A radar vital signs detection method in complex environments

Abstract

With the growing demand for non-contact monitoring of vital signs such as respiration and heartbeat, frequency-modulated continuous wave (FMCW) radars have emerged as a promising solution for precise analysis of these signals. However, in complex environments such as indoors or inside vehicles, masking effects significantly degrade the accuracy of the target’s distance. Additionally, multiple harmonics of the respiration frequency can easily leak into the heartbeat frequency range, resulting in biased heart rate estimation. To address these challenges, we propose the Matrix Coefficient Selection Method (MCSM), a robust distance detection approach that suppresses interference between targets and mitigates the impact of other obstacles in the environment, thereby improving the robustness of distance detection. Inspired by the harmonic mitigation techniques employed in power systems, we propose the Recursive Least Squares Respiratory Harmonic Suppression (RLSRHS) method, which is derived from an improved adaptive filter structure, to suppress respiratory harmonics. Simulation experiments demonstrate that the MCSM method reduces the MAE by approximately 40% at distance detection compared to traditional methods, while the accuracy of heart rate estimation after RLSRHS respiratory harmonic suppression reaches 83%. Extensive actual experiments, compared with contact instruments such as electrocardiogram monitors, Xiaomi wristbands, and respiratory sensors, show that the error is about 4%.

Introduction

Non-contact monitoring facilitates continuous tracking of vital signs, such as heart rate (HR) and respiratory rate (RR), without the need for direct physical contact, marking a substantial advancement in modern healthcare¹. Unlike other non-contact methods, such as infrared and ultrasound^2,3, radar technology utilizes electromagnetic waves, remaining unaffected by ambient light or temperature and eliminating the need for image capture, thereby enhancing privacy. With its high resolution and sensitivity, radar is capable of accurately detecting subtle respiratory and cardiac fluctuations. This advanced technology has extensive applications across critical care⁴, health management for elderly and chronic patients⁵, automotive industry⁶ (monitoring driver’s vital signs for safe driving), post-disaster life detection⁷, and precision agricultural monitoring⁸.

Unlike continuous wave (CW) radar⁹ and Impulse Radio Ultra-Wideband(IR-UWB) radar¹⁰, frequency modulated continuous wave (FMCW) radar is capable of extracting both frequency and phase information by transmitting a continuous wave signal with a linearly varying frequency over time and receiving the target’s reflected signal. This enables precise measurement of the target’s distance and vital signs^11–13.

In radar-based vital sign detection, the studies^14,15 utilized the maximum mean amplitude and average power, respectively, to detect the range of real targets. However, in complex environments, targets with large reflection power may obscure the real target, making it difficult to detect. The work in¹⁶ employed a product parameter based on both the amplitude and phase of the signal to determine the target range. This approach relies not only on signal amplitude but also on phase information, and its performance degrades when uniformly distributed clutter is present in the environment. Therefore, it is necessary to suppress both static and dynamic clutter in the environment. Traditional methods include the I/Q curve length method, amplitude variance analysis, and Moving Target Indication (MTI) techniques. The I/Q curve length method enhances target discrimination by analyzing the geometric characteristics of I/Q trajectories^17,18, but it is highly sensitive to noise and requires careful threshold selection. MTI can effectively suppress static clutter, but it tends to filter out low-velocity micro-motions, such as chest wall movements, leading to target loss^19,20. Background modeling can efficiently remove various types of clutter but requires frequent recalibration and shows poor adaptability in dynamic environments^21,22. The amplitude variance method has low computational complexity but is sensitive to random noise and non-periodic motion²³. In most cases, indoor environments are complex (see Fig. 1), containing both strong static reflections and dynamic clutter (e.g., from fans), making it difficult to distinguish the real target.

Fig. 1.

Masking effects and harmonic interference in complex environments.

Moreover, respiration activity introduces strong harmonic components in the HR frequency band, which can mask or distort the heartbeat signal (see Fig. 1). To address this problem, various respiration harmonic suppression methods have been proposed. Traditional frequency-domain filtering methods, such as band-pass filtering, notch filtering, or peak analysis^24–28, reduce harmonic interference by constraining or suppressing specific frequency bands, these methods are simple and real-time efficient. However, because the RR changes dynamically, fixed-bandwidth filters cannot adapt well to individual or postural variations, often causing signal distortion or loss of HR components. Another class of methods is time-domain reconstruction^29,30, which reconstructs the time-domain respiratory signal and its harmonics from the spectrum and removes corresponding components from the complex signal to recover the HR. These methods perform well for steady-state respiration but suffer from modeling inaccuracy and noise artifacts when the RR is unstable or subject to dynamic motion. Phase inversion and demodulation methods eliminate baseband DC offsets via arctangent demodulation³¹, thereby suppressing harmonics, its performance strongly depends on I/Q channel balance, when the target distance changes or the signal drifts, recalibration is required, reducing robustness in practical applications. Recently, signal decomposition techniques such as Empirical Mode Decomposition (EMD), Variational Mode Decomposition (VMD), and Empirical Wavelet Transform (EWT), as well as deep learning–based methods^32–36, have been used to separate harmonics and HR signals. Nevertheless, these methods are computationally intensive and parameter-sensitive, making real-time monitoring difficult.In comparison, adaptive filtering methods^37–39 exhibit better suppression performance in non-stationary environments by automatically adjusting filter parameters according to signal variations. However, their performance still depends on filter design and update strategy—if the filter coefficients converge too slowly or the reference signal is improperly chosen, residual respiration harmonics or excessive attenuation of the HR signal may occur.

To address the above two difficulties, this paper proposes the Matrix Coefficient Selection Method (MCSM) to improve the target distance detection performance in complex environments and the Recursive Least Squares adaptive notch filtering (RLSRHS) to suppress the respiratory harmonic. The main contributions of this paper are as follows:

• This paper introduces MCSM method based on the Range–Doppler spectrum, aimed at enhancing the accuracy and robustness of target distance estimation in cluttered environments. Unlike traditional approaches that struggle with strong reflectors or random environmental motion, the proposed MCSM framework utilizes low-frequency zero setting and autocorrelation method to effectively suppress static clutter and non periodic dynamic interference, significantly improving the reliability of distance estimation and the stability of multi-target detection under complex environmental conditions.

• Inspired by harmonic mitigation techniques in power systems^40,41, this work is the first to introduce Recursive Least Squares (RLS) adaptive filtering into vital signs measurement tasks. We propose RLSRHS algorithm that automatically removes respiratory harmonics.Unlike existing approaches such as band-pass filtering, time-domain reconstruction, or modal decomposition, the proposed method requires no manual tuning of optimal parameters. The adaptive filter automatically adjusts its coefficients in response to signal variations, making it particularly suitable for non-stationary signals.

• Simulation experiments show that the MCSM method can effectively improve the robustness of distance detection in complex environments, while the RLSRHS method can effectively suppress interference from respiratory harmonics and enhance HR monitoring performance. Extensive actual experiments, including comparisons with ECG monitoring devices, bracelets, and breath sensors, further validate the results of the simulation experiments.

The rest of the paper is organized as follows: Methods explains the working principle of FMCW radar, algorithms explains the principles and processes of the two algorithms. Result evaluates the performance of the proposed methods using an experimental platform, and Conclusion concludes the paper.

Methods

Physiological basis

All methods were carried out in accordance with relevant guidelines and regulations. All experimental protocols were approved by the Ethics Committee of Xiamen University. Informed consent was obtained from all participants prior to participation in the study. Vital signs are a set of medical parameters that indicate a person’s health status and physiological functions, providing clues to potential diseases as well as trends in recovery or deterioration. The main vital signs include four types: Body Temperature (BT), Blood Pressure (BP), RR, and HR. These parameters vary depending on age, gender, body weight, and health status. Under specific conditions, these parameters may also differ due to an individual’s physical or psychological activities. For example, individuals engaged in physical exercise may exhibit higher body temperature, RR, and HR. The normal ranges for RR and HR in healthy adults are presented in Table 1.

Table 1.

Displacement and frequency parameters of respiration and heartbeat in normal adults.

		Chest measurement	Back measurement
Vital signs	Frequency (Hz)	Amplitude (mm)	Amplitude (mm)
Respiratory	0.1–0.5	1–12	0.1–0.5
Heartbeat	0.8–2.0	0.1–0.5	0.01–0.2

Vital sign signal model based on the FMCW radar

A typical FMCW radar emits a series of signals, known as chirps, over a given time range, with the instantaneous frequency increasing linearly over time. By transmitting multiple chirp signals within a single frame, the FMCW radar can model the reflected echo signals received from the human body as follows,

1

where is the carrier frequency, and B is the sweep bandwidth, is the actual sweep time, is the power of the received signal, is the initial phase of the transmitted signal, and is the time delay.After the mixing process, we get,

2

where R(t) is the distance between the antenna and the body, and c is the speed of light, denotes the wavelength of the electromagnetic wave.When the radar system and the target are fixed, the distance relationship between the antenna and the human body is affected by the rise and fall of the thorax, and the movement of the human body’s vital signs can be expressed as maintaining a small movement r(t) around ,

3

where r(t) consists of the respiratory signal, the heartbeat signal, and the noise,

4

where represents the displacement caused by breathing, represents the displacement caused by heartbeat, and is Gaussian white noise with variance 0. And both respiratory and heartbeat signals can be regarded as periodic signals, so they can be expressed as,

5

where and denote the range of body surface displacements for respiration and heartbeat, respectively, and denote the frequency values of human respiration and heartbeat, respectively, and and denote the initial phases of respiration and heartbeat signals, respectively.Since , the effect of r(t) on the frequency term can be neglected, therefore equation (2) can be rearranged as follows:

6

Then performing FFT for fast-time dimension gives distance information and performing FFT for slow-time dimension gives vital signs information.

Algorithms

System overview and working principle

The workflow of the whole system is shown in Fig. 2. Firstly, the received echo signal and the radar transmission signal are mixed to obtain the IF signal. Second, the IF signal is pre-processed (e.g. IQ correction). Third, the real target signal is extracted by the MCSM algorithm for distance localisation of the target. Fourth, extract phase from the distance dimension of the target, harmonic suppression using RLSRHS algorithm to achieve accurate separation of respiratory and heartbeat signals. Finally, heartbeat and respiration waveforms were plotted and HR and respiration rate were evaluated.

Fig. 2.

System overview. MCSM algorithm module in red represents strong reflectors(interference), green represents target, blue represents RR, yellow represents HR, purple and orange represents respiratory harmonics, and all others are noise components.

Matrix coefficient selection method (MCSM) based on distance dimension

The above analysis shows that the correct selection of the distance dimension where the target is located is crucial; if the correct location of the target is not found, then the extracted vital sign signals about the target are erroneous and the subsequent results obtained are wrong. In order to improve the accuracy of vital signs detection, it is necessary to reduce the erroneous results due to the misjudgment of the distance dimension, so we propose the MCSM algorithm.

The main flow of the algorithm is as follows: FFT is performed on the IF signal in the fast time dimension to obtain a one-dimensional distance spectrogram, and FFT is performed again on the one-dimensional distance spectrogram in the slow time dimension to obtain a two-dimensional distance spectrogram, which is also called the distance-Doppler spectrogram, in which the fast time dimension coordinate corresponds to the distance of the target and the slow time dimension coordinate corresponds to the Doppler frequency. The two-dimensional distance spectrogram is carried out to remove the low-frequency information, after which the signal autocorrelation process is carried out, and the obtained matrix coefficients are used to select the distance units on the one-dimensional distance spectrogram, and the distance unit containing the target information is selected to complete the correct distance selection, and the algorithmic flowchart is shown in Fig. 3a.

Fig. 3.

(a) Is the MCSM algorithm flowchart, and (b) is the RLSRHS algorithm flowchart.

For the echo IF signal, assuming that the number of targets located at different distances is k, the number of sampling points in each chirp cycle is N, and the number of chirps used in a frame is M, where T denotes the pulse repetition period, and represents the sampling interval in the fast-time dimension, the expression for the IF signal reflected back from the k targets (including the strong stationary interference targets) is:

7

Performing the FFT operation on the IF signal in the fast time and slow time dimensions, respectively, where p and q are the distance index and Doppler index indices, yields:

8

The above equation is a two-dimensional spectral matrix, due to the interference of clutters in the surrounding environment, such as tables, walls, and fans, the reflection amplitude of some of these obstacles is much larger than the vital signs signal, resulting in a very weak vital signs signal on the two-dimensional spectrogram. The Doppler frequency of the 2D spectrogram does not allow direct target finding.

In the two-dimensional spectrum, these existing disturbances are manifested as DC components and low-frequency fluctuations (i.e., Doppler frequencies below a certain threshold, such as 0.05 Hz). These disturbances are primarily concentrated in the zero and low-frequency regions of the spectrum. To mitigate their influence, interference removal processing is applied to each range unit. Specifically, the DC and low-frequency components are suppressed within the two-dimensional spectrum. The number of frequency bins to be suppressed, denoted as , is determined by the Doppler frequency resolution and the disturbance frequency threshold, calculated as

9

where represents the maximum Doppler frequency to be suppressed (e.g., 0.05 Hz), and is the Doppler frequency resolution. The interference suppression operation can thus be expressed as

10

The data after removing zero and low dimension were processed for a vital sign signal autocorrelation. Autocorrelation plays an important role in extracting periodic signals that are masked by noise and identifying fundamental frequencies in harmonic frequencies of complex signals. Since the respiratory signal and heartbeat signal are signals with certain periodicity, a vital sign signal autocorrelation is performed on the data on the basis of removing the low-frequency operation, that is, autocorrelation processing is performed on all Doppler dimensions of each range dimension signal obtained after processing by formula (11).

11

For each distance unit, a matrix coefficient can be obtained, and the distance unit where the vital signs target signal is located can be obtained by obtaining the maximum matrix coefficient.

12

After defining the distance unit of the target, the signal at the corresponding range bin is extracted from the one-dimensional range spectrum. The signal subjected to phase unwrapping to remove discontinuities caused by phase wrapping. Based on the unwrapped phase, the vital-sign information of the target is further extracted, including the respiratory signal and the heartbeat signal .

Recursive least squares respiratory harmonic suppression (RLSRHS) based on adaptive notch suppression of respiratory harmonics

After selecting the appropriate range unit, the vital sign signal corresponding to that distance can be extracted, which includes both the respiratory and heartbeat components of the measured subject. Ideally, the acquired human vital sign signal can be expressed as,

13

Generally, and belong to distinct frequency bands and can be separated by appropriate bandpass filtering. However, in practice, due to the presence of respiratory harmonics and the fact that the amplitude induced by respiration is much larger than the amplitude induced by heartbeat, multiple harmonics of the respiratory frequency may extend into the heartbeat frequency band. As a result, these harmonics are often misidentified as heartbeat components, leading to estimation errors where the calculated may satisfy , as illustrated in Eq. 14,

14

Since the amplitudes of respiratory harmonics decrease as the harmonic order increases, suitable upper and lower harmonic indices and can be determined according to the range in which the respiratory harmonics overlap with the heartbeat frequency band,

15

where and denote the maximum and minimum RR (in beats per minute), and and denote the maximum and minimum RR, respectively.

Table 2 shows preliminary statistical results of HR and RR distributions for different age groups obtained from Zhongshan Hospital, Fudan University. As shown, the average resting HR of healthy adults typically ranges from 70 to 75 beats per minute, while the RR generally changes slightly, about 16 to 18 times per minute. Considering residual components and the influence of frequency resolution, and are empirically set to 5 and 3, respectively.

Table 2.

Comparison of 24-h HR indicators under daily activity among different age groups⁴².

Group	Sample size	Average HR (beats/min)	Average RR (beats/min)
Young group	19
Middle-aged group	50
Elderly group	40

Algorithm 1.

RLS Procedure

Based on this principle, the RLSRHS algorithm is proposed. The flowchart of the RLSRHS algorithm is shown in Fig. 3b, and Recursive Least Squares (RLS) filter procedure is detailed in Alg.1. In the algorithm, denotes the filter coefficient vector, is a small positive initialization constant, is the identity matrix, is the gain vector, and is the forgetting factor.

The detailed steps of the RLSRHS algorithm are as follows:Demodulation of the obtained signals containing vital signs is performed to obtain r(t),and the fundamental frequency of respiration is estimated by Rife algorithm ⁴³.Since the respiratory harmonic frequencies are integer multiples of the fundamental frequency , the respiratory harmonic frequency vector is constructed as,

16

The corresponding reference signal is expressed as,

17

The signal vector is multiplied by a set of filter coefficients to obtain the output,

18

Then, and are fed into the RLS filter to update the filter coefficients and output the harmonic-suppressed result e(t), with the above steps recursively iterated multiple times.

Result

Experimental setup

This section verifies the effectiveness and superiority of the proposed vital sign detection algorithm. First, the MCSM and RLSRHS algorithms were individually evaluated and compared with existing methods. The results demonstrate that the proposed approach effectively suppresses interference and mitigates the influence of respiratory harmonics, thereby significantly improving the accuracy of HR and RR estimation. Moreover, it exhibits robust performance under various signal-to-noise ratio (SNR) conditions, outperforming the compared algorithms. Subsequently, the algorithm was further validated and analyzed in multiple complex actual environments, and the experimental results confirm its strong applicability and stability in practical scenarios. The FMCW radar signal and vital sign parameter configurations used in the experiments are summarized in Table 3, where the simulation and actual experiments share identical waveform settings.

Table 3.

Waveform parameters and vital sign parameters.

	Parameter	Value
Radar waveform	Speed of light c	m/s
	Frequency	77 GHz
	Bandwidth B	4 GHz
	Wavelength	0.0039 m
	Chirp duration	52 s
	Chirp period T	50 ms
	Sampling frequency	5 MHz
	Number of sampling points N	256
	Number of chirps M	256
Vital sign	Target range	0.2–2 m
	Breathing amplitude	2 mm
	Heart amplitude	0.5 mm
	Breathing frequency	0.3 Hz
	Heart frequency	1.1 Hz
	Breathing harmonics	0.6 Hz, 0.9 Hz, 1.2 Hz

In the experimental setup, individual vital sign data were collected using a 77 GHz millimeter-wave radar (IWR1443, Texas Instruments, USA) in conjunction with a DCA1000EVM data acquisition board. The experimental platform is illustrated in Fig. 4. The millimeter-wave radar board is connected to the data acquisition board via the _HD_CONN_ and _60_PIN_RADAR_CONN_ interfaces, while data transmission between the two devices is achieved through an Ethernet cable. Additionally, the DCA1000EVM board is connected to the host computer via USB interfaces, enabling device control and data recording, thus forming a complete radar-based vital sign acquisition system.

Fig. 4.

Experimental radar wiring diagram.

MCSM experiment

Simulation experiment

Multiple target scenarios were simulated within a range of 0.2–2 m, encompassing both single- and multi-target cases, while introducing static as well as non-periodic dynamic clutter into the environment.Taking the targets located at 1 m and 1.6 m as examples, two-dimensional range spectra containing target position information were obtained through the aforementioned signal processing procedure, as illustrated in Fig. 5a and b. The results clearly show that the presence of surrounding obstacles and spectral broadening effects significantly increase the complexity of the range spectrum. Reflections(static and non-periodic dynamic clutter) from environmental objects introduce interference signals, resulting in spurious peaks that do not correspond to real targets. Meanwhile, the responses of actual targets in the range spectrum are relatively weak, making it difficult to accurately determine their positions based solely on range information. This phenomenon closely reflects the actual challenges faced by radar systems in complex environments and highlights the key difficulty of achieving precise target localization in vital sign monitoring tasks.

Fig. 5.

(a) Is a 2D spectrogram in the distance-slow time dimension (non-target is static clutter), and (b) is a plot of the distance-dimensional results in a single time dimension, (c) is a plot of the results after MCSM processing.

To effectively address the aforementioned issue, the proposed MCSM algorithm was applied to process the radar echo signals, as illustrated in Fig. 5c. Compared with Fig. 5a and b , the MCSM algorithm demonstrates superior target identification capability. By exploiting the inherent periodic characteristics of the signals through its distinctive modeling and processing mechanism, the algorithm effectively suppresses environmental interference and spectral broadening, thereby enabling clearer discrimination of the target’s vital sign signal from complex background clutter, even when partially obscured by obstacles.This result is of great significance for vital sign monitoring, as accurate identification of the target range cell is the key prerequisite for reliable extraction of physiological signals such as respiration and heartbeat. Only when the range cell corresponding to the target is correctly determined can subsequent signal estimation and analysis achieve high precision and stability, forming the foundation for accurate vital sign monitoring.

To quantitatively evaluate the performance and robustness of the proposed MCSM algorithm, the range cell positions were estimated from FMCW radar echo signals. Considering the distributed echo characteristics of the human thoracic region across multiple range cells, measurements with an error less than 4% were regarded as valid detections in practical applications. The detection accuracy of the algorithm was defined as the ratio of valid measurements to the total number of measurements, the estimation error and accuracy was computed according to Eq. 19,

19

Experiments were conducted over a target range of 0.2–2 m under multiple simulated and actual conditions, with varying levels of additive white Gaussian noise introduced to create different signal-to-noise ratio (SNR) environments. The target range estimation results under different SNRs were then compared with those obtained using the methods reported in literature^14–16, as shown in Fig. 6.

Fig. 6.

Comparison of ranging accuracy and MAE in different Gaussian white noise, with results for a single person at the top and multiple people at the bottom.

Simulation results indicate that as the level of additive white Gaussian noise increases, the proposed range estimation algorithm maintains high localization accuracy. This robustness arises from the algorithm’s reliance on the intrinsic periodic characteristics of the signal, rather than solely on amplitude or phase information. Consequently, it exhibits stronger resistance to noise interference. In both single-target and multi-target scenarios, the proposed method consistently achieves precise range estimation even under complex and noisy conditions. Furthermore, compared with other benchmark algorithms, the proposed approach demonstrates significantly lower mean absolute error (MAE), particularly in multi-person localization scenarios, where its distance estimation accuracy and stability are markedly superior to the other three methods.

Verification experiment

To verify the ranging performance of the proposed MCSM algorithm in actual environments, measurement experiments were conducted in multiple scenarios with known target distances, as illustrated in Fig. 7. For each scenario, hundreds of data samples were collected. The estimated target distances were compared with the ground-truth values to comprehensively evaluate the accuracy and stability of the proposed method under various environmental conditions. By averaging the ranging accuracy obtained across different experimental scenarios, the comparative results of the actual measurements were derived, as shown in Fig. 8a. It can be observed that the proposed algorithm achieves an accuracy of approximately 98% for both single- and dual-target cases, which is significantly higher than that of the other three algorithms. Furthermore, as illustrated in Fig. 8b, the proposed method consistently outperforms the compared approaches at various target distances, exhibiting a lower MAE and superior measurement stability.

Fig. 7.

MCSM experimental scenario.

Fig. 8.

(a) Is accuracy of single and two-person actual distance detection, and (b) is comparison of MAE for measured results at different distances.

RLSRHS experiments

Simulation experiment

The simulation results of the proposed RLSRHS algorithm are presented in Fig. 9. Figure 9a illustrates the original signal containing only the desired respiratory and heartbeat frequencies with added Gaussian white noise, and its corresponding spectrum is shown in Fig. 9e. In Fig. 9b, the second-, third-, and fourth-order harmonics of the respiratory signal are introduced to simulate a realistic scenario, with the corresponding spectrum shown in Fig. 9f. It can be observed that the respiratory harmonics severely interfere with the estimation of the heartbeat frequency. Figure 9c depicts the difference between the original vital sign signal and the filter output, representing the result after harmonic suppression, and its spectrum is shown in Fig. 9g, where the respiratory harmonic interference is effectively attenuated. Figure 9d shows the final output of the filter, while Fig. 9h presents its convergence process. The results indicate that the filter achieves convergence within a short period, demonstrating the rapid response and effectiveness of the RLSRHS algorithm in suppressing respiratory harmonic interference.

Fig. 9.

RLSRHS algorithm simulation results.

To verify the performance advantage of the proposed RLSRHS algorithm, comparative analyses were conducted against several existing harmonic removal methods. First, to investigate the differences in suppression mechanisms among various approaches, the proposed RLSRHS algorithm was compared with a frequency-domain respiratory signal reconstruction method³⁰. This reconstruction method performs a Fourier transform on the signal to identify the amplitude and phase of the fundamental respiratory frequency and its higher-order harmonics, reconstructs the respiratory components in the time domain, and subtracts them from the original signal to achieve harmonic suppression. The comparative results are shown in Fig. 10. Under SNR of 0 dB, −3 dB, and −6 dB, the proposed RLSRHS algorithm consistently exhibits superior harmonic suppression performance compared to the reconstruction method. This improvement is primarily attributed to the fact that FFT-based reconstruction can accurately recover phase information only when the signal satisfies the periodic truncation condition, where spectral leakage is minimal. In contrast, when the signal does not meet this condition, the accuracy of frequency and phase estimation degrades significantly. The proposed RLSRHS algorithm, however, relies solely on the estimation of the fundamental respiratory frequency, which can be further refined using the Rife frequency estimation technique, thereby enhancing the overall suppression of respiratory harmonics.

Fig. 10.

Comparison of the performance of RLSRHS and³⁰ method under different SNRs.

To further validate the superiority and effectiveness of the proposed RLS algorithm in adaptive filtering, a comparative analysis was conducted against the classical LMS adaptive notch filter³⁹. Although the two algorithms share a similar structural framework, they differ fundamentally in their coefficient update strategies: the LMS algorithm iteratively adjusts filter weights using the gradient descent method, whereas the RLS algorithm minimizes the weighted least squares error, enabling faster convergence and enhanced dynamic tracking capability. In the experimental setup, both adaptive filtering algorithms were simulated under identical parameter configurations. The estimation error between the measured and true values was computed according to Eq. 19, and detections with an error smaller than 1% (corresponding to the minimum accuracy requirement for HR estimation) were regarded as valid. The accuracy was then obtained by calculating the ratio of valid detections to the total number of measurements, as summarized in Table 4.

Table 4.

Comparison of HR Estimation Accuracy Using Different Methods.

Method used	Accuracy
None	46%
LMS39	57%
RLS[ours]	83%

The simulation results demonstrate that incorporating an adaptive filter effectively mitigates the interference of respiratory harmonics on HR extraction, thereby significantly improving the accuracy of HR estimation. Compared with the conventional LMS adaptive filter, the RLS filter exhibits superior performance in both detection accuracy and stability, enabling more robust and reliable HR monitoring.

Verification experiment

To validate the practical effectiveness of the proposed RLSRHS algorithm, multiple experimental trials were conducted involving several participants under various conditions. The harmonic suppression performance of the algorithm was first evaluated in actual environments, with the experimental setup shown in Fig. 11, where the millimeter-wave radar was positioned approximately 0.8 m in front of the subject. The measured radar vital-sign spectra are presented in Fig. 12. As observed, the reconstruction-based method shows limited capability in suppressing second- and third-order harmonics. Although the LMS adaptive filter effectively reduces these harmonics, it simultaneously attenuates the HR component and introduces additional frequency artifacts, thereby degrading the HR estimation accuracy. In contrast, the proposed RLSRHS algorithm successfully suppresses harmonic interference while preserving the essential characteristics of the HR signal. The dominant peaks corresponding to the respiration and HR frequencies remain clearly distinguishable after filtering, enabling accurate and reliable vital-sign estimation.

Fig. 11.

RLSRHS experimental scenario.

Fig. 12.

RLSRHS experimental comparison chart, with black, blue, orange red, and yellow circles representing RR, respiratory harmonics, HR, and other interference frequencies, respectively.

Comprehensive experiment

To comprehensively evaluate the performance of the proposed algorithm, experiments were conducted under three different scenarios, and the results were compared with those obtained from commercial monitoring devices such as an electrocardiograph (ECG) monitor and a Xiaomi smart band. The waveform configuration used in all comprehensive experiments was identical to that in the previous practical validation experiments, as summarized in Table 3.

Scenario 1: Comparison with cardiac monitor at rest

In the first experiment, vital-sign data were collected from a subject in a sedentary resting state. The experimental setup is illustrated in Fig. 13. The millimeter-wave radar was positioned directly in front of the subject to measure respiration and HR in real time, while an ECG monitor was connected to the subject via cables to provide reference measurements for validating the radar-based results.

Fig. 13.

Scenario 1 experiment setup.

Figure 14 presents the results of a single measurement obtained using both the radar and the ECG monitor. As shown, the ECG monitor measured a HR of 60 beats per minute (bpm) and a respiration rate of 18 breaths per minute (brpm), while the radar estimated corresponding values of 58.7 bpm and 17.1 brpm. The close agreement between the two sets of results demonstrates the accuracy and reliability of the proposed algorithm for vital-sign detection under resting conditions.

Fig. 14.

Comparison chart of single measurement between ECG monitor and radar.

To further quantify the performance of the proposed method, the mean relative error (MRE) and root mean square error (RMSE) of the respiration rate and HR were calculated, as defined in Eq. 20,

20

where denotes the measured value, represents the reference value obtained from the ECG monitor, and N is the total number of samples, MRE represents the mean relative error, while RMSE represents the number of deviations.

Figure 15 illustrates the vital-sign detection results obtained from the radar and the ECG monitor over a period of time. The RR measurements from both systems exhibit highly consistent trends. Since the HR signal has a relatively weak amplitude and is susceptible to noise interference, a median filter was applied to the radar signal to remove outliers and enhance stability. In the figure, the blue dashed line represents the radar HR results before median filtering, the red solid line denotes the radar HR results after filtering, and the yellow solid line indicates the HR obtained from the ECG monitor. The results demonstrate that, after median filtering, the radar-derived HR closely matches that of the ECG monitor, confirming the effectiveness and robustness of the proposed method for HR estimation. The radar-estimated respiration rate achieved an MRE of 4.47% and an RMSE of 1.054, demonstrating strong consistency with the ECG measurements. For HR estimation, after applying the filtering algorithm, the MRE decreased from 5.79 to 4.60%, and the RMSE was reduced from 4.32 to 3.45, indicating that the filtering process effectively suppressed interference and improved detection stability. Overall, these error levels are within the acceptable range for clinical vital-sign monitoring accuracy⁴⁴, confirming that the proposed radar-based method can reliably and accurately reflect the subject’s actual respiration and HR.

Fig. 15.

Comparison of radar and ECG monitor measurements over a period of time.

Furthermore, to evaluate the adaptability of the proposed algorithm under varying respiratory conditions, vital-sign detection experiments were conducted across multiple breathing patterns. Table 5 lists the changes in respiratory state at different time intervals, while Fig. 16 presents the detection results of a single subject over approximately 192 s. The results indicate that, even when the subject continuously changed breathing patterns during the experiment, the radar-based measurements remained in good agreement with those obtained from the ECG monitor.The radar-estimated RR achieved an MRE of 19.95% and an RMSE of 4.17. The relatively higher RR error can be attributed to the rapid and irregular variations in the subject’s breathing during the experiment, which caused significant fluctuations in the instantaneous amplitude and frequency of the respiratory signal. For HR estimation, after applying the filtering algorithm, the MRE decreased from 8.89 to 5.35%, and the RMSE was reduced from 8.16 to 4.64, demonstrating that the filtering process effectively suppressed interference and improved detection stability.

Table 5.

Time status table.

Time start(s)	End time(s)	Status
0	15	Steady breathing
15	30	Rapid breathing
30	60	Steady breathing
60	90	Slow breathing
90	130	Steady breathing
130	160	Rapid breathing
160	192	Steady breathing

Fig. 16.

Results of RR and HR of subjects in different states over a period of time.

Scenario 2: Comparison with bracelet and breath sensor under exercise condition

In this experimental scenario, two different contact-based devices were used to measure the subject’s HR and RR during motion. A subject was first tested in a sedentary resting state to collect baseline vital-sign data (as shown in Fig. 17), followed by simultaneous monitoring during a walking experiment. The subject wore a Xiaomi bracelet band on the left wrist to record HR and attached a respiratory sensor to the abdomen to measure RR. The subject walked steadily at a normal pace indoors to evaluate the performance of the proposed algorithm under dynamic conditions.

Fig. 17.

Scenario 2 experiment setup.

The results of a single measurement are shown in Fig. 18. As illustrated, the Xiaomi bracelet band measured a HR of 67 beats per minute (bpm), and the respiratory sensor measured a respiration rate of 20.4 breaths per minute (brpm). The radar estimated corresponding values of 68.03 bpm for HR and 20.17 brpm for respiration rate. The high consistency among the three measurement systems further confirms the accuracy and reliability of the proposed algorithm for vital-sign detection under dynamic motion conditions.

Fig. 18.

Comparison chart of single measurement.

The statistical results and corresponding error analysis are summarized in Table 6. As shown, the HR (HR) values obtained from the radar closely match those recorded by the Xiaomi bracelet band, indicating a high level of accuracy and consistency between the two measurement methods. In contrast, the respiration rate (RR) measurements exhibit a wider error variation. This discrepancy is primarily attributed to the subject’s walking motion, where natural rhythmic movements of the abdomen, including slight displacement and compression, can interfere with the respiratory sensor’s ability to capture consistent readings, thereby increasing RR measurement error. When using the Xiaomi bracelet band as a reference, the radar-derived HR results maintained a relatively low error range, typically within 0–4%, which falls well within the expected tolerance of this experimental setup. This demonstrates that the radar-based measurement system provides reliable performance and can serve as a viable alternative or complementary technology to traditional wearable devices for vital-sign monitoring during motion. These findings confirm the feasibility and potential of radar sensing for accurate, non-contact physiological monitoring under dynamic conditions.

Table 6.

HR and RR comparison chart.

Number	HR (times/min)			RR (times/min)
	Radar	Xiaomi bracelet	Error rate	Radar	Respiration sensor	Error rate
1	68	67	1.4%	20.1	20.4	1.5%
2	99	97	2.1%	27.1	29.5	8.1%
3	78	78	0%	17.3	18.0	3.9%
4	102	104	1.8%	25.4	25.0	1.6%
5	87	90	3.3%	19.8	20.1	1.5%
6	100	106	5.7%	24.3	26.3	8.2%
7	70	70	1.4%	17.6	19.3	8.8%
8	101	100	1.0%	22.0	22.4	1.7%
9	75	76	1.3%	19.0	19.5	2.5%
10	95	94	1.0%	26.2	26.0	0.8%

Scenario 3: Multi-target monitoring

In this experimental scenario, the respiration and RR of two targets located at different radial distances were simultaneously measured. Target 1 was positioned approximately 0.76 m from the radar, while Target 2 was located at a distance of about 1.33 m. During the experiment, Target 1 maintained a rapid breathing pattern, whereas Target 2 exhibited a steady and regular respiratory rhythm. The experimental setup is illustrated in Fig. 19.

Fig. 19.

Scenario 3 experiment setup.

In Fig. 20, the blue solid line represents the RR and HR of Target 1, while the red solid line represents those of Target 2; in Fig. 17b, the black dashed line indicates the HR trend of Target 1. It can be observed that Target 1, which maintains rapid breathing, consistently exhibits a higher RR than Target 2, which breathes steadily. During the first half of the measurement period, both targets’ RR remain within similar ranges; in the latter half, the HR of Target 1 gradually increases due to rapid breathing, as reflected by the upward trend in its HR curve. Long-term monitoring of multiple targets’ RR and HR enables simultaneous capture of vital signs from multiple individuals, and the observed trends can be used for timely intervention when necessary, effectively reducing the risk of fatal cardiovascular or pulmonary events.

Fig. 20.

RR and HR results for two subjects at different distances and conditions.

Conclusion

For non-contact vital signs detection using FMCW radar, the accuracy mainly depends on the correct selection of distance units and the accurate estimation of frequency. To address these two key factors, we propose two methods:MCSM based on vital sign sign signals to accurately select distance units, and RLSRHS to suppress the effect of respiratory harmonics on heartbeat frequency estimation. Through extensive simulation experiments and real data experiments on these two methods, we find that the method in this paper is able to extract the desired vital sign-related parameters more accurately. The measured results show that the MCSM distance selection method significantly improves the accuracy of target distance detection and demonstrates good robustness in complex environments with low signal-to-noise ratios. Meanwhile, the RLSRHS adaptive trapping method effectively reduces the influence of breathing harmonics. The validity and reliability of these algorithms are verified by comparing the detection results with those from ECG monitors and contact devices such as bracelets. Overall, our proposed method significantly improves the accuracy of vital signs detection.

Author contributions

C.Z. and H.L. conceived the study and supervised the overall project,conducted the experiments, and wrote the main manuscript text. Y.Z. developed the radar signal processing algorithms.G.F. assisted with data analysis and figure preparation. X.C. and D.Y. reviewed and edited the manuscript. All authors reviewed and approved the final version of the manuscript.

Data Availability

The data that support the findings of this study are available from the corresponding author upon request.

Declarations

Approval for human experiments

All methods were carried out in accordance with relevant guidelines and regulations. All experimental protocols were approved by the Ethics Committee of Xiamen University. Informed consent was obtained from all participants prior to participation in the study.

Competing interests

The authors declare no competing interests.