FDM MIMO Spaceborne SAR Tomography by Minimum Redundancy Wavenumber Illumination

This work investigates a new concept to finely resolve the vertical structure of natural media, such as snow, ice, and vegetation, by using a formation of spaceborne synthetic aperture radars (SARs) mounted onboard different satellites. The formation is assumed to operate in multiple-input-multiple-output (MIMO) mode by implementing a frequency-division multiplexing (FDM) access scheme, where all satellites transmit simultaneously on different frequency bands and receive the echoes scattered by the Earth's surface in all transmitted bands. In doing so, a formation on N satellites is used to produce N-2 SAR images. By the principle of diffraction tomography, each of these images represents a distinct set of wavenumbers, i.e., a distinct region of the spatial spectrum of the observed scene. The vertical separation between any two sets of wavenumbers defines the interferometric differential wavenumber, which determines the sensitivity of that particular pair to the vertical structure of the observed scene. Fine vertical resolution is achieved by developing a novel approach to set the satellite positions in such a way that the resulting interferometric differential wavenumbers form an almost uniformly spaced array of maximum length under the constraint of a given height of ambiguity and interferometric coherence magnitude. As a result, we show two examples where formations of four or five satellites are deployed to provide the equivalent of 17 and 26 monostatic acquisitions, respectively. Such figures are comparable to the best airborne and ground-based systems available as of today and indicate the concrete possibility to image the vertical structure of natural targets from space at fine resolution. The concept here developed to deploy the formation is referred to as minimum redundancy wavenumber illumination (MRWI), as it is shown to be a generalization to distributed targets of the principle of minimum redundancy virtual array (MRVA) used in array theory. The analysis is supported by results from synthetic data generated by numerical simulations.