Scalar and vector multistatic radar data models

Abstract

In the second part of the thesis we develop a vector multistatic data model incorporating polarization and antenna effects from transmitters and receivers modeled as long thin dipoles. We derive the model beginning with the potential formulation of Maxwell's equations and describe radiation from a transmitting antenna, scattering from a moving target, and reception at a receiving antenna in both the time and frequency domains. This model is developed from beginning to end with the transmit waveform and scattering behavior of the target left arbitrary and we obtain physical intuition, greater understanding and control of assumptions, and the ability to carefully model the desired multistatic scenario by formulating our data model from first principles. Following formulation of the data model we derive two imaging operations that combine the data collected at each receiver, first assuming that the contributions from all transmitters in the scene are separable and then assuming that the contributions from all transmitting antennas cannot be separated and must be treated as a unit.

We then utilize the presented data model and imaging operations to simulate multiple antenna geometries and transmission schemes. Scattering behavior of the target is modeled with both a bistatic scattering matrix based on physical optics for a perfectly electrically conducting flat rectangular plate and a general complex scattering matrix. Simulations exhibit the angle and polarization dependent scattering behavior and cross-polarization of the incident electric field consistent with the scattering models. The images formed under both the separable and nonseparable assumptions are comparable when waveforms with low cross-correlation are used. We approach the multistatic radar problem by combining an electromagnetic data model with signal processing to obtain an image, but the data model can also be used to generate high-quality data for a variety of applications.

The aim of this thesis is to further the theory for multistatic imaging of moving targets through the development and simulation of scalar and vector radar data models and accompanying imaging operations. In the first part of the thesis we investigate scalar representations of multistatic radar data. We begin by comparing two different approaches for developing a multistatic ambiguity function (MAF), a tool used to assess performance of the waveforms and geometry of a multistatic radar system jointly. One approach is deterministic in nature, originating from the scalar wave equation, and the other is statistical, relying on a Neyman-Pearson defined weighting of received data. Although the two methods are fundamentally different in formulation, they are shown to yield similar results. We then build on the data model for the existing deterministically derived MAF with the inclusion of antenna beam patterns by relating the current density on the radiating and receiving antennas to a far-field spatial weighting factor. From this model we develop an imaging formula in position and velocity that can be interpreted in terms of filtered backprojection or matched filtering and a corresponding ambiguity function or point-spread function. We use the resulting data model and MAF to examine scenarios with various geometries and transmit waveforms and we show that the performance of a multistatic system depends critically on the system geometry and transmitted waveforms.