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

Authors:
Y.I. Abramovich;N.K. Spencer;A.Y. Gorokhov
Affiliations:
Intelligence, Surveillance, & Reconnaissance Div., Defence Sci. & Technol. Organ., Adelaide, SA, Australia;-;-
Venue:
IEEE Transactions on Signal Processing
Year:
2004

Citing 0
Cited 6

Two-set adaptive detection-estimation of Gaussian sources in Gaussian noise

Signal Processing - Special section: New trends and findings in antenna array processing for radar
Second-order asynchronous interference cancellation: regularized semi-blind technique and non-asymptotic maximum likelihood benchmark

Signal Processing - Special section: Multimodal human-computer interfaces
Non-stationary multiple-antenna interference cancellation for unsynchronized OFDM systems with distributed training

Signal Processing
DOA estimator performance assessment in the pre-asymptotic domain using the likelihood principle

Signal Processing
Detection-estimation of very close emitters: performance breakdown, ambiguity, and general statistical analysis of maximum-likelihood estimation

IEEE Transactions on Signal Processing
Invariance properties of the likelihood ratio for covariance matrix estimation in some complex elliptically contoured distributions

Journal of Multivariate Analysis

Quantified Score

Hi-index	35.69

Visualization

Abstract

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.