Leaky least mean fourth adaptive algorithm

In this work, a leakage-based variant of the least mean fourth (LMF) algorithm, the leaky least mean fourth (LLMF) algorithm, is proposed. This algorithm will help mitigate the weight drift problem experienced in the conventional LMF algorithm. The main aim of this work is to derive the LLMF adaptive algorithm, analyse its convergence behaviour, and examine its performance in different noise environments. Furthermore, the tracking and transient analysis of the proposed LLMF algorithm are carried out using the energy-conservation relation framework. Finally, a number of simulation results are carried out to corroborate the theoretical findings, and show improved performance obtained through the use of LLMF over the conventional LMF algorithm in a weight drift scenario.