Elsevier

Signal Processing

Volume 80, Issue 9, September 2000, Pages 1697-1719
Signal Processing

Step-size control for acoustic echo cancellation filters – an overview

https://doi.org/10.1016/S0165-1684(00)00082-7Get rights and content

Abstract

In this paper we present an overview about several approaches for controlling the step size for adaptive echo cancellation filters in hands-free telephones. First an optimal step size is derived. For the determination of this step size the power of a non-measurable signal has to be estimated. Detection and estimation methods for the determination of this power and for the determination of the optimal step size can be grouped into four classes. For each class, several principles, which differ in their reliability and in their complexity, are presented. Possibilities for combining elements from each class to create an entire step size control unit are also described. An outlook on detector combinations based on neuronal networks concludes this paper.

Zusammenfassung

In diesem Artikel werden verschiedene Ansätze zur Schrittweitensteuerung für adaptive Echokompensationsfilter in Freisprechtelefonen zusammengefaßt dargestellt. Zunächst wird dazu eine optimale Schrittweite hergeleitet. Zur Bestimmung dieser Schrittweite muß die Leistung eines nicht unmittelbar meßbaren Signals geschätzt werden. Detektions- bzw. Schätzverfahren zur Bestimmung dieser Leistung bzw. Bestimmung der Schrittweite können in vier Klassen unterteilt werden. Zu jeder dieser Klassen werden verschiedene Prinzipien, die sich hinsichtlich ihrer Zuverlässigkeit und ihres Aufwands unterscheiden, vorgestellt. Kombinationsmöglichkeiten einzelner Elemente dieser Klassen zu einer gesamten Schrittweitensteuerung werden im Anschluß beschrieben. Ein Ausblick auf Möglichkeiten der Detektorkombination mittels neuronaler Netze schließt diesen Artikel.

Résumé

Nous présentons dans cet article un survol des différentes approches pour le contrôle du pas des filtres adaptatifs d'annulation d’écho dans les téléphones mains-libres. Tout d'abord une valeur de pas optimale est dérivée. Pour la détermination de cette valeur de pas la puissance d'un signal non mesurable doit être estimée. Les méthodes de détection et d'estimation pour la détermination de cette puissance et pour la détermination du pas optimal peuvent être regroupées en quatre classes. Pour chaque classe, plusieurs principes qui différent en termes de fiabilité et de complexité sont présentés. Les possibilités de combinaison d’éléments de chaque classe pour créer une unité complète de contôle du pas sont également décrites. Un aperçu sur les combinaisons de détecteurs basées sur les réseaux neuronaux conclut cet article.

Introduction

Comfortable hands-free telephones reduce the acoustic coupling between the loudspeaker and the microphone by computing a (digital) replica c(k) of the loudspeaker–enclosure–microphone (LEM) system, shown in Fig. 1 [13], [16], [17]. The part of the microphone signal y(k) which originates in the remote speakers signal x(k) can be eliminated by subtracting the estimated echo signald̂(k)=x(k)∗c(k)=i=0x(k−i)ci(k)from the microphone signal y(k), where ci(k) denotes the ith coefficient of the impulse response at time index k.

Due to the movements of the local speaker, door openings, or temperature variations, the impulse response h(k) of the LEM system is time variant. Therefore, one single adaptation of the filter coefficients at the beginning of communication and a subsequent freezing of the filter coefficients is not sufficient for a permanent echo reduction. Since the filter c(k) should be able to track variations of the LEM system, it should be adaptive. For obtaining simpler adaptive algorithms, finite impulse response (FIR) filters are preferable to infinite impulse response (IIR) filters. The impulse response of the adaptive filter can be written in vector notationc(k)=(c0(k),c1(k),…,cN−1(k))T,where N−1 is the order of the adaptive filter. The LEM system can also be modeled as an FIR filterh(k)=(h0(k),h1(k),…,hN−1(k))T,in combination with an additional locally generated signal n(k). Usually, the impulse response of the LEM system has infinite order. An adaptive algorithm for the update of the filter c(k) has to be constructed in such a way that the filter c(k) converges to the LEM system impulse response h(k). Therefore only the first N coefficients are considered within the vector h(k). The noncancelled echo signalnt(k)=i=Nx(k−i)hi(k),caused by the tail (hN(k),…,h(k))T of the LEM impulse response is modeled as part of the local signal n(k). Further components of the signal n(k) are local background noise nb(k), the signal of the local speaker ns(k), and distortions due to nonlinearities of nonideal loudspeakers, amplifiers, etc., nn(k). The signal n(k) with its four componentsn(k)=nt(k)+nb(k)+ns(k)+nn(k)adds to the error signal ε(k)=x(k)T(h(k)−c(k)) generated by the mismatch of the adaptive filter:e(k)=ε(k)+n(k).The excitation vector x(k)=[x(k),x(k−1),…,x(k−N+1)]T contains the last N samples of the input signal. In contrast to the disturbed error signal e(k), the undisturbed error signal ε(k) is not accessible. Adaptive algorithms use the signal e(k) in their feedback loop. If no control mechanism is implemented, the presence of the local signal n(k) may lead to stability problems of the adaptive algorithm. For the adaptation of the filter c(k) several well-known adaptive algorithms [8], [14], [2], [20] such as

  • the Recursive Least Squares (RLS) algorithm,

  • the Affine Projection (AP) algorithm, or

  • the Normalized Least Mean Square (NLMS) algorithm


can be applied. They differ mainly in their convergence speed and their computational complexity. All algorithms have in common that they compute the new filter vector c(k+1) by correcting the old estimation c(k) with an innovation term Δ(k), weighted by a step size α(k):c(k+1)=c(k)+α(k)Δ(k).Details of the algorithm-dependent innovation vector Δ(k) are given in [14]. This aspect of the adaptive algorithms will not be addressed in this paper.

The step size α(k) can vary within the interval [0,2). In the absence of distortions (n(k)=0), the non-weighted adaptation step can be performed by simply setting the step size α(k) to one. In the presence of distortions, the step size should be reduced with increasing power of local distortions, with decreasing power of the excitation signal, and with better convergence of the adaptive filter.

Unfortunately a simple power estimate of the error signal e(k) cannot be used for the step-size control. Both local distortions and variations of the LEM impulse response lead to an increase of the error signal. In turn a different choice of the step-size parameter α(k) is required. In the first case, the step size should be reduced to avoid a divergence of the adaptive filter. Values of the step size close to one are required in the second case, to permit fast adaptation to the new impulse response. Therefore, more sophisticated control algorithms are required for setting the step size conveniently.

The paper is organized as follows: First an optimal step size based on a mean square error criterion is derived. Since the power of the non-accessible undisturbed error signal ε(k) is required to compute this optimal step size, the basic principle for estimating the power of this signal is presented in the next section. Afterwards, an overview about several detection and estimation methods is given. It is shown that they can be grouped into four classes. In Section 5, possible combinations of the detectors for designing an entire step size control method are presented and an example for one possible combined control method is given. Conclusions and an outlook are presented at the end of the paper.

Section snippets

Derivation of an optimal step size and basic control principles

In the following, an optimal step size for the NLMS algorithm is derived. The main reasons for choosing this algorithm are its high robustness against finite arithmetical precision and its simplicity compared to the other adaptive algorithms. The NLMS algorithm is therefore usually chosen for real-time implementations. Nevertheless, the proposed control methods are independent of the adaptive algorithm and may therefore also be applied to other algorithms.

At the end of this section, traditional

Basic principle for estimating the optimal step size

For the estimation of the optimal step size according to Eq. (15), it is necessary to estimate the power of the undisturbed error signal, which is not accessible.

Since the LEM system and the adaptive FIR filter provide a parallel structure, the signal ε(k) can be noted as ε(k)=xT(k)·[h(k)−c(k)].

For white remote excitation x(k), the estimated power of the undisturbed error signal can be noted as E{ε2(k)}=E{x2(k)}·E{||h(k)−c(k)||2}, where the second factor, the system distance, indicates the echo

Detection and estimation methods

In this section, several detection methods are introduced. To limit the extent of this overview, only the basic principles, or simulation examples, respectively, with input signals chosen to demonstrate the detection principles are presented. Details about real-time implementation, computational complexity, and reliability can be found in the corresponding references.

All detectors/estimators mentioned here can be grouped into four classes. As mentioned above (derivation of the optimal step

Overview of the detectors and examples for combined control methods

After having described some of the most important detection principles in the previous section, we now present an overview about the possibilities for combining these detectors into an entire step-size control. At the end of this section, one of the possible detector combinations is presented and its performance is demonstrated via simulations.

Conclusions and outlook

In this paper the step-size control for acoustic echo cancellation filters was explained and an overview of various control structures was given. The step size control is an essential part of the hands-free telephone system, i.e., the quality of the entire system is influenced mainly by the efficiency of the control method. An increase of the performance of Digital Signal Processors (DSPs) over the next few years will allow the implementation of faster and therefore more complex adaptive

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