GLRT-Based Detection-Estimation for Undersampled Training Conditions

For sensors where the number of available independent identically distributed training samples T is less than the number of antenna array elements M, we propose nondegenerate properly normalized likelihood ratio (LR) tests (both standard and scale-invariant) to support detection-estimation of m point sources (m < T) in white noise, based on a generalized likelihood-ratio test (GLRT) approach. We demonstrate that these tests can detect MUSIC-specific ldquooutliersrdquo in the direction-of-arrival (DOA) estimation of closely spaced independent sources caused by insufficient training volume and/or signal-to-noise ratio (SNR). We then compare the performance of the introduced LRs to other test statistics available in this undersampled regime. We show that a search for solutions that increase the introduced LR allows us to replace the detected outliers by proper DOA estimates. This ldquopredict and curerdquo process leverages the SNR ldquogaprdquo between MUSIC breakdown and breakdown of maximum-likelihood estimation itself. The resultant LR maximization makes the associated covariance model statistically ldquoas likelyrdquo as the true covariance matrix and removes the vast percentage of outliers in certain scenarios.