Radar

Automotive radars send a chirp, a radio signal whose frequency sweeps upward. The echo comes back as a delayed copy. Mixing the two gives a beat tone whose pitch is proportional to range. Radio waves pass through rain, fog, and dust, so radar keeps working when cameras and LiDAR struggle.

Target 1 range Target 2 is farther by Target 1 speed (toward the radar) Chirp bandwidth

Range and speed from a chirp

The chirp sweeps bandwidth $B$ in time $T$, so its slope is $S = B / T$. An echo from range $R$ arrives after $\tau = 2R / c$, and mixing it with the outgoing chirp leaves a beat frequency. Motion adds a Doppler shift at wavelength $\lambda$:

$$f_b = S\,\tau = \frac{2 S R}{c} \qquad R = \frac{c\, f_b}{2S} \qquad f_D = \frac{2v}{\lambda} \qquad \Delta R = \frac{c}{2B}$$

$\Delta R$ is the range resolution: two targets closer than this blur into one peak.

What to notice

Farther targets give a bigger gap between the two chirps and a higher beat frequency. In the range profile below, lower the bandwidth and the two peaks merge into one. A 77 GHz car radar with 1 GHz of bandwidth separates targets 15 cm apart. Speed comes from the Doppler shift, measured directly rather than by comparing positions over time, which is a big advantage for tracking cars.

The trade-off is angular resolution. Radar beams are wide, so radar knows well how far and how fast, but less well exactly where.