Carrier frequency of chirp signal

Question

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.

Answer 1

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.