Adaptive signal processing with the gradually increasing filter length (GRINFIL) method

This dissertation introduces a new adaptation technique which greatly improves the convergence rate of stochastic gradient based adaptive filtering algorithms. Our method starts the adaptation with a short filter length and then increases the filter length as the previous one becomes insufficient in getting us any closer to the optimum solution. We call this approach the gradually increasing filter length (GRINFIL) adaptation algorithm. We also show how this method can be best utilized by side selective extension of the filter (GRINFIL-SSE). Then to illustrate the power of the GRINFIL approach, we present examples on least-mean-squares adaptation, and single- and multi-channel blind equalization. We show especially how this new method can be used to significantly increase the convergence rate of all Bussgang type blind equalizers. We also derive a closed-form expression for the minimum achievable inter-symbol interference (ISI) for a given equalizer length for the blind equalization problem. After this, we apply our method on adaptive subband filtering and combine and contrast the advantages of subband filtering and adaptation by GRINFIL. We show that the GRINFIL method can be applied on the subband filters to improve the convergence rate, and it may even be considered to replace subband filtering.