A noise constrained least mean fourth adaptive algorithm

In this work, a noise-constrained least mean fourth (NCLMF) adaptive algorithm is proposed. Based on the fact that in many practical applications an accurate estimate of the measurement noise variance 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. The main aim of this paper is to derive the NCLMF adaptive algorithm, analyze its convergence behaviour, and assess its performance in different noise environments. Moreover, the concept of energy conservation is used to carry out the rigorous steady-state analysis. Finally, a number of simulation results 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.