Closed-form 2D angle estimation with uniform circular array via phase mode excitation and ESPRIT

The UCA-ESPRIT algorithm represents a significant advance in the area of 2D arrival angle estimation. It is a closed form algorithm for use in conjunction with uniform circular arrays (UCAs) that provides automatically paired source azimuth and elevation angle estimates. In contrast, the algorithms for 2D arrival angle estimation to date have required expensive spectral searches, iterative solutions to multi-dimensional optimization problems, or ad-hoc schemes for pairing direction cosine estimates with respect to each of a number of different array axes. UCA-ESPRIT is fundamentally different from ESPRIT in that it is not based on a displacement invariance array structure but rather is based on phase mode excitation and hinges on a recursive relationship between Bessel functions. In the final stage of UCA-ESPRIT, the ith eigenvalue has the form μ_i=sin θ_ie(jφ_i) where θ_i and φ_i are the azimuth and elevation angles of the ith source