Bounds on maximum likelihood ratio-part I: application to antenna array detection-estimation with perfect wavefront coherence

The multiple hypothesis testing problem of the detection-estimation of an unknown number of independent Gaussian point sources is adequately addressed by likelihood ratio (LR) maximization over the set of admissible covariance matrix models. We introduce nonasymptotic lower and upper bounds for the...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2004-06, Vol.52 (6), p.1524-1536
Main Authors: Abramovich, Y.I., Spencer, N.K., Gorokhov, A.Y.
Format: Article
Language:English
Subjects:
Antenna arrays
Applied sciences
Coherence
Covariance matrix
Detection, estimation, filtering, equalization, prediction
Economic models
Electric breakdown
Estimates
Exact sciences and technology
Hypothesis testing
Information, signal and communications theory
Lower bounds
Mathematical models
Maximization
Maximum likelihood detection
Maximum likelihood estimation
Parameter estimation
Performance analysis
Point sources
Recognition
Signal and communications theory
Signal, noise
Studies
Telecommunications and information theory
Testing
Upper bound
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Summary:The multiple hypothesis testing problem of the detection-estimation of an unknown number of independent Gaussian point sources is adequately addressed by likelihood ratio (LR) maximization over the set of admissible covariance matrix models. We introduce nonasymptotic lower and upper bounds for the maximum LR. Since LR optimization is generally a nonconvex multiextremal problem, any practical solution could now be tested against these bounds, enabling a high probability of recognizing nonoptimal solutions. We demonstrate that in many applications, the lower bound is quite tight, with approximate maximum likelihood (ML) techniques often unable to approach this bound. The introduced lower bound analysis is shown to be very efficient in determining whether or not performance breakdown has occurred for subspace-based direction-of-arrival (DOA) estimation techniques. We also demonstrate that by proper LR maximization, we can extend the range of signal-to-noise ratio (SNR) values and/or number of data samples wherein accurate parameter estimates are produced. Yet, when the SNR and/or sample size falls below a certain limit for a given scenario, we show that ML estimation suffers from a discontinuity in the parameter estimates: a phenomenon that cannot be eliminated within the ML paradigm.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2004.827199