# Residual Echo Suppression Considering Harmonic Distortion and Temporal Correlation
###### Abstract  
In acoustic echo cancellation, a certain level of residual echo resides in the output of the linear echo canceller because of the nonlinearity of the power amplifier, loudspeaker, and acoustic transfer function in addition to the estimation error of the linear echo canceller. The residual echo in the current frame is correlated not only to the linear echo estimates for the harmonically-related frequency bins in the current frame, but also with linear echo estimates, residual echo estimates, and microphone signals in adjacent frames. In this paper, we propose a residual echo suppression scheme considering harmonic distortion and temporal correlation in the short-time Fourier transform domain. To exploit residual echo estimates and microphone signals in past frames without the adverse effect of the near-end speech and noise, we adopt a double-talk detector which is tuned to have a low false rejection rate of double-talks. Experimental results show that the proposed method outperformed the conventional approach in terms of the echo return loss enhancement during single-talk periods and the perceptual evaluation of speech quality scores during double-talk periods. a +
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estimating system noise power, which showed fast convergence speed and small steady-state mean square error. The linear filtering approach cannot completely remove the acoustic echo as the echo is not a linear function of the far-end signal. The nonlinearity arise mainly from the nonlinear response of the power amplifier and loudspeaker, as well as from the nonlinear acoustic transfer function and the misalignment of the linear echo canceller. In order to suppress nonlinear echo components, AEC based on a nonlinear adaptive filter has been proposed [14; 15; 16; 17]. Volterra filter-based methods [14; 15; 16] were proposed to model the nonlinear relationship between far-end and acoustic echo signals with polynomial models. Unfortunately, these methods exhibited slow convergence rates [21]. [PERSON] et al. [17] also employed a polynomil model in a Kalman filter-based framework when multiple microphone signals were available. AES algorithms analogous to speech enhancement techniques that estimates spectral gain functions such as Wiener filtering have also been proposed, and demonstrated an impressive performance with low computational complexity [18; 19; 20]. Another class of approach is placing a separate module after the linear echo canceller to clean up the residual echo left after the linear AEC or AES, which is called residual echo suppression (RES) [22; 23; 24; 25; 26; 27; 28]. [PERSON] et al. [22] suggested a spectral subtraction scheme to remove the residual echo by assuming that the spectral magnitude of the residual echo is proportional to that of the linear echo estimate. [PERSON] and [PERSON] [23] proposed a statistical model based RES incorporating four hypotheses according to the existence of the near-end speech and residual echo. [PERSON] et al. [24] proposed a RES that estimates residual echo from the far-end signal using an artificial neural network. In [25; 26], RES based on deep neural networks have been proposed and have shown good performance, while requiring heavy computation. Another class of approaches is based on adaptive filters [27; 28] that showed decent performance with a reasonable computational cost [21]. [PERSON] et al. [28] proposed harmonic distortion RES (HDRES) in short-time Fourier transform (STFT) domain, which models the residual echo as a linear function of the linear echo estimates in the frequency bins that can make a harmonic distortion in the current frequency bin. In this paper, we extend HDRES in [28] by modeling the residual echo in the current time-frequency bin as a function of the linear echo estimate, residual echo estimate, and microphone signals in adjacent frames as well as the linear echo estimates in the harmonically-related frequency bins in the current frame.