非線性回音消除的設計與分析

Abstract

回音消除(AEC)的應用上，喇叭經常被過度驅動，造成輸出訊號的非線性失真，而限制其效能。近年來，非線性和線性的串接式AEC 適應性濾波器架構被提出來，在這個架構中，LMS 適應性法則被用來調整濾波器的係數，但收歛性分析仍不清楚。我們在上一個年度「非線性回音消除之研究」中，假設「非線性」 和 「線性」相互獨立的條件之下我們已推導出濾波器係數的收歛公式。 在未來第一年的「高階互相關法則(HOC)的非線性AEC收斂特性研究」中，我們嘗試將HOC用在 「線性和非線性」 濾波器係數的混合系統。目前我們初步發現，HOC法則在低的SNR條件之估計係數較為準確，我們的研究目標將在:以HOC的法則之下AEC性能的收斂性分析。 在未來第二年「AEC濾波器之非線性與線性係數共同調整與補償方法研究」 中，首先我們針對非線性AEC中，「非線性」 和 「線性」共同調整時，深入研究它們的收斂特性。其次，我們研究另一種 「喇叭非線性失真補償等化器」的架構。這種等化器，稱為 「事先等化器」。其目的是將喇叭非線性失真予以等化，等化之後的喇叭即視為線性。但這種非線性等化大多不存在，因此如何確保喇叭的輸出 「不失真』便是一個主要的課題。 在未來第三年 「多聲道AEC研究與應用」中，由於聲道之間相互耦合的問題，而變得較為複雜。最近多聲道AEC的研究則著重在局部部份調整係數，來降低聲道的相關性，但並沒有詳細的收斂性分析，未來我們希望分析其收斂性。尤其在NLMS演算法中，缺點就是收斂速度慢，故我們將考慮一種最佳步伐演算法，每一個閥(tap)有自己的時變收斂步伐，利用房間的響應強度指數下降模型，預期有較快的收斂速度。另外我們可以將濾波器係數片段化，以降低運算複雜度。

Hands-free telephone usually suffers from the annoying acoustic echo problem. A linear adaptive filter is commonly used for acoustic echo cancellation (AEC). However, overdriving the power amplifier of loudspeaker will incur nonlinear distortion. Recently, several nonlinear AEC structures have been proposed to compensate this kind of distortion. The cascaded nonlinear AEC structure has fewer coefficients than the Volterra filter and has less computational complexity, if it is updated by the NLMS algorithm. Convergent analysis of the cascaded nonlinear AEC has been performed in our last year project. In the coming first year, a higher order correlation(HOC) algorithm using a white Gaussian training signal will be studied for nonlinear AEC. With comparable complexity as NLMS, it is most effective at small SNR. With comparable complexity as NLMS, it is most effective at small SNR. Computer simulations demonstrate that the proposed algorithm has a smaller steady-state echo and it is also very robust to background noise. The convergence rates of nonlinear AEC coefficients and its residual echo power are derived analytically. In the second year, we focus on the adaptation of nonlinear echo cancellation and compensation. We will examine the convergent behaviors of nonlinear and linear coefficients. We will also examine the alternative of using a nonlinear compensator to linearize the loudspeaker. In the third year, we will study a multi-loudspeaker AEC system. Due to highly correlated channel responses, NLMS fails to track these channels. With coefficients being partially updated, the ill effect to interchannel correlation can be reduced. An optimum step-size NLMS will be proposed and further simplified to speed up convergence according to the exponentially decaying room impulse response. We will perform convergence analysis to support its effectiveness.