Acoustic Feedback Solution #9 – Adaptive Feedback
The last blog on hearing aid acoustic feedback was several weeks ago, with promises of a continuation on this topic. However, a couple of separate, unfortunate deaths to two audiology/hearing aid industry icons resulted in blogs about them. This blog will continue with the acoustic feedback discussion.
Acoustic Feedback in Hearing Aids
Because of the delay between the last feedback blog and this one, it is appropriate to redefine the topic. Acoustic feedback in hearing aids refers to the acoustical coupling between the speaker (loudspeaker/receiver) of the hearing aid and the microphone(s) as illustrated in Figure 17. This shows the so-called forward amplification path modified in such a way that it is stable in conjunction with the feedback path. Perhaps the most common approach to this is the use of the notch filter described in Hearing Aid Acoustic Feedback III. However, other approaches have involved phase equalizing of the open-loop response and the use of time-varying elements such as frequency shifting, delay, and phase modulation.
The level at which acoustic feedback occurs is dependent therefore on the physical fit of the ear piece, any venting, the volume of the ear canal, distance between the transducers, geometric configuration of the hearing aid, and the acoustics outside the ear that are constantly changing (reverberation, ear with hearing aid close to objects, jaw movement, time variability in the feedback path, other sounds in the environment, etc.), among other things. Because of this coupling, the amplified sound from the speaker can be picked up and reamplified by the hearing aid. When this happens, the hearing aid produces severe distortion of the desired signal and an annoying howling/squealing sound when the hearing aid gain is increased. This limits the maximum stable gain to the point where low-energy signals fall below the required hearing compensation requirement of the patient. In order to increase the gain to a sufficient level without the system becoming unstable, some kind of feedback suppression is called for. This is more of an issue for those patients who require substantial gain to fit their more severe hearing losses, of for those with even milder hearing losses who use some kind of open fitting, or when the hearing aid transducers are in close approximation to each other.
Previous blogs in Wayne’s World described various approaches to managing hearing aid acoustic feedback in the feedforward path (Acoustic Feedback I, II, III, IV) using these techniques. They included overall gain reduction, high-frequency gain reduction, electronic damping of high-frequency peaks, phase equalization, time-varying elements (such as frequency shifting, delay, phase modulation), bandpass filtering, echo cancellation, channel equalization, and notch filtering.
However, feedforward alone techniques suffer because they do not consider the transfer function (measured response of the output of an amplifying system relative to its input) appropriately. In real listening situations when wearing hearing aids, the acoustic path transfer function can vary significantly depending on the acoustic environment as well as the in-situ response, meaning that it is not a static transfer function. Understanding this suggests that effective acoustic feedback cancellers for hearing aids must be adaptive, as shown in Figure 18. Feedback canceling algorithms estimate the feedback signal and then adaptively subtract this estimate from the microphone signal, so that ideally, only the desired signal is preserved at the input of the forward path.
Adaptive Feedback Cancellation
But, adaptive in which way? One way to differentiate adaptive feedback cancellation is to identify which of two categories they fit: continuous or non-continuous adaptation. Both types have been developed for hearing aids, so what is the difference?
Non-continuous adaptation systems periodically use a training sequence such as a white noise at the output of the hearing aid for adaptation of the feedback canceller coefficients. This training sequence in which the coefficients of the feedback canceller are adapted, occurs only when instability is detected for loud sounds causing feedback , or when the input signal level is low and thus requires more gain, leading to instability  of the microphone input signal.
The feedback-cancellation system described updates the estimated feedback path whenever changes are detected in the feedback behavior. When a change is detected, the normal hearing-aid processing is interrupted, a pseudorandom probe signal is injected into the system, and a set of filter coefficients is adjusted to give an estimate of the feedback path. The hearing aid is then returned to normal operation with the feedback-cancellation filter as part of the system.
The interfering nature of such a training sequence when feedback occurs reduces the SNR (signal-to-noise ratio), and as a result, is best for those individuals who have a severe hearing loss and who would not be affected by the white noise of the training sequence. Both of these approaches may be objectionable because adaptation is limited only to those situations where either howling (Kates, 1991) or silence (Maxwell and Zurek, 1995) intervals are detected.
Continuous adaptation feedback systems (CAF) constantly adapt the filter coefficients based on the input signal and do not require a training sequence, and are therefore preferred (Figure 19). As diagrammed, the adaptive filter W(z) attempts to continuously estimate the feedback transfer function F(z). However, the primary disadvantage of these type systems is that the response signal d(n) is the addition of the feedback signal y(n) and the input signal x(n), which are correlated. As a result, such an adaptive filter cannot properly estimate the feedback path (it is biased) when the desired signal is spectrally colored* (speech or music, as examples). In this case, the CAF tends to cancel the desired signal instead of the feedback signal, so that the desired signal gets distorted.
Adaptive algorithms generally estimate filter coefficients based on some kind of optimization criterion. The criterion very often used is that which minimizes the mean square error signal, or LMS (least means square), which is the signal following subtraction of the adaptive filter’s output signal. This was used as early as 1983 by Nunley, et. al.  when they developed the first wearable digital hearing aid. LMS was used for both noise reduction and for feedback management, but it did not attempt to decorrelate the input and output signals.
A number of methods have been used to reduce the correlation issue mentioned previously.
Fast-Adaptive Decorrelation Filters
A problem with this approach is that the filter adaptation speed may be explicitly lowered for highly correlated input signals, such as speech or tonal excitation in general, and raised whenever feedback occurs. Additionally, the distinction between feedback and tonal signals cannot easily be obtained.
Delay – Time or Frequency – It was not until 1989 that a delay was added to the LMS-based adaptive filter to decorrelate the feedback signal y(n) and the input signal x(n) so that the feedback path could be accurately estimated  (Figure 20).
Frequency-domain Delay – Figure 21 diagrams the use of a frequency-domain delay approach to decorrelate the input signal x(n) to the input of the adaptive filter s(n)  In this model, the delay is placed in the forward path using real-time DSP (digital signal processing) evaluation, but again, with no analytical justification for the amount of delay.
Spectrum Compression – Nonlinear compression processing approach was another proposed method to decorrelate the input signal x(n) and the adaptive filter s(n)  This was placed before the output stage of the hearing aid.
However, none of these decorrelation methods is a straightforward solution because many additional problems occurred in trying to implement these approaches. More sophisticated approaches had to be developed.
*Spectral coloring refers to the fact that certain spectral components are stronger than other spectral components. A spectrally colored signal may be a broadband (e.g. speech signal) and well as a narrowband signal (e.g. sinusoid or alarm signal).
Next week: Adaptive Feedback – continued.
- Kates, 1991. Results from a computer simulation, IEEE Trans. Signal Processing, Vol. 39, pp. 553-562↵
- Maxwell and Zurek, 1995. Reducing acoustic feedback in hearing aids, IEEE Trans. Speech Audio Processing, Vol. 4, pp 304-313↵
- Nunley J, Staab W, Steadman J, Wechsler P, and Spencer B. 1983. A wearable digital hearing aid, Hearing Journal vol. 36: 29, 31↵
- Bustamante D, Worrall T, Williamson M. 1989. Measurement of adaptive suppression of acoustic feedback in hearing aids, Prod. 1989 IEEE ICASSP, pp. 2017-2020↵
- Estermann P. and Kaelin A. 1994. Feedback cancellation in hearing aids: results from using frequency-domain adaptive filters, in Proc. 1994 IEEE ISCAS, pp. 257-260.↵
- Joson H, Asano F, Suzuki Y, and Sone T. 1993. Adaptive feedback cancellation with frequency compression for hearing aids. JASA, Vol. 94, pp. 3248-3254, Dec.↵