### Abstract

We consider an adaptive linear prediction based feedback canceller for hearing aids that exploits two (an external and a shaped) noise signals for a bias-less adaptive estimation. In particular, the bias in the estimate of the feedback path is reduced by synthesizing the high-frequency spectrum of the reinforced signal using a shaped noise signal. Moreover, a second shaped (probe) noise signal is used to reduce the closed-loop signal correlation between the acoustic input and the loudspeaker signal at low frequencies. A power-transfer-function analysis of the system is provided, from which the effect of the system parameters and adaptive algorithms [normalized least mean square (NLMS) and recursive least square (RLS)] on the rate of convergence, the steady-state behaviour and the stability of the feedback canceller is explicitly found. The derived expressions are verified through computer simulations. It is found that, as compared to feedback canceller without probe noise, the cost of achieving an unbiased estimate of the feedback path using the feedback canceller with probe noise is a higher steady-state misadjustment for the RLS algorithm, whereas a slower convergence and a higher tracking error for the NLMS algorithm.

Original language | English |
---|---|

Journal | Signal Processing |

Volume | 157 |

Pages (from-to) | 45-61 |

Number of pages | 17 |

ISSN | 0165-1684 |

DOIs | |

Publication status | Published - 1 Apr 2019 |

### Fingerprint

### Keywords

- Adaptive filters
- Band-limited LPC vocoder
- Convergence rate
- Feedback cancellation
- Hearing-aid
- Power transfer function
- Probe noise

### Cite this

*Signal Processing*,

*157*, 45-61. https://doi.org/10.1016/j.sigpro.2018.11.003

}

*Signal Processing*, vol. 157, pp. 45-61. https://doi.org/10.1016/j.sigpro.2018.11.003

**Mean Square Performance Evaluation in Frequency Domain for an Improved Adaptive Feedback Cancellation in Hearing Aids.** / Kar, Asutosh; Anand, A.; Østergaard, Jan; Jensen, Søren Holdt; Swarmy, M.N.S.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - Mean Square Performance Evaluation in Frequency Domain for an Improved Adaptive Feedback Cancellation in Hearing Aids

AU - Kar, Asutosh

AU - Anand, A.

AU - Østergaard, Jan

AU - Jensen, Søren Holdt

AU - Swarmy, M.N.S.

PY - 2019/4/1

Y1 - 2019/4/1

N2 - We consider an adaptive linear prediction based feedback canceller for hearing aids that exploits two (an external and a shaped) noise signals for a bias-less adaptive estimation. In particular, the bias in the estimate of the feedback path is reduced by synthesizing the high-frequency spectrum of the reinforced signal using a shaped noise signal. Moreover, a second shaped (probe) noise signal is used to reduce the closed-loop signal correlation between the acoustic input and the loudspeaker signal at low frequencies. A power-transfer-function analysis of the system is provided, from which the effect of the system parameters and adaptive algorithms [normalized least mean square (NLMS) and recursive least square (RLS)] on the rate of convergence, the steady-state behaviour and the stability of the feedback canceller is explicitly found. The derived expressions are verified through computer simulations. It is found that, as compared to feedback canceller without probe noise, the cost of achieving an unbiased estimate of the feedback path using the feedback canceller with probe noise is a higher steady-state misadjustment for the RLS algorithm, whereas a slower convergence and a higher tracking error for the NLMS algorithm.

AB - We consider an adaptive linear prediction based feedback canceller for hearing aids that exploits two (an external and a shaped) noise signals for a bias-less adaptive estimation. In particular, the bias in the estimate of the feedback path is reduced by synthesizing the high-frequency spectrum of the reinforced signal using a shaped noise signal. Moreover, a second shaped (probe) noise signal is used to reduce the closed-loop signal correlation between the acoustic input and the loudspeaker signal at low frequencies. A power-transfer-function analysis of the system is provided, from which the effect of the system parameters and adaptive algorithms [normalized least mean square (NLMS) and recursive least square (RLS)] on the rate of convergence, the steady-state behaviour and the stability of the feedback canceller is explicitly found. The derived expressions are verified through computer simulations. It is found that, as compared to feedback canceller without probe noise, the cost of achieving an unbiased estimate of the feedback path using the feedback canceller with probe noise is a higher steady-state misadjustment for the RLS algorithm, whereas a slower convergence and a higher tracking error for the NLMS algorithm.

KW - Adaptive filters

KW - Band-limited LPC vocoder

KW - Convergence rate

KW - Feedback cancellation

KW - Hearing-aid

KW - Power transfer function

KW - Probe noise

UR - http://www.scopus.com/inward/record.url?scp=85056852034&partnerID=8YFLogxK

U2 - 10.1016/j.sigpro.2018.11.003

DO - 10.1016/j.sigpro.2018.11.003

M3 - Journal article

VL - 157

SP - 45

EP - 61

JO - Signal Processing

JF - Signal Processing

SN - 0165-1684

ER -