# Crowded Space: A Review on Radar Measurements for Space Debris Monitoring and Tracking
## 3 US SSN Radar Measurements
Interestingly enough, the radar measurements of the smallest debris tracked were used to demonstrate the non-spherical shape of the debris by comparing the detected RCS at different frequencies, as shown in Figure 3. As can be seen from the figure, the RCS of the object scales with the frequency. Figure 1: Results from TRADEX 1994 state-and-chase activities [14]. Reprinted with permission courtesy of MIT Lincoln Laboratory, Lexington, Massachusetts. Figure 2: Results from ALTAIR 1994 tracking activities [14]. Reprinted with permission courtesy of MIT Lincoln Laboratory, Lexington, Massachusetts. Another important US SSN facility, with plenty of information published in the open literature, is the Haystack radar. As for the KREMS radars, the Haystack is a collateral sensor within the SSN [12]. The Haystack radar is a monopulse X-band (10 GHz) 36 m diameter tracking radar located in Tyngsboro, MA [16,17]. It can operate in two different modes based on the waveform code, with a peak power of 400 kW, and it is able to detect a piece of debris as small as 1 cm diameter in beam park mode at ranges greater than 1000 km [16,17]. Between 1990 and 1994, the Haystack radar was employed to collect data from space debris for nearly 2500 h [16]. The data were collected taking into account different elevation (el)/azimuth (az) angles: 90\({}^{\circ}\) el, 20\({}^{\circ}\) el/180\({}^{\circ}\) az, and 10\({}^{\circ}\) el/180\({}^{\circ}\) az. In 1993, two more staring angles were added: 20\({}^{\circ}\) el/90\({}^{\circ}\) az, and 90\({}^{\circ}\) with extended range. Figures 4 and 5 show the results of the debris campaign in terms of altitude vs. inclination and altitude vs. diameter. The debris are clustered between 350 and 1600 km altitude, with diameters between 0.003 m and 7 m.  
Figure 4: Altitude vs. inclination at different elevation angles for 1990–94 Haystack radar measurements [16]. Reprinted from Advances in Space Research, copyright 1995, with permission from Elsevier. Figure 3: Results from joint debris tracks for the smallest debris, comparing VHF (ALTAIR), L-band (TRADEX), and C-band (ALCOR) radar cross section (RCS) vs. UHF (ALTAIR) RCS [14]. Reprinted with permission courtesy of MIT Lincoln Laboratory, Lexington, Massachusetts. Data from the latter measurement campaign, after the insertion of the two additional staring angles, were integrated with the debris population detected by the Haystack Auxiliary radar (HAX), after 1993. The HAX is a 12 m parabolic dish also located in Tyngsboro [18]. Its operating frequency is higher than the Haystack, at 16.7 GHz, and it is able to transmit a circularly polarized signal with a peak power of 40 kW [18]. The HAX is complementary to the Haystack radar, having a wider field of view but less sensitivity. An aggregate of 263.1 h of data collected by the Haystack radar (with 75\({}^{\circ}\) el/90\({}^{\circ}\) az pointing angle) and 372.1 h of data collected by the HAX in 1994, were compared in terms of debris flux and discrimination from altitude intervals. In Figure 6, the debris flux measurement comparison between the two collected populations is shown as a function of debris diameter. The model reported in these figures refers to ORDEM96 and the old NASA debris environmental model. Specifically, Figure 6a shows an overlap of the Haystack and HAX curves for sizes from about 1 to 4 cm; however, below 1 cm the HAX curve starts to flatten (which indicates a zero detection probability), whereas the Haystack curve maintains its  
Figure 5: Altitude vs. diameter at different elevation angles for 1990–94 Haystack radar measurements [16]. Reprinted from Advances in Space Research, Copyright 1995, with permission from Elsevier. Figure 6: Comparison of Haystack and HAX measured debris size distributions for the altitude intervals 450–550 km (**a**) and 850–950 km (**b**) [18]. Reprinted from Proceedings of the Second European Conference on Space Debris, Copyright 1997, with permission from NASA. slope until 3-4 mm.