Quasi-Newton least-mean fourth adaptive algorithm

This paper proposes a new Newton-based adaptive filtering algorithm, namely the Quasi-Newton Least-Mean Fourth (QNLMF) algorithm. The main goal is to have a higher order adaptive filter that usually fits the non-Gaussian signals with an improved performance behavior, which is achieved using the Newton numerical method. Both the convergence analysis and the steady-state performance analysis are derived. More importantly, unlike other stochastic based algorithms, the step size parameter that controls the convergence of the QNLMF is independent of the statistics of the input signal, and consequently, the analytical assessments show that the proposed algorithm enjoys an independent performance from the input signal eigenvalue spread. Finally, a number of simulation experiments are carried out to corroborate the theoretical findings.