# Interaural Coherence Estimation for Speech Processing in Reverberant Environment
## 1 Introduction  
In a real situation, influences of the surrounding environment, such as multiple speakers, external noise sources, reverberation, etc., distort target speech information such that the performance of speech recognition methods get worse [1]. Among the causes of speech distortion, multiple speakers and external noise sources are additive noises, which have a low correlation with the target speech, making it easy to extract information about the target speech. Reverberation, on the other hand, is convolutive noise caused by the sound waves reflected by the surrounding walls or objects. In reverberant speech, both direct speech and reverberation, which is attenuated direct speech with a time delay, are involved. The reverberant speech has a high correlation with target speech; hence, it is difficult to extract the target information. Thus, the performance of speech separation decreases because the reverberation changes the amplitude and phase of time-frequency bins of direct speech [2,3]; moreover, speech recognition performance is also degraded.  
On the other hand, humans recognize speech accurately even in real reverberant environments. In the human hearing system, a direct source and early reflections are emphasized, and late reflections are suppressed, which is called the precedence effect [4, 5, 6]. By implementing the precedence effect with a computational algorithm based on the relationship between reverberation and interaural coherence(IC), previous studies attempted to solve reverberation problems. The ideal coherence between signals obtained from two microphones for the diffuse source reflected off the walls can be represented in the form of a square value of the sinc function in the frequency domain [7, 8]. If the two microphones are apart far enough, the IC appears close to zero for diffuse sources and close to one for direct sources at most frequencies. Based on these characteristics, the performance is improved by applying IC to the direction of arrival (DoA) estimation of the speaker [9], speech, or source separation [10] and dereverberation [11, 12, 13] in a reverberation environment.  
To get the best performance of the various speech preprocessing algorithms that use coherence, the estimated ICs of reverberant speech should match the ideal IC. Most of the algorithms [9, 10, 11, 12, 13] use the IC in the form of an infinite impulse response (IIR) filter in the calculation of power spectral densities. Due to recursive nature of the IIR filter, all of the past data have influence on the IC estimation, which may give an adversary effect on non-stationary speech data. Since the utterance changes continuously in speech, using all the past data will make coherence estimation different from the ideal coherence. Therefore, we propose a new IC estimation method of speech using a finite number of data in the form of a finite impulse response (FIR) filter to accurately estimate it close to the ideal IC. The optimal number of data required for estimating IC varies according to gender, frequency, and reverberation time; hence, the optimal IC estimation parameters should be determined by considering these factors. The performance of the proposed method is compared with that of the conventional IC estimation method through a numerical experiment using real speech data and measured room impulse responses.  
The structure of this paper is organized as follows: Section 2 presents a new IC estimation method and theoretical validation of the proposed method. In Section 3, the optimal IC estimation parameters are determined based on gender, frequency, and reverberation time, and compared to the conventional IC estimation method for the estimation accuracy of IC. Sections 4 and 5 present the discussion and conclusions, respectively.