Paper Info
Title
IEEE-STD-1057 Three Parameter Sine Wave Fit for SNR Estimation: Performance Analysis and Alternative Estimators
Abstract
This paper considers the three-parameter-fit sine wave model. Under a Gaussian noise assumption, it is known that the three-parameter fit given in IEEE Standards 1057 and 1241 coincides with the method of maximum likelihood (ML), which is known for its favorable properties in large samples. Under coherent sampling assumption, the Cramér-Rao Bound of an unbiased estimator (UE) of the signal-to-noise ratio (SNR) is derived followed by an exact finite-sample analysis of the ML estimator of SNR derived from the three-parameter fit, revealing its nonsymmetric F-distribution. Exact expressions for the bias, variance, and the mean squared error (MSE) of the ML estimator are then derived, revealing that the ML estimator in finite samples is far from optimal in terms of precision and accuracy. With the ML estimator as a starting point, several alternative estimators are derived, which outperform the method of ML. In particular, a UE is derived, with lower variance compared with the ML for small sample size. In addition, estimators are derived based on constrained minimization of the MSE. The theoretical findings are illustrated by simulations, showing an excellent agreement between theory and practice. Simulations using quantized data are also used to show the performance of the derived estimators mimicking an analog-to-digital converter (ADC) testing scenario. Furthermore, the derived estimators are applied to coherently and noncoherently sampled measurement data from a 12-bit ADC and, for small number of samples, all are shown to outperform the original estimate, showing the practical relevance of the theoretical findings.
Year
DOI
Venue
2014
10.1109/TIM.2013.2293226
Instrumentation and Measurement, IEEE Transactions  
Keywords
Field
DocType
Gaussian noise,IEEE standards,analogue-digital conversion,maximum likelihood estimation,mean square error methods,signal processing,ADC testing,Cramér-Rao bound,Gaussian noise assumption,IEEE standards 1241,IEEE-STD-1057,ML estimator,MSE,SNR estimation,analog-to-digital converter,coherent sampling assumption,finite-sample analysis,maximum likelihood method,mean squared error,nonsymmetric F-distribution,signal-to-noise ratio,three-parameter-fit sine wave model,unbiased estimator,Cramér--Rao bound (CRB),Cram??r??Rao bound (CRB),maximum-likelihood (ML) estimation,signal-to-noise ratio (SNR),sine-fit,unbiased estimator (UE),unbiased estimator (UE).
Efficient estimator,Applied mathematics,Minimum-variance unbiased estimator,Minimax estimator,Signal-to-noise ratio,Mean squared error,Bias of an estimator,Electronic engineering,Estimation theory,Statistics,Mathematics,Estimator
Journal
Volume
Issue
ISSN
63
6
0018-9456
Citations 
PageRank 
References 
4
0.60
8
Authors
3
Name
Order
Citations
PageRank
Senay Negusse140.94
Peter Handel277691.45
Per Zetterberg320924.11