# Carrier frequency of chirp signal

I am computing the link budget for a communication-radar (CoRadar) system. The formula for maximum distance, in communication, is:

$$d_{max} = \sqrt{\frac{P_t}{\tau}\frac{G_t G_{r, comm} \lambda^2}{(4\pi^2)FkT_0 B_w SNR_{comm}}}$$

where,

$$P_t$$ is the transmitted power

$$\tau$$ is the duty cycle

$$G_t$$ is the transmission antenna gain

$$G_{r, comm}$$ is the communication receiver antenna gain

$$\lambda$$ is the wavelength

$$F$$ is the noise factor

$$k$$ is the Boltzmann's constant

$$T_0$$ is the noise reference temperature

$$B_w$$ is the bandwidth

$$SNR_{comm}$$ is the $$SNR$$ of the communication system

I am using a LFM chirp signal that sweeps from $$3.5\times10^6$$ to $$8.5\times10^6$$. Which would be the frequency, which would be associated to a wavalength $$\lambda$$, that should I use for the formula? $$8.5\times10^6$$? Or, $$\frac{8.5\times10^6 + 3.5\times10^6}{2} = 6\times10^6$$ (i.e. a middle point)?

And which would be the bandwidth? $$8.5\times10^6 - 3.5\times10^6 = 5\times10^6$$?

Many thanks.

## 1 Answer

In my experience in the radar industry, most people use the center frequency of the chirp for such calculations; in your case, that would be 6MHz. Since your bandwidth is only 5MHz this is probably fine. You'd start to run into issues with that calculation if your bandwidth was much wider, say several GHz.

• Ok. I have also been looking on the internet, and I was wondering if you could help me with a doubt, if a radar, using a LFCW signal, is working at 5.3GHz and has a bandwidth of 50MHz, does it mean that the chirp signal sweeps from 5.3GHz - 25MHz to 5.3GHz + 25MHz ? – DaDSPGuy Mar 27 '19 at 19:06
• Yes, that is typically how one would express that: the bandwidth is generally centered on the carrier – matthewjpollard Mar 27 '19 at 19:11