NLMS演算法收斂步伐調整之回音消除

Abstract

基於簡單性和實用性，回音消除最常用的演算法就是NLMS演算法。然而，NLMS演算法最大的缺點就是收斂速度太慢，因為其使用固定的收斂步伐(step-size)。我們提出一種調整收斂步伐的新方法稱為理想步伐NLMS演算法。所謂的『理想』是指這種收斂步伐在每次疊代時可以提供最小閥係數誤差的均方誤差(MSE)，以致於和其他演算法比較起來有最快的收斂速度。每一個閥(tap)有自己的、隨閥係數誤差改變而調整的收斂步伐。在偵測雙邊對話方面，我們分析了J. C. Liu所提出來的方法。它是利用計數器的概念在殘響回音突然變大時，用一段短時間內去記錄事件發生的次數。回音衰減量(ERLE)被用來表示使用不同門限(threshold)的成本。最後，電腦模擬將用來驗證支持之前的分析。

The most often used algorithm for acoustic echo cancellation is normalized least mean square (NLMS) algorithm due to its simplicity and robustness. However, the major drawback of NLMS algorithm is its slow convergence rate due to its constant step-size. We propose a new approach of adjusting step-size called optimum step-size NLMS. The word “optimum” means the step-size can provide the minimum tap coefficient error mean square error at each iteration step which leads the fastest convergence rate than other algorithms. Each tap has its individual time-variant step-size which adjusts with tap coefficient error variance. We analyze double talk detector proposed by J. C. Liu. It uses the concept of counter to record number of abrupt events happened during a short period when an abrupt change in residual echo. Echo return loss enhancement (ERLE) is used to indicate the cost of using different threshold. Finally, computer simulations will be presented to support the analysis.