Radio Detection and Ranging

RADAR is a method of using a radio to detect and find the distance to objects.

Types

1. Pulse based RADAR
   • requires high power
   • required for ranging
2. Continuous Wave RADAR
   • cannot range
   • can find velocity
   • types are sawtooth (for range), triangular (for range and velocity ambiguity resolution), sinusoidal, and stepped-frequency modulation

RADAR equations

Ranging

$$P_r=P_t\frac{G^2{\lambda }^2{\sigma }^2}{(4\pi {)}^3{r}^4}$$

where,
$P_r$ is Receive power
$P_t$ is transmit power
$G$ is Antenna Gain
$\lambda$ is wavelength of carrier frequency
$\sigma$ is radar cross section
$r$ is range.

Range resolution

$$\mathrm{\Delta }R=\tau c/2$$

$\tau$ is pylse width $c$ is speed of light

So $1\mu s$ = 150 m of resolution.

Bandwidth

$ BW = 1 / \tau $

$ \Delta R = c / (2 . BW) $

where,
BW is bandwidth, and
$\tau$ is pulse width.

Velocity

$$f_{reflected}-f_{transmitted}=\mathrm{\Delta }f=\frac{2v_{target}}{c}f$$

Doppler frequency is the frequency change based on the target relative to the radar. This is caused by wave expansion or contraction.

Beat frequency : Difference between original and doppler frequency($f_c$).