I am currently doing a project in the area of optical inter-satellite communication (GEO-LEO).
I am using a optical carrier of 281 THz, and the Doppler shift corresponding to it is ±7 GHz. I introduced this Doppler shift in the transmitted signal $S$ as an offset like
$$ S \cdot e^{j 2 \pi f_\mathrm{doppler}} $$
At the receiver, I am using a Costas Loop as a demodulator. I have to do Doppler shift compensation to recover the signal. Guess, I have to add an offset compensator in the local oscillator.
Can anybody help me in doing this?