Fundamental limitations for DOA and polarization estimation with applications in array signal processing

Using a generic electromagnetic model based on the spherical vector harmonics, we provide the Cramer-Rao lower bound (CRB) for direction-on-arrival (DOA) and polarization estimation with arbitrary multiport antennas. By reciprocity, the receiving multiport antenna is characterized in terms of the transmission matrix from incident voltage waves to multipole coefficients of the outgoing spherical vector waves. Explicit results of the CRB for the Gaussian case is given in terms of the transmission matrix, the spherical vector harmonics and its spatial derivatives. Numerical examples are included to illustrate the results.