Analysis of the deficient length prediction error method in a hearing aid´s feedback canceller

This work presents a statistical analysis of the deficient length Least Mean Square algorithm combined with the prediction error method applied to feedback cancellation in hearing aids. Deterministic recursive equations to the mean coefficient behaviour of the adaptive filters were derived in order to assess the performance of the algorithm. The expected theoretical behaviour was compared with Monte Carlo simulations and practical experimental results, showing a very good agreement. The theoretical results can be useful to minimize the complexity of the canceller with a controlled performance loss.