Detection of more uncorrelated Gaussian sources than sensors using fully augmentable sparse antenna arrays

We introduce a new approach to the detection problem for “fully augmentable” arrays (whose set of intersensor differences is complete). We propose a transformation of the directly augmented (non-positive-definite) Toeplitz matrix into a p.d. Toeplitz matrix T_μ with the proper number of equal minimum eigenvalues, appropriate for the candidate number of sources μ. Comparison of the results of these best-fit transformations over the range of candidates then allows us to select the most likely number of sources mˆ using traditional criteria. Simulation results demonstrate the high performance of this method