A statistical noise constrained least mean fourth adaptive algorithm

In this work, a statistical noise-constrained least mean fourth (SN CLMF) adaptive algorithm is proposed. Based on the fact that in many practical applications an accurate estimate of the fourth- order moment of the noise is available, or can be easily estimated, the learning speed of the LMF algorithm can be then increased considerably by adding a constraint to it. This noise constrained LMF algorithm can be seen as a variable step-size LMF algorithm. Moreover, the concept of energy conservation is used to carry out the rigorous steady-state analysis. Finally, a number of simulations are carried out to corroborate the theoretical findings, and as expected, improved performance is obtained through the use of this technique over the traditional LMF algorithm.