Resolution and sidelobe structure analysis for RF tomography

Abstract

Abstract-Radio frequency (RF) tomography utilizes a network of spatially diverse sensors to trade geometric diversity for bandwidth, permitting images to be formed with narrowband waveforms. Such a constellation of sensors produces a sparsely and irregularly spaced set of Fourier space samples, complicating the definition and analysis of resolution for these systems. We present an analysis of resolution for RF tomography based on the Cramér Rao Bound (CRB) for estimation of target position and velocity. This approach allows the resolution for a given sensor configuration to be determined with minimal computational cost, thus providing a useful design tool for sensor placement and frequency selection for RF tomography. We also explore the impact of Fourier space "filling" with bistatic geometries on sidelobe structure of the ambiguity function. Several simulation results are presented to validate the resolution calculations from the CRB and to illustrate the importance of sensor placement for RF tomographic imaging.

Resolution optimization with irregularly sampled Fourier data

“…Specifically, we prove that the area of the CRLB uncertainty ellipse defined by the corresponding Fisher information matrix (FIM) [19] is directly proportional to the half-peakpower contour of the quadratically approximated imaging PSF when a uniform DCF is used. The PSF-CRLB equivalence proof provides a theoretical validation of previous experimental comparisons [20,21] between PSF isocurves and the CRLB ellipse. Section 4 first describes the Frobenius objective K w (z, z ) − δ(z, z ) 2 F originally used by Fang et al [16], then the method is extended to included additive measurement noise, leading to a modification which properly combines information from the sample geometry with a priori knowledge of the signal-to-noise ratio (SNR).…”

“…The algorithms in this paper are written in terms of pixel-independent Fourier locations as in (21), but can easily be applied in a pixel-dependent fashion to account for spherical wavefronts and/or undulating terrain maps.…”

“…. , 1] T , (33) collapses to the area of the Cramer-Rao uncertainty ellipse for positional error (see, e.g., [21]) when data are considered Fourier samples for a point scatterer in additive white Gaussian noise. Consider a single point scatterer located at unknown position z with unit scattering strength.…”

“…This implies that the volume of the (quadratically approximated) PSF isocurve and the volume of the Cramer-Rao positional error ellipse must also be proportional up to a noise-level-dependent scale factor. Specifically, as noted in [21], the volume of the positional error ellipsoid can be computed as…”

Sub-Aperture Partitioning Method for Three-Dimensional Wide-Angle Synthetic Aperture Radar Imaging with Non-Uniform Sampling

“…Furthermore, after partitioning Fisher information matrix, the CRLB sub-matrix CRLB xyz of the target position (x, y, z) was obtained through matrix decomposition and matrix inversion [24]…”