# Estimation of Human Body Vital Signs Based on 60 GHz Doppler Radar Using a Bound-Constrained Optimization Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Nonlinearity in Doppler Radar Vital-Signal Detection

#### 2.1. Arctangent Demodulation

#### 2.2. Complex Demodulation

## 3. Numerical Spectrum Analysis

#### 3.1. Without Noise

#### 3.2. With Noise

#### 3.3. Choice of the Demodulation Technique

## 4. Vital-Sign Detection Using Optimization Algorithms

#### 4.1. Description of the Problem

#### 4.2. Numerical Results

#### 4.2.1. Without Noise, with Ambiguity

#### 4.2.2. Noise Influence on the Optimization

#### 4.2.3. Observation-Time Influence on the Optimization

## 5. Large-Scale Constrained Bound: PSO Parallel Optimization

#### 5.1. Normal Case

#### 5.2. No-Breath Case

#### 5.3. With a Random Body Motion

#### 5.4. Experimental Measurements

`&`Schwarz ZVA67 and do not exhibit phase drift between each other. A photo of the setup is given in Figure 12. The antennas are directed to the chest of an adult at a distance of 2 m.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

WSN | Wireless sensor network |

IQ | In-phase quadrature |

LO | Local oscillator |

EEMD | Ensemble empirical mode decomposition |

CW | Continuous wave |

CDF | Cumulative distribution function |

LSM | Least-square minimization |

GA | Genetic algorithm |

PSO | Particle swarm optimization |

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**Figure 2.**Spectral representation of the noiseless baseband signals, using (

**a**) arctangent demodulation and (

**b**) complex demodulation. ${m}_{r}=1.0$ mm, ${m}_{h}=0.08$ mm. ${f}_{h}=4{f}_{r}=72$ bpm (i.e., ambiguity). Red line and blue square line represent different mutual phases (${\varphi}_{r}$ and ${\varphi}_{h}$, respectively).

**Figure 3.**Spectral representation of the baseband signals, using the arctangent demodulation technique. ${m}_{r}=1.0$ mm, ${m}_{h}=0.08$ mm. ${f}_{h}=4{f}_{r}=72$ bpm (i.e., ambiguity).

**Figure 4.**Obtained CDF with optimization in (

**a**) time domain and (

**b**) frequency domain. Three optimization algorithms are compared (namely, GA, PSO, and LSM). Without noise. ${m}_{r}=1.0$ mm, ${m}_{h}=0.08$ mm, and ${f}_{h}=4{f}_{r}=72$ bpm (i.e., ambiguity).

**Figure 5.**CDFs of different optimization procedures with SNRs at the receiver of (

**a**) 10 dB and (

**b**) 6 dB. ${m}_{r}=1.0$ mm, ${m}_{h}=0.08$ mm, and ${f}_{h}=4{f}_{r}=72$ bpm (i.e., ambiguity).

**Figure 6.**CDFs of different optimization procedures for obervation time duration of (

**a**) 5 s and (

**b**) 20 s. ${m}_{r}=1.0$ mm, ${m}_{h}=0.08$ mm, ${f}_{h}=4{f}_{r}=72$ bpm (i.e., ambiguity), and SNR = 10 dB.

**Figure 7.**CDFs of different optimization procedures with a large–scale constrained bound. SNR = 10 dB, ${m}_{r}=2$ mm, ${m}_{h}=0.3$ mm, ${f}_{r}=\left(\right)open="["\; close="]">12,25$ bpm, and ${f}_{h}=\left(\right)open="["\; close="]">60,100$ bpm. (

**a**) Estimation error on f

_{h}, (

**b**) Estimation error on f

_{r}.

**Figure 8.**CDFs of PSO optimization procedure executed in four sub-bounds for (

**a**) normal case: ${f}_{r}=\left(\right)open="["\; close="]">12,25$ bpm, ${f}_{h}=\left(\right)open="["\; close="]">60,100$ bpm, and (

**b**) rapid case: ${f}_{r}=\left(\right)open="["\; close="]">25,72$ bpm, ${f}_{h}=\left(\right)open="["\; close="]">100,180$ bpm. SNR = 10 dB. ${m}_{r}=2$ mm, ${m}_{h}=0.3$ mm.

**Figure 9.**CDFs of PSO optimization procedure executed in four subranges. The person under test does not breathe but has a normal heart rate. ${m}_{r}=0$ mm, ${m}_{h}=0.3$ mm, and ${f}_{h}=\left(\right)open="["\; close="]">60,100$ bpm. SNR = 10 dB.

**Figure 10.**CDFs of PSO optimization procedure in four subranges and arctangent direct peak detection. SNR = 10 dB, and with a random body motion. ${m}_{r}$, ${m}_{h}$, ${f}_{r}$, and ${f}_{h}$ take random values within ranges indicated in Table 1. Results are obtained for 1000 generations.

**Figure 14.**CDFs of PSO optimization procedure in four subranges and arctangent direct peak detection.

${\mathit{f}}_{\mathit{r}}$ (bpm) | ${\mathit{f}}_{\mathit{h}}$ (bpm) | ${\mathit{m}}_{\mathit{r}}$ (mm) | ${\mathit{m}}_{\mathit{h}}$ (mm) | ||
---|---|---|---|---|---|

At rest | lb | 12 | 48 | 0 | 0.05 |

ub | 30 | 90 | 6.0 | 1.0 | |

After sport | lb | 30 | 90 | 0 | 0.05 |

ub | 60 | 180 | 6.0 | 1.0 |

Working Domain | Methods | Advantages | Disadvantages | |
---|---|---|---|---|

Frequency domain | Peak detection | Arctangent demodulation | Fast, No ambiguity | Sensitive to noise and to random body movements, Needs accurate DC offset compensation |

Complex demodulation | Fast, Robust to noise | Intermodulation, ambiguity | ||

Optimization | LSM, GA, and PSO | Handle ambiguity | At least 10 s time window, Not adaptable to nonstationary signal | |

Time domain | Optimization | LSM | Converge quickly | Sensitive to initial estimates, Easy to fall into local minima |

GA | Robustness, Stable | Computationally expensive if applied to large bounds | ||

PSO | Converges more quickly than GA | |||

PSO in parallel | Robust, Less optimization time | Multiple processors required |

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**MDPI and ACS Style**

Zhang, T.; Sarrazin, J.; Valerio, G.; Istrate, D.
Estimation of Human Body Vital Signs Based on 60 GHz Doppler Radar Using a Bound-Constrained Optimization Algorithm. *Sensors* **2018**, *18*, 2254.
https://doi.org/10.3390/s18072254

**AMA Style**

Zhang T, Sarrazin J, Valerio G, Istrate D.
Estimation of Human Body Vital Signs Based on 60 GHz Doppler Radar Using a Bound-Constrained Optimization Algorithm. *Sensors*. 2018; 18(7):2254.
https://doi.org/10.3390/s18072254

**Chicago/Turabian Style**

Zhang, Ting, Julien Sarrazin, Guido Valerio, and Dan Istrate.
2018. "Estimation of Human Body Vital Signs Based on 60 GHz Doppler Radar Using a Bound-Constrained Optimization Algorithm" *Sensors* 18, no. 7: 2254.
https://doi.org/10.3390/s18072254