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curriculum/Radar Systems
section 15 of 163 min read

15. Things to Try

  1. Compute the maximum unambiguous range for a radar with PRF = 2 kHz: Runamb=c/(2⋅2000)=75R_{unamb} = c/(2 \cdot 2000) = 75 km. Then the blind speeds at λ=3\lambda = 3 cm are vblind,n=n⋅30v_{blind,n} = n \cdot 30 m/s, so 0, 30, 60, 90 m/s. A target at 30 m/s along the line of sight is invisible to MTI without PRF stagger.

  2. Solve the radar equation for a counter-drone radar: Pt=10P_t = 10 W, G=25G = 25 dBi, f=24f = 24 GHz, σ=0.01\sigma = 0.01 m², Smin=−110S_{min} = -110 dBm. With λ=1.25\lambda = 1.25 cm you get R≈100R \approx 100 m, realistic for short-range counter-drone.

  3. Implement a simple FMCW radar in Python. Generate a chirp, simulate an echo from a few targets, compute the beat-frequency spectrum, identify the peaks:

python
import numpy as np
import matplotlib.pyplot as plt
 
c = 3e8
f0 = 77e9
B = 1e9                # 1 GHz chirp bandwidth → 15 cm range res
T_chirp = 100e-6
fs = 5e6                # baseband sample rate
N = int(fs * T_chirp)
t = np.arange(N) / fs
 
ranges = [50, 80, 150]   # meters
amps = [1.0, 0.7, 0.4]
beat = np.zeros(N, dtype=complex)
for R, A in zip(ranges, amps):
    tau = 2 * R / c
    f_b = (B / T_chirp) * tau
    beat += A * np.exp(1j * 2 * np.pi * f_b * t)
beat += 0.05 * (np.random.randn(N) + 1j*np.random.randn(N))
 
# Range FFT
F = np.fft.fft(beat * np.hanning(N))
freqs = np.fft.fftfreq(N, 1/fs)
range_axis = freqs * c * T_chirp / (2 * B)
mask = freqs >= 0
 
plt.plot(range_axis[mask], 20*np.log10(np.abs(F[mask])+1e-9))
plt.xlim(0, 200)
plt.xlabel("Range (m)")
plt.ylabel("Magnitude (dB)")
plt.title("FMCW range spectrum: peaks at the targets")
plt.show()

You should see clean peaks at 50, 80, and 150 meters. Adjust B and watch the range resolution change.

  1. Build a Doppler-only motion sensor. A 24-GHz CW radar module costs a few dollars on AliExpress. Hook it up to an op-amp and a microcontroller, observe the audio-frequency Doppler signal as you walk past, and compute your speed from the FFT.

  2. Read about the Hülsmeyer Telemobiloskop, then about Watson-Watt's 1935 demonstration where he detected a Heyford bomber 8 miles out using a 12-meter wavelength.

  3. Try an SDR-based passive radar. With an inexpensive RTL-SDR and a couple of antennas, you can use commercial FM radio or DVB-T transmitters as opportunistic illuminators and detect aircraft passively. KrakenSDR's passive radar mode is a friendly entry point.