Convex Combination of LMF and ZA-LMF for Variable Sparse System Identification

The objective of this work is to introduce a convex combination of two filters to perform a variable sparse system identification. The first filter is based on the Least Mean Fourth algorithm (LMF), whereas the second is based on its sparse aware version, i.e., the Zero-attractor-LMF (ZA-LMF) algorithm. The convex combination is proposed to solve the sparsity problem under non-Gaussian noise environments. The universality study of the filter indicates that the convex combination always chooses the component filter that offers the lowest Excess Mean Square Error (EMSE) possible. Computer Simulations are performed to confirm the theoretical findings.

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