Doppler Synthetic Aperture Radar Interferometry: A Novel SAR Interferometry for Height Mapping using Ultra-Narrowband Waveforms
Birsen Yazıcı1,∗, Il-Young Son1 and H. Cagri Yanik
Abstract. This paper introduces a new and novel radar interferometry based on Doppler synthetic aperture radar (Doppler-SAR) paradigm. Conventional SAR interferometry relies on wideband transmitted waveforms to obtain high range resolution. Topography of a surface is directly related to the range difference between two antennas configured at different positions. Doppler-SAR is a novel imaging modality that uses ultra-narrowband continuous waves (UNCW). It takes advantage of high resolution Doppler information provided by UNCWs to form high resolution SAR images.
We introduced the theory of Doppler-SAR interferometry. We derived interferometric phase model and develop the equations of height mapping. Unlike conventional SAR interferometry, we show that the topography of a scene is related to the difference in Doppler between two antennas configured at different velocities. While the conventional SAR interferometry uses range, Doppler and Doppler due to interferometric phase in height mapping, Doppler-SAR interferometry uses Doppler, Doppler-rate and Doppler-rate due to interferometric phase in height mapping. We demonstrate our theory in numerical simulations.
Doppler-SAR interferometry offers the advantages of long-range, robust, environmentally friendly operations; low-power, low-cost, lightweight systems suitable for low-payload platforms, such as micro-satellites; and passive applications using sources of opportunity transmitting UNCW.
Synthetic Aperture Radar (SAR) interferometry is a powerful tool in mapping surface topography and monitoring dynamic processes. This tool is now an integral part of wide range of applications in many disciplines including environmental remote sensing, geosciences and climate research, earthquake and volcanic research, mapping of Earth’s topography, ocean surface current monitoring, hazard and disaster monitoring, as well as defense and security related research .
Basic principles of SAR interferometry were originally developed in radio astronomy [2, 3]. Interferometric processing techniques and systems were later developed and applied to Earth observation [4, 5, 6, 7, 8].
SAR interferometry exploits phase differences of two or more SAR images to extract more information about a medium than present in a single SAR image  . Conventional SAR interferometry relies on wideband transmitted waveforms to obtain high range resolution [10, 1, 11, 12, 13]. The phase difference of two wideband SAR images are related to range difference. There are many different interferometric methods depending on the configuration of imaging parameters in space, time, frequency etc . When two images are acquired from different look-directions, the phase difference is related to the topography of a surface.
In this paper, we develop the basic principles of a new and novel interferometric method based on Doppler-SAR paradigm to determine topography of a surface. Unlike conventional SAR, Doppler-SAR uses ultra-narrowband continuous waves (CW) to form high resolution images [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]. Conventional SAR takes advantage of high range resolution and range-rate due to the movement of SAR antenna for high resolution imaging. Doppler-SAR, on the other hand, takes advantage of high temporal Doppler resolution provided by UNCWs and Doppler-rate for high resolution imaging.
We develop the phase relationship between two Doppler-SAR images and show that the phase difference is related to Doppler difference. We approximate this phase difference as Doppler-rate and derive the equations of height mapping for Doppler-SAR interferometry.
Conventional wideband SAR interferometry for height mapping requires two different look-directions. Doppler-SAR interferometry provides a new degree of freedom in system design by allowing antennas to have the same look-direction, but different velocities to obtain height mapping. Additional advantages of Doppler-SAR interferometry include the following: (i) Small, lightweight, inexpensive, easy-to-design and calibrate hardware, high Signal-to-Noise-Ratio(SNR) and long effective range of operation. All of these make Doppler-SAR interferometry a suitable modality for applications requiring high SNR, long range of operation and low payload platforms such as micro-satellites or small uninhabited aerial vehicles. (ii) Effective use of electromagnetic spectrum and environmentally friendly illumination. (iii) Passive applications. Doppler-SAR may not require dedicated transmitters, since existing Radio
Frequency (RF) signals of opportunity often have the ultra-narrowband properties.
To the best of our knowledge, this is the first interferometric method that is developed in Doppler-SAR paradigm. We present the theory for two monostatic Doppler-SAR. However, the method can be easily be extended to bistatic and multi-static configurations and synthetic aperture imaging applications in acoustics.
The rest of the paper is organized as follows: In Section 2, SAR geometry and notation are defined. In Section 3, wideband SAR image formation, layover effect and basic principles of wideband SAR interferometry are described in a perspective relevant to our subsequent development. In Section 4, Doppler-SAR data model, image formation and layover are summarized. Section 5 introduces the basic principles of Doppler-SAR interferometry and compares the results to wideband SAR case. Section 6 presents numerical simulations and Section 7 concludes the paper.