An Extended Version of the NLMF Algorithm Based on Proportionate Krylov Subspace Projections

The Krylov proportionate normalized least mean square (KPNLMS) algorithm extended the use of proportional update idea of the PNLMS (proportionate normalized LMS) algorithm to the non-sparse (dispersive) systems. This paper deals with the mean fourth minimization of the error and proposes Krylov proportionate normalized least mean fourth algorithm (KPNLMF). First, the PNLMF (proportionate NLMF) algorithm is derived, then Krylov subspace projection technique is applied to the PNLMF algorithm to obtain the KPNLMF algorithm. While fully exploiting the fast convergence property of the PNLMF algorithm, the system to be identified does not need to be sparse in the KPNLMF algorithm due to the Krylov subspace projection technique. In our simulations, the KPNLMF algorithm converges faster than the KPNLMS algorithm when both algorithms converge to the same system mismatch value. The KPNLMF algorithm achieves this without any increase in the computational complexity. Further numerical examples comparing the KPNLMF with the NLMF and the KPNLMS algorithms support the fast convergence of the KPNLMF algorithm.