Adaptive combination of affine projection and NLMS algorithms based on variable step-sizes

Considering the filters with variable step-sizes outperform their fixed step-sizes versions and the combination algorithms with proper mixing parameters outperform their components, a combination algorithm consisting of improved variable step-size affine projection (I-VSSAP) and normalized least mean square (I-VSSNLMS) algorithms, of which the former is fast and the latter is slow, is proposed for stationary environment. Different from the combination algorithms whose components are updated independently, the variable step-sizes components are adapted using the same input and error signals, and their step-sizes are derived via the mean-square deviation (MSD) of the overall filter. Therefore, the components reflect the working state of the combination filter more accurately than their fixed step-sizes versions. The mixing parameter is obtained by minimizing the MSD and gradually decreases from 1 to 0. Therefore the proposed algorithm has a performance similar to I-VSSAP and I-VSSNLMS in the initial stage and steady-state respectively. Simulations confirm that the proposed algorithm outperforms its components and its fixed step-sizes version. The mixing parameter is artificially set to 0 when the difference between the MSDs of two adjacent iterations is below a user-defined threshold, then the proposed algorithm degrades to I-VSSNLMS and exhibits a less computational complexity than AP algorithm.