Cramer-Rao Lower Bounds for Polarimetric 2D Direction of Arrival Estimation

It is a well known fact that antennas behave differently when excited with differently polarized electromagnetic waves. This effect has significant importance in the field of direction finding since each antenna array comprises a pair of polarimetric array manifolds. Consequently, this fact has also to be taken into account when calculating Cramer-Rao Lower Bounds (CRLBs) for direction of arrival (DoA) estimation. However, the polarimetric behavior of the antenna array is not always taken into account in the literature. This may lead to unrealistic results especially in cases where calibration data of real antenna arrays are used. To this end, we demonstrate three different reception models suitable for direction of arrival estimation. The first model, although widely used in the DoA estimation community, does not inherently incorporate polarization effects. The second model incorporates the waves' states of polarization but treats this information as nuisance parameters. The third type of model includes the states of polarization into the set of parameters to be estimated. We give CRLBs for each of the models presented in this work. Additionally, we also give the reduced CRLB that only calculates parameters that are of interest. Moreover, our CRLBs are based on the constrained CRLB using the Moore-Penrose pseudoinverse of the Fisher information matrix (FIM).