Detecting Instability Potentials in Regularization for Fast Affine Projection Algorithms

In fast affine projection (FAP) adaptation algorithms, it is needed to explicitly or implicitly perform a matrix inversion, during which a small positive regularization factor plays an important role in keeping the algorithm stable and optimized. While existing schemes choose the regularization factor based on certain system criteria not related to the inversion, this paper proposes a simple scheme that dynamically diagnoses the inversion process itself for potentials of instability. This work paves the way for further studies on "minimal regularization and step-size control" technique. A FAP adopting this technique can be compared with FAPs with existing regularization schemes for convergence and steady state performance.