System model of doppler shifted laser

Hello all,

I am trying to model a received laser signal, x(t), reflected off a moving target. I am currently trying to model for both frequency change due to Doppler shifting as well as a time-varying phase shift, θ(t), due to the continuous change in distance from the target. My current model is as follows:

x(t) = cos(2∏(f+f0(t))t + θ(t)),

where f0(t) is the Doppler effect at time t and θ(t)=(distance at time t)/wavelength. I do not assume constant velocity so the f0(t) may change over time. It appears that trying to simulate both phase and frequency shifts simultaneously does not accurately model what I expect.

If there is a constant velocity it will introduce a constant frequency shift. However, if there is a constant velocity, this implies the target is in motion and therefore the phase constantly changes with respect to the distance from the target. In turn, the constant phase change appears to offset the frequency change.

I am not sure if this physical model is correct. Any comments or suggestions are welcome. Thank you.