Hello guys.

So a little background to explain
my problem. I work for a company that provides Internet
on board high speed train. For that we use a satellite
link. As you can imagine we face a Doppler shift
when the train is moving.

I would like to
be able to reproduce the Doppler shift in lab to
be able to test satellite technology without having
to go on a train to face the Doppler shift. At around
12.5 GHz (Ku Band) the Doppler shift is about 3.5
KHz (with a train running at 83.3 m/s). As i can
only integrate a device after the LNB, i have to
works in L Band. However the Doppler shift as to
be the same.

I want to reproduce the worst
case frequency shift, so the shift has to remain
constant (which simplify my problem).

Then
only way i see to create that is by creating a constant
phase derivation with a device like a Digital Phase
Shifter on the IF signal (L Band after transposition
by the LNB) since a phase derivation results in
a frequency shift.

Where i got stuck is
when i try to put numbers on the derivation i have
to apply on my signal. Using the formula of the
Instantaneous Frequency and the Instantaneous Phase
and after integration i came to:

Phi(t)=
2*PI*Fo*t + 2*PI*Fshift*t

Phi(t) being the
instantaneous phase

Fo being the original frequency

Fshift being the Doppler shift

From that
i conclude that:

Phi(t) = Phio(t) + PhiShift(t)

Phio(t) being the instantaneous phase of Fo

PhiShift(t) beinf the instantaneous phase of Fshift

Then i conclude that:

PhiShift(t) = 2*PI*Fshift*t

It appaers then that to create a frequency shift,
i need to apply a constant phase derivation over
which is TOTALLY independant from the frequency
i am working at. For example, whatever i am working
at 12.5 Ghz or at 1.2 Gz (after conversion by the
LNB with a LO@11.3Ghz) which sound to me a bit...
wierd.

I must miss something somewhere but
i can't figure out what and where. Can someone help
me with this understanding?