An Adaptive Feedback Equalization Algorithm For Digital Hearing Aids

Abstract

A method is described for adaptively equalizing the ubiquitous feedback path of a hearing aid in order to stabilize the system. The algorithm utilizes an LMS adaptive filter and is implemented in digital form. An additional 10 to 15 dB of stable gain margin has been demonstrated. INTRODUCTION System instability is a commonly cited problem with regard to highpower hearing aids, where it is desirable to achieve high acoustic gains, and with intheear devices, where acoustical and mechanical isolation between input and output is difficult to achieve. Instability is a result of feedback due to 1) acoustic leakage around the earmold and through the vent in the earmold and 2) mechanical coupling between receiver and microphone As is well known, when the open loop gain of a system with feedback is greater than unity and has a phase which is a multiple of 2n radians, the system will oscillate [l], thereby causing a serious degradation of signal quality. In addition, if the open loop gain is close to but less than unity, the system response will be highly underdamped and will exhibit a response sharply divergent from the desired frequency-gain characteristic prescribed for the hearing-impaired patient. Current methods for reducing hearing aid instability are limited to the use of tightly fitting m o l d s . However, this is difficult to achieve without causing discomfort for the patient. A number of methods of feedback suppression have been proposed. For example, Egolf and Larson [2] have studied two methods, one, a time delay notch filter system and, two, an active feedback cancellation system. They report improvements of between 6 and 8 dB in closed loop gain margin with both approaches and, if conditions are carefully controlled, up to 15 to 20 dJ3 [3]. The algorithm described herein, is similar to the active feedback cancellation system, and stabilizes the hearing aid by adaptively cancelling its feedback path. Since the algorithm is adaptive, it can accommodate to changes in the feedback characteristic of the hearing aid. Equalization is accomplished with a Widrow LMS adaptive filter [4]. The adaptive process is driven by an internally generated pseudorandom signal presented at threshold and subthreshold levels similar to that used by Schroeder [5]. The algorithm has been refined for implementation on small digital processing structures. THE FEEDBACK EQUALIZATION MODEL The equalized hearing aid model is shown in the figure where Hm and Hr represent the microphone and receiver characteristics, respectively, Hf represents the undesirable acoustic and mechanical feedback paths, H represents a filter function that when multiplied by Hm and Hr yields the prescribed acoustic fkequencygain function for the patient, and & represents the adaptive equalization filter. X, Y, and N represent the input sound pressure at the hearing aid microphone, the sound pressure in the ear canal, and the pseudorandom probe signal, respectively. The closed-loop transfer characteristic for the system in the figure can be expressed as: The term in the numerator, Hm H Hr, is the prescribed frequency-gain function that is desired. The term, H(Hm Hf Hr &), in the denominator, represents the openloop gain of the system. The system will be unstable if this term is greater than unity and the phase is a multiple of 2x radians. If the term in the denominator of Equation 1 is zero, that is He = HmHfHr, then the system will be stable and the overall response will be the prescribed one. In theory it should be possible to achieve as much stable acoustic gain as desired with equalization. In practice, however, the maximum stable gain is limited by the degree of cancellation that can be achieved between I& and HmHfHr. These limitations are discussed below. THE ADAPTIVE ALGORITHM The cancellation of HmHfHr is achieved with an adaptive algorithm that adjusts the coefficients of & to minimize, in the least-mean-square sense, the error function, E, as shown in the figure. The error is a function of the difference between the external feedback path and the equalizing filter and can be expressed as: E =Hm X + (Hm Hf Hr He) (N + Z) (2) If the variables, N, Z, and N are uncorrelated, it is easy to see that the e m r can only be minimized by adjusting the equalization filter, l & . . A recursive expression for adapting the coefficients (tap weights) of can be derived from Equation 2 and is the same as for the Widrow adaptive LMS filter [5]. The recursive expression is: FIR filter can cancel the acoustic and mechanical feedback paths. Mismatch Ck(n+l) = Cdn) + B e(n) x(nk) (3) filter can be caused by the presence of processing noise and input signal, X, in the error term. If the noise and input signals are wideband, which is generally true for processing noise and speech, the mismatch ACKNOWLEDGEMENTS This work was supported by the Rehabilitation Research and Development Service of the Department of Veterans Affairs, the National Aeronautics and Space Administration, and the 3M Company. N REFERENCES AND FOOTNOTE [l] Nyquist, H., "Regeneration theory", Bell System Technical Journal, Vol. 11, 1932, pp. 126-147. 121 Egolf, David P. and Larson, Vernon D., "Acoustic Feed back Suppression in Hearing Aids", Department of Veteran Affairs Rehabilitation R&D Progress Reports, 1984, pp. 163-164. [3] Egolf, David P. and Larson, Vernon D., "Studies of Acoustic Feedback in Hearing Aids", Department of Veteran Affairs Rehabilitation R&D Progress Reports, 1986, p. 315. [4] Widrow B., Glover, J.R., McCool J.M., Kaunitz, J., Williams C.S., Hearn, R.H., Ziedler J.R., Dong, E., and Goodlin, R.C., "Adaptive noise cancelling: principles and applications," Proceedings of the EEE, Vol. 63, No. 12, pp. 16921716. December 1975. [!7J Schmeder, M.R., "Integrated-impulse'method of measuring sound decay without using impulses", J. Acoust. SOC. Am. * Also presented at the the Twelfth Annual International Conference of E E E EMBS. 66(2), Aug. 1979, pp. 497-500.