Stochastic Model for the LMS Algorithm with Symmetric/Antisymmetric Properties
Augusto Cesar Becker,
Eduardo Vinicius Kuhn,
Marcos Vinicius Matsuo,
Jacob Benesty,
Constantin Paleologu,
Laura-Maria Dogariu,
Silviu Ciochină
Affiliations
Augusto Cesar Becker
LAPSE—Electronics and Signal Processing Laboratory, Department of Electronics Engineering, Federal University of Technology-Paraná, Toledo 85902-490, PR, Brazil
Eduardo Vinicius Kuhn
LAPSE—Electronics and Signal Processing Laboratory, Department of Electronics Engineering, Federal University of Technology-Paraná, Toledo 85902-490, PR, Brazil
Marcos Vinicius Matsuo
GEPS—Electronics and Signal Processing Group, Department of Control, Automation, and Computation, Federal University of Santa Catarina, Blumenau 89036-004, SC, Brazil
Jacob Benesty
National Institute of Scientific Research—Energy, Materials, and Telecommunications, University of Quebec, Montreal, QC H5A 1K6, Canada
Constantin Paleologu
Department of Telecommunications, Faculty of Electronics, Telecommunications, and Information Technology, University Politehnica of Bucharest, 060042 Bucharest, Romania
Laura-Maria Dogariu
Department of Telecommunications, Faculty of Electronics, Telecommunications, and Information Technology, University Politehnica of Bucharest, 060042 Bucharest, Romania
Silviu Ciochină
Department of Telecommunications, Faculty of Electronics, Telecommunications, and Information Technology, University Politehnica of Bucharest, 060042 Bucharest, Romania
This paper presents a stochastic model for the least-mean-square algorithm with symmetric/antisymmetric properties (LMS-SAS), operating in a system identification setup with Gaussian input data. Specifically, model expressions are derived to describe the mean weight behavior of the (global and virtual) adaptive filters, learning curves, and evolution of some correlation-like matrices, which allow predicting the algorithm behavior. Simulation results are shown and discussed, confirming the accuracy of the proposed model for both transient and steady-state phases.
