Paper Info
Title
A variable step-size zero attracting proportionate normalized least mean square algorithm
Abstract
The proportionate normalized least mean square (PNLMS) algorithm and its variants are by far the most popular adaptive filters that are used to identify sparse systems. The convergence speed of the PNLMS algorithm, though very high initially, however, slows down at a later stage, even becoming worse than sparsity agnostic adaptive filters like the NLMS. In this paper, we address this problem by introducing a carefully constructed l1 norm (of the coefficients) penalty in the PNLMS cost function which favors sparsity. This results in certain “zero attractor” terms in the PNLMS weight update equation which help in the shrinkage of the coefficients, especially the inactive taps, thereby arresting the slowing down of convergence and also producing lesser steady state excess mean square error (EMSE). We also demonstrate both analytically and also intuitively, that the EMSE can not, however, be reduced significantly by the zero attractors due to some fundamental shortcoming of the PNLMS algorithm, and propose methods to counter it by deploying a variable step size and also a variable proportionality constant for the zero attractors. Simulation results confirm excellent performance of the proposed algorithm vis-a-vis existing methods.
Year
DOI
Venue
2014
10.1109/ISCAS.2014.6865353
Circuits and Systems
Keywords
Field
DocType
adaptive filters,least mean squares methods,EMSE,PNLMS algorithm,PNLMS cost function,PNLMS weight update equation,adaptive filters,l1 norm penalty,proportionate normalized least mean square algorithm,steady state excess mean square error,variable step size,zero attractor terms,Adaptive Filter,Convergence Speed,Excess Mean Square Error,PNLMS Algorithm,Zero Attractor
Discrete mathematics,Applied mathematics,Control theory,Normalized least mean square algorithm,Recursive least squares filter,Mathematics
Conference
ISSN
Citations 
PageRank 
0271-4302
1
0.36
References 
Authors
13
2
Name
Order
Citations
PageRank
Rajib Lochan Das1354.97
Mrityunjoy Chakraborty212428.63