Two Bicomplex and One Multicomplex Least Mean Square algorithms
This work provides incremental improvements for signal processing or adaptive filtering applications by generalizing LMS algorithms to higher-dimensional number systems.
The authors tackled the problem of extending LMS algorithms to bicomplex and multicomplex domains by introducing new gradient operators, resulting in the formulation of BLMS and MLMS algorithms as extensions of classical real and complex LMS methods.
We study and introduce new gradient operators in the complex and bicomplex settings, inspired from the well-known Least Mean Square (LMS) algorithm invented in 1960 by Widrow and Hoff for Adaptive Linear Neuron (ADALINE). These gradient operators will be used to formulate new learning rules for the Bicomplex Least Mean Square (BLMS) algorithms and we will also formulate these learning rules will for the case of multicomplex LMS algorithms (MLMS). This approach extends both the classical real and complex LMS algorithms.