CONVERGENCE AND STEADY-STATE PROPERTIES OF THE LEAST-MEAN MIXED-NORM (LMMN) ADAPTIVE ALGORITHM

Convergence and steady-state analyses of a least-mean mixed-norm adapt ive algorithm are presented. This is formed as a convex mixture of the mean-square and the mean-fourth cost functions. The local exponential stability of the algorithm is shown by application of the determinist ic averaging analysis and the total stability theorem. A theoretical m isadjustment expression is then obtained by using the ordinary-differe ntial-equation method. Simulation studies are presented to support the theoretical findings. The results demonstrate the advantage of mixing error norms in adaptive filtering when the measurement noise is compo sed combination of long-tail and short-tail distributions.