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.