High-resolution DOA estimation by algebraic phase unwrapping algorithm

A common strategy among modern high-resolution direction-of-arrival (DOA) estimation schemes is their systematic translation from the DOA estimation problem to a global nonlinear optimization problem: find all (local) minima or maxima of certain univariate functions, defined as the values on the unit circle, of carefully designed complex self-reciprocal univariate Laurent polynomials. We present, for this highly nonlinear optimization problem, an algebraic (finite step) algorithm to compute the complete minima-maxima distributions along the unit circle, i.e., the exact number of minima or maxima located on an arbitrarily chosen sub-arc of the unit circle. This algorithm can serve as a powerful mathematical tool for the high-resolution DOA estimation problem. The key idea of the proposed algorithm is essentially based on the use of the generalized Sturm sequence developed originally for the exact solution to the algebraic multidimensional phase unwrapping problem (Yamada I. et al, IEEE Trans. Sig. Process., vol.46, p.1639-64, 1998).