Two variable step-size adaptive algorithms for non-Gaussian interference environment using fractionally lower-order moment minimization

Two variable step-size adaptive algorithms using fractionally lower-order moment minimization are proposed for system identification in non-Gaussian interference environment. The two algorithms automatically adjust their step sizes and adapt the weight vector by minimizing the p-th moment of the a posteriori error, where p is the order with 1⩽p⩽2, thus they are named as variable step-size normalized least mean p-th norm (VSS-NLMP) algorithms. The proposed adaptive VSS-NLMP algorithms are applied to both real- and complex-valued systems using low-complexity time-averaging estimation of the lower-order moments. Simulation results show that the misalignment of the proposed VSS-NLMP algorithms with a smaller p converges faster and achieves lower steady-state error in impulsive interference and/or colored input environment. The adaptive VSS-NLMP algorithms also perform better than the adaptive fixed step-size (FSS) NLMP in both Gaussian and finite-variance impulsive interference environments. A theoretical model for the steady-state excess mean-square error is also provided for both Gaussian and Bernoulli–Gaussian interference.