Bounds on maximum likelihood ratio-Part II: application to antenna array detection-estimation with imperfect wavefront coherence

The maximum likelihood ratio (LR) lower bound analysis introduced in our previous papers is applied to support the detection-estimation of multiple Gaussian spread (distributed, scattered) sources. Since angular spreading eliminates any "noise eigensubspace" from the spatial covariance matrix, traditional detection techniques based on the equality of noise-subspace eigenvalues are not applicable here. Brute-force "focusing", which is based on the Schur-Hadamard inverse, is shown to be inefficient. Our technique is based on generalized likelihood-ratio test (GLRT) principles and involves LR maximization over the set of admissible covariance matrix models. The introduced technique yields results that statistically exceed the LR generated by the exact covariance matrix, which is used as the lower bound. High optimization efficiency drives high detection-estimation performance that, nevertheless, breaks down under certain threshold conditions. It is demonstrated that this breakdown phenomenon is not curable within the maximum likelihood (ML) paradigm since these highly erroneous solutions are still "better" than the true covariance matrix (as measured by the LR).