Step-size control for acoustic echo cancellation filters – an overview
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 signalfrom 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 notationwhere N−1 is the order of the adaptive filter. The LEM system can also be modeled as an FIR filterin 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 has to be constructed in such a way that the filter converges to the LEM system impulse response . Therefore only the first N coefficients are considered within the vector . The noncancelled echo signalcaused 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 componentsadds to the error signal generated by the mismatch of the adaptive filter:The excitation vector 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 several well-known adaptive algorithms [8], [14], [2], [20] such as
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the Recursive Least Squares (RLS) algorithm,
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the Affine Projection (AP) algorithm, or
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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 by correcting the old estimation with an innovation term , weighted by a step size α(k):Details of the algorithm-dependent innovation vector 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 .
For white remote excitation x(k), the estimated power of the undisturbed error signal can be noted as , 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
References (37)
The hands-free telephone problem – an annotated bibliography
Signal Processing
(1992)- J. Benesty, D.R. Morgan, J.H. Cho, A family of doubletalk detectors based on cross-correlation, Proceedings of the...
- et al.
J. Tilp, Acoustic echo control
Signal Process. Mag.
(1999) - C. Breining, A Robust Fuzzy Logic-Based Step Gain Control for Adaptive Filters in Acoustic Echo Cancellation, IEEE...
- C. Breining, G. Alt, On using MLPs for stepsize control in echo cancellation for hands-free telephone sets, Proceedings...
- C. Breining, State detection for hands-free telephone sets by means of a self-organizing map, Proceedings of the COST...
Steuerung eines Kommunikationsterminals mit Freisprecheinrichtung, VDI-Fortschritt-Berichte, Reihe 10, No. 570
(1999)Practical application of adaptation control for NLMS-algorithms used for echo cancellation with speech signals
(1995)Adaptive Filtering – Algorithms and Practical Implementations
(1997)- H. Ezzaidi, I. Bourmeyster, J. Rouat, A new algorithm for double talk detection and separation in the context of...