# Coherent Radar — How do we justify it?

How can we justify doing coherent radar when the phase of the return is unknown?

For instance, after a reflection, assuming a stationary target, we should get something akin to:

$$x_{rx}(t) = |\alpha| e^{\angle\alpha} x_{tx}(t) = |\alpha| e^{j 2 \pi f_{tx} t + \phi_{tx} + \angle \alpha}$$

however $$\alpha$$ is generally unknown. It is highly dependent on the material of the target, the angle of the waveform's impingement, and the frequency bands used.

So why do we not always do incoherent radar? Why do all these methods for coherent radar exist? Where are they useful?

• Consider FMCW radar where we transmit a chirp and determine range to target based on the frequency difference between the local oscillator and the reflected signal. How would you do that non-coherently and how would the range accuracy compare? – Dan Boschen Dec 5 '19 at 18:27