The Cramer-Rao bound on frequency estimates of signals closely spaced in frequency

This paper examines the Cramer-Rao (CR) lower bound on the variance of frequency estimates for the problem of n signals closely spaced in frequency. The main results presented are simple analytic expressions for the CR bound in terms of the maximum frequency separation, delta omega , SNR, and the nu...

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Bibliographic Details
Published in:IEEE transactions on signal processing 1992-06, Vol.40 (6), p.1507-1517
Main Author: Lee, H.B.
Format: Article
Language:English
Subjects:
Chromium
Frequency estimation
Performance analysis
Sampling methods
Signal analysis
Signal resolution
Signal to noise ratio
Source separation
Spatial resolution
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Summary:This paper examines the Cramer-Rao (CR) lower bound on the variance of frequency estimates for the problem of n signals closely spaced in frequency. The main results presented are simple analytic expressions for the CR bound in terms of the maximum frequency separation, delta omega , SNR, and the number of data vectors, N, that are valid for small delta omega . The results are applicable to the conditional (deterministic) signal model. The results show that the CR bound on frequency estimates is proportional to ( delta omega )/sup -2(n-1)//N*SNR. Therefore, the bound increases rapidly as the signal separation is reduced. Examples indicate that the expressions closely approximate the exact CR bounds whenever the signal separation is smaller than one resolution cell. Based upon the results, it is argued that the threshold SNR at which an unbiased estimator can resolve n closely spaced signals is at least proportional to ( delta omega )/sup -2n//N. The results are quite general and apply to many different types of temporal and spatial sampling grids.< >
ISSN:1053-587X
1941-0476
DOI:10.1109/78.139253