## 1 Introduction  
In the current century, the smartphones and other communication devices have been an important part of human life, where it is impossible to have social communications without them [1,2]. One of the principal parts in these smartphones is the signal processing platform. This part has an important role in the telecommunication and audio signal processing. Denoising and dereverberation are two main sections in the signal processing and enhancement platforms, which is the aim of this article, to increase the performance of speech enhancement algorithms [3]. Increasing the number of sensors improves the accuracy of denoising algorithms due to the spatial spectrum extension by providing the proper information. The definition of accuracy in the enhancement algorithms is how the enhanced signal is closer to the original signal with a high level of noise elimination and less distortion. Therefore, the speech enhancement is the main part in such applications as: hearing aid systems, mobile communication, speaker localization and tracking, speech recognition, voice activity detection (VAD), speaker identification, etc. The denoising algorithms should be implemented in a way to keep the speech intelligibility in an acceptable range and to remove a high level of noise and reverberation. Then, the signal-to-noise ratio (SNR) cannot be the only specific factor for comparing the speech enhancement methods. The qualitative criteria such as: perceptual evaluation of speech quality (PESQ) [4], mean opinion score (MOS) [5], and short-time objective intelligibility (STOI) [6] are very useful to show the performance of denoising methods in comparison with other previous works along with quantitative criteria such as: overall SNR and segmental SNR (SegSNR) [7]. The performance of the denoising algorithms is calculated by considering the qualitative and quantitative criteria at the same time, which are the proper measurements for comparison with other previous works. In recent years, many of the single and multi-channel methods have been proposed for speech enhancement. The single-channel methods are still challenging strategies for the speech enhancement due to the limited information. The traditional speech enhancement methods such as the Wiener filter (WF) and distributed multichannel WF (DB-MWF) [8,9], spectral subtraction [10,11], and statistical-model-based [12,13] have superior performances in stationary noisy environments but the stability and accuracy of these methods are strongly decreased in non-stationary noisy conditions. However, existing noise estimation methods such as minima-controlled recursive averaging [14,15] and minimum statistics [11,16] follow the stationary noise energy. However, they do not have the ability to follow the non-stationary noise energy. For example, the method proposed in [16] is presented to estimate the power spectral density (PSD) of a non-stationary noise signal. This method can be considered in combination with any speech enhancement algorithm, which requires the noise PSD estimation. The presented method follows the spectral minima in each frequency band by minimizing conditional mean square error (MSE) criteria in each time frame, which develops the optimal smoothing parameter for recursive smoothing of the PSD of the noisy speech signal. Therefore, an unbiased noise estimator is presented based on the optimally smoothed PSD estimation and the analysis of the statistics of spectral minima. Therefore, the noise estimation accuracy in some methods [15,16] is affected when the noise is non-stationary. A group of speech enhancement methods are proposed based on a priori information of speech signals such as the auto-regressive hidden Markov model (ARHMM) [17,18,19]. The noise and speech signals are modeled as an auto-regressive (AR) process in these methods. In addition, the hidden Markov model (HMM) is implemented for modeling the prior information of speech and noise features. For example, the methods in [18,19] are considered for modeling the speech and noise spectrum shape.