Abstract—System identification is one of the most important applications of adaptive filter algorithms. Some systems such as echo response that must be identified by the echo canceller have sparse nature. Classic adaptive filter algorithms like LMS or NLMS have poor performance in this way. Proportionate NLMS (PNLMS) algorithm has been developed to make improve poorly performance of NLMS in system identification, unfortunately it suffers from slow down during adaption process. To solve this problem, the concept of proportionate adaptation is extended to the normalized subband adaptive filter (NSAF), and three types proportionate normalized subband adaptive filter (PNSAF) algorithms are established in this paper. Proposed algorithms are proportionate normalized subband adaptive filter ++ (PNSAF++), the set-membership PNSAF (SM-PNSAF) and the set-membership PNSAF++ (SM-PNSAF++). Here we demonstrate that PNSAF++ algorithm improve the convergence rate of PNSAF in sparse channels. The SM-PNSAF and SM-PNSAF++ also exhibit good performance with significant reduction in the overall computational complexity compared with the ordinary PNSAF. The simulation results show good performance of the proposed algorithms.

Index Terms—Proportionate normalized subband adaptive filter, set-membership, sparse system identification.

The authors are with the Shahid Rajaiee Teaching Training university of Tehran (SRTTU), Department of Electrical and Computer Engineering, Lavizan 16788, Tehran, Iran (e-mail: mshams@srttu.edu,sima.kadkhodazadeh@gmail.com).

Cite: Mohammad Shams Esfand Abadi and Sima Kadkhodazadeh, "The Novel Proportionate Normalized Subband Adaptive Filter Algorithms for Sparse System Identification," International Journal of Computer and Electrical Engineering vol. 4, no. 4, pp. 577-581, 2012.