2-D angle estimation with spherical arrays for scalar fields by means of Unitary spherical ESPRIT

The geometric configuration of the antenna array is of great importance for the performance of direction-of-arrival (DOA) estimation algorithms. Uniform circular arrays (UCAs) provide 360deg azimuthal coverage, thanks to their circular symmetry in the azimuth direction which is exploited by applying phase-mode excitation. Yet, the source elevation cannot be estimated with the same accuracy as the source azimuth angle. Moreover, a 180deg ambiguity typically appears in the elevation angle because the azimuth plane is often a symmetry plane for the array geometry. A spherical array, where the antenna elements are distributed over a sphere, overcomes these disadvantages. However, distributing the elements more or less uniformly over the sphere is a lot more complex than in the case of a UCA. In order to avoid spatial aliasing effects due to the limited number of antenna elements over the sphere, special strategies are required to distribute the antenna elements over a sphere such as equi-angle sampling, Gaussian sampling and nearly uniform sampling. In spherical phase-mode processing for spherical antenna arrays is proposed, which is similar to the phase-mode processing for UCAs. This processing technique, which is essentially a spherical Fourier transform of the element-space manifold, is the basis to develop an ESPRIT-based DOA estimation algorithm. For paired azimuth and elevation estimation, we propose an ESPRIT algorithm that incorporates all relevant phase modes, after transformation into beamspace, to fully exploit the spatial properties of the spherical array. The eigenvalues of a matrix directly yield the DOA estimates. The Unitary spherical ESPRIT algorithm is outlined in Section 2. The results of the simulations in Section 3 demonstrate that the algorithm is capable of estimating the DOAs with a high accuracy.