save extra costs in terms of arithmetic operations required by the WL-DR-RLS-DCD with higher values for \(N_{it}\). It can be noted that even the convergence speeds associated with values \(\alpha_{\mathrm{r}}>0.5\) (i.e., when the stereo effect is altered) cannot match the misalignment performance of using \(\alpha_{\mathrm{r}}=0.33\) and \(N_{it}>1\). All normalized misalignment curves corresponding to \(N_{it}=1\) require more than \(10^{6}\) iterations to reach steady state (i.e., around \(-25\) dB), which exceeds the boundaries of the presented simulation interval. Figure 3: Misalignment of the WL-DR-RLS-DCD algorithm for different values of \(N_{it}\) and different values of the pre-distortion parameter \(\alpha_{\rm r}\). The input signal is an AR(1) sequence with the pole 0.95, and the length of the four unknown impulse responses is \(L=128\) and \(\lambda=1-1/(64L)\). Figure 2: Misalignment of the WL-DR-RLS-DCD algorithm for different values of \(N_{it}\). The input signal is an AR(1) sequence with the pole 0.95, and it is pre-distorted (\(\alpha_{\rm r}=0.33\)) or not pre-distorted at all (\(\alpha_{\rm r}=0\)). The length of the four unknown impulse responses is \(L=128\) and \(\lambda=1-1/(64L)\). The last experiment is presented in Figure 4. The input signal is a speech sequence. The unknown impulse responses are longer than the ones employed in the previous scenarios and are changed after half of the simulation is completed by shifting them 25 positions to the right (tracking scenario). We compared the performances of the WL-DR-RLS-DCD for the same value of \(\alpha_{\mathrm{r}}\) and different number \(N_{it}\) of DR iterations. As a reference, we also added the corresponding results for the lowest and highest value of \(N_{it}\) when the input signal is not pre-distorted. It can be noted that as the number of DR iterations increases, the tracking capabilities of the WL-DR-RLS-DCD improve, and the corresponding steady-state accuracy is diminished. Moreover, the versions of WL-DR-RLS-DCD which work without a pre-distorted input signal cannot match the performance of the algorithm employed with pre-processed input data.