# Frequency Comb-Based Ground-Penetrating Bioradar: System Implementation and Signal Processing

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Basics

#### 2.1. Bioradar Measuring Principle

#### 2.2. Frequency Comb CW Radar

**Requirement 1**:$${f}_{s}=M\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\Delta {f}_{\mathrm{tx}}.$$

**Requirement 2**:$$L=k\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}4M,\mathrm{with}\phantom{\rule{4.pt}{0ex}}k\in \mathbb{N}.$$

#### 2.3. Ground-Penetrating Bioradar

## 3. System Description: SDR-Based Bioradar

^{2}project, the bioradar system was integrated into a UAS. The antennas were built into the feet of the landing gear to ensure direct contact with the ground after landing [38]. However, a safe landing spot for UAS cannot be found on all debris fields. To overcome this problem, in the SORTIE project, we propose to design a standalone ground-penetrating radar (GPR) that can be unloaded on the rubble by the UAS with a rope without landing. The UAS communicates with the bioradar wirelessly.

## 4. Signal Processing

#### 4.1. Pre-Processing: Radar Frequency Domain to Spatial Domain

#### 4.2. FFT: Time Domain to Breathing Frequency Domain

#### 4.3. Continuous Wavelet Transform (CWT): Time–Frequency Analysis

## 5. Experiment with Two Persons

## 6. Field Measurement

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. GNU Radio Flow Graph

## Appendix B. Field Measurement Plots

**Figure A2.**Measurement Nr.1 in scenario shown in Figure 16a: (

**a**) top: preprocessed time-domain signal of the first range bin; bottom: FFT of the signal in the upper plot. (

**b**) CWT of the signal in (

**a**).

**Figure A3.**Measurement Nr.3 in scenario shown in Figure 16b: (

**a**) top: preprocessed time-domain signal of the first range bin; bottom: FFT of the signal in the upper plot. (

**b**) CWT of the signal in (

**a**).

**Figure A4.**Measurement Nr.5 in scenario shown in Figure 16c: (

**a**) top: preprocessed time-domain signal of the first range bin; bottom: FFT of the signal in the upper plot. (

**b**) CWT of the signal in (

**a**).

**Figure A5.**Measurement Nr.7 in scenario shown in Figure 16d: (

**a**) top: preprocessed time-domain signal of the first range bin; bottom: FFT of the signal in the upper plot. (

**b**) CWT of the signal in (

**a**).

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**Figure 2.**Polar plot of two $s\left[l\right]$ examples: (

**a**) $M=3$, odd. The comb has three tones. For $l=1$ and 2, these tones equally distribute on the unit circle, and their complex sum is zero. For $l=3$, the three tones overlap at −j. (

**b**) $M=4$, even. The comb has four tones. For $l=4$, the four tones overlap at j.

**Figure 3.**For transmitting: (

**a**) The pre-defined waveform in sample time domain. Samples $l=1\dots 128$ built one complete wave. (

**b**) The spectrum of the waveform $s\left[l\right]$ with a length $L=4096$.

**Figure 4.**Illustration of a bioradar operation scenario. A person is trapped underneath rubble piles. A bioradar is on top of the rubble pile. All objects in the environment reflect the transmitted radar signal. A non-trapped person and a vibrating tree are out of the range window.

**Figure 5.**Block diagram of the software-defined radio bioradar. The SDR block is modified from [40]. Next Section shows a detailed version of the signal processing process.

**Figure 6.**Signal processing procedure. Step 1, pre-processing, includes four sub-steps: N times FFT, N times IFFT, decompose the signal into M range intervals and keep the first $M/2$ sub-signals, and highpass filter them. In step 2, another FFT is applied to these sub-signals, respectively. The result of the second step is a plot and three values. Step 3 calculates the time-frequency distribution of the sub-signal from ${R}_{person}$ and results in a diagram and two values. With the results from steps 2 and 3, the decision about whether life is detected can be determined in Step 4.

**Figure 7.**(

**a**) Photograph of the Bioradar (adrv9364-z7020) with two Vivaldi antennas. (

**b**) A test person sits in front of the test setup.

**Figure 9.**(

**a**) The 32 points of raw data of one frame, linear scale of Figure 8b. (

**b**) The IFFT of the magnitude in (

**a**).

**Figure 10.**(

**a**) The real part of the time domain decomposed signal for the first three ranges of the measurement shown in Figure 7. Range-1 $\approx 0\phantom{\rule{4pt}{0ex}}$ to $2.5$ m, range-2 $\approx 2.5\phantom{\rule{4pt}{0ex}}$ to 5 m, range-3 $\approx 5\phantom{\rule{4pt}{0ex}}$ to $7.5$ m. (

**b**) The corresponding filtered signals.

**Figure 11.**(

**a**) FFT of the filtered signals of the first three range bins shown in Figure 10; (

**b**) The breathing frequency–range plot.

**Figure 12.**The CWT time-frequency distribution of the range-2 signal in Figure 10b. (

**a**) The distribution for frequency $f\in $ [0, 1 Hz]. (

**b**) The 1D representation of (

**a**): the strongest peak of each time point. The mode value of the curve is marked in red.

**Figure 13.**The CWT time–frequency distribution of the range-1 signal in Figure 10b. (

**a**) The distribution for frequency $f\in $ [0, 1 Hz]. (

**b**) The 1D representation of (

**a**): The strongest peak of each time point. The mode value of the curve is marked in red.

**Figure 14.**A bioradar experiment with two people. (

**a**) Photograph of the experiment setup. Person 1 sits in the first range interval, and person 2 sits in the third range interval. (

**b**) The breathing frequency–distance plot.

**Figure 15.**Block diagram of the prototype bioradar system. Relevant software used on the Raspberry Pi is illustrated with white blocks.

**Figure 16.**Measurement scenarios: (

**a**) A tunnel covered with a wooden plate. (

**b**) A concrete tube. (

**c**) A building with wooden floors. The test person lay on the ground floor. The bioradar was placed on the first floor. (

**d**) A building with reinforced concrete floors. The test person lay on the ground floor. The bioradar was placed on the first floor.

Parameter | Symbol | Value |
---|---|---|

sampling frequency | ${f}_{s}$ | $61.44$ MHz |

number of tones in the frequency comb | M | 32 |

number of samples in waveform $s\left[l\right]$ | L | 4096 |

bandwidth | $BW$ | $59.52$ MHz |

start frequency | ${f}_{\mathrm{tx}}\left[1\right]$ | $-29.28$ MHz |

stop frequency | ${f}_{\mathrm{tx}}\left[M\right]$ | $30.24$ MHz |

Parameter | Symbol | Value |
---|---|---|

sampling frequency | ${f}_{s}$ | $61.44$ MHz |

LO-frequency of the receiver | ${f}_{\mathrm{Rx}}$ | $1.3$ GHz |

LO-frequency of the transmitter | ${f}_{\mathrm{Tx}}$ | $1.3007$ GHz |

transmitting waveform | $s\left[l\right]$ | see Equation (5) and Table 1 |

number of samples per receiving frame | L | 4096 |

number of frames | N | 20k |

frame rate | ${f}_{s,frame}$ | 225 Hz |

measurement duration | ${T}_{\mathrm{meas}}$ | about 86 s |

Nr. | Scenario | ${\mathit{f}}_{\mathbf{resp},\mathbf{fft}}$ | ${\mathit{f}}_{\mathbf{resp},\mathbf{cwt}}$ | ${\mathit{PR}}_{\mathbf{fft}}$ | $\mathbf{\Delta}{\mathit{f}}_{\mathbf{resp}}$ | Life Detected |
---|---|---|---|---|---|---|

1 | (a) | $0.27$ Hz | $0.29$ Hz | $17.45$ dB | $7.1\%$ | yes |

2 | (a) | $0.30$ Hz | $0.30$ Hz | $17.94$ dB | $0\%$ | yes |

3 | (b) | $0.25$ Hz | $0.26$ Hz | $18.25$ dB | $0.4\%$ | yes |

4 | (b) | $0.13$ Hz | $0.27$ Hz | $7.35$ dB | $70\%$ | no |

5 | (c) | $0.32$ Hz | $0.32$ Hz | $22.35$ dB | $0\%$ | yes |

6 | (c) | $0.13$ Hz | $0.13$ Hz | $21.02$ dB | $0\%$ | yes |

7 | (d) | $0.15$ Hz | $0.64$ Hz | $12.52$ dB | $124\%$ | no |

8 | (d) | $0.09$ Hz | $0.12$ Hz | $12.99$ dB | $28.6\%$ | no |

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## Share and Cite

**MDPI and ACS Style**

Shi, D.; Gidion, G.; Aftab, T.; Reindl, L.M.; Rupitsch, S.J.
Frequency Comb-Based Ground-Penetrating Bioradar: System Implementation and Signal Processing. *Sensors* **2023**, *23*, 1335.
https://doi.org/10.3390/s23031335

**AMA Style**

Shi D, Gidion G, Aftab T, Reindl LM, Rupitsch SJ.
Frequency Comb-Based Ground-Penetrating Bioradar: System Implementation and Signal Processing. *Sensors*. 2023; 23(3):1335.
https://doi.org/10.3390/s23031335

**Chicago/Turabian Style**

Shi, Di, Gunnar Gidion, Taimur Aftab, Leonhard M. Reindl, and Stefan J. Rupitsch.
2023. "Frequency Comb-Based Ground-Penetrating Bioradar: System Implementation and Signal Processing" *Sensors* 23, no. 3: 1335.
https://doi.org/10.3390/s23031335