Fast communication: On the steady-state mean squared error of the fixed-point LMS algorithm

Authors:
Mohamed Ghanassi;Benoít Champagne;Peter Kabal
Affiliations:
Department of Electrical & Computer Engineering, McGill University, 3480 University Street Montreal, Quebec, Canada H3A 2A7;Department of Electrical & Computer Engineering, McGill University, 3480 University Street Montreal, Quebec, Canada H3A 2A7;Department of Electrical & Computer Engineering, McGill University, 3480 University Street Montreal, Quebec, Canada H3A 2A7
Venue:
Signal Processing
Year:
2007

Citing 5
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A nonlinear analytical model for the quantized LMS algorithm-thearbitrary step size case

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Abstract

This communication studies the quantization effects on the steady-state performance of a fixed-point implementation of the Least Mean Squares (LMS) adaptive algorithm. Based on experimental observations, we introduce a new intermediate mode of operation and develop a simplified theoretical approach to explain the behaviour caused by quantization effects in this mode. We also review the stall mode and provide a new expression that predicts the discontinuous behaviour of the steady-state mean squared error as a function of the input signal power. Combined with a previous analysis of quantization effects in stochastic gradient mode, this study provides analytical expressions for the steady-state mean squared error for the full range of step-size values. We present experimental results that are in a good agreement with theoretical predictions to validate our model.