Statistical Noise-Constrained Least Mean Fourth adaptive algorithms

Abstract

In this thesis, two constrained least mean fourth adaptive algorithms are proposed. These are based on the fact that in many practical applications, an accurate estimate of the measurement noise statistics is available or can be easily estimated. The proposed algorithms, namely the Statistical Noise-Constrained Least Mean Fourth (SNCLMF) and the Noise-Constrained Least Mean Fourth (NCLMF) are a type of variable step-size LMF algorithms. The main aim of this research is to derive the SNCLMF and NCLMF adaptive algorithms and assess their performance in different noise environments. More specifically, both the convergence analysis and the steady-state performance analysis are derived. Furthermore, the tracking analysis and the transient analysis of the proposed algorithms are also presented. In this work, unlike the work carried out in the literature, the concept of energy conservation is employed to carry out the analysis. Finally, a number of simulation results are carried out to corroborate the theoretical findings, and as it was expected, an improved performance is obtained through the use of these algorithms over the traditional LMF algorithm.