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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.

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