Mathematical Model for Developing Ideal Synthetic Aperture Radars

Researchers from the Skolkovo Institute of Science and Technology (Skoltech) and the Massachusetts Institute of Technology (MIT) have collaborated to develop a model aiming to assist engineers in creating and selecting the most potential conceptual designs of satellite radar systems.

Mathematical Model for Developing Ideal Synthetic Aperture Radars.

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Alessandro Golkar and Ksenia Osipova from Skoltech and Giuseppe Cataldo, a former student from MIT who is currently working at the Goddard Space Flight Center in NASA, contributed to the study.

The optimization of the designs of these quickly evolving instruments promotes faster and more efficient capabilities of the model in the better mapping and monitoring of storms, floods and landslides.

The study was published in the journal Acta Astronautica.

Satellite imaging of the Earth was employed to monitor agriculture land use, coastal change, ocean ice cover and hostile weather events. These observations are done in different bands of the electromagnetic spectrum, including radio waves. Different from optical or infrared imagers, radars track targets independently concerning their illumination, bypass clouds, and usually operate well in any weather.

The radar needs to be physically larger to offer the same resolution as shorter wavelength instruments. This requirement makes it hard to mount in a satellite. One possible solution is using synthetic aperture radars.

SARs obtains high resolution by artificially enhancing their aperture or antenna “size.” Affixed on a satellite, a SARs emits a radar pulse and travels a specific distance before the pulse returns and is received at a different location. The distance traveled is then factored into the virtual size of the antenna, as if it were much larger, which translates into a better image quality with a comparatively small antenna.

SARs is equipped historically on large and expensive satellite despite its aperture inflation trick because the radars are bulky and consume a lot of power. This factor has been changing with the development of smaller and lighter SARs. The technology is in the early stages of development but is evolving at a faster pace, already finding applications in oil spill detection and surveillance.

With the increasing number of smaller satellites in the orbit, SARs engineers are searching for the one that is a feasible carrier for miniaturizing radars. This news is certainly relevant as a recent study presents dozens of so-called micro- or nanosatellite-based SARs operations that together could broadly outperform traditional large SAR projects, considering cost-efficiency.

With the available range of extensive options, it is becoming more difficult to balance radar performance characteristics against other properties of a SAR launch mission. A few of the available variables are the orbits, radar and satellite models, with their physical dimension and an array of characteristics, including power consumption and data rate.

This complexity demands a computational technique to support the future designs of SARs-based Earth observation missions.

To fulfill this requirement, a study led by Skoltech demonstrated a mathematical model for developing ideal SARs conceptual designs. The model optimizes SARs properties with an approach called trade space exploration.

This term, which is a combination of “trade-off” and “playspace,” means that the model will support the designer in the early stages of the analysis of the several trade-offs involved in the process. This enables quick evaluation of several design alternatives and identification of ideal solutions to pursue.

The study proposes the applications of the model by looking at radar instruments on a wide range of small satellite platforms. A total of 1265 feasible radar designs were screened to find 44 optimal ones for different radio frequencies. The researchers concluded that the small satellites are a feasible platform for the higher frequency range of 8 to 12 GHz and 4 to 8 GHz radars, but not for the 1 to 2 GHz band.

The conditions for producing the latter type of feasible SARs are discussed along with feasibility bounds and technical limitations on the associated instruments and spacecraft requirements. Pulse repetition frequency is the key limiting factor on the SARs trade space. in other words, this is the most powerful factor - ahead of power consumption, antenna size, data rate, etc. - for screening the radar configuration to a limited array of feasible designs.

In a different analysis, the researchers consider radars for the very small 3U CubeSat platform, identifying 44 optimal designs among about 13,000 feasible candidates. The research unravels the operational limitations needed for the development of such innovative miniaturized radars.

The researchers concluded that SARs for CubeSats are feasible from an instrument-level perspective and suggest their design for the application at the mission level, together with the usage in spacecraft design.

The model exhibited in the study is applicable for radar systems mounted on a single satellite. It is also possible to extend the capability for the future, for combining SAR satellites into constellations.

Journal Reference:

Golkar, A., et al. (2021) Small satellite synthetic aperture radar (SAR) design: A trade space exploration model. Acta Astronautica.


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