ACOUSTIC FEEDBACK CANCELLATION FOR HEARING-AIDS, USING MULTI-DELAY FILTER Thomas FILLON and Jacques PRADO ENST - Signal and Image Processing Dept 46 rue Barrault, 75634 PARIS cedex 13, FRANCE Contact : { fillon, prado } @tsi.enst.fr ABSTRACT Acoustic feedback cancellation in hearing-aid needs robust and efficient adaptive filter techniques. In this paper, we propose a method based on the Generalized- Multi-Delay Filter algorithm. This algorithm is par- ticulary attractive in the hearing-aid context because it requires only small size transforms. We derive a new method for the step-size control which improves the behavior of the algorithm and enables to reach the stability conditions in hearing-aid. 1. INTRODUCTION In a hearing-aid device, the acoustic feedback path be- tween the receiver and the microphone is the source of instability for the whole closed-loop system. When the system is unstable the device sound quality is de- teriorated since distortion and high-level self-sustaining oscillations can set-up. These phenomenons are very unpleasant for the hearing-impaired and limit the po- tential gain of the device. This study proposes to introduce in the hearing aids context an improved transform domain echo can- cellation algorithm, called Generalized Multi-Delay Fil- ter (GMDFα) in a specific implementation using the Fast Hartley Transform (FHT). This implementation was initially introduced in [6] and is derived from time-domain Block Least Mean Square (BLMS) adap- tive filtering. This technique was originally developed for hand- free-telephones and modern teleconferencing systems. Its basic idea consists in a segmentation of the feed- back path impulse response estimation which is up- dated directly in the Hartley domain. It also takes advantage of the FHT as a real transform having the self-inverting property. In spite of GMDFα efficiency, it is not sufficient to reach the stability conditions in the particular context of hearing-aid without a better control of the step-size of the adaptation process. To achieve this goal, the present paper proposes a new transform domain nor- malization strategy at marginal computational cost. 2. FEEDBACK IN HEARING AID In a hearing aid system (described in Figure 1), the acoustic source signal s[n], where n is the time index, is corrupted by the additive feedback signal u[n] origi- nating from the output signal y[n] leaking back to the input. In classical acoustic echo cancellation system, these signals are usually named : • s[n] : the near-end talker signal, • u[n] : the echo signal, • y[n] : the far-end talker signal. Hence, without feedback reduction, the closed-loop system transfer function is : T (z)= z -D .G(z) 1 − z -D .G(z).H(z) (1) where the intended hearing loss compensation and the feedback path transfer functions are approximated re- spectively by G(z) and H(z). D is the time delay introduced by the algorithm in samples. s[n] Echo Path HEARING-AID y[n] x[n] H(z) Adapt. Filter  u[n] u[n] v[n]  H(z) Hearing-loss compensation z -D .G(z) Figure 1: Hearing-aid device with its intended trans- fer function G(z) and an adaptive filter  H(z) estimat- ing the feedback path H(z) Assuming that G(z) and  H(z) are two linear time- invariant transfer functions, self-oscillation phenomenon can occur and causes unpleasant whistling sound if it