Thermal noise in the ground and spacecraft receivers

4.7 Thermal noise in the ground and spacecraft receivers

Finite signal-to-noise ratios in the up- and downlinks cause white phase noise. For observations to date, the signal-to-noise ratio (SNR) of the downlink dominates. The one-sided spectral density of phase fluctuations due to finite SNR, $S φ$ , is $≃$ 1 / (SNR in 1 Hz band) rad² Hz^–1. The associated Allan deviation [23

] is $∘ ------ ≃ 3BS φ ∕(2πν0τ)$ , where $B$ is the bandwidth of the detection system and assuming $2πB τ ≫ 1$ . For Cassini gravitational wave observations, B is typically $≃$ 1 Hz and the typical X- or Ka-band SNR in a 1 Hz bandwidth can be 45 dB or more. At $τ$ = 1000 s finite link SNR contributes negligibly to the overall noise budget in current generation Doppler experiments (see Table 2).