It was a difficult decision to accept, but the Mars Express experiment with the USRP and GNU Radio is not going to happen this time!
It’s a shame because the link budget looked quite promising. An optimistic estimate gives almost 20 dB signal to noise ratio, which is more than we need, so the problem is not there. The problem is with the X-band down converter. I was looking at the KU LNC 8084 from Kuhne, which together with the KU LNA 133 BH low noise amplifier gives a total G/T of more than 30 dB/K. Unfortunately, there are two problems with this down converter:
- The price is slightly above what my budget can allow here and now
- There is a 2 week delivery time
For the sake of the experiment I could have lived with either one of the two, but not both. I know, I know… the two weeks are so close that I might even get lucky and receive it in time. But it would need to be in my hands on Tuesday, March 2, preferably on Monday to allow proper integration and testing, and that is closer to 10 days than to 14.
Using the S-band signal is not very promising either. Here, the link budget doesn’t go up due to the low power of the transmitter (5W). We can get a few dB above the noise floor if we use a filter no wider than 10 Hz – and that’s no fun when you are trying to measure Doppler shift.
Concerning the Doppler shift, I have been looking at the ephemeris generated by JPL Horizons web interface. At this time of the year, Mars and Earth are moving away from each other so the Doppler shift will be dominated by the range rate between the two planets. The orbit of Mars Express around Mars can be observed by this Doppler shift oscillating between two values. On March 3, the oscillation will be roughly between 7.3 to 12.5 km/s resulting in a Doppler shift between 200 and 350 kHz with a period of 7 hours:
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Date__(UT)__HR:MN Azi_(a-appr)_Elev delta deldot S-O-T /r
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2010-Mar-03 12:00 *r 44.3857 0.0718 0.78932354310229 11.1852087 137.6854 /T
2010-Mar-03 12:30 * 50.5231 3.1913 0.78946087508986 11.6142978 137.6635 /T
2010-Mar-03 13:00 * 56.5265 6.5964 0.78960254573254 11.9176387 137.6415 /T
2010-Mar-03 13:30 * 62.4270 10.2445 0.78974736351007 12.1426231 137.6193 /T
2010-Mar-03 14:00 * 68.2648 14.0936 0.78989453336189 12.3108050 137.5969 /T
2010-Mar-03 14:30 * 74.0891 18.1025 0.79004342478087 12.4288177 137.5742 /T
2010-Mar-03 15:00 * 79.9584 22.2300 0.79019340567595 12.4891937 137.5514 /T
2010-Mar-03 15:30 * 85.9418 26.4339 0.79034362769204 12.4603569 137.5283 /T
2010-Mar-03 16:00 * 92.1210 30.6697 0.79049254590969 12.2459365 137.5050 /T
2010-Mar-03 16:30 * 98.5934 34.8883 0.79063632341205 11.5023192 137.4814 /T
2010-Mar-03 17:00 C 105.4752 39.0329 0.79076193096873 8.8729735 137.4577 /T
2010-Mar-03 17:30 N 112.9049 43.0339 0.79085460119582 7.7994185 137.4351 /T
2010-Mar-03 18:00 N 121.0408 46.8078 0.79096079023597 9.7083822 137.4134 /T
2010-Mar-03 18:30 A 130.0480 50.2537 0.79108469006353 10.7829081 137.3915 /T
2010-Mar-03 19:00 140.0731 53.2460 0.79121862213031 11.4324332 137.3693 /T
2010-Mar-03 19:30 151.1869 55.6385 0.79135901132806 11.8780500 137.3470 /T
2010-Mar-03 20:00 163.3031 57.2784 0.79150401404296 12.2087075 137.3244 /T
2010-Mar-03 20:30 176.1098 58.0358 0.79165251591848 12.4639928 137.3017 /T
2010-Mar-03 21:00 t 189.0909 57.8425 0.79180373020367 12.6611863 137.2789 /T
2010-Mar-03 21:30 201.6721 56.7165 0.79195699075542 12.8035934 137.2558 /T
2010-Mar-03 22:00 m 213.4087 54.7551 0.79211158678530 12.8795690 137.2326 /T
2010-Mar-03 22:30 m 224.0838 52.1019 0.79226652008935 12.8488984 137.2092 /T
2010-Mar-03 23:00 m 233.6851 48.9097 0.79241990790189 12.5882130 137.1856 /T
2010-Mar-03 23:30 m 242.3230 45.3178 0.79256684230434 11.6337681 137.1618 /T
2010-Mar-04 00:00 m 250.1570 41.4426 0.79269056949806 8.4958690 137.1381 /T
2010-Mar-04 00:30 m 257.3492 37.3764 0.79278746204570 8.6897914 137.1158 /T
2010-Mar-04 01:00 m 264.0503 33.1954 0.79290340477852 10.4123533 137.0940 /T
2010-Mar-04 01:30 m 270.3909 28.9637 0.79303487629095 11.3531489 137.0722 /T
2010-Mar-04 02:00 m 276.4794 24.7346 0.79317518946651 11.9281843 137.0502 /T
2010-Mar-04 02:30 m 282.4067 20.5555 0.79332120377351 12.3189920 137.0281 /T
2010-Mar-04 03:00 m 288.2493 16.4696 0.79347121486610 12.6006078 137.0058 /T
2010-Mar-04 03:30 m 294.0717 12.5188 0.79362414053192 12.8071911 136.9835 /T
2010-Mar-04 04:00 Am 299.9287 8.7442 0.79377918105395 12.9534316 136.9610 /T
2010-Mar-04 04:30 Am 305.8659 5.1872 0.79393563141900 13.0406358 136.9384 /T
2010-Mar-04 05:00 Nm 311.9199 1.8902 0.79409271234490 13.0538218 136.9157 /T
Delta is the range in AU, deldot is the range rate in km/s. The S-O-T parameter is also interesting in general because it gives the angle between the Sun and the target as seen from the observer. It is important because having the Sun in the field of view of the antenna can increase the sky noise significantly.
The interesting question is still the magnitude of the perturbations caused by Phobos. 1 Hz? 10 Hz? 100 Hz? I don’t know but I am trying to convince myself that a relative Doppler shift of 10 Hz should be detectable with the USRP and GNU Radio, provided that the local oscillator of the down converter is stable. Fortunately, this is an experiment that I can do!