A cumulant based variable step size adaptive algorithm

An adaptive step size selection rule for least mean squares (LMS) adaptive algorithms is introduced. The step size sequence is adjusted using the kurtosis of the estimation error, thus the performance degradation due to the existence of noise with a strong variance. The proposed algorithm traces changes in the noise statistics and optimally adapts itself, exhibiting a reduced steady state error. Simulation results illustrate the algorithm´s superior performance and confirm its ability to optimally adapt to time varying noise environments. The convergence behavior of the algorithm is also addressed