Manifold Ambiguity and Performance Analysis for Electric-Measurement-OnlyPolarization Sensitive Arrays

Direction-of-arrival and polarisation estimation is an important issue in array signal processing. Among various polarisation sensitive arrays (PSAs), arrays with only measurements of the electric field are most extensively applied in practice. In this study, the manifold ambiguity of such electric-measurement-only PSA is investigated to evaluate the uniqueness of parameter estimation. For co-centred PSAs and spatially-spread PSAs, the necessary and sufficient conditions of linearly dependent steering vectors are established based on the cosine similarity. Furthermore, for various arrays, the explicit parameter sets corresponding to trivial manifold ambiguity are provided. Moreover, for the noisy case, the closed-form Cramer-Rao bounds for arbitrary PSAs are also presented to evaluate the performance bound of parameter estimation with the considered arrays. Simulations and experimental results of high-frequency radar further reveal the influences of array configurations on the identifiability and performance bound of PSAs, and verify the corresponding theoretical results. The presented results can be easily generalised to other PSAs containing magnetic measurements, which provide guidelines for designing the spatial and polarimetric configuration of PSAs to ensure unambiguous and accurate parameter estimation.