On the convergence, steady-state, and tracking analysis of the SRLMMN algorithm

In this work, a novel algorithm named sign regressor least mean mixed-norm (SRLMMN) algorithm is proposed as an alternative to the well-known least mean mixed-norm (LMMN) algorithm. The SRLMMN algorithm is a hybrid version of the sign regressor least mean square (SRLMS) and sign regressor least mean fourth (SRLMF) algorithms. Analytical expressions are derived to describe the convergence, steady-state, and tracking behavior of the proposed SRLMMN algorithm. To validate our theoretical findings, a system identification problem is considered for this purpose. It is shown that there is a very close correspondence between theory and simulation. Finally, it is also shown that the SRLMMN algorithm is robust enough in tracking the variations in the channel.