## 1 Introduction
A binaural method for STP parameters estimation is proposed in this paper with a directional pitch predictor based on the harmonic model and maximum likelihood (ML) criteria for pitch features estimations. These parameters are calculated just based on 2-microphones signals equivalent to human ears. [PERSON] et al. [26] proposed a simultaneous noise-reverberation enhancement method for text-to-speech (TTS) systems. The recorded voices in noisy-reverberant environments affects the quality of the TTS systems. A simple way is to increase the quality of the prerecorded speech signals for the TTS training system by speech enhancement methods such as: noise suppression and dereverberation algorithms. Then, a recurrent neural network is considered in this paper for the speech enhancement. The neural network is trained by parallel data of clean speech and recorded speech with low quality. The low quality speech signal is obtainedby the addition of environmental noise and convolution between the room impulse response and the clean speech. The separated neural networks are trained by only-noise, only-reverberation, and noisy-reverberant data. The quality of the training data with a low quality speech signal is highly improved by the use of this neural network. [PERSON] et al. [27] proposed a model-based method for speech enhancement in modulation domain by the use of a Kalman filter. The proposed predictor models the estimated amplitude spectral dynamically from the speech and noise to calculate the minimum mean square error (MMSE) of the speech amplitude spectrum taking into account that the noise and speech are additive in the complex plane. The stationary Gaussian model is proposed to consider the dynamic noise amplitude as same as the dynamic speech amplitude, which is a mixture of Gaussian models that the centers are located in a complex plane. In our article, a multi-channel speech enhancement method is introduced based on the proposed circular nested microphone array in combination with the sub-band affine projection algorithm (CNMA-SBAPA). A nested microphone array increases the accuracy of the speech enhancement methods by increasing the information. Nevertheless, spatial aliasing is one of the challenges when microphone arrays are used. Firstly, a uniform circular nested microphone array (CNMA) is proposed for eliminating the spatial aliasing. Additionally, the array dimensions are designed in a way to be applicable in the real conditions. The speech components are variable in frequency bands. Therefore, a sub-band processing method is considered for speech signals. This method provides the high frequency resolution in low speech frequency components. Finally, the affine projection algorithm (APA), as an adaptive method for the speech enhancement, is implemented on sub-band signals from the circular nested microphone array (NMA). Since each APA block is implemented on a sub-band with specific information, the accuracy and speed of convergence are increased in this condition. In the last step, the synthesis filters are used to generate the enhanced speech signal. The proposed system with sub-band APA is compared by the quantitative (segmental SNR), qualitative (PESQ, MOS, and STOI) criteria, and speed of convergence with the least mean square (LMS), traditional APA, recursive least square (RLS), distributed multichannel Wiener filter (DB-MWF), and multichannel nonnegative matrix factorization-minimum variance distortionless response (MNMF-MVDR) algorithms on real and simulated data under white and colored noisy conditions. The results show the superiority of the proposed system in comparison with other previous works in all environmental conditions. Section 2 shows the microphone signal model and the proposed uniform circular nested microphone array. Section 3 includes the proposed sub-band algorithm with analysis and synthesis filter banks in combination with the sub-band APA. The results on real and simulated data are discussed in Section 4. Section 5 includes some conclusions.