Convergence and tracking analysis of a constrained least mean fourth adaptive algorithm

It is a well established fact that the addition of a constraint to an adaptive algorithm improves its performance properties. Consequently, in this work, a noise-constrained least mean fourth (NCLMF) adaptive algorithm is developed. The NCLMF algorithm is based on a constrained minimization problem that includes knowledge of the noise variance. Moreover, this noise constrained LMF algorithm can be seen as a variable-step-size LMF algorithm. The convergence analysis as well the tracking analysis of the NCLMF adaptive algorithm are developed using the concept of energy conservation. Finally, simulation results are presented to demonstrate the superiority of the NCLMF algorithm over the conventional LMF algorithm as well corroborating the theoretical findings.