Multiple signal detection and estimation using atomic decomposition and EM

An algorithm to detect and estimate a linear mixture of deterministic signals corrupted by white Gaussian noise is presented. The number of signals is assumed to be unknown, and the noise power can be either known or unknown. The algorithm is based on an information-theoretic criterion in which the...

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Bibliographic Details
Published in:IEEE transactions on aerospace and electronic systems 2006-01, Vol.42 (1), p.84-102
Main Authors: Lopez-Risueno, G., Grajal, J.
Format: Article
Language:English
Subjects:
Algorithms
Computer simulation
Criteria
Decomposition
Estimates
False alarms
Maximization
Maximum likelihood detection
Maximum likelihood estimation
Noise
Parameter estimation
Radar detection
Radar signal processing
Radiometry
Signal detection
Signal processing
Signal processing algorithms
Signal to noise ratio
Studies
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Summary:An algorithm to detect and estimate a linear mixture of deterministic signals corrupted by white Gaussian noise is presented. The number of signals is assumed to be unknown, and the noise power can be either known or unknown. The algorithm is based on an information-theoretic criterion in which the probability of false alarm can be adjusted; typical information criteria, such as the Akaike (AIC) and the minimum description length (MDL) criteria, can be regarded as particular cases of it for given probabilities of false alarm. The proposed approach includes the use of the atomic decomposition and the expectation maximization (EM) algorithms to efficiently approximate the signal maximum likelihood estimate. For the first time, upper-bounds for the probabilities of underestimation and overestimation of the number of signals are obtained. In addition, the constant false-alarm rate (CFAR) characteristic is shown, and the statistical efficiency of the signal parameter estimation is discussed and illustrated by simulation. Numerical experiments show the suitability of the algorithm for signal interception by using synthetic and real-life radar signals.
ISSN:0018-9251
1557-9603
DOI:10.1109/TAES.2006.1603407