Monday, 22 October 2012

The Doppler effect on satellite signals

Everyone is familiar with the Doppler effect in sound waves—the varying pitch of a police car siren as it speeds past you. The Doppler effect also occurs for other types of waves such as radio waves. However, since the speed of light is much larger than the speed of sound, you have to be moving a lot faster to experience it. Satellites orbit the earth pretty fast: 30 kilometres per second (at 400km altitude). At these speeds, the Doppler effect is significant.

The Doppler frequency shift is
Δf = - fvrelative c,
where f0 is the rest frequency, vrelative is the relative velocity between you and the satellite, and c is the speed of light.

For a typical cubesat using UHF frequencies,  f0 = 437 MHz and vrelative varies from -7 km/s to +7 km/s. Thus, Δf varies from -10 kHz to +10 kHz.

Here is a spectrogram of FITSAT-1's Morse beacon that was recently received by a Carpcomm Ground Station 1:


At this resolution, you can easily read off the Morse dots and dashes. But more interestingly, notice how the frequency decreases over time. This is exactly due to the Doppler effect! The frequency decreases as the satellite flies away with increasing relative velocity as it nears the horizon. The green curve is the predicted Δf calculated from the satellite's orbital parameters (essentially using Newton or Kepler's laws).

This is how it sounds:



Because of this frequency shift, you can't just tune to a fixed frequency to decode the signal. You need to continuously track it as it varies during the pass. The Carpcomm cloud software-defined radio processing system has built in algorithms for doing this so that you don't have to worry about it.

Big Bang Theory Reference

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