IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 58, NO. 9, SEPTEMBER 2009 3177 Modified LMS-Based Feedback-Reduction Subsystems in Digital Hearing Aids Based on WOLA Filter Bank Raúl Vicen-Bueno, Almudena Martínez-Leira, Roberto Gil-Pita, Member, IEEE, and Manuel Rosa-Zurera, Senior Member, IEEE Abstract—Digital hearing aids usually suffer from acoustic feed- back. This feedback corrupts the speech signal, causes instability, and damages the speech intelligibility. To solve these problems, an acoustic feedback reduction (AFR) subsystem using adaptive algo- rithms such as the least mean square (LMS) algorithm is needed. Although this algorithm has a reduced computational cost, it is very unstable. To avoid this situation, other AFR subsystems based on modifications of the LMS algorithm are used. Such algorithms are given as follows: 1) normalized LMS (NLMS); 2) filtered-X LMS (FXLMS); and 3) normalized FXLMS (NFXLMS). These algorithms are tested in three digital hearing aid categories: 1) in the ear (ITE); 2) in the canal (ITC); and behind the ear (BTE). The first and second categories under study suffer from great feedback effects due to the short distance between the loudspeaker and the microphone, whereas the third category suffers from these effects due to the high signal level at the hearing aid output; thus, robust AFR subsystems are needed. The added stable gains (ASGs) over the limit gain when AFR subsystems are working in the digital hearing aids are studied for all the categories. The ASG is de- termined as a tradeoff between two measurements: 1) segmented signal-to-noise ratio (objective measurement) and 2) speech qual- ity (subjective measurement). The results show how the digital hearing aids that work with AFR subsystems adapted with the NLMS or the NFXLMS algorithms can achieve up to 18 dB of increase over the limit gain. After analyzing the results, it is ob- served that the subjective measurement always limits the achieved ASG, but when the NLMS algorithm is used, it is appreciated that the objective measurement is a good approximation for esti- mating the maximum achieved ASG. Finally, taking into consider- ation the hearing aid performances and the computational cost of each AFR subsystem implementation, an AFR subsystem based on the NLMS algorithm to adapt feedback-reduction filters that are 128 coefficients long is proposed. Manuscript received January 30, 2008; revised August 27, 2008. First published May 26, 2009; current version published August 12, 2009. This work was supported in part by the Comunidad de Madrid/Universidad de Alcalá under Projects CCG06-UAH/TIC-0378 and CCG07-UAH/TIC-1572 and in part by the Spanish Ministry of Education and Science under Project TEC2006- 13883-C04-04/TCM. This paper is based on Acoustic Feedback Reduction Based on Filtered-X LMS and Normalized Filtered-X LMS Algorithms in Digital Hearing Aids based on WOLA filterbank by R. Vicen-Bueno, A. Martínez-Leira, R. Gil-Pita, and M. Rosa-Zurera, which appeared in the Proceedings of the IEEE International Symposium on Intelligent Signal Processing (WISP 2007). The Associate Editor coordinating the review process for this paper was Dr. Annamaria Varkonyi-Koczy. R. Vicen-Bueno, R. Gil-Pita, and M. Rosa-Zurera are with the Department of Signal Theory and Communications, Escuela Politécnica Superior, Universi- dad de Alcalá, 28805 Madrid, Spain (e-mail: raul.vicen@uah.es; roberto.gil@ uah.es; manuel.rosa@uah.es). A. Martínez-Leira is with Dimetronic Signals, 28830 Madrid, Spain (e-mail: almudena.martinez@servext.dimetronic.es). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2009.2017150 Index Terms—Acoustic feedback reduction (AFR), digital hear- ing aids, filtered-X LMS (FXLMS), least mean square (LMS), normalized FXLMS (NFXLMS), normalized LMS (NLMS), weighted overlap-add (WOLA) filter bank. I. I NTRODUCTION D IGITAL hearing aids are widely used by hearing-impaired people to improve the speech intelligibility and their quality of life. However, hearing-aid performance is usually degraded due to acoustic feedback, which generates other prob- lems. This phenomenon is produced when the sound propa- gates from the loudspeaker to the microphone. This situation maintained over time causes instability and a high frequency oscillation that can be perceived by the hearing-impaired people if its level exceeds their hearing thresholds. As a consequence, these effects limit the maximum gain that the hearing aid can perform and reduce the sound quality when the gain is close to the limit. To mitigate acoustic feedback, several methods based on adaptive algorithms have been used in the literature for feed- back reduction. The least mean square (LMS) algorithm [1], [2] is a commonly used algorithm in practical hearing-aid applica- tions due to its simplicity and low computational complexity. However, it can easily become unstable. Other feedback- reduction subsystems are developed from the LMS algorithm to mitigate its instability, e.g., the normalized LMS (NLMS) [3]. In this case, the adaptation parameter of the LMS algorithm is automatically updated and normalized according to the esti- mation of the algorithm output signal power. Other researchers propose a different way of updating the adaptation parameter, which is known as the sum method [4], [5]. This method is based on an estimation of the powers of the feedback-reduction subsystem output signal and its error signal. This estimation is used every algorithm iteration to update the adaptation parame- ter. Currently, the trend is to use feedback-reduction subsystems based on the filtered-X LMS (FXLMS) algorithm [6], [7] due to its robustness. Several researchers propose a variant of the FXLMS algorithm, i.e., the denominated normalized FXLMS (NFXLMS) [8], which updates the adaptation parameter ac- cording to the sum method. Thus, in the NFXLMS algorithm, the adaptation parameter is updated through an estimate of the powers of the feedback-reduction subsystem output signal filtered by the primary path filter and the error signal filtered by the secondary path filter. Independently of the algorithm used to automatically adapt the feedback-reduction filter, it is 0018-9456/$26.00 © 2009 IEEE