# Effective Dereverberation with a Lower Complexity at Presence of the Noise
## 4 Experiments and Evaluation
### Acoustic Scenario and Experimental Setup  
The observation signals are generated the same as described in [34], and the TIMIT corpus [35] is used for the simulation. As shown in Figure 2, the length, width, and height of the room are 4, 3, and 3 m, respectively. A uniform linear microphone array with eight microphones is placed on a table for receiving speech signals from all angles in the room, the microphone spacing is 0.04 m, and the linear microphone array has a height of 0.75 m with the table. Meanwhile, there are 20 speech source positions in the room. Eight source positions, namely Tar.1, Tar.2, Tar.3, Tar.6, Tar.7, Tar.8, Tar.10, and Tar. 20, are chosen for the test (Figure 2), and 100 utterances are selected for each position. The selection of the source positions is based on their symmetry in Figure 2, that is, Tar.1 and Tar.2 are similar to Tar.5 and Tar.4, Tar.15 and Tar.16, Tar.19 and Tar.18, respectively. Tar.3 is similar to Tar.17. Tar.6 is similar to Tar.11. Tar.7 is similar to Tar.9, Tar.12 and Tar.14. Tar.8 is similar to Tar.13. These eight source positions are represented in Figure 2. Babble noise is used to obtain the reverberate speech with noise, the input signal-to-noise ratio (SNR) is set to \(-5\), 0, 5, and 10 dB, and the reverberation time \(T_{60}\) is set to 100, 400, 500, 600, 700, and 800 ms. When investigating the dependence of the algorithm on the order \(L\) of the linear prediction filter and the effect of the different initializations of the PSD on the proposed method, we selected the speech signal from the first position as the evaluation object. When comparing with the reference methods, all 800 utterances of the eight aforementioned locations in Figure 2 were utilized.  
The speech signal is sampled at 16 kHz, a Hanning window with a length of 512 samples has 50% overlap for analyzing the speech signal, and a 512-point STFT is used for the windowed speech signal. The frame number for each batch in the MVDR beamforming is set to 70. The delay \(D\) that preserves the early reflections is set to 1, and the order \(L\) of the linear prediction filter is set to 10. The state transition matrix \(\mathbf{A}\) (\(l\)) = \(\alpha\mathbf{I}\), where \(\alpha\) = 0.998. Similar to the default setting in [12], we let 10 \(\log_{10}(\varphi_{\text{e}})\) = \(-4\) dB and 10 \(\log_{10}(\varphi_{\text{e}1})\) = \(-4\) dB in (56) and (57), whereas 10 \(\log_{10}\) (\(1-\beta\)) = \(-25\) dB in (58) and (59).  
To evaluate the proposed algorithm, we choose the perceptual evaluation of speech quality (PESQ) [36], the short-time objective intelligibility (STOI) [37], the cepstral distance (CD) [38], the frequency-weighted segmental SNR (fwSegSNR) [39], and the signal-to-interference ratio (SIR) [39] as the measures, where the reverberation and noise are considered as the interference. These measures have a reasonable evaluation of the perception of reverberation and the overall quality of speech [40]. The CD focuses on reflecting the distortion of the speech spectrum: the lower the CD, the less overall speech distortion. The PESQ, STOI, fwSegSNR, and SIR can better demonstrate the reduction in reverberation and noise.