A hybrid approach for sparse adaptive filters under highly colored inputs

We address an adaptive filtering problem for sparse linear systems excited by highly colored input signals. A proportionate approach is known to accelerate the convergence speed by exploiting the sparseness of the systems, while a transformdomain approach is known to alleviate the decay of the convergence rate for highly colored inputs. We highlight the improved proportionate NLMS (IPNLMS) and transform-domain NLMS (TD-NLMS) algorithms. The present experimental results show that the gain of IPNLMS against TD-NLMS changes from positive to negative as the input auto-correlation becomes strong. We propose a hybrid approach of IPNLMS and TD-NLMS, taking the advantages of both algorithms by means of a timevariant convex combination of the two matrices employed by those algorithms. Numerical examples show the efficacy of the proposed algorithm.