## 1 Introduction
Therefore, the spectrum gain is calculated instead of the whole spectrum for the speech and noise signals. The noise-spectrum gain estimation is adapted by the fast variations of the signal energy, which is known as non-stationary noise. [PERSON] and [PERSON] [20] proposed a novel method based on the normalized fractional of the two-channel least mean square (LMS) algorithm for enhancing the speech signal. The presented algorithm is known as fractional LMS, which is obtained by considering the fractional terms in the calculation of filter coefficients of the standard LMS algorithm. The normalization is a proper strategy to improve the performance of the LMS algorithm. Therefore, a normalization step is implemented on the fractional LMS in order to promote the performance of the enhancement method. The proposed two-channel method has a higher performance in terms of the MSE criteria in comparison with other works. [PERSON] and [PERSON] [21] proposed a recursive least square (RLS)-based adaptive filter for the application of speech enhancement. The segmentation step is considered for the microphone signals to provide a better stationary of the speech signals. In the following, the adaptive filter coefficients are calculated based on the modified version of the RLS method. The filter coefficients are calculated in a way to have the least distortion in the enhanced speech signals. The presented method has a high performance in the presence of white noise for a different range of SNRs. [PERSON] et al. [22] proposed a method for estimation of the short-time linear prediction parameters of the Wiener filter. In the presented work, a speech signal spectrum modeling is proposed based on the prior information of the speech linear prediction in order to model the noise as same as the speech signal. The difference between the proposed method with other previous works is the use of multiplicative update rule for better estimation of the coefficients. [PERSON] et al. [23] introduced a framework for the speech enhancement based on an ad-hoc microphone array. A subarray is considered for coherence calculation in the speech signal. A coherence measurement is proposed based on the speech quality in the entrance of the array in order to select the subarrays in the local speech enhancements, when more than one subarray is used. The proposed method is evaluated based on quantitative and qualitative criteria such as: array gains, speech distortion ratio, PESQ, and STOI to show the superiority of the algorithm. [PERSON] et al. [24] proposed an unsupervised speech enhancement method based on the non-negative matrix factorization and sub-band beamforming for robust speech recognition against the noise. In the recent years, the minimum variance distortionless response (MVDR) beamforming is widely used to achieve the speech enhancement because this method properly works when there are steering vectors for the speech signal and spatial covariance matrix for the noise. In the presented algorithm, an unsupervised method decomposes each time-frequency bin to the sum of the noise and signal by implementing the multi-channel non-negative matrix factorization (MNMF). The presented method estimates the spatial covariance matrix (SCM) for the signal and noise by the use of spectral noise and speech features. In this paper, the online MVDR beamforming is proposed via an adaptive update for the MNMF parameters. [PERSON] et al. [25] proposed a speech enhancement model-based method to increase the speech perception for auditory earphones applications. In the proposed method, a binaural speech enhancement framework is introduced, which is implemented by a speech production approach. The proposed speech enhancement framework is based on a Kalman filter, which is presented to use the speech production dynamic in the procedure of the speech enhancement. The Kalman filter needs to have an estimation from the short time predictor (STP) of clean speech, noise, and the pitch estimation of the clean speech.