LODESTONETechnical report TR-2026-01 · revision 3Հայերեն
Contents
  1. Cover and contents
  2. 1Introduction
  3. 2State of the art
  4. 3Physics of detection and identification
  5. 4System architecture
  6. 5Induction subsystem
  7. 6Radar subsystem
  8. 7Positioning and timing
  9. 8Signal processing and machine learning
  10. 9Work plan
  11. 10Team and responsibilities
  12. 11Budget and funding
  13. 12Risks, safety and quality
  14. AAppendices
Chapter 6

Radar subsystem

Stepped-frequency ground-penetrating radar on the ADALM-Pluto.

The radar subsystem measures depth and shape. It does not identify the metal, but it provides the independent depth estimate that the induction measurement needs, and its false alarms have different causes from those of induction.

6.1Why not induction on the SDR

The ADALM-Pluto uses the AD9363 transceiver, specified from 325 MHz to 3.8 GHz and commonly operated from 70 MHz to 6 GHz with the AD9364 firmware profile. Induction needs kilohertz frequencies, four orders of magnitude lower. The SDR is therefore used as a radar, and induction is handled by the codec (Chapter 5).

6.2Stepped-frequency continuous-wave radar

An SFCW radar transmits one frequency at a time and records the complex echo at each step. An inverse FFT of the sweep gives the echo as a function of range. The method needs neither a fast pulse generator nor a fast analog-to-digital converter, which suits an SDR.

PC · Python + pyadi-iio subtract background → window → IFFT → matrix pencil USB ADALM-Pluto AD9363 · 12-bit TX PLL + RX PLL · one ref clock TX1 RX1 PA LNA TX Vivaldi RX Vivaldi direct TX → RX coupling · removed by background subtraction soil · εr ≈ 4–25 · lossy metal target rings at its resonance · Γ ≈ −1 rock: weaker echo, no phase flip depth d
Figure 6.1.Radar subsystem. The power amplifier and the low-noise amplifier are used in their intended band. Both antennas are shielded and backed with absorber so that they look into the ground.
Figure 6.2.Simulated SFCW measurement: 251 steps from 0.5 to 3 GHz, three reflectors in soil with \(\varepsilon_r = 9\). After a Hann window and inverse FFT the ground surface, a metal object at 35 cm and a stone at 80 cm are separated.

Table 6.1.Radar parameters.

QuantityRelationValue
Sweep0.5 to 3.0 GHz, 10 MHz steps251 steps
Range resolution in soil\(\Delta R = v/2B\), \(v = c/\sqrt{\varepsilon_r}\), \(\varepsilon_r = 9\)2.0 cm
Range resolution in air\(c/2B\)6.0 cm
Unambiguous range in soil\(v/2\Delta f\)5 m
Sweep timelimited by synthesiser retuningabout 0.3 s
Averaging gain\(\sqrt{N}\)+20 dB for 100 sweeps

Low frequencies penetrate further and high frequencies resolve more detail. Because the whole sweep is recorded, the band can be windowed after the measurement. Typical penetration is more than a metre in dry sand and a few tens of centimetres in wet clay.

6.3Phase coherence

The AD9363 has separate transmit and receive synthesisers locked to one reference. After each retune their relative phase can change, and SFCW processing depends on phase. The second receive channel of the AD9363, available on Pluto revision C and later after enabling the two-channel firmware mode, is therefore used as a reference. A directional coupler feeds a small part of the transmit signal into it, and each echo is divided by the reference:

$$S(f_k) = \frac{\mathrm{RX1}(f_k)}{\mathrm{RX2}(f_k)}.$$

Both receive channels share one synthesiser, so the division cancels the retuning phase.

6.4Structural resonances

A metal object that is comparable in size to half a wavelength resonates. For an elongated object of length \(L\) the first resonance is approximately

$$f_1 \approx \frac{c}{2L\sqrt{\varepsilon_r}}.$$
Figure 6.3.First structural resonance as a function of object length in air and in soil (\(\varepsilon_r \approx 9\)), with the AD9363 bands shaded. Objects from a few centimetres to about one metre resonate within the band when buried.

The late part of a radar echo is a sum of damped oscillations, one per resonance. Their poles depend on the size and shape of the object but not on the viewing angle, which makes them usable as a signature. They are estimated with the matrix-pencil method. Metal reflects almost completely with inverted phase (\(\Gamma \approx -1\)), while stones and voids reflect partly without inversion. The echo polarity is therefore a second test for metal. Resonances of coin-sized objects lie near 2.5 GHz in soil, where attenuation is high; the radar is aimed at objects of about 5 cm and larger.

6.5Antennas and amplifiers

Two Vivaldi antennas on FR4 cover the sweep. The lowest usable frequency requires an aperture of about half a wavelength: roughly 30 cm for 0.5 GHz. The Pluto delivers up to about +7 dBm, so a power amplifier is used on transmit and a low-noise amplifier on receive. The antennas are placed close to the ground and shielded on top, which improves the signal and also keeps the emission directed into the soil (Chapter 12).

GPR · SFCW on the AD9363 • position and depth • size & shape (resonance poles) • metal vs non-metal (Γ ≈ −1) Induction · kHz coil • time constant τ • ferrous vs non-ferrous • conductivity class Fusion match τ + poles against a target library Classification "aluminium can, ~10 cm long, 35 cm deep"
Figure 6.4.Fusion of radar and induction. Each sensor answers questions the other cannot. The combination follows established dual-sensor detectors (Chapter 2).