Deterministic CRB and manifold ambiguity analysis for polarization sensitive arrays

Direction-of-arrival (DOA) and polarization estimation based on polarization sensitive arrays is a meaningful topic in the field of array signal processing. In this paper, the closed- form Cramer-Rao bounds (CRBs) for arbitrary polarimetric array configurations, under the deterministic signal assumption, are derived for known and unknown waveforms. In terms of the manifold ambiguity, the existence as well as the necessary and sufficient conditions of trivial ambiguity are investigated for arrays with identical vector sensors. Moreover, taking a uniform linear array (ULA) with tripoles for instance, the explicit expression of the deterministic CRB, in terms of 2D DOA and polarization parameters, is presented for the single source case. Then the concrete parameters resulting in trivial ambiguity are given, which further reveals a link between the CRB and the ambiguity of spatial-polarization steering vectors. Finally, the above theoretical analyses are verified through simulation results.