Common part estimation of acoustic feedback paths in hearing aids optimizing maximum stable gain

The computational complexity and convergence speed of adaptive feedback cancellation algorithms depend on the number of adaptive parameters used to model the acoustic feedback path. To reduce the number of adaptive parameters it has been proposed to decompose the acoustic feedback path as the convolution of a (time-invariant) common part and a (time-varying) variable part. Typically the problem of estimating all the required coefficients has been formulated as a least-squares optimization problem. In contrast, in this paper we propose to formulate the estimation problem as a minmax optimization problem and show how this is associated with the maximum stable gain of a hearing aid. Experimental results using measured acoustic feedback paths from a two-microphone behind-the-ear hearing aid show that the proposed minmax optimization outperforms the least-squares optimization in terms of maximum stable gain. Furthermore, the robustness of proposed common part decomposition for different feedback paths is evaluated.