## 5 Performance Evaluation
### Results and Analysis  
Figure 2 depicts the mean LSD for Habets LRSV estimator using \(\kappa\) obtained by different methods, including the measured ground truth \(\kappa\)(fullband and subband), proposed \(\kappa\) estimator, conventional \(\kappa\) estimator and the scanning method. As shown in Figure 2, an scanning-optimal \(\kappa\) can be obtained for each AIR as the corresponding \(\overline{LSD_{late}}\) reaches a minimum during the scanning process, and it can be observed that such scanning-optimal \(\kappa\) is far from the measured ground truth \(\kappa\), which alerts us that the measured \(\kappa\) may not be the optimal \(\kappa\) for Habets LRSV estimator. Although the measured fullband \(\kappa\) performs better for \(AIR_{4}\) and the measured subband \(\kappa\) performs better for \(AIR_{2}\), they perform poorly for other AIRs. As for the proposed \(\kappa\) estimator, the \(\overline{LSD_{late}}\) value exhibits a minimum for three AIRs, and is close to the minimum for other AIRs. It suggests that the proposed \(\kappa\) estimator performs not only much better than the conventional \(\kappa\) estimator and measured ground truth \(\kappa\) (both fullband and subband), but even as well as the scanning-optimal \(\kappa\) obtained by scan method. It is worth mentioning that the scanning-optimal \(\kappa\) may not be the real optimal \(\kappa\), but it still can be seen as an appropriate \(\kappa\) considering the experimental results. Figure 3 shows the averaged log error obtained using all RIRs for varying RSNR. As the RSNR decreases, all estimators show a more and more positive bias, which means the LRSV estimator performs worse with background noise and should be used after a denoising algorithm. However, the 'length' of the whisker bars of the proposed \(\kappa\) estimator is always shorter than other methods. In other words, the proposed \(\kappa\) estimator yields lower variance, which suggests that the proposed \(\kappa\) estimator is more robust with background noise. Figure 2: Plot of \(\overline{LSD}\) as a function of \(\kappa\) for (**a**–**f**): \(AIR_{1}\sim AIR_{6}\). \(\overline{LSD}\) for the measured ground truth \(\kappa\)(fullband and subband), proposed \(\kappa\) estimator and conventional \(\kappa\) estimator are presented as reference lines for comparison. (**a**) \(AIR_{1}\); (**b**) \(AIR_{2}\); (**c**) \(AIR_{3}\); (**d**) \(AIR_{4}\); (**e**) \(AIR_{5}\); (**f**) \(AIR_{6}\). Figure 4 compares the measured ground truth \(\kappa\) with the scanning-optimal \(\kappa\), and as depicted in it, the scanning-optimal \(\kappa\) is not obviously related to the measured ground truth \(\kappa\). It precludes us from simply applying a bias correction to the measured \(\kappa\), which is sometimes used in practical. The reason for the mismatch between the measured ground truth \(\kappa\) and the scanning-optimal \(\kappa\) may be that the generalized statistical model is a simplified approximation of AIR, which causes the error of estimation in Equation (6) and the error will vary with the anechoic speech signal \(\lambda_{s}(k,l)\). Hence, in order to compensate that error, the value of \(\kappa\) needs to be modified, which makes the measured ground truth \(\kappa\) not the scanning-optimal \(\kappa\) for [PERSON] LRSV estimator. To prove the above viewpoint, 13 different anechoic speech signals of 15 s length are used to obtain corresponding scanning-optimal \(\kappa\) for each AIR. The results are shown in Figure 5.  
Figure 4: Plots of the measured ground truth \(\kappa\) and the scanning-optimal \(\kappa\) for each AIR. Figure 3: Mean and standard deviation of log error \(e(k,l)\) for different RSNR. The means are indicated by symbols (circle, cross, etc. ), and the semi-variances are indicated by whisker bars. It can be seen that for different speech signals, the scanning-optimal \(\kappa\) changes randomly and can differ by up to 0.54, which reveals that the optimal \(\kappa\) for Habets LRSV estimator may be not only related to DRR but also related to the speech signal.