# Doppler Radar Vital Signs Detection Method Based on Higher Order Cyclostationary

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Doppler Radar Vital Sign Model

#### 2.2. Cyclostationary Detection Theory

## 3. Statistical Property Analysis of Higher Order Cyclostationary Detection

#### 3.1. The Almost Sure Convergence of the Time Varying Cyclic-Moments and the Sample Cyclic-Moments

#### 3.2. The Relation Analysis Between the Finite-Time Average and the Ensemble Average

## 4. Experiment and Analysis

#### 4.1. The Detection of the Heartbeat and Respiration Rate under Different SNR for Simulation Signals

#### 4.2. The Detection of the Heartbeat and Respiration Rate Using the Doppler Radar Signal for a Single Subject

#### 4.3. The Detection of the Heartbeat Rate Using the Doppler Radar Signal for Different Subjects

#### 4.4. The Detection of the Respiration Rate Using the Doppler Radar Signal for Multiple Subjects

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Spectral correlation function (SCF) of the second-order cyclostationary signal $B(t)$ in (8), where noise and subject movement interferences are ignored.

**Figure 2.**TOCC of $B(t)$ in (5). (

**a**) TOCC of the received signal; (

**b**) TOCC of the received signal (here ${a}_{h}=0.02$ cm).

**Figure 4.**TOCC of the received signal. (

**a**) TOCC of the received signal; (

**b**) Test statistic (purple line denotes the threshold); (

**c**) TOCC of the received signal in Hilbert space.

**Figure 5.**Estimated means and variances of the heart and respiration for 20 realizations of TOCC in each SNR levels (SIR = 0 dB).

**Figure 7.**Doppler radar signal and reference signals ECG and RW. (

**a**) Received radar signal (

**top**) and power spectrum density (PSD) of the radar signal (

**bottom**); (

**b**) RW (

**top**) and ECG (

**bottom**).

**Figure 8.**TOCC of the received radar signal. (

**a**) TOCC 2-D graph; (

**b**) Test statistic (purple line denotes the threshold, here PFA = 0.001); (

**c**) The detected results of the heart and respiration rates with the record time increased in the 3 s steps (bottom: heart, top: respiration, Ref indicates the reference).

**Figure 9.**Estimated results of the heartbeat in the state of holding breath. (

**a**) TOCC estimators of Subject1, Subject2, Subject3 and Subject3 plus motion; (

**b**) Test statistic; (

**c**) FFT spectrum corresponding to the Subject1, Subject2, Subject3 and Subject3 plus motion.

**Figure 10.**Estimated respiration frequencies and statistic of the received recorded respiration signal under the four different tempos. (

**a**) TOCCs of R1, R2, R3, R4 (distance = 30 cm); (

**b**) Fourier spectrum (distance = 30 cm); (

**c**) Test statistic of (

**a**); (

**d**) TOCCs of R1, R2, R3, R4 (distance = 50 cm); (

**e**) Fourier spectrums (distance = 50 cm); (

**f**) Test statistic of (

**d**).

Components | Frequency | Power Output | Operating Voltage | Sensitivity | Gain | Noise |
---|---|---|---|---|---|---|

Specifications | 10.587 GHz | 10 dBm | +5 V ± 0.25 V | −86 dBm | 8 dBi | <10 $\mathsf{\mu}$V |

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**MDPI and ACS Style**

Yu, Z.; Zhao, D.; Zhang, Z.
Doppler Radar Vital Signs Detection Method Based on Higher Order Cyclostationary. *Sensors* **2018**, *18*, 47.
https://doi.org/10.3390/s18010047

**AMA Style**

Yu Z, Zhao D, Zhang Z.
Doppler Radar Vital Signs Detection Method Based on Higher Order Cyclostationary. *Sensors*. 2018; 18(1):47.
https://doi.org/10.3390/s18010047

**Chicago/Turabian Style**

Yu, Zhibin, Duo Zhao, and Zhiqiang Zhang.
2018. "Doppler Radar Vital Signs Detection Method Based on Higher Order Cyclostationary" *Sensors* 18, no. 1: 47.
https://doi.org/10.3390/s18010047