## 4 Results and Discussion
The microphone, sound, and noise sources were selected in the simulations with exactly the same real conditions for the results to be comparable in these two conditions. Figure 9 shows the time-domain and spectrum of the male speech signal. The reverberation effect was considered in the experiments to provide the simulation conditions similar to the real scenarios. The image model was implemented in the simulations to produce the reverberation effect similar to the real conditions [41]. The image model produced the room impulse response between the source and microphone by considering the speaker position, microphone  
Figure 8: The real recording room in the speech processing laboratory, FBK, Trento, Italy. Figure 7: A view of the simulated room with the positions of speakers, noise source, and microphones. Figure 9: The time-domain and spectrum for the male speech signal. location, sampling frequency, room dimension, room reflection coefficients, impulse response length, and reverberation time. The received signal to the microphone was simulated by the convolution between the generated impulse response by the image method and the source signal. The impulse response was generated for the noise and speech sources because both receive the same effect of the room reverberation. In addition, noise was additive with the speech signal in the microphone positions. The room reverberation time was selected as \(RT_{60}=350\) ms, which was considered for a room with a low level of reverberation to be the same as the real conditions. To generate the noisy signal, five types of noise were considered for the simulated and real data such as white noise, babble noise, train noise, car noise, and restaurant noise. Figure 10 shows the time-domain and spectrum for these noisy signals according to a SNR = 0 dB. The noise signal duration was 12.5 s, the same as the speech signal. Figure 10: _Cont._  
Figure 10: The time-domain and spectrum for a noisy speech signal with (**a**) white noise, (**b**) babble noise, (**c**) train noise, (**d**) car noise, and (**e**) restaurant noise according to a signal-to-noise ratio (SNR) = 0 dB. The Hamming window with a length of 30 ms was selected for signal blocking to keep the stationarity of the signal in the short time. The projection order was considered as \(N=4\) to keep the computational complexity in an acceptable range in addition to a proper accuracy of the algorithm. Additionally, the step sizes were chosen as \(\mu_{12}=1\) and \(\mu_{21}=1\) to provide the fast convergence for the proposed SBAPA in the real-time implementations. The evaluations in this article were implemented by the use of MATLAB software version 2019b on a PC with processor Inter Core i7-7700k, 4.20 GHz, and with 32 GB RAM to be able to implement the proposed algorithm in the real-time conditions. The proposed SBAPA in combination with a proposed circular nested microphone array (CNMA-SBAPA) was compared with the LMS [20], traditional APA [31], RLS [21], DB-MWF [9], and MNMF-MVDR [24] algorithms. These methods were compared because all of them are based on the adaptive filters and multi-channel beamforming as a main category for comparison. There are many methods for comparison with the proposed algorithm but the comparison should be based on the common theme in implementations. Therefore, the adaptive filter-based algorithms were selected for this comparison. The qualitative and quantitative criteria were considered to show the superiority of the proposed method in comparison with other previous works. For this purpose, the SegSNR [7], PESQ [4], MOS [5], and STOI [6] criteria were selected for the comparison.