Likelihood ratio tests are used in a range of detection-estimation problems, but normally cannot be extended to cases where training data volume T is smaller than the dimension M of the observations. We propose a non-degenerate normalized LR test that can be used for detection-estimation in such under-sampled training conditions. The LR is formed based on non-degenerate band extension of the original degenerate sample covariance matrix. This LR is then applied within a generalized likelihood

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... io test framework to an array processing problem where the presence of closely spaced signal can be robustly detected, but their individual directions of arrival cannot be fully resolved by subspace-based DOA techniques such as MUSIC. In that case, MUSIC produces direction of arrival estimates for some sources with very large errors (outliers). We use the under-sampled likelihood ratio to detect the presence of such MUSIC outliers and provide corrected DOA estimates. Index Terms-maximum likelihood estimation, direction of arrival estimation, array signal processing, parameter estimation, signal resolution.