Reference
Excellent Youtube video: Jon Kraft “Build Your Own Drone Tracking Radar 1-6” Build Your Own Drone Tracking Radar: Part 1 (youtube.com)
Introduction
Jon is an engineer from Analog Device. He gave a series of Youtube video of building radar and very good explanation of the basic prinicples.
Radar Classification
As shown in the figure below. Radar has two main categories: Pulsed Radars and CW (Continuous Wave) Radars.
In this video sequence, we focus on CW Radars (speed only) -> Frequency Modulated CW (speed + distance).
Here’s a comparison of Pulse Radar and Continuous Wave (CW) Radar in table form, highlighting their pros and cons:
| Feature | Pulse Radar | Continuous Wave (CW) Radar |
|---|---|---|
| Applications | Used in long-range applications (e.g., weather, aviation) | Common in speed detection (e.g., police radar) |
| Operation | Sends short bursts of energy (pulses) | Continuously transmits a signal |
| Range Detection | Can measure distance using time delay | Limited range; primarily detects speed |
| Resolution | High resolution due to short pulse duration | Lower resolution; less accurate range measurement |
| Target Detection | Good for detecting stationary and moving targets | Excellent for tracking moving targets |
| Interference | Less susceptible to jamming | More susceptible to jamming |
| Complexity | Generally more complex due to pulse processing | Simpler design and implementation |
| Power Consumption | Higher power consumption during pulses | Typically lower power consumption |
| Cost | Generally more expensive due to complexity | Usually cheaper due to simpler design |
Summary:
- Pulse Radar Pros: Long-range detection, high resolution, versatile applications.
- Pulse Radar Cons: More complex and expensive, higher power consumption.
- CW Radar Pros: Simple design, effective for speed detection, lower cost.
- CW Radar Cons: Limited range, lower resolution, more vulnerable to interference.
Radar Block Diagram
Transmitting path: Waveform generator -> Up-converter -> PA (Power Amplifier) -> Antenna Receiving path: Low-Noise-Amplifier (LNA) -> Down-converter -> DSP for range and speed
RF is homodyne transceiver: Transmitter and Receiver use the same LO (Local Oscillator). IF is created by waveform generator and receiver, i.e. high speed DAC and ADC.
Radar Configuration
In these videos, it uses PLUTO + Phaser.
- costs: ~$2300.
- RF: 10GHz
- IF: 2.2GHz
- Modulation BW: 500MHz?
RF: 10GHz depends on the regulation, resolution, and channel characteristics (rain, …). IF: < 20% of the RF frequency BW: < 5% of the RF frequency
Radar Fundmental Formula
Receiving Power: Friis Transmission Equation
\[P_{R, \max}=P_T G_T\left(\frac{\lambda}{4 \pi R}\right)^2 G_R\]
When it applies to Radar, assuming $G_T = G_R = G$ for simplication (usually it is not the case!), the reflection can be thought as a re-broatcast of the EM waves on a sphere with surface area $4\pi r^2$. We can use a simple ratio of $\sigma_s$ Radar cross section (unit: area) vs. $4 \pi r^2$ (sphere area) to make the unit right.
\[P_r= P_t G^2 \left(\frac{\lambda}{4 \pi r}\right)^2 \left(\frac{\sigma_s}{4\pi r^2}\right) =P_t \frac{G^2 \cdot \lambda^2 \cdot \sigma_S}{(4 \pi)^3 \cdot r^4}\]
Comment
- Wavelength: physical parameter
- Radar cross section and range, r, are specifications
- Antenna gain: another whole subject. One important parameter is the antenna array for beam-forming.
- Pt is typically a fixed parameter, but heavily depending on pulse radar vs. CW radar.
- Pulse radar: need very high peak power to get a good range and range resolution
- CW radar: constant (lower) power to operate
Pulse Radar (only range and range resolution)
- Distance: $R = \Delta t \cdot c / 2$ : 1 us = 150m
- Range resolution: $\Delta R = \tau \cdot c /2$ where $\tau$ is the pulse width
- BW of the pulse: BW = $1/ \tau$. Therefore $\Delta R= \frac{c}{2 BW}$ $\Delta R$ = 1m -> BW = 150 MHz -> $\tau$ = 6.6 ns.
- $P_r = P_t \frac{G^2 \lambda^2 \sigma_s}{(4 \pi)^3 r^4}$
CW Radar (only speed)
$f_{reflected} - f_{transmitted} = \Delta f = \frac{2 v_{target} f}{c}$
- Example: f = 2.4 GHz and car velocity is 100 mph (160 km/hr): $\Delta f$ = 716 Hz
- Example: f = 10 GHz and car velocity is 100 mph (160 km/hr): $\Delta f$ = 2982 Hz
FMCW (Frequency Modulated Continuous Wave) - (Range + Speed)
FMCW uses chirped continuous waveform.
Beat frequency: proportional to time delay -> FFT for range estimation. By detecting $f_b$ converting $t_d$, we can get the range of the car. By checking the Doppler frequency shift, we can get the velocity of the car.
\(f_b = \frac{2 R B}{c T_s}\) where $c$ is speed of light, $f_b$ beat frequency, $B$ bandwidth of the chirp, $T_s$ chipr ramp time
- Example $f_b = \frac{2\cdot 500 MHz}{c \cdot 500 us}$ = 6.7 kHz/m
- Example:
There is another method to use clipped triangular mode. At the top and bottom of the chirp keep the same frequencies, it can be used for the Dopper frequency shift.
Fast Time is the ramp speed of the chirp. It’s for the ranging purpose. Slow Time is the period of the chirp. It’s movement of the object over slow time. But I din’t think it’s related to Doppler frequency.
Antenna Diversity
Future Work
I think it’s a good topic to use AI for the 3D cube and use learning base for radar detection.
