## 6 Experimental Evaluation  
The performance of the different estimators and speech enhancement algorithms discussed along this paper is evaluated by means of objective speech quality and intelligibility metrics. Two different well-known objective metrics are used:  
* The Perceptual Evaluation Speech Quality (PESQ) [37] metric is utilized to evaluate the speech quality of the enhanced speech signal. This metric gives a mean opinion score between one and five. The higher the PESQ values, the better the speech quality. * The Short-Time Objective Intelligibility (STOI) [38] metric is intended to evaluate the speech intelligibility of the enhanced speech signal. The resulting score is a value between zero and one. The higher the STOI value, the better the speech intelligibility. PESQ and STOI are both intrusive metrics, which means that they need a clean reference. As a reference, we use the clean speech signal at the reference microphone, \(x_{1}(n)\). Additionally, in order to evaluate the RTF estimation accuracy, we use the speech distortion (SD) index [2]. This index measures the distortion level on the clean speech signal at the beamformer output, namely \(\tilde{x}_{1}(n)\) (inverse STFT of \(\mathbf{F}^{H}(t,f)\mathbf{X}(t,f)\)). The idea behind using this metric is that, because of the distortionless property of MVDR, more accurate RTF estimates should yield lower speech distortion. The SD index is measured segmentally across the speech signal, in such a way that the SD value at the \(i\)-th segment is obtained as\[SD(i)=\frac{\sum\limits_{n=(i-1)T}^{iT-1}\left|x_{1}(n)-\tilde{x}_{1}(n)\right|^{2 }}{\sum\limits_{n=(i-1)T}^{iT-1}\left|x_{1}(n)\right|^{2}}, \tag{76}\]  
where \(T\) is the number of samples per segment. The segmental SD values are averaged to achieve the final SD index, which is a value between zero and one. The lower the SD value, the lower the speech distortion. As in Reference [5], silence frames are excluded from this evaluation by means of calculating the median of the segment-wise signal power and removing those segments with a power 15 dB lower than that median. We evaluate the proposed algorithms by using simulated dual-channel noisy speech recordings from a dual-microphone smartphone. Two different databases were developed for each device use mode: close-talk (CT) and far-talk (FT). To simulate the recordings, clean speech signals are filtered using dual-channel acoustic impulse responses and real dual-channel environmental noise is added at different signal-to-noise ratios (SNRs). We evaluate four different reverberation environments and eight different noises, which are matched as indicated in Table 1, yielding eight different acoustic environments (including both reverberation and noise). Details about the methodology used to obtain the acoustic impulse responses and the noises can be found in References [15; 39]. Clean speech signals are obtained from the TIMIT database [40; 41] and downsampled to 16 kHz. In particular, a total of 850 clean speech utterances from different speakers are employed. All the utterances have a length of around seven seconds, which is achieved by same-speaker utterance concatenation. Two different sets are then defined, namely training and test. Speakers do not overlap across sets. Moreover, the number of utterances from female and male speakers is balanced. The distribution of utterances and the number of speakers in the training and test sets are indicated in Table 2.  
The training set consists of reverberated clean speech utterances and is only used to estimate the _a priori_ statistics for the eKF-RTF estimator. Such utterances were obtained by filtering each clean speech utterance with a set of dual-channel acoustic impulse responses which model four reverberant environments, thereby yielding a total of 2800 training utterances. Sixteen different acoustic impulse responses were considered for each acoustic environment. For each utterance, the impulse response was randomly selected.