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Feature extraction 
The feature extraction pipeline of the speech recogniser is shown in Fig. 8. Each acquired audio channel is processed by the PNCC extraction block that computes the feature coefficients. Then, the Multichannel Histogram Equal ization (MHEQ) stage exploits the feature streams to produce a single feature vector per frame. Notice that for simplicity the “PNCC Extractor” is shown as a single block Fig. 8, however each channel is processed by a dedicated block. PNCCs were chosen instead of the more common Mel-Frequency Cepstral Coefficients (MFCCs) (Davis & Mermelstein, 1980) because at the cost of a 420 modest increment of computational burden they give superior accuracies in degraded acoustic conditions (Kim & Stern, 2012). The steps for the extraction of PNCCs are showed in Fig. 9. The figure shows in blue colour the stages which the PNCC pipeline shares with the MFCCs one, in red the additional stages, and in yellow the modified stages. Without entering into the details, an important 425 processing stage of PNCCs is the “Medium-Time Processing” one, where the signal is processed in segments 50-120 ms long to obtain an estimate of the signal floor level. The other additional processing stages are the “Time-Frequency Normalization”, and the “Mean Power Normalization”. The first takes the transfer function at the output of the “Medium-Time Processing” and employs 430 it to modulate the “Gammatone Frequency Integration” output. The second, normalizes the signal power dividing the input by a running average of the overall power. In PNCCs, the logarithm non-linearity of the MFCC pipeline is replaced with a “Power-Function Non-Linearity”, i.e., the same non-linearity employed in Perceptual Linear Prediction (PLP) coefficients (Hermansky, 1990). Here, 435 however the exponent is set to 1/15 instead of 1/3 as in PLP. The final step, i.e., the “DCT” computation, is in common with MFCCs. In this paper, the sampling frequency of the speech signals is 16 kHz and PNCC are parametrised as in Kim & Stern (2012). The PNCC extractor produces four streams composed of 13 feature coefficients. 440 MHEQ (Squartini et al., 2012) is a variant of the single channel HEQ algorithm (De La Torre et al., 2005) able to exploit the information of multiple audio channels. Compared to conventional beamforming techniques, MHEQ is able to produce similar results with a reduced computational burden and without the need of a source localization algorithm. Single channel HEQ reduces 445 the mismatch between training and testing condition by transforming the probability distribution of the input signals into the one of the signals employed in the acoustic model training phase. This requires the estimation of the cumulative distribution function of the input signals, and the calculation of the inverse of the cumulative distribution function of the training set signals. Without 450 entering into the details, MHEQ consists in computing the average of the feature streams and the average of the cumulative distribution functions estimated separately from each stream. Then, the results are employed as in the single channel HEQ. The final feature vector is composed of 13 static coefficients plus their first 455 and second derivatives, for a total of 39 coefficients.