Sparsity Aware Hybrid Adaptive Algorithms for Modeling Acoustic Paths

Modeling of acoustic paths may be considered as a sparse system identification problem, owing to the sparse nature of the many acoustic impulse responses. Adaptive algorithms based on the concept of proportionate filtering as well as the ones based on zero attraction has been widely used for sparse system identification. A re-weighted zero attraction least mean square (RZA-LMS) algorithm is a popular sparse adaptive algorithm and is effective for modeling sparse as well as non-sparse systems. However, it offers a slow initial convergence, which will slow down the system identification process. The improved proportionate normalized least mean square (IPNLMS) algorithm offers a fast initial convergence and is effective for sparse system identification. But the steady state mean square error offered by the algorithm is not as effective as that offered by RZA-LMS algorithm. In an endeavour to achieve sparse system identification with improved initial convergence speed and enhanced steady state mean square error, this paper proposes a modeling scheme based on a convex combination of IPNLMS and RZA-LMS algorithms. The new scheme has been shown to be effective in modeling sparse systems including an acoustic feedback path in a behind the ear digital hearing aid.