# Pulse Radar with Field-Programmable Gate Array Range Compression for Real Time Displacement and Vibration Monitoring

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

**Notations**: t

_{del}: radar-to-target round trip delay, c: speed of light, R

_{0}: radar-to-target fixed range component, ΔR(t): radar-to-target variable range component, τ: chirp duration, α: chirp angular rate, f

_{0}: carrier frequency, φ

_{0}: initial phase, δφ: phase shift, K: number of simultaneous multiplications, N: length of the input sequence, δr: range bin width, σ

_{displ}: displacement standard deviation, λ: wavelength, SNR: Signal-to-Noise Ratio.

## 2. Principle of Pulse Radar Displacement Monitoring

_{del}is dependent on the radar-to-target range, with expression (1):

_{0}is the fixed range component, and ΔR(t) is the variable range component, which describes displacement or vibration.

_{0}is the carrier frequency and φ

_{0}is the initial phase.

_{del}.

_{0}.

## 3. System Overview

## 4. Pulse Radar Baseband Implementation on the USRP Platform

## 5. Baseband Range Compression

Algorithm 1: Cross-Correlation Computation | |

Inputs: S_RX1, S_RX2Output: XCORR | |

1 | for n = 1 to (3136-448) do |

2 | BUFFER2 = flip(S_RX2(n to n + 447)) |

3 | for k = 0 to 447 do |

4 | XCORR[n] = XCORR[n] + conjugate(S_RX1[k])*BUFFER2[k] |

5 | end for |

6 | end for |

7 | return XCORR |

^{2}[16]. The bandwidth of the receiver is 160 MHz and the required signal to noise ratio is 10dB, in order to perform displacement measurements with a certain standard deviation, as it will be described in section 7. The radar equation is used in order to determine the measurement range at a value of 92 m.

## 6. Host Side Interface

_{s}. The sampling frequency equals 120 Msps. Therefore, the range bin width is:

_{0}= 5.755 GHz.

## 7. Validation and Experimental Results

#### 7.1. Outdoor Displacement Measurement

#### 7.2. Real Time Target Vibration Spectrum Monitoring

#### 7.3. Indoor Vibration Measurement

#### 7.4. Outdoor Vibration Measurement

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

USRP | Universal Software Radar Peripheral |

FPGA | Field-Programmable Gate Array |

FMCW | Frequency-Modulation Continuous Wave |

SAR | Synthetic Aperture Radar, |

UAV | Unmanned Aerial Vehicle |

PRF | Pulse Repetition Frequency |

PRI | Pulse Repetition Interval |

SNR | Signal to Noise Ratio |

## Appendix A

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**Figure 1.**Displacement measurement geometry. Target is placed at a fixed range R

_{0}. The target’s displacement or vibration is described by ΔR(t). ΔR(t) is much smaller than R

_{0}.

**Figure 3.**Pulse radar FPGA implementation overview. Two different clock domains exist: system clock and sampling clock. The system clock was chosen based on the implementation timing constraints. The two domains are linked by the “Start trigger 2” signal and by the RX memory contents.

**Figure 4.**I samples of RX1 and RX2 signals, with their corresponding time domain duration, as received by the platform when a close target is placed in front of the radar.

**Figure 5.**Cross-correlation block diagram, as well as the related blocks that operate in the system clock domain. The contents of the RX1 memory are dumped in the corresponding buffer. Then, the contents of the second memory are dumped in “Buffer 2”. The two buffers are actually shift registers composed of cascaded FFs (flip-flops). The multiplications and partial results summation are performed each clock period. The magnitude and phase of the obtained range profile are sent to the host computer using FIFOs.

**Figure 6.**Timing diagram of the operations performed during a PRI. The sampling clock period is denoted Tsamp_clk and the system clock period is denoted Tsys_clk. The system clock period is four times greater than the sampling clock period. The time available for data transfer from FPGA to host and additional host processing is the time left after the end of cross-correlation computation until the next PRI.

**Figure 7.**Resulted signals from FPGA range compression, based on the RX1 and RX2 signals plotted in Figure 4, as displayed on the host interface. The peak in the first plot indicates the delay between the two signals.

**Figure 8.**Displacement measurement errors at 7.5 m and at 30 m range. Note the slightly larger error for the 30 m range.

**Figure 9.**Displacement measurement errors at 30 m range for 30 consecutive steps in the same direction, with a step size of 5 mm.

**Figure 10.**Standard deviation of the displacement measurement versus signal-to-noise ratio, in the simulated, theoretical and experimental cases.

**Figure 11.**(

**a**) Vibrating target mechanical fixture drawing. An audio speaker is used as the vibrating element, with a metallic plate mounted on the dust cap. A linear potentiometer is used to sense the vibration amplitude. (

**b**) Photography of the assembled mechanical fixture mounted on a tripod.

**Figure 12.**Vibration monitoring on the vibrating target, set at a 12 Hz frequency. Data from 256 radar pulses was used for the computation of this spectrum. The fundamental component at 12 Hz is the most powerful, followed by weak harmonics at 24 Hz and 36 Hz.

**Figure 13.**Indoor vibration amplitude measurement results, for a frequency range from 5 Hz to 50 Hz (half the PRF of the radar, in order to prevent aliasing). The indoor target was placed at a range of 3 m.

**Figure 14.**Outdoor vibration amplitude measurement results, for a frequency range from 5 Hz to 50 Hz. The radar to target range was approximately 10 m.

Radar System | Parameters |
---|---|

Carrier frequency | 5.755 GHz |

Transmitted power | 30 dBm |

Chirp bandwidth | 40 MHz |

Range resolution cell | 3.75 m |

Maximum detectable target range | 92 m |

Transmit pulse duration | 3.73 μs |

Receive window duration | 26.13 μs |

Cross-correlation computation time | 121.63 μs |

Pulse Repetition Interval | 10 ms |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Tudose, M.-L.; Anghel, A.; Cacoveanu, R.; Datcu, M.
Pulse Radar with Field-Programmable Gate Array Range Compression for Real Time Displacement and Vibration Monitoring. *Sensors* **2019**, *19*, 82.
https://doi.org/10.3390/s19010082

**AMA Style**

Tudose M-L, Anghel A, Cacoveanu R, Datcu M.
Pulse Radar with Field-Programmable Gate Array Range Compression for Real Time Displacement and Vibration Monitoring. *Sensors*. 2019; 19(1):82.
https://doi.org/10.3390/s19010082

**Chicago/Turabian Style**

Tudose, Mihai-Liviu, Andrei Anghel, Remus Cacoveanu, and Mihai Datcu.
2019. "Pulse Radar with Field-Programmable Gate Array Range Compression for Real Time Displacement and Vibration Monitoring" *Sensors* 19, no. 1: 82.
https://doi.org/10.3390/s19010082