In this paper, solutions for combined feedback and noise suppression in hearing aids are developed. The techniques presented are based on the generalized sidelobe canceller (GSC) and adaptive feedback canceller (AFC), with a prediction error method (PEM) adaptation to avoid speech distortion. Two possible cascades of GSC-based noise reduction and AFC, namely an ldquoAFC firstrdquo and a ldquoGSC first,rdquo as well as a truly integrated solution that jointly suppresses feedback and noise are discussed. The integrated solution (called PEM-GFIC) achieves optimum synergies between noise and feedback suppression at the lowest computational cost. In addition, it cancels more feedback than the generalized echo and interference canceller, a joint solution for echo and noise suppression. In the cascaded solutions, the feedback and noise suppression filters are not always optimally exploited. For high input SNRs, ldquoAFC firstrdquo scheme generally may achieve better feedback cancellation because of its larger number of degrees of freedom. However, noise reduction by the GSC-stage seriously affects the feedback cancellation performance. At low SNRs, ldquoGSC firstrdquo generally achieves more feedback cancellation than PEM-GFIC at the expense of worse noise reduction. At high hearing aid gains and/or large SNRs, the noise reduction stage however negatively affects the performance of the feedback cancellation filter, resulting in a worse feedback and noise suppression compared to PEM-GFIC.

We derive a fast QRD-least-squares lattice (QRD-LSL) based unconstrained optimal filtering algorithm for multichannel acoustic noise reduction. As known from the literature, the unconstrained optimal filtering approach is an alternative to the popular GSC beamforming, which does not rely on a priori information and hence possesses improved robustness. The optimal filtering problem involved is special in that the desired response signal is not known explicitly. The derivation of the QRD-LSL algorithm is based on a significantly reorganized version of a QRD-RLS-based unconstrained optimal filtering scheme. Overall an order of magnitude complexity reduction is obtained without any performance penalty, which makes this new approach affordable for real time implementation.

The so-called affine projection algorithm (APA) has become a popular method in adaptive filtering applications and fast versions of it have been developed previously, such as fast affine projection (FAP) and the frequency domain block exact fast affine projection (BEFAP). While it is known that regularization is an absolute necessity in affine projection based adaptive filtering algorithms, FAP and BEFAP rely on an implicit "small regularization parameter" assumption. In this paper, a block exact affine projection algorithm (BE-APA) is derived that does not rely on the assumption of a small regularization parameter. It is an exact frequency domain translation of the original AP algorithm, and still has about the same complexity as, block exact FAR Unlike BEFAP, it can be used with strong regularization. It is then extended to incorporate an alternative to explicit regularization that is based on so-called "sparse" equations.