Convex combination of adaptive filters based on the logarithmic cost

In this work, we propose a novel convex combination algorithm incorporating two different-step-size adaptive filters derived from the logarithmic cost function. Recently, to incorporate the advantages of the different-order-norm-based cost functions without the need of a priori knowledge on signal statistics, the cost function using a logarithmic penalty was introduced. There are two different versions depend on the decision of the base cost function, and these algorithms possess the mixed-norm properties themselves. However, these algorithms still have the trade off related to step size. The convex combination algorithm is applied to cope with this trade off, and the suitable mixing parameter adaptation algorithm is designed based on the logarithmic cost. In the simulation on system identification scenario, the simulation results show that the proposed algorithm properly combines the advantages of two different-step-size component filters.