Detection-estimation of more uncorrelated Gaussian sources than sensors in nonuniform linear antenna arrays .I. Fully augmentable arrays

Previous studies dealing with direction-of-arrival (DOA) estimation for uncorrelated planes waves incident on nonuniform M-sensor arrays assumed that the number of signal sources m was known or had already been estimated. In the “conventional” case (m<M), traditional detection techniques such as Akaike´s information criterion (AIC) and minimum description length (MDL) that are based on the equality of several smallest eigenvalues in the covariance matrix may be applied, although we demonstrate that these results can be misleading for nonuniform arrays. In the “superior” case (m⩾M), these standard techniques are not applicable. We introduce a new approach to the detection problem for “fully augmentable” arrays (whose set of intersensor differences is complete). We show that the well-known direct augmentation approach applied to the sample covariance matrix is not a solution by itself since the resulting Toeplitz matrix is generally not positive definite for realistic sample volumes. We propose a transformation of this augmented matrix into a positive definite Toeplitz matrix T_μ with the proper number of equal minimum eigenvalues that are appropriate for the candidate number of sources μ. Comparison of the results of these best-fit transformations over the permissible range of candidates then allows us to select the most likely number of sources mˆ using traditional criteria and yields uniquely defined DOAs. Simulation results demonstrate the high performance of this method. Since detection techniques for superior scenarios have not been previously described in the literature, we compare our method with the standard AIC and MDL techniques in a conventional case with similar Cramer-Rao bound (CRB) and find that it has a similar detection performance