Performance Analysis of $l_0$ Norm Constrained Recursive Least Squares Algorithm

Samrat Mukhopadhyay; Bijit Kumar Das; Mrityunjoy Chakraborty

Performance Analysis of $l_0$ Norm Constrained Recursive Least Squares Algorithm

Information Theory 2016-02-11 v1 math.IT Adaptation and Self-Organizing Systems Methodology

Authors: Samrat Mukhopadhyay , Bijit Kumar Das , Mrityunjoy Chakraborty

Abstract

Performance analysis of $l_0$ norm constrained Recursive least Squares (RLS) algorithm is attempted in this paper. Though the performance pretty attractive compared to its various alternatives, no thorough study of theoretical analysis has been performed. Like the popular $l_0$ Least Mean Squares (LMS) algorithm, in $l_0$ RLS, a $l_0$ norm penalty is added to provide zero tap attractions on the instantaneous filter taps. A thorough theoretical performance analysis has been conducted in this paper with white Gaussian input data under assumptions suitable for many practical scenarios. An expression for steady state MSD is derived and analyzed for variations of different sets of predefined variables. Also a Taylor series expansion based approximate linear evolution of the instantaneous MSD has been performed. Finally numerical simulations are carried out to corroborate the theoretical analysis and are shown to match well for a wide range of parameters.

Keywords

sparse optimization randomized algorithm convex optimization

Cite

@article{arxiv.1602.03283,
  title  = {Performance Analysis of $l_0$ Norm Constrained Recursive Least Squares Algorithm},
  author = {Samrat Mukhopadhyay and Bijit Kumar Das and Mrityunjoy Chakraborty},
  journal= {arXiv preprint arXiv:1602.03283},
  year   = {2016}
}

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15 pages, 5 figures

Performance Analysis of $l_0$ Norm Constrained Recursive Least Squares Algorithm

Abstract

Keywords

Cite

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