Application of MUSIC to arrays with multiple invariances

This paper describes generalizations of the MUSIC and root-MUSIC algorithms for direction of arrival (DOA) estimation to arrays composed of multiple translated subarrays. The advantage of these new approaches is that the DOAs can be estimated using either a one-dimensional search or by rooting a polynomial, as opposed to a multidimensional search as required by the Multiple Invariance (MI)-ESPRIT algorithm. While MI-MUSIC and root-MI-MUSIC are not statistically efficient like MI-ESPRIT, they do perform better than a single invariance implementation of ESPRIT, and are thus better suited for finding the initial conditions required by the MI-ESPRIT search. subarray responses for a given source are related by a constant on the unit circle. Although the proposed MI-MUSIC., algorithm does not share the statistical optimality of MIESPRIT, it provides more accurate initial estimates than regular ESPRIT since it is always able to exploit all array invariances and enforce the aforementioned unit circle constraint. We also show how the root-MUSIC technique can be extended to MI arrays. The root-MUSIC approach is attractive since it eliminates the need for even a onedimensional search for the DOA parameters. While the standard version of root-MUSIC finds the zeros of a scalar polynomial to estimate the DOAs, the MI version requires calculation of the zeros of a matrix polynomial. The asymptotic performance of root-h1I-MUSIC will be equivalent to that of MI-MUSIC, and hence is suboptimal.