A method for calculating lateral surface area of bistatic radar beam overlap

Abstract

It has been shown that bistatic radars using radio telescopes as receivers can be used to increase the sensitivity of orbital debris measurements over traditional terrestrial monostatic radar. A method to calculate the lateral surface area of a bistatic radar is needed to evaluate the efficacy of a proposed bistatic radar configuration for orbital debris measurements. For over three decades, models of the orbital debris (OD) environment in low Earth orbit (LEO) have been developed to assess the risk posed by OD to spacecraft. While terrestrial radar measures debris 3 mm and larger and in situ measurements provide data for debris smaller than 1 mm, no good data sources exist for debris between 1 mm and 3 mm in size. This results in large variations between competing OD models. It also happens to be the size regime which poses the highest mission-ending risk to spacecraft. It is, therefore, of interest to investigate potential new data sources for this under-sampled size regime. There are many radars and radio telescopes that could be combined to create sensitive bistatic radars that could potentially bridge the size gap. In addition to sensitivity, it is necessary to predict the expected count rate of a candidate sensor to evaluate its performance. NASA’s Orbital Debris Engineering Model (ORDEM) can be used to predict the flux of debris passing through the line of sight of a radar or telescope. This flux is related to a count rate through the calculation of the lateral surface area of the sensor. While this can be done easily for monostatic radars, a method for calculating the lateral surface area of a bistatic radar is needed. This new method of calculation has been developed and is described. The new method maps the radar beam overlap in 3D space, calculating the area of the complex surface formed by the gain product of the two antennas. Comparisons of the monostatic and new bistatic lateral surface area calculation methods for the monostatic case are presented. Results of a sample lateral surface area calculation for a bistatic radar observation configuration currently employed by NASA are shown. Finally, a guide for total error as a function of baseline and target altitude is established.