Detection-estimation of distributed Gaussian sources

The problem of estimating the number of independent homogeneously distributed (spread) Gaussian sources and their parameters impinging upon a uniform linear antenna array is considered for scenarios with a priori known angular spreading. This new method adopts the generalised likelihood ratio test (GLRT) methodology, based on LR maximisation, supported by a statistical nonasymptotic scenario-free lower bound analysis. The introduced LR maximisation yields results that statistically exceed the LR generated by the exact covariance matrix. High LR optimisation efficiency drives very high detection-estimation performance that, nevertheless, breaks down under certain threshold conditions. It is demonstrated that this breakdown phenomenon is not curable within the ML paradigm, since these highly incorrect solutions are still "better" than the actual covariance matrix as measured by the LR.