# Maximum Range of FMCW Radar

I am performing some simulations for FMCW radar for target detection. I am working with a dechirp on receive system. Therefore, the target distance can be determined from the Intermediate Frequency or beat frequency.

$$F_{beat} = \frac{\text{rate}_{\text{chirp}} \cdot 2 \text{dist}_{\text{target}}}{c}$$

I realised that the maximum theoretical distance that can be detected by the radar is determined by $$F_s$$ (sampling frequency). What is the relationship between the two? Is there a particular formula or concept that links both parameters?

They are related, and their relationship is so subtle that you may not realize that your equation already shows the relationship. Let's make the relationship explicit between the generated beat frequencies $$f_b$$ and the chirp with pulse width $$\tau$$ and bandwidth $$\beta$$:
$$f_b = \frac{2R\beta}{c\tau}$$
If everything remained the same, then processing out to a larger range $$R$$ requires a larger $$f_b$$, and thus you must be able to sample it. Then, this means that you need to increase the sample rate $$f_s$$.