Alexander Stenger

Adaptation of a memoryless preprocessor for nonlinear acoustic echo cancelling

Abstract Acoustic echo cancellers (AECs) in todays hands-free telephones rely on the assumption of a linear echo path. However, low-cost audio equipment or constraints of portable communication systems cause nonlinear distortions in the loudspeaker and its amplifier, which limit the echo reduction of linear AECs. Such an echo path can be modelled by a memoryless nonlinear function preceding the linear FIR filter. Algorithms for joint adaptation of both stages and stepsize normalizations are derived. As examples for the preprocessor a hard-clipping curve and a polynomial are considered. Fast convergence of the latter is achieved with signal orthogonalization or RLS adaptation. Adaptation stepsize control mechanisms are derived using a novel system distance measure. Experiments under adverse conditions and with real hardware demonstrate robust convergence with both models, and an echo reduction improvement by up to 10 dB at amplitude peaks. For a straightforward implementation, computational cost is increased by factor 1.5–4.5 compared to a linear AEC, but ways for complexity reduction are outlined.

Nonlinear acoustic echo cancellation with 2nd order adaptive Volterra filters

Acoustic echo cancellers in todays speakerphones or video conferencing systems rely on the assumption of a linear echo path. Low-cost audio equipment or constraints of portable communication systems cause nonlinear distortions, which limit the echo return loss enhancement achievable by linear adaptation schemes. These distortions are a super-position of different effects, which can be modelled either as memoryless nonlinearities or as nonlinear systems with memory. Proper adaptation schemes for both cases of nonlinearities are discussed. An echo canceller for nonlinear systems with memory based on an adaptive second order Volterra filter is presented. Its performance is demonstrated by measurements with small loudspeakers. The results show an improvement in the echo return loss enhancement of 7 dB over a conventional linear adaptive filter. The additional computational requirement for the presented Volterra filter is comparable to that of existing acoustic echo cancellers.

Steady-state performance limitations of subband adaptive filters

Nonperfect filterbanks used for subband adaptive filtering (SAF) are known to impose limitations on the steady-state performance of such systems. In this paper, we quantify the minimum mean-square error (MMSE) and the accuracy with which the overall SAF system can model an unknown system that it is set to identify. First, in case of MMSE limits, the error is evaluated based on a power spectral density description of aliased signal components, which is accessible via a source model for the subband signals that we derive. Approximations of the MMSE can be embedded in a signal-to-alias ratio (SAR), which is a factor by which the error power can be reduced by adaptive filtering. With simplifications, SAR only depends on the filterbanks. Second, in case of modeling, we link the accuracy of the SAF system to the filterbank mismatch in perfect reconstruction. When using modulated filterbanks, both error limits-MMSE and inaccuracy-can be linked to the prototype. We explicitly derive this for generalized DFT modulated filterbanks and demonstrate the validity of the analytical error limits and their approximations for a number of examples, whereby the analytically predicted limits of error quantities compare favorably with simulations.

Nonlinear acoustic echo cancellation with fast converging memoryless preprocessor

Low-cost audio components in hands-free telephone applications call for nonlinear adaptive echo cancellation (AEC). It has been demonstrated that a cascade of a polynomial and an FIR filter can cancel such nonlinear echoes (Stenger and Rabenstein 1998). Another technique employs a hard-clipping curve with LMS adapted saturation parameter (Nollet and Jones 1997). For both cascaded systems we derive an LMS-type adaptation using a common framework, and propose stepsize normalizations for both approaches. To achieve sufficiently fast convergence for practical use, an RLS-type adaptation for the polynomial is derived and experimentally verified. Both techniques are compared using real hardware and speech signals, and show robust convergence behaviour and an echo reduction gain of up to 10 dB compared to a linear AEC.

Polyphase analysis of subband adaptive filters

Based on a polyphase analysis of a subband adaptive filter (SAF) system, it is possible to calculate the optimum subband impulse responses to which the SAF system will converge. We give some insight into how these optimum impulse responses are calculated, and discuss two applications of our technique. Firstly, the performance limitations of an SAF system can be explored with respect to the minimum mean square error performance. Secondly, fullband impulse responses can be correctly projected into the subband domain, which is required for example for translating constraints for subband adaptive beamforming. Examples for both applications are presented.

Measuring performance limits of subband adaptive systems

We discuss a method to measure the convergence limits of general subband adaptive systems due to non-ideal filter banks. Aliasing caused in such filter bank presents a distortion to the subband adaptive system which forms a lower limit for the minimum mean squared error. The accuracy of the achievable model is given by the transfer function of the filter bank. To measure both aliasing and filter bank distortions, we employ the measurement technique by Heinle and Schussler (see Proc. IEEE International Conference on Acoustics, Speech and Signal Processing, Atlanta, GA, p.2754-57, 1996). The presented approach is applicable to a wide range of subband adaptive filter systems. Examples for the measured limits are presented.

Zufallssignale und LTI-Systeme

Nach der Beschreibung von Zufallssignalen durch Korrelationsfunktionen und Leistungsdichtespektren wenden wir diese neuen Werkzeuge jetzt an, um die Reaktion von LTI-Systemen auf Zufallssignale zu untersuchen. Dabei interessieren wir uns nicht fur den genauen Verlauf des Ausgangssignals eines LTI-Systems, wenn am Eingang eine spezielle Musterfunktion eines Zufallsprozesses anliegt. Stattdessen beschreiben wir den Systemausgang ebenfalls durch einen Zufallsprozes und suchen die Erwartungswerte des Ausgangsprozesses in Abhangigkeit von den Erwartungswerten des Eingangsprozesses.

Stabilität und rückgekoppelte Systeme

Neben der Kausalitat eines Systems ist ein zweites wichtiges Kriterium fur die Realisierung eines Systems seine Stabilitat. Die Stabilitat eines Systems stellt sicher, das bei beschranktem Eingangssignal auch das Ausgangssignal nicht uber alle Grenzen anwachst. Diese Bedingung ist zu erfullen, wenn kontinuierliche Systeme auf der Grundlage des physikalischen Gesetzes der Energieerhaltung realisiert werden sollen (d.h. mit elektrischen, optischen, mechanischen, hydraulischen, pneumatischen, etc. Methoden). Aber auch fur diskrete Systeme ist die Einhaltung gewisser Schranken fur die Signalamplituden notwendig, da sonst der zulassige Zahlenbereich der verwendeten Rechner uberschritten wird. In diesem Kapitel werden wir zunachst die Zusammenhange zwischen Stabilitat, Frequenzgang und Impulsantwort allgemeiner LTI-Systeme untersuchen. Danach beschranken wir uns auf kausale Systeme und betrachten Stabilitatstests anhand des Pol-Nullstellen-Diagramms. Abschliesend diskutieren wir einige typische Anwendungen ruckgekoppelter Systeme. Wir werden wiederum kontinuierliche und diskrete Systeme parallel behandeln.

Zeitdiskrete LTI-Systeme

Nach den zeitdiskreten Signalen und ihrer Beschreibung im Frequenzbereich behandeln wir jetzt Systeme, deren Ein- und Ausgangssignale zeitdiskret sind. Auch die Systeme selbst nennt man kurz zeitdiskrete Systeme. Wir hatten sie bereits kurz in Kapitel 1.2.5 erwahnt, aber dann zugunsten der kontinuierlichen Systeme zuruckgestellt.

Diskrete Signale und ihr Spektrum

In den Kapiteln 1 bis 10 haben wir machtige Werkzeuge fur den Umgang mit kontinuierlichen Signalen und Systemen kennengelernt. Den Ubergang von in der Natur vorkommenden kontinuierlichen Signalen zu abgetasteten Signalen, die fur eine digitale Verarbeitung notig sind, haben wir in Kapitel 11 vollzogen. Der Definitionsbereich der abgetasteten Signale war immer noch eine kontinuierliche (Zeit)-Variable, so das wir die bekannten Werkzeuge, u.a. die Fourier-Transformation, verwenden konnten.