Multistatic passive polarimetric radar imaging

Abstract

This thesis studies the exploitation of polarimetric diversity in passive radar imaging. To this end, we develop a novel polarimetric data model and show that by exploiting polarimetric diversity, passive radar can better exploit spatial diversity than that of polarimetrically non- diverse case and hence improve its performance. We also present and study optimization- based algorithms applied to simultaneous recovery of reflectivity and polarization states of extended targets.

Next, we apply a generalization of the Wirtinger flow algorithm, recently developed and analyzed by Yonel et. al., to the multistatic radar imaging problem, as an efficient alternative to low-rank matrix recovery. Leveraging the theoretical work by Yonel et. al., we establish that the lifted data model for the multistatic radar satisfies the sufficient condition for exact recovery by the generalized Wirtinger flow. This exact recovery result is limited to the data model that does not take polarimetry into account. However, we show that application of the algorithm to polarimetric data for simultaneous recovery of polarization state and reflectivity is straight forward. Furthermore, our result has broader implications for multistatic passive radar as it shows that the data model satsifies the restricted isometry property for rank- 1 real positive semi-definite matrices. Simulated experiments are provided to verify the theoretical result. We also perform a comparison study with LRMR method and show that generalized Wirtinger flow outperforms LRMR for the extended target reconstruction task under multistatic passive radar scenario.

The second part of the thesis explores the reconstruction of extended targets. First, we leverage the inherent fourth order tensor structure of the lifted scene to simultaneously recover polarization state and reflectivity of extended targets for a polarimetrically diverse multistatic passive radar setting. We show that the problem can be recast as a low-rank matrix recovery (LRMR) problem and solve it using forward-backward splitting algorithm.

Next part of the thesis mathematically analyzes the detection performance under this scheme in terms of signal/system parameters. We perform the analysis in both asymptotic (as number of data samples go to infinity) and non-asymptotic regimes under a specified figure-of-merit. In each case, we compare the detection performance between the case with polarimetric diversity and the case without. Simulations are performed to validate the idea that exploiting polarimetric diversity improves detection performance.

In the first part of this thesis, a polarimetric data model for targets in linear motion is derived from first principles by modeling anisotropic scattering explicitly. The data model is then used in a detection scheme under a generalized likelihood ratio test (GLRT) frame- work. In addition, we derive a method of estimating the target’s polarization state in this framework. We consider two cases unified under the GLRT framework: 1) A case where we have direct-path signals available. That is, where we have additional signals gathered from antennas pointed in direct-line-of-sight to a source of opportunity. 2) A case where we do not have such signals available.