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A Matrix Extension Built Under-Sampled Likelihood Ratio Test with Application to MUSIC Breakdown Prediction and Cure

Ben A. Johnson1, and Yuri I. Abramovich2
1. RLM Management, Pty. Ltd., Edinburgh, Australia and Institute of Telecommunications Research, UniSA, Mawson Lakes, Australia
2. ISR Division, Defence Science and Technology Organisation
Abstract—Likelihood ratio tests are used in a rangeof detection-estimation problems, but normally cannot beextended to cases where training data volume T is smallerthan the dimension M of the observations. We proposea non-degenerate normalized LR test that can be usedfor detection-estimation in such under-sampled trainingconditions. The LR is formed based on non-degenerateband extension of the original degenerate sample covariancematrix. This LR is then applied within a generalized likelihoodratio test framework to an array processing problemwhere the presence of closely spaced signal can be robustlydetected, but their individual directions of arrival cannot befully resolved by subspace-based DOA techniques such asMUSIC. In that case, MUSIC produces direction of arrivalestimates for some sources with very large errors (outliers).We use the under-sampled likelihood ratio to detect thepresence of such MUSIC outliers and provide correctedDOA estimates.

Index Terms—maximum likelihood estimation, directionof arrival estimation, array signal processing, parameterestimation, signal resolution.

Cite: Ben A. Johnson, and Yuri I. Abramovich, "A Matrix Extension Built Under-Sampled Likelihood Ratio Test with Application to MUSIC Breakdown Prediction and Cure," Journal of Communications, vol. 2, no. 3, pp. 64-72, 2007.
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