# Dual-Mic Speech Enhancement Based on TF-GSC with Leakage Suppression and Signal Recovery
## 1 Introduction  
Multi-channel speech enhancement is an essential part for many applications, such as mobile phones, smart TVs, and smart speakers [1, 2]. Compared to a single-channel approach, multi-channel speech enhancement can utilize not only spectral information, but also spatial information using multiple microphones, which makes it possible to achieve better performance. Popular examples of spatial filters include multi-channel Wiener filters [1, 3, 4, 5, 6], adaptive beamformers [2, 7, 8], and nonlinear filters [9, 10, 11, 12, 13, 14, 15, 16].  
One of the useful implementations of adaptive beamformers [17] is the generalized sidelobe canceller (GSC) [17], which consists of a fixed beamformer (FBF) that tries to pass only the signals from the desired direction, a blocking matrix (BM) that attempts to filter out the signals from the desired direction, and an adaptive noise canceller (ANC) that removes the signals related to the BM output from the FBF output. The transfer function (TF)-GSC (TF-GSC) [18, 19, 20, 21, 22, 23, 24, 25, 26, 27] is one of the most popular algorithms for GSC, which steers a beam to a desired source based on the estimated acoustic TF [2] ratio vector and achieves high noise reduction performance while maintaining low speech distortion [28]. However, the steering error [29] arising from an inaccurate TF ratio estimation may introduce signal leakage in the BM output and speech distortion in the FBF output, which degrades the performance of speech enhancement, especially in the presence of diffuse or nonstationary noise.  
One of the typical remedies to this problem is to equip a single-channel speech enhancement module as a post-processor [9, 10, 11, 12, 13, 14, 15, 16]. The spectral gain based on the optimally modified log spectral amplitude (OM-LSA) estimator [30] is applied to the output of theTF-GSC in [12; 13; 14], where the transient beam-to-reference ratio (TBRR) [31] is utilized for hypothesis testing [32] to determine if the input contains desired speech, transient interference, or stationary noises, which in turn affects the estimation of a priori signal absence probability, a priori signal-to-noise ratio (SNR), noise power spectra, and spectral gain function. In [15; 16], the results of the hypothesis testing were further utilized in the parameter updates for the TF-GSC. Nevertheless, a certain amount of the steering error is practically inevitable, resulting in signal leakage in the BM output and signal attenuation in the FBF output, which limits the performance of speech enhancement using TF-GSC.  
In this paper, we propose to modify the outputs of the FBF and the BM by utilizing both of the outputs and the microphone signals. Specifically, we applied a gain function similar to the square-root Wiener filter to the BM output to suppress the desired speech signal leaking into it. Moreover, the attenuated signal in the FBF output was recovered to an extent by adding back a certain amount of appropriate microphone signals. The experimental results show that the proposed TF-GSC achieved better performance than the conventional TF-GSC for various noise scenarios. Moreover, the proposed method can provide consistent performance for various directions of arrivals (DoAs) of the desired and interfering sources in contrast to the conventional TF-GSC.  
The remainder of this paper is organized as follows. Section 2 summarizes the conventional TF-GSC and the postfiltering. The proposed TF-GSC with leakage suppression and signal recovery is introduced in Section 3. Section 4 outlines the experimental results. Finally, a conclusion is provided in Section 5.