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 adaptive 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 deterministic averaging analysis and the total stability theorem. A theoretical misadjustment expression is then obtained by using the ordinary-differential-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 composed of a linear combination of long-tail and short-tail noise distributions