Multichannel broadband Fano theory for arbitrary lossless antennas with applications in DOA estimation

In this paper, we consider fundamental limitations for DOA estimation with arbitrary lossless antennas or antenna arrays inserted inside a sphere. Spherical vector modes and their associated equivalent circuits and Q factor approximations are employed as a general framework for the analysis. The classical broadband matching theory by Fano is extended to a general multiport S-parameter model of the antennas and fundamental bounds are given for the scattering parameters with respect to bandwidth and electrical size of the sphere. Finally, assuming a statistical signal model with Gaussian receiver noise, the Cramer-Rao lower bound is used to derive fundamental upper bounds for the performance of DOA estimation by a sphere.