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# WiCG: in-body cardiac motion sensing based on a mix-medium Wi-Fi fresnel zone model

Pei Wang, Anlan Yu, Xujun Ma, Rong Zheng, Jingfu Dong, Zhaoxin Chang, Duo Zhang, Djamal Zeghlache, Daqing Zhang

► To cite this version:

Pei Wang, Anlan Yu, Xujun Ma, Rong Zheng, Jingfu Dong, et al. WiCG: in-body cardiac motion sensing based on a mix-medium Wi-Fi fresnel zone model. IEEE Transactions on Mobile Computing, 2025, 24 (10), pp.1-15. 10.1109/TMC.2025.3564843. hal-05215250

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# WiCG: In-Body Cardiac Motion Sensing Based on a Mix-Medium Wi-Fi Fresnel Zone Model

Pei Wang, Graduate Student Member, IEEE, Anlan Yu, Xujun Ma, Member, IEEE, Rong Zheng, Senior Member, IEEE, Jingfu Dong, Member, IEEE, Zhaoxin Chang, Duo Zhang, Djamal Zeghlache, Life Member, IEEE, and Daqing Zhang, Fellow, IEEE

**Abstract**—Cardiovascular diseases (CVDs) are a leading cause of mortality worldwide, highlighting the critical need for accurate and continuous heart health monitoring. Electrocardiograms (ECG), considered as the golden standard for diagnosing and monitoring heart-related conditions, offer precise measurements but require direct skin contact, limiting their practicality for long-term and everyday use. On the other hand, existing RF sensing techniques that analyze signals reflected off the skin struggle to distinguish micro cardiac motions of the heart due to weak motion amplitude and respiration interference at the chest wall. To overcome these limitations, we introduce WiCG, a novel contact-less cardiac motion monitoring system that employs 2.4 GHz Wi-Fi signals to penetrate the chest and detect subtle cardiac movements. A mix-medium Wi-Fi Fresnel zone model is developed to explain the enhanced phase sensitivity of in-body Wi-Fi signals, which is crucial for accurately detecting cardiac motions. By strategically positioning antennas near the heart, WiCG captures ventricular motions effectively. A novel cardiac Doppler method is proposed to suppress phase noise and interference from static paths and extract the time interval between the systole and diastole of the ventricular. Extensive experiments demonstrate that the proposed system can robustly estimate the R-R and Q-T intervals of human cardiac cycles across 21 subjects and different environments with an average accuracy of 99.22% and 92.8%, achieving performance comparable to ECG.

**Index Terms**—Cardiac cycle estimation, Wi-Fi, In-body sensing, Fresnel zone model.

## I. INTRODUCTION

CARDIOVASCULAR diseases (CVDs) have become a major threat to human health [1]–[4]. According to the World Health Organization (WHO), an estimated 17.9 million people died from CVDs in 2019, representing 32% of all global deaths. Of these deaths, 85% were due to heart attack

This work was supported by in part by the European Union through the Horizon EIC pathfinder challenge project SUSTAIN under Grant 101071179 and in part by the Innovative Medicines Initiative 2 Joint Undertaking under IDEA-FAST project under Grant 853981.

Pei Wang, Xujun Ma, Zhaoxin Chang, Djamal Zeghlache and Daqing Zhang are with the SAMOVAR, Télécom SudParis, Institut Polytechnique de Paris, 91120 Palaiseau, France (e-mail: pei.wang@telecom-sudparis.eu; xujun.ma@telecom sudparis.eu; zhaoxin.chang@telecom-sudparis.eu; djamal.zeghlache@telecom-sudparis.eu; daqing.zhang@telecom-sudparis.eu)

Rong Zheng is with the Department of Computing and Software, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada (email: rzheng@mcmaster.ca)

Anlan Yu, Duo Zhang and Jingfu Dong are with the School of Computer Science, Peking University, No.5 Yiheyuan Road, Haidian District, Beijing, P.R. China (email: yal6040@pku.edu.cn; jf200203@bupt.edu.cn; zhangduo@stu.pku.edu.cn)

Manuscript received 17 May 2023; revised 05 Nov. 2023; accepted XX XXX. XXXX. Date of publication XX XXX. XXXX; date of current version XX XXX.XXXX. (Corresponding author: Xujun Ma.)

<figure><img src="image_3.png" /><figcaption>Fig. 1: WiCG Output VS. ECG Output.</figcaption></figure>

and stroke [5]. To evaluate the health status of hearts, it's crucial to evaluate the rhythmic coordination between the actions of its main functional chambers, the atria, and the ventricles. In a healthy heart, these chambers work in tandem with a highly synchronized rhythm to efficiently pump blood throughout the body, ensuring an adequate oxygen supply to the organs. However, when CVDs occur, deviations in rhythm between the cardiac motions can lead to irregularities. By carefully examining these deviations, clinical experts can diagnose specific heart conditions. For example, atrial fibrillation causes irregular R-R intervals between consecutive ventricular contractions [6], and Long Q-T Syndrome could be characterized by the prolonged Q-T intervals from ventricular systole to diastole [7]. As heart attacks happen acutely with little warning, such rhythm deviations may not be easily discovered during brief consultations with doctors. Therefore, to better diagnose, manage, and prevent heart diseases, it is essential to continuously monitor cardiac activities over the long term [8], [9]. Clinically, the Electrocardiogram (ECG), which measures the electrical activity of the heart, is considered to be the golden standard for diagnosing and monitoring many heart-related conditions [10]–[15]. From ECG, specific intervals of atrial and ventricular activity can be clearly identified from the peaks corresponding to the P-wave, QRS complex, and T-wave. However, the use of an ECG device is limited by the need to attach sticky electrodes to the patient's skin at specific positions. This requirement hinders its long-term use at home, especially for patients with burnt or sensitive skin. Alternatively, Photoplethysmography (PPG) can extract R-R intervals and blood oxygen measurements using sensors embedded in smart watches, finger or ear clips. Machine Learning algorithms enable researchers to utilize PPG data for CVD diagnosis [16]–[20]. However, the quality of PPG
data highly depends on the firm contact between the sensors and human skin, which can lead to discomfort over prolonged use, and low accuracy when sweating.

Apart from sensors that require direct skin contact, contact-less sensing techniques are also exploited for heart monitoring. Researchers in [21], [22] use piezoelectric sensors inside the pillows/mattresses to capture the Ballistocardiography (BCG) signal for detecting CVDs. However, since the piezoelectric sensors are highly sensitive to body movements, patients must remain still during data collection. Furthermore, BCG recordings capture the combined activities from all the cardiac chambers and large vessels, lacking detailed information on cardiac movements such as Q-T interval. Seismocardiography (SCG) [23], [24] records heart vibrations using accelerometers placed on the chest area. Similar to BCG, SCG data is significantly influenced by respiration and body movements, and can only be used to estimate R-R intervals. Such restrictions greatly limit its usage in continuous monitoring of cardiac activities.

Recently, RF sensing offers an attractive alternative for long-term monitoring due to its non-contact nature. Many works have exploited Wi-Fi signals for remote human respiration monitoring [25]–[31] and activity detection [32]–[37]. However, unlike respiration, which causes centimeter-level displacement of the chest wall, cardiac-induced motions result in only millimeter-level chest wall displacements due to the covering of the sternum and the thickness of thoracic tissues. Such minute displacements are challenging to detect using Wi-Fi signals due to their limited bandwidth and large wavelength in the air. MmWave radars have shown promise in monitoring cardiac activities [38]–[47]. By filtering out low-frequency respiration signals, the R-R intervals between adjacent heart beats can be readily estimated from radar measurements. However, the performance of these approaches heavily relies on the quality of the received signals. Accurate estimations are possible only when the radar is directly facing one's chest area and there is little physical movement.

As shown in TABLE I existing heart monitoring solutions suffer from high cost, discomfort, limited granularity, or restrictive usability. Can we detect the subtle motions of the human heart without skin contact? Indeed, the answer is a resounding yes. It is known that low-frequency RF signals can penetrate human body tissues when the Tx-Rx antennae are placed close to the skin. However, the sensing mechanisms for in-body RF cardiac activity monitoring are not yet well explored. What is the effective sensing range of wireless signals inside the human body? What level of accuracy can be achieved in detecting internal physiological activities through such signals? In this paper, we develop WiCG, a novel in-body Wi-Fi cardiac motion sensing system by leveraging the capability of low-frequency RF signals to penetrate human body tissues [48]. As shown in Figure 1, the TX-RX antenna pair of a Wi-Fi device is placed over the heart area separated by normal clothing. The transmitted signal penetrates the human tissue, and upon being reflected by the heart, it is received by the receiving antenna. When properly positioned, WiCG can directly capture the cardiac movements without any close contact with human skin.

In realizing non-contact in-body cardiac motion sensing using Wi-Fi, we focus on three key design considerations. **First, a theoretically-sound system model is essential.** Due to the different dielectric constants of the human body and air, the wavelength and attenuation coefficient of the signal change after it penetrates the skin. In this paper, a mix-medium Fresnel zone model is introduced and validated experimentally to characterize the properties of RF signals in media with different dielectric constants. **Second, to extract fine-grained cardiac motions, a high-quality signal needs to be captured.** The informativeness of the received signal is influenced by several factors. As the TX-RX antenna is placed on the chest, the interference from the chest displacement caused by respiration, direct over-air transmission, and multipath reflections from fat layers and bones is non-negligible. Additionally, the thickness of the chest cavity varies at different positions within the heart area, causing the signal to penetrate different tissues to reach the heart. Therefore, it is important to have a principled way to decide the best placement positions for TX-RX that maximizes the received signal quality. **Third, the usability of the system is key for its applicability in practice.** Specifically, users should not require professional supervision or extensive medical knowledge to be able to set up and use the system.

In summary, this paper develops novel techniques for in-body Wi-Fi cardiac motion sensing and makes the following contributions:

* To the best of our knowledge, this is the first work to sense fine-grained cardiac motions using commodity Wi-Fi devices. The principled design is based on the properties of electromagnetic propagation in different mediums.

* A mix-medium Fresnel Zone model is introduced to characterize the interaction of RF signals with static and dynamic surfaces. We have experimentally verified the reduced wavelength and concentrated sensing coverage of 2.4GHz signals in a medium with a dielectric coefficient similar to that of the human body. These properties make Wi-Fi signals an excellent candidate for in-body cardiac motion sensing.

* A robust cardiac interval extraction method is developed that can successfully suppress the interferences from respiration and other multipath reflections.

* A new metric is introduced to assess and guide antenna placement on the human body. The resulting guideline is easy to follow by new users after no more than 15-min of initial training.

* We implement WiCG for human cardiac motion sensing. Extensive experiments show that the proposed system can robustly detect R-R and Q-T intervals of the human cardiac cycle in different environments at an average accuracy of 99.20% and 93.4%, respectively, compared with that obtained with an ECG device.

The rest of the paper is organized as follows. Section II introduces the preliminary of human cardiac motion and signal characteristics in different mediums. Section III presents the mix-medium Wi-Fi Fresnel zone model and demonstrates the
<table><caption>TABLE I: Comparison with existing approaches in terms of cardiac monitoring.</caption><thead><tr><th>Tech</th><th>Cost</th><th>Is skin contact?</th><th>Clinical setup required?</th><th>Working Principle</th><th>Output Features</th></tr></thead><tbody><tr><td>Electrocardiogram (ECG)</td><td>>$2000</td><td>Yes</td><td>Yes</td><td>Human electromyographic (EMG) signals</td><td>ECG Waveform</td></tr><tr><td>Ultrasound equipment</td><td>>$20000</td><td>Yes</td><td>Yes</td><td>Ultrasound imaging</td><td>Sonographic images</td></tr><tr><td>FMCW Radar</td><td>$300-1000</td><td>No</td><td>No</td><td>Radar-based sensing of subtle vital signs</td><td>Heartbeat interval</td></tr><tr><td>WiCG</td><td>&lt;$50</td><td>No</td><td>No</td><td>Mix-Medium Wi-Fi Fresnel Zone Model</td><td>R-R interval &amp; Q-T interval</td></tr></tbody></table>

sensing cover in water. In Section IV, the system design and workflows of WiCG are described. Section V reports the evaluation results. Limitations are discussed in the Section VI. Section VII reviews related works, and conclusions and future work are discussed in Section VIII.

## II. BACKGROUND

### A. Human Heart Anatomy and Cardiac Motions

<figure><img src="image_4.png" /><figcaption>Fig. 2: Heart structure and its location inside the chest.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3: Cardiac cycle intervals in ECG.</figcaption></figure>

The human heart is a muscular organ located slightly to the left of the chest's midline, as shown in Figure 2. It's roughly the size of a fist and is responsible for pumping blood throughout the body, delivering oxygen and nutrients to cells while removing waste [49], [50]. Positioned at the upper part of the heart, the atria are deeper from the surface of the body [51]. They consist of the right atrium, receiving deoxygenated blood from the body, and the left atrium, receiving oxygenated blood from the lungs, both functioning primarily as intake chambers that prepare blood for the subsequent pumping phase. In contrast, the ventricles are located at the lower part of the heart and are shallower from the body's surface [51]. The right ventricle sends deoxygenated blood to the lungs for oxygenation, while the left ventricle pumps oxygen-rich blood to the systemic circulation.

The cardiac cycle is mainly driven by the systole and diastole of the ventricular. As the ventricle begins to systole, the pressure exceeds that of the corresponding atrium, resulting in the closure of the atrioventricular valves. With increased ventricular pressure, the semilunar valves open, allowing blood to leave the ventricle. The arterial blood is pumped throughout the body and pulmonary trunk, and the venous blood is squeezed pulmonary trunk. During the ventricular diastole, as a precipitous fall in the intra-ventricular pressure. The ventricular pressure becomes less than the atrial pressure, and the atrioventricular valves open. The blood outflows the atria to fill the ventricles, and the volume accounts for about 2/3 of the blood that is in the ventricle before it contracts. The

systole and diastole of the ventricular are the most powerful and rapid cardiac activities of the heart, and maintain the heart's regulation of blood flow in the human body.

Electrocardiography (ECG) measures the electrical activity of the heart over a period of time. It detects the electrical signals generated by the polarization and depolarization of cardiac tissue and translates them into a waveform. In ECG, the R-R and Q-T intervals are critical in assessing cardiac function and rhythm. As shown in Figure 3, the R-R interval, measuring the time between consecutive R waves, is indicative of heart rate and rhythmic regularity, with its variability reflecting autonomic control of the heart [52]. The Q-T interval, extending from the onset of the QRS complex to the end of the T wave, encompasses both ventricular depolarization and repolarization. The duration of Q-T intervals is heart rate-dependent. The prolongation of Q-T intervals is a risk factor for Torsades of Pointes and sudden cardiac death [53], [54]. Its prolongation suggests a first-degree heart block and shortening potentially indicating pre-excitation syndromes [9], [55], [56]. Accurate measurement and interpretation of these intervals are essential for the diagnosis and management of a multitude of cardiac conditions.

### B. Wi-Fi Signal Propagation in Different Mediums

In order to leverage Wi-Fi signals for in-body cardiac motion detection, it is essential to understand the penetration properties of RF signals inside the human body. Thus, we begin with the analysis of RF signal attenuation in the medium in two main Wi-Fi bands, i.e., 2.4GHz and 5GHz.

When a signal propagates in a uniform medium, its energy will attenuate over distance following [57]:

$$P' = e^{-\beta l} P, \qquad (1)$$

where $P$ represents the signal power at the source, $P'$ represents the signal power attenuated by the medium, $l$ represents the distance the signal propagates in the medium, and $\beta$ is the attenuation factor determined by the medium property. Specifically, we have:

$$\beta = \frac{2\pi}{\lambda_0} \sqrt{\frac{\sqrt{\varepsilon'^2 + \varepsilon''^2} - \varepsilon'}{2}}, \qquad (2)$$

where $\lambda_0$ is the wavelength of the signal in vacuum, $\varepsilon'$ is the dielectric constant and $\varepsilon''$ is the loss factor of the medium. $\varepsilon'$ and $\varepsilon''$ correspond to the real and imaginary parts of the complex permittivity of the medium $\varepsilon = \varepsilon' - j\varepsilon''$, respectively.

In the 2.4GHz and 5GHz Wi-Fi frequency bands, the complex permittivity of air can be approximate as constant 1, i.e. $\varepsilon^{air} \approx 1$, and $\beta^{air} \approx 0$, $e^{-\beta^{air}l} \approx e^{-0 \times l} = 1$. Therefore in this paper, the energy attenuation caused by air is negligible
and is omitted. On the other hand, given that the human body is composed of approximately 60% water, the dielectric properties of water dominate the overall dielectric behavior of in-body tissues. Therefore, for simplicity, we regard the permittivity of the human body the same to that of the water in the subsequent analysis.

At room temperature (25°C), the complex permittivity of water in the 2.4GHz and 5GHz frequency bands are $\epsilon_{2.4GHz} = \epsilon_{water}' - j\epsilon_{water}'' = 78 - 12.5j$, and $\epsilon_{5GHz} = \epsilon_{water}' - j\epsilon_{water}'' = 73.73 - 17.81j$ [58], [59]. Accordingly, the attenuation factors of 2.4GHz and 5GHz Wi-Fi signals in water are $\beta_{2.4GHz}^{water} = 35.46$ and $\beta_{5GHz}^{water} = 107.83$. Therefore, 2.4GHz signals attenuate much slower than 5GHz signals in water. Under the same transmitted signal power, 2.4GHz signals can penetrate more deeply, making them better suited to detect motion within the medium.

When Wi-Fi signals enter different mediums, their signal wavelength will change. The wavelength $\lambda$, frequency $f$, and wave speed $v$ of electromagnetic waves in the medium have the following relationship:

$$ \lambda = \frac{v}{f}. \qquad (3) $$

In different mediums, the frequency of the electromagnetic wave remains unchanged, while the speed of electromagnetic waves is slower than the speed of light in vacuum (i.e., $c$). The wave speed in the medium depends on the dielectric constant $\epsilon'$ of the medium: $v = \frac{c}{\sqrt{\epsilon'}}$. As a result, the wavelength of electromagnetic waves in the medium will be:

$$ \lambda = \frac{c}{\sqrt{\epsilon' f}}. \qquad (4) $$

From equation 4, we can observe that for electromagnetic waves of the same frequency, the wavelength shortens when propagating in a medium with a larger dielectric constant. For example, with a dielectric constant approximately equal to 1, the wavelength of a 2.4GHz Wi-Fi signal is around 12.5 cm in air. The dielectric constant of water is around 75, and thus the wavelength of a 2.4GHz Wi-Fi signal in water is shortened to about 1.44 cm.

### III. SYSTEM MODEL AND FEASIBILITY STUDY

In this section, we introduce a mix-medium Fresnel zone model to characterize how Wi-Fi signal propagates through body tissues and validate it empirically using controlled experiments.

#### A. Mix-Medium Wi-Fi Fresnel Zone

In a Wi-Fi sensing system, in addition to the LoS (Line-of-Sight) path, signals from Tx to Rx may propagate along multiple reflection paths. Among these signal paths, ones that do not change are referred to as static paths, whereas paths that vary are called dynamic paths. Therefore, the received Wi-Fi CSI signal can be decomposed into a superposition of static component $H_s(f, t)$ and a dynamic component $H_d(f, t)$:

$$ H(f, t) = H_s(f, t) + H_d(f, t). \qquad (5) $$

The superposition of static and dynamic signals results in increased total signal amplitude when they are in-phase and decreased amplitude when they are out-of-phase, which can be described by the Fresnel zone model [34]. As illustrated in Figure 4, consider Tx-Rx separation of distance $d$ and a set of ellipses with foci at the Tx and Rx. Signals reflected from a target at distances $r_T$ to Tx and $r_R$ incurs a phase shift of $\frac{2\pi(r_T+r_R)}{\lambda}$.

<figure><img src="image_6.png" /><figcaption>Fig. 4: Fresnel zones. Fresnel zones in water are denser than those in air.</figcaption></figure>

The boundary of the i-th Fresnel zone refers to the ellipse when the phase difference between the reflected path and the direct path of the signal is $i\pi$. Therefore, The boundary of the i-th Fresnel zone can be described by the following equation:

$$ r_T + r_R = \frac{\lambda i}{2} + d. \qquad (6) $$

From equation 6, it can be observed that when other conditions are the same, the smaller the wavelength of the electromagnetic wave, the smaller the range of the i-th Fresnel zone. As discussed in Section II-B, in a medium with a smaller dielectric constant (i.e., air), the RF signal wavelength is larger, leading to a larger i-th Fresnel zone boundary (bottom half of Figure 4); in a medium with a larger dielectric constant (i.e., human body or water), signal wavelength is smaller (top half of Figure 4), leading to a smaller i-th Fresnel zone boundary.

<figure><img src="image_7.png" /><figcaption>(a) When an object moves (b) When an object moves in air, the dynamic signal in water, the dynamic signal rotates by $\theta_{air}$. rotates by $\theta_{water}$.</figcaption></figure>

Fig. 5: When an object moves the same distance in water, the dynamic signal rotates by a greater number of degrees due to the higher density of Fresnel zone boundaries in water compared to air.

Having a denser Fresnel zone implies that the signal is more sensitive to changes in the dynamic path length. Consider an object crossing the Fresnel zones and moving from A to B over a short distance $d$. As shown in Figure 5a, when the object moves in the air, since $d$ is smaller than the distance between the neighboring even Fresnel zone and the odd Fresnel zone,
$H_d$ rotates by $\theta_{air}$, which is much less than $\pi$. In contrast, when the object moves the same distance in water shown in Figure 5b, it cuts more than 3 Fresnel zones resulting in a larger rotation phase $\theta_{water}$. From this example, it is evident that the same small displacement of a reflective surface causes a much greater change in signal phase in water than in air, resulting in enhanced sensing sensitivity.

<figure><img src="image_8.png" /><figcaption>(a) Metal plate moves in (b) Metal plate moves in air. water.</figcaption></figure>

<caption>Fig. 6: Experiment setups.</caption>

To verify this key insight experimentally, we use a pair of commercial Intel 5300 network cards and a Universal Software Radio Peripheral (USRP) B210 that is transmitting a continuous wave signal with a center frequency at 2.4GHz to conduct verification experiments separately. The LoS length of the two USRP antennas is 5 cm. A 10cm*10cm iron plate is mounted on a high-precision sliding track, which moves at 2cm/s. The sliding track starts at 5 cm away from the LoS, and moves to 10 cm. Two scenarios are tested. In the first case (Figure 6a), the metal plate moves in the air. In the second case (Figure 6b), the metal plate is immersed in water <fnref n="1" />, with the USRP antenna placed on the side wall of the water tank.

Figure 7 and Figure 8 show the theoretical prediction and experimental results of the signal characteristics in two scenarios respectively. The dynamic signal rotates less than one circle when the plate moves 5cm in the air (i.e., the phase change is less than $2\pi$). When the plate moves in water, the dynamic signal rotates more than 7 cycles (i.e., the phase change exceeds $14\pi$), exhibiting roughly 7× greater phase sensitivity compared with the detection in the air. The measurements from USRP and Intel 5300 network card both exhibit good consistency with the theoretical values and with one another.

## B. In-Medium Sensing Coverage

Sensing Signal-to-Noise-ratio (SSNR) characterizes the quality of Wi-Fi CSI signals for sensing, which can be described as [60]:

$$SSNR = \frac{P_d}{P_i} = \frac{\lambda^2 P_T G_t G_r \sigma}{(4\pi)^3 (r_T r_R)^2 P_i}, \quad (7)$$

where $P_i$ is the power of the interference signal, $P_t$ and $P_d$ represent the power of the transmitted and received signals, $G_t$ and $G_r$ represent the gains of the transmitting and receiving antennas respectively, and $\sigma$ represents the radar cross section (RCS) of the sensing target. For a given sensing system setting and a fixed target, these quantities are all constant. Therefore, $K = \frac{P_t G_t G_r \sigma}{(4\pi)^3 P_i}$ is a constant.

In sensing tasks, a target can be detected only when the SSNR is greater than a certain threshold, denoted by $SSNR_{min}$. The region where $SSNR \ge SSNR_{min}$ is called sensing coverage. Signals from target motion inside this region are sufficiently strong compared to the interference signal to be detectable.

Since Wi-Fi signal will undergo attenuation in the medium as described in Section II-B, the sensing coverage will be reduced. In a lossy medium such as water, when the reflection path length is $r_T+r_R$, the reflected signal energy from a target will experience attenuation of $e^{-\beta(r_T+r_R)}$. The SSNR is given by:

$$SSNR = \frac{e^{-\beta(r_T+r_R)} \lambda^2 P_T G_t G_r \sigma}{(4\pi)^3 (r_T r_R)^2 P_i}. \quad (8)$$

Thus, the sensing coverage satisfies:

$$r_T r_R e^{\frac{\beta(r_T+r_R)}{2}} \le \lambda \sqrt{\frac{P_t G_t G_r \sigma}{(4\pi)^3 P_i SSNR_{min}}}. \quad (9)$$

Since both the attenuation factor $\beta$ and the signal wavelength $\lambda$ are related to the complex dielectric constant of the medium, there exist different sensing coverage areas in different mediums. In particular, the large attenuation factor of signals in water results in smaller sensing coverage compared to that over air. This limited sensing coverage restricts the reflection of signals to a small area within a lossy medium, thereby enabling more localized sensing.

To verify this key insight experimentally, we use a similar setup as in Section 3.2 except that a metal ball (with approximately 100% reflectivity) is mounted on the sliding track (Figure 9b). By combining the horizontal movements (parallel to the LOS) of the sliding tracking and the vertical movements of the slider head, the metal ball can be placed at various positions in the tank as shown in Figure 9b. By calculating the signal power of the received signal, when the metal ball is at different positions, we can estimate the sensing coverage in the water. Good matches can be found between the theoretical sensing coverage derived from Equation 9 (Figure 10a) and the experimental sensing coverage results tested by USRP (Figure 10b) and Inter 5300 network card (Figure 10c). Therefore, in lossy mediums, the sensing coverage is more concentrated. In the context of cardiac motion sensing, restricting the coverage areas enhances the signals reflected from the heart and eliminates interference from the lung motion.

# IV. WI-FI-BASED IN-BODY CARDIAC CYCLE MONITORING

## A. System Overview

Recall that the R-R interval corresponds to the time interval between two adjacent heartbeats and the Q-T interval between

<footnote n="1">¹Water is chosen because of its similar permittivity to human body tissues.</footnote>
<figure><img src="image_9.png" /><figcaption>(a) Theoretical results.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>(b) USRP experiment results.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>(c) Wi-Fi experiment results.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>(a) Theoretical results.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>(b) USRP experiment results.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>(c) Wi-Fi experiment results.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>(a) Metal ball moves in water.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>(b) Moving trajectories of metal ball.</figcaption></figure>

<caption>Fig. 9: Experiment setup.</caption>

ventricular contraction and relaxation. To accurately estimate these intervals, it's essential to position the transceiver antennas properly on the chest, within the heart area. Specifically, we fix the distance between the receiving antenna and the transmitting antenna to 0.5 cm. Additionally, a reference antenna (receiving antenna 2) is placed far away from the transmitting and receiving (outside the heart area) on the human body to help eliminate the phase noise of Wi-Fi signals.

The overall data processing flow of WiCG is summarized in Figure 11. It consists of three modules: Data Collection, Data Preprocessing, and Cardiac Cycles Extraction. In the Data Collection module, CSI signals are collected from the receiving antenna and reference antenna. In the Preprocessing module, a low-pass filter is applied after the calculation of CSI ratio [28], to eliminate the phase noise in Wi-Fi signals. In the Cardiac Doppler Calculation module, a cardiac Doppler method is employed to calculate the Doppler speed variations caused by cardiac motions. Finally, the R-R interval and Q-T interval are estimated from the detected time instances.

## B. Data Preprocessing

The CSI signals captured by commercial Wi-Fi devices contain significant noise, which impedes the detection of cardiac motions accurately. The noise in amplitude primarily stems from the power amplifier in the RF chain, while the phase shift noise mainly originates from the Carrier Frequency Offset (CFO) and Sampling Frequency Offset (SFO) [28].

<figure><img src="image_17.png" /><figcaption>(a) Simulation results.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>(b) USRP Measurement results.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>(c) Wi-Fi Measurement results.</figcaption></figure>

<caption>Fig. 10: Attenuation of RF signals in water. Tx and Rx antennas are 10 cm apart. Different colors represent the relative power of signals.</caption>

With the consideration of both sources of noise, the CSI at the *i*-th antenna can be written as:

$$H_i(f, t) = A_n(f, t)e^{-j\theta_n(f, t)}(H_{i,s}(f) + H_{i,d}(f, t)), \quad (10)$$

where $A_n(f, t)$ is the impulse noise in amplitude, and $\theta_n(f, t)$ is the phase shift noise. $H_{i,s}$ and $H_{i,d}$ are the channel
<figure><img src="image_20.png" /><figcaption>Fig. 11: System Diagram.</figcaption></figure>

responses of the static and dynamic paths.

The CSI ratio technique [28] is grounded in the observation that both amplitude noise and phase shift noise are consistent across all antennas on the same receiver. This allows for the cancellation of these noises by computing the ratios between the CSIs across antennas. In WiCG, the TX-RX antenna pair

<figure><img src="image_21.png" /><figcaption>(a) Raw Signal. Phase shift noise hinders extracting fine cardiac patterns.</figcaption></figure>

<caption>(b) After CSI ratio and filtering. phase changes induced by cardiac activities and respiration are visible and exhibit different patterns.</caption>

<caption>Fig. 12: Signal on the complex plane before and after preprocessing. Different colors represent the time order of signals.</caption>

is placed on the human body next to the ventricle, to capture its motion. The reference antenna is placed outside the heart area, collecting a reference signal. This reference signal is used as the common denominator in the CSI ratio calculations to cancel the amplitude and phase noise of signals from the first and second antennas. Therefore, signals from ventricle motions can be denoised as follows:

$$H(f, t) = \frac{H_1(f, t)}{H_2(f, t)} = \frac{A_n(f, t)e^{-j\theta_n(f, t)}(H_{1,s}(f) + H_{1,d}(f, t))}{A_n(f, t)e^{-j\theta_n(f, t)}(H_{2,s}(f) + H_{2,d}(f, t))} \\ = \frac{H_{1,s}(f) + H_{1,d}(f, t)}{H_{2,s}(f) + H_{2,d}(f, t)}. \qquad (11)$$

After computing the CSI ratios, we apply a low-pass filter with a 10Hz cut-off frequency to filter out the remaining high-frequency noise in the signal.

Figure 12a shows the raw CSI signals collected from the antennas placed in the ventricular area. The distribution of the signal on the complex plane exhibits a broad circular shape, indicative of the presence of phase shift noise. After eliminating the phase shift noise through CSI ratio and low-pass filtering, as shown in Figure 12b, effects of both respiration

and heart beat signals are clearly visible in the complex plane. Specifically, the segments with longer periods correspond to the chest displacement caused by respiration, whereas the segments with shorter periods are due to heartbeats.

### C. Cardiac Doppler for Robust Cardiac Interval Extraction

<figure><img src="image_22.png" /><figcaption>(a) Multipath environment 1: Static paths has little impact on signal amplitude fluctuations</figcaption></figure>

<caption>(b) Multipath environment 2: Static paths distort signal amplitude fluctuations</caption>

<figure><img src="image_23.png" /><figcaption>Fig. 14: Wi-Fi cardiac waveform and ECG waveform.</figcaption></figure>

After mitigating CFO and SFO, the next step is to extract cardiac motion intervals from the pre-processed signals. The resulting signal consists of two parts, the static component due to reflection from the environment, and the dynamic component, due to the reflection from cardiac motion and respiration. To accurately extract the cardiac motion timings, we must remove the interference from the static component first. Specifically, the resulting signal rotates periodically in the IQ domain due to respiration and cardiac motions. However, the amplitude of the signal variations depends on the static component.

The static component of the signal determines the position and orientation of the signal in the IQ domain, different static components will lead to different fluctuation patterns in signal amplitude. Without loss of generality, as shown in Figure 13. Suppose a CSI signal segment with two cardiac cycles, which consists of the static component and cardiac
motion component. i.e., $H = H_s + H_c$. In the first multipath environment (Figure 13a), the signal amplitude of $H$ fluctuates twice, such that valid cardiac waveform can be detected. However, Figure 13b illustrates that when the multipath environment changes, the signal static component changes correspondingly, which significantly alters the cardiac signal waveform. The signal amplitude fluctuates four times, which means the cardiac waveform is distorted and the fluctuation frequency is doubled. Meanwhile, the variation of the signal is tiny, leading to a low signal-to-noise ratio. Therefore, to accurately restore the fluctuation pattern of the dynamic component in the signal, the interference caused by the static component must be eliminated.

To solve this problem, we first use a bandpass filter with the passband frequency of $1Hz-8Hz$ to filter out the interference from respiration and high-frequency noise. In WiCG, we then propose a novel cardiac Doppler calculation method. As mentioned above, when the heart circulates blood flow over the body, the ventricles systole and diastole rapidly, which will cause significant Doppler speed changes. At the same time, the static component in CSI changes little during a short interval. Therefore, by taking the difference between consecutive samples, we can effectively eliminate the static component. Specifically, the difference between two adjacent samples can be expressed as:

$$D(t) = H_{t+\Delta t} - H_t = \Delta(H_S) + \Delta(Ae^{-j2\pi\frac{d(t)}{\lambda}}) \\ = \Delta(Ae^{-j2\pi\frac{d(t)}{\lambda}}), \quad (12)$$

where $\Delta t$ is the sample interval. Since the change in the static component is close to 0, $D(t)$ is independent of the static CSI component. Based on [61], $D(t)$ can be further expressed as:

$$D(t) = 2ASin(\frac{\Delta\theta(t)}{2})e^{j(\theta(t)+\frac{\Delta\theta(t)}{2}+\frac{\pi}{2})}, \quad (13)$$

where $\theta(t) = -2\pi\frac{d(t)}{\lambda}$, and $\Delta\theta(t) = \theta(t + \Delta t) - \theta(t)$ represents the phase variation of the dynamic CSI component during interval $\Delta t$. As $\Delta t$ is short, $2ASin(\frac{\Delta\theta(t)}{2}) \approx 2A\frac{\Delta\theta(t)}{2} = A\Delta\theta(t)$. Therefore:

$$\begin{aligned} |D(t)| &= |2ASin(\frac{\Delta\theta(t)}{2})e^{j(\theta(t)+\frac{\Delta\theta(t)}{2}+\frac{\pi}{2})}| \\ &= A|\Delta\theta(t)| = A| - 2\pi \frac{d(t+\Delta t) - d(t)}{\lambda}| \quad (14) \\ &= A| - 2\pi \frac{V_{doppler} * \Delta t}{\lambda}|. \end{aligned}$$

In other words, $|D(t)| \propto V_{doppler}$. As the timing of ventricular systole and diastole correspond to the moments when the Doppler speed changes significantly. Thus, instead of estimating the displacement of the heart surface over time, we calculate $|D(t)|$ from CSI samples as it is strongly correlated with ventricular motions and does not suffer from the interference of static components. In practice, we first calculate $|D(t)|$, and then the timing when $|D(t)|$ changes rapidly, corresponding to the time points of ventricular systole and diastole. In WiCG we calculate $|D(t)|$ in discrete time as:

$$\begin{aligned} D(t_n) &= H(f, t_{n+1}) - H(f, t_n) \\ &= \frac{H_1(f, t_{n+1})}{H_2(f, t_{n+1})} - \frac{H_1(f, t_n)}{H_2(f, t_n)}. \end{aligned} \quad (15)$$

Figure 14 illustrates 5 seconds of signals from the receiving antenna and the corresponding ECG data. The signal in red corresponds to the amplitude of the receiving signal with the static component. The signal in blue corresponds to the Doppler speed variation calculated by the proposed method. Compared to the ECG signals (Subfigure III) there are multiple prominent peaks in the red signal (Subfigure I). Though it is possible to determine the interval between two heartbeats, i.e. the R-R interval. Micro heart motions such as Q-wave are hard to detect. In contrast, two distinctive peaks corresponding to the Q-peak and the end of T-wave of the ECG are evident consistently in the Doppler speed profile. From these peaks, both the R-R interval and Q-T interval can be obtained.

For the cardiac Doppler signal, to estimate Q-T and R-R intervals. We first find the largest peaks in which the time interval threshold between peaks is set to 600ms (Corresponding heart rate is 100 beats per minute). Denoting the timing of these peaks as $T_{systole}^i$, which means the systole timing of $ith$ heartbeat. This gives all the peaks corresponding to the Q-wave, and R-R interval can then be calculated as: $R - R_{Interval} = T_{systole}^{i+1} - T_{systole}^i$. Next, according to the clinical experience [62], the systole timing and diastole timing have the relationship that $T_{systole}^i + 350ms \le T_{diastole}^i \le \frac{T_{systole}^{i+1} - T_{systole}^i}{2}$. Therefore, after we find the $T_{systole}^i$, we set the highest peak in $[T_{systole}^i + 350ms, \frac{T_{systole}^{i+1} - T_{systole}^i}{2}]$ as the $T_{diastole}^i$. The Q-T interval can be calculated as: $Q - T_{Interval} = T_{diastole}^i - T_{systole}^i$.

## D. Antenna Placement to Maximize Sensing Signal Quality

The surface of the human chest cavity is uneven in the heart area, and the 3D structure of the heart itself is also an irregular cone. When a signal travels from the body surface to the heart, it must pass through different tissues depending on the location. For example, in some positions, the signal must penetrate the ribs, while in others, it must pass through the lung lobes. Therefore, different patterns of signals can be detected when the antennas are placed at different positions in the heart area. In this section, we investigate the best place for antenna placement such that cardiac motions can be stably and robustly detected.

<figure><img src="image_24.png" /><figcaption>Fig. 15: Cardiac Doppler waveform from different positions.</figcaption></figure>

Following medical convention, we use the human ribs and other easily identifiable anatomical features to annotate relative positions to the heart within the chest cavity. As shown in
Figure 15a, in an average adult, the upper and lower borders of the heart are between the second and sixth ribs of the human body, respectively. The right border is 0.5-1cm away from the right side of the sternum and the left border runs along the lower left side to below the left nipple [62]. Consequently, we consider 2 different positions as shown in Figure 15a, Position 1 is located between the 3rd and 4th ribs, and Position 2 is located between the 4th and 5th ribs. Positions 1 and 2 (P1 and P2) are both along the sternum. The antennas are placed at the gap between ribs to eliminate signal blockage from the ribs. 10-second data is collected from each position as shown in Figure 15b. Signals from P1 are quite noisy. In each heartbeat, only one clear peak can be found, the second peak corresponding to the end of the T-wave is masked by surrounding noise, making it impossible to extract Q-T intervals. The signal in P2 has visible peaks corresponding to the cardiac motions. For each heartbeat, two peaks can be detected, one corresponds to the Q-peak and the second corresponds to the end of the T-wave. This comparison shows that cardiac Doppler signals extracted from different positions have varying signal-to-noise ratios (SNR). In general, the cardiac Doppler signal with high SNR is associated with more stable and accurate Q-T intervals.

<figure><img src="image_25.png" /><figcaption>Fig. 16: Cardiac Doppler SNR distribution for different persons.</figcaption></figure>

To assess the quality of signals at various positions, we introduce a new metric called $SNR_{Doppler}$, which is defined as

$$SNR_{Doppler} = \text{average}\left(\frac{P(T_{\text{diastole}}^{i})}{\text{Mean}(P([T_{\text{systole}, i}^{i}, T_{\text{systole}}^{i+1}]))}\right), \quad (16)$$

where, $P(t)$ means the signal amplitude at time t, $T_{\text{diastole}}^{i}$ and $T_{\text{systole}}^{i}$ are the diastole timing in the $i$th heartbeat and the systole timing of the $i + 1$th heartbeat from the start of the data collection, respectively. In Figure 16, we show the normalized heatmap of $SNR_{Doppler}$ at 9 positions for three subjects. Positions with the brighter color correspond to higher $SNR_{Doppler}$ values. The result shows that the best detection area is between the 4th and 5th, and 5th and 6th ribs, close to the sternum. One plausible explanation is that in this particular area, there are no organs between the heart and the body surface, whereas in other positions, lung lobes lie between the two. Therefore, we provide the following guidelines for antenna placement for optimal WiCG operation.

**Guideline 1 (Antenna placement):** To obtain the best sensing signal quality, the antenna pair consisting of a transmitting antenna and a receiving antenna should be placed between the 4th and 5th, or 5th and 6th of the ribs close to the sternum.

<table><caption>TABLE II: BMI for each Subject.</caption><thead><tr><th>Subject</th><th>Gender</th><th>BMI</th><th>Subject</th><th>Gender</th><th>BMI</th><th>Subject</th><th>Gender</th><th>BMI</th></tr></thead><tbody><tr><td>S1</td><td>Male</td><td>21.2</td><td>S8</td><td>Male</td><td>25.4</td><td>S15</td><td>Male</td><td>20.2</td></tr><tr><td>S2</td><td>Male</td><td>23.2</td><td>S9</td><td>Male</td><td>22.2</td><td>S16</td><td>Female</td><td>25.4</td></tr><tr><td>S3</td><td>Male</td><td>20.7</td><td>S10</td><td>Male</td><td>24.2</td><td>S17</td><td>Female</td><td>23.1</td></tr><tr><td>S4</td><td>Male</td><td>23.1</td><td>S11</td><td>Male</td><td>23.2</td><td>S18</td><td>Female</td><td>20.1</td></tr><tr><td>S5</td><td>Male</td><td>20.95</td><td>S12</td><td>Male</td><td>22.5</td><td>S19</td><td>Female</td><td>22.3</td></tr><tr><td>S6</td><td>Male</td><td>19.6</td><td>S13</td><td>Male</td><td>27.1</td><td>S20</td><td>Female</td><td>25.3</td></tr><tr><td>S7</td><td>Male</td><td>28.1</td><td>S14</td><td>Male</td><td>20.3</td><td>S21</td><td>Female</td><td>21.2</td></tr></tbody></table>

The reference antenna should be placed far away from the antenna pair and outside the heart area.

## V. EVALUATION

In this section, we conducted a comprehensive assessment of our system's capability to accurately measure cardiac cycles under diverse conditions.

### A. Experiment Setup

<figure><img src="image_26.png" /><figcaption>(a) Commodity Wi-Fi (b) Heal Force (c) Placement of transmitter (Tx) and re-ECG monitor. devices. receiver (Rx).</figcaption></figure>

<caption>Fig. 17: Experiment hardware.</caption>

We employ two GIGABYTE mini-PCs equipped with off-the-shelf Intel 5300 Wi-Fi card as transceivers (Figure 17a), both are configured to run at 2.457GHz Wi-Fi band with a sampling rate of 1000 Hz. The transmitter and receiver are equipped with three 3-cm long omni-directional antennas, respectively. The ground-truth cardiac activities are recorded by a Heal Force Prince 180B ECG monitor (Figure 17b). The placements of Wi-Fi transceivers following Guideline 1 as shown in Figure 17c.

21 volunteers, including 6 females and 15 males have been recruited to evaluate WiCG $^2$. Their BMIs range from 19.6 (healthy weight) to 28 (overweight) as shown in TABLE II. The subjects are asked to wear the system in 4 different postures (i.e. sitting, standing, supinating, and prostrating) in 3 different environments (i.e. living room, bedroom, and office). Each test lasts 5 minutes. Therefore, a total of 900 minutes of data is collected (15 subjects × 4 postures × 3 environments × 5 minutes).

The accuracy of estimated cardiac intervals is measured by Mean Relative Error (MRE), defined as:

$$ 
\begin{aligned}
\text{Accuracy} &= (1 - \text{MRE}) \times 100\% \\
&= (1 - \frac{1}{N} \sum_{i=1}^{N} \left| \frac{y_i - \hat{y}_i}{y_i} \right|) \times 100\%,
\end{aligned} 
\quad (17) $$

where N is the number of cardiac cycles, $y_i$ and $\hat{y}_i$ are the $i$-th cardiac interval (i.e. R-R and Q-T intervals) measured by ECG and WiCG respectively.

<footnote>$^2$The experimental protocol has been approved by the research ethic board.</footnote>
## B. Overall Performance

<figure><img src="image_27.png" /><figcaption>Fig. 18: Distribution of absolute errors.</figcaption></figure>

We find that the average accuracy of R-R intervals is 99.22%. For the more fine-grained Q-T intervals, the system maintains a relatively high accuracy, averaging at 92.8%. These numbers are on par with what is achievable using resting ECG machines in the market is typically within ±5% to ±10% errors. Figure 18 shows the Cumulative Distribution Function (CDF) of the absolute errors for cardiac interval extraction. It can be observed that 80% of the estimation errors for R-R interval are less than 8 ms. while, the 80-quantile estimation errors in Q-T intervals are less than 21 ms. According to medical literature, this level of accuracy is acceptable and can be used to detect potential cardiac health problems [63].

## C. Robustness of WiCG

<figure><img src="image_28.png" /><figcaption>Fig. 19: Absolute errors and accuracy of R-R and Q-T interval estimation for different subjects.</figcaption></figure>

### 1) Subject variations

For different individuals, both the relative accuracy and absolute errors are shown in Figure 19. Indeed, variations in performance can be observed among subjects. For R-R interval estimation, the accuracy for all the subjects varies between 98.2% – 98.8%, and the maximum absolute error is only 13 ms. For the Q-T interval estimation, the estimation accuracy varies between 89% – 94.1%, which corresponds to a maximum absolute measurement error of about 50 ms. Subject 6 (low-weight subject) achieves 94% measurement accuracy, while subject 7 (over-weight subject) experience a slight drop in accuracy at 91%. Notably, the system maintains high accuracy independent of gender. Thus, it is reasonable to conclude that, gender-associated morphological variations have negligible impact on WiCG measurement accuracy.

<figure><img src="image_29.png" /><figcaption>Fig. 20: Experiment setups of different postures and corresponding testing result.</figcaption></figure>

### 2) Impact of body posture.

In this experiment, measurements are collected while subjects are in four body postures (sitting, standing, supine, and prostrate) as shown in Figure 20. Experiment results (Figure 22) indicate that the estimation accuracy for the R-R interval remains consistently high across all postures, with 99.19%, 99.13%, 99.48%, and 99.69% accuracy during sitting, standing, supine, and postures, respectively. The accuracy of Q-T intervals varies slightly from 93.31% to 94.00% across different postures. Notably, in prostrate posture, the antenna is closer to the heart resulting in more accurate estimations of accuracy values for Q-T interval. In contrast, for standing and sitting postures, minor body movements lead to a slight decrease in the accuracy of Q-T measurements. Furthermore, in the supine posture, the accuracy for the Q-T intervals is observed at 93.8%.

### 3) Impact of Environments

<figure><img src="image_30.png" /><figcaption>Fig. 21: Different environments for evaluation.</figcaption></figure>

To evaluate multipath signal propagation can be successfully eliminated in WiCG, we conduct experiments in three environments: a living room (Figure 21a), a bedroom (Figure 21b), and an office space (Figure 21c). Each of these environments exhibits unique signal multipath characteristics. As shown in Figure 23, the average accuracy for the R-R interval in these environments is 99.37%, 99.10%, and 99.70%, respectively.
For the Q-T interval, the accuracy is 93.60%, 93.28%, and 94.06%, respectively. These results underscore the capability of WiCG to reliably extract cardiac cycles in varied daily settings, despite the presence of complex multipath effects.

<figure><img src="image_31.png" /><figcaption>Fig. 22: Results of different Fig. 23: Results of different postures. environment.</figcaption></figure>

4) Impact of Clothing

Next, we consider clothing with different thicknesses, i.e., an undergarment, a sweater, and a hoody. The materials of these clothes are all cotton. Three subjects with different BMIs (19.6, 23.2 and 28) were asked to put on these three different types of clothing. As shown in Figure 24, undergarment represents the thinnest material, while the hoody is the thickest. As shown in Figure 25, the accuracy of the R-R interval measurements across these clothing are similar. However, the discrepancy can be explained by the reduced SSNR for Q-T interval when the antennas are further away from the chest. Therefore, it is recommended that users deploy the system underneath thick clothes in practice.

<figure><img src="image_32.png" /><figcaption>Fig. 24: Clothing types.</figcaption></figure>

<caption>Fig. 25: Accuracy impact of the thickness of clothing.</caption>

To evaluate the impact of metal clothing accessories, we placed three coins near the sensing antennas to simulate the effect of metal buttons, as shown in Figure 26. A 10-second experiment captured 12 cardiac cycles, with mean errors of 16 ms for R-R intervals and 80 ms for Q-T intervals—comparable to the overall WiCG performance. This suggests that metallic buttons in typical clothing configurations do not significantly affect measurement accuracy. The likely reason is that Wi-Fi signals have a wavelength of 12.5 cm outside the body, so the small displacements of the coins caused by breathing induce only minor signal variations, which have minimal impact on in-body sensing.

D. Long-term monitoring experiment

To evaluate the system's performance across different times of the day, we conducted intermittent assessments at different

<figure><img src="image_33.png" /><figcaption>Fig. 26: Experiment setups and corresponding testing result under metal clothing accessories interference.</figcaption></figure>

<figure><img src="image_34.png" /><figcaption>Fig. 27: Absolute error and accuracy of R-R and Q-T interval estimation for one subject over one day.</figcaption></figure>

times of a single day. Specifically, from 10:00 AM to 6:00 PM, we measured the R-R intervals and Q-T intervals of a subject (Subject 1) using WiCG for 2-minute periods every hour. During the test, the subject sat at a table and remained still. As shown in Figure 27, the R-R interval accuracy fluctuates between 99.1% and 99.8%, while the Q-T interval accuracy ranges from 90.5% to 95.2%. This result is comparable to cross-subject evaluation results, demonstrating the long-term consistency of the system performance over a day.

E. Impact of CSI sampling rate.

<figure><img src="image_35.png" /><figcaption>Fig. 28: Experiment result over different CSI sampling rate.</figcaption></figure>

In WiCG, we collect CSI data by transmitting packets at a fixed rate in the Injection Frame Mode [64]. To investigate the impact of different sampling rates on the measurement accuracy, we experiment with different sampling frequencies,
namely, 1000Hz, 500Hz and 200Hz. The measurement results are shown in Figure 28. Within 3.5-s time window, WiCG collects five complete heartbeat cycles at a sampling frequency of 1000 Hz. Compared with ECG signals, the waveform peaks from WiCG match well with the timing of Q and T waves, achieving a mean error of 11 ms for R-R intervals and 25 ms for Q-T intervals. When the sampling frequency is reduced to 500 Hz, a noticeable temporal drift could be observed in the WiCG output, yielding an increased mean error to 15 ms for R-R intervals and 40 ms for Q-T intervals. Further reducing the sampling frequency to 200 Hz causes significant peak blurring and makes it hard to extract proper features. In this case, the mean error dramatically increases to 28 ms for R-R intervals and 70 ms for Q-T intervals.

## F. Use Study

WiCG is designed for in-home long-term monitoring. Thus, it is important that users are able to collect quality data without interventions from medical professionals. To evaluate its usability, we carry out a simple user study. In the study, each participant is first taught to identify and count their ribs. Then, they are asked to follow the placement guideline (Section IV-D) and try 3 or 4 different positions. The $SNR_{Doppler}$ is calculated according to Equation 16 and the best location is fed back to the participants. We find that, on average, the process takes 15 minutes per subject during the initial trials. Once participants become familiar with the counting method and the system, the time can be further reduced. After they have learned the method of using the system, It takes an average of 5 minutes per subject to get accurate results with WiCG.

# VI. DISCUSSION AND LIMITATION

**Environmental Interference.** The presence of nearby interference (like fans or other individuals) can disrupt the system's ability to monitor cardiac motions. This disruption occurs because the system's sensing range extends broadly through the air, meaning any activity within this range can affect the signal integrity.

**Daily Activity Challenges.** Accurate cardiac motion measurement becomes challenging when the user is engaged in daily activities (such as walking). Movement leads to significant shifts in the antenna's relative position with respect to the atria and ventricles, which in turn, results in drastic changes in the received signals.

**Antenna deployment constraints.** The WiCG system requires three Wi-Fi antennas for cardiac signal measurements with one antenna connected to the transmitter and two receiving antennas connected to the receiver via cables. To ensure precise positioning, we fix the transmitting antenna and one receiving antenna on the chest using a strap, while the second receiving antenna is placed away from the heart as a reference signal to eliminate SFO and CFO. In the future, to improve usability hardware modification is necessary. For example, a portable system can be implemented comprising only two antennas and a signal-generation circuit. Such a

system operates under the same principle as WiCG but can be easily clipped on clothes without any straps or cables.

**Simultaneous Monitoring.** The system operates with a single Wi-Fi transmitter (Tx) and two receivers (Rx) setup to monitor an individual's cardiac activity, requiring the placement of the Wi-Fi antenna directly on the person's chest. Consequently, it's not feasible to monitor multiple individuals simultaneously with a single system. In scenarios where concurrent monitoring of multiple individuals is required (like in a hospital ward), each person must be equipped with his/her own system. However, when multiple systems are used in proximity to monitor cardiac activity, the signals do not interfere with each other due to the signal energy being concentrated around the antenna of each system.

# VII. RELATED WORK

## A. Wi-Fi CSI-based Vital Sign Sensing

Owing to the low cost and pervasiveness of commercial Wi-Fi devices, Wi-Fi CSI signals have been widely used for vital sign monitoring. Building on the recent studies on Wi-Fi sensing, respiration monitoring is achieved with robust performance independent of human position and orientation [28], [34], [65], [66]. Besides respiration monitoring, some recent works explore the possibility of heart rate detection [67]–[72]. These methods use special algorithms such as wavelet transform or machine learning techniques to extract the heart beat rates in the spectrum. Due to the limited SSNR of commodity Wi-Fi devices, however, these methods are both unreliable and require special experimental requirements.

## B. Radar-based Cardiac Motion Sensing

Radar-based sensing overcomes the CFO issue of Wi-Fi devices as coherent signals are shared between the TX and RX, thus outperforming Wi-Fi in terms of SSNR [73]. By increasing the sensing frequency of the radar system, the sensing performance could be further improved [39], [42], [44], [74]–[79]. Based on a 24GHz biomedical radar with single-input-single-output (SISO) configuration, Dong et al propose novel vectors analytic demodulation (VAD) method [39] and parameterized respiratory filter technique [79] to efficiently mitigate the strong respiration interference reflected from the whole chest area, such that R-R intervals could be reliably detected. To reduce the strength of respiration interference, Multiple-input-Multiple-output (MIMO) radar with beamforming capability is much more favorable. Xu et al. leverage Off-The-Shelf (COTS) MIMO mmWave radar to estimate R-R intervals in driving environments [42]. Li et al. build 10T10R 4D imaging radar and propose a variational mode separation algorithm to profile the R-R intervals of multiple subjects. Despite numerous attempts, there is no reliable solution with mmWave radar systems to achieve accurate monitoring of key cardiac Q-T intervals.

## C. Near-field Cardiac Sensing

For the near-field RF sensing techniques [80]–[85]. Bi et al. presents the potential of in-body cardiac motion detection by
simply attaching TX and RX antennas of a 2.4Ghz Doppler radar on the heart area [84]. Gao et al. find that the recovered waveform trajectory of in-body cardiac motion could be modeled as the superposition of atrium and ventricle motion [85]. Hui et al. demonstrate the high sensitivity of near-field cardiac sensing by using the ultrahigh-frequency (UHF) band signal to couple considerable power into the thoracic [81], [82]. Li et al. develop the near-field sensing theory by investigating the electromagnetic characteristics inside the body and measuring R-T intervals using UHF band signal from USRP. In this work, we propose WiCG, the first cardiac motion monitor based on commodity Wi-Fi devices, grasping new insights for near-field cardiac sensing and enabling accurate monitoring of key cardiac intervals (R-R and Q-T) based on the mix-medium Fresnel zone model.

## VIII. CONCLUSION

In this work, we presented WiCG, a pioneering system for non-contact cardiac motion monitoring using commodity Wi-Fi devices. By leveraging a mix-medium Fresnel zone model, WiCG is capable of precisely detecting cardiac motions within the human body. The system's design, which includes the strategic placement of Wi-Fi antennas and a spatial-projection method, allows for the measurement of ventricular motions, leading to the accurate extraction of cardiac intervals. Our evaluations under diverse conditions confirm the robustness and reliability of WiCG in monitoring R-R and Q-T intervals. While challenges remain, such as environmental interference and dynamic activity, the results highlight the potential of in-body Wi-Fi sensing for cardiac health monitoring. This study paves the way for further research in mix-medium Wi-Fi sensing and its applications in personal health monitoring.

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**Pei Wang** (Student Member, IEEE) received the MS degree in computer science and technology from Northwestern Polytechnical University, Xi'an, China, in 2020. He is currently working toward the Ph.D degree at the Ambient Intelligence and Pervasive System Group, Institut Polytechnique de Paris, France. His current research interests include biomedical applications of microwave, millimeter-wave, and ubiquitous wireless sensing.

**Anlan Yu** Anlan Yu (Student Member, IEEE) received his Bachelor's degree in computer science from Peking University in 2023 and is currently pursuing a PhD degree there. His research interests include mobile computing and ubiquitous computing.

**Xujun Ma** (Member, IEEE) received the Ph.D. degree in information and communication engineering from Southeast University, Nanjing, China, in 2020. Since 2020, he has been a Postdoctoral Research Fellow with the Ambient Intelligence and Pervasive System Group, Télécom SudParis, Évry, France. His current research interests include biomedical applications of microwave, millimeter-wave CMOS circuit design, and wireless sensing. He was the Second-Place Award recipient of the Student Paper Competition of 2019 IEEE-IMBioC.

**Rong Zheng** (Senior Member, IEEE) received her Ph.D. degree from Dept. of Computer Science, University of Illinois at Urbana-Champaign and earned her M.E. and B.E. in Electrical Engineering from Tsinghua University, P.R. China.She is now a Professor in the Dept. of Computing and Software in McMaster University, Canada. She was on the faculty of the Department of Computer Science, University of Houston from 2004 to 2012. Rong Zheng's research interests include mobile computing, data analytics and networked systems. She is currently Tier-1 Canada research chair in Mobile Computing. She was awarded the NSERC Discovery Accelerator Supplement in 2019 and received the National Science Foundation CAREER Award in 2006, and was a Joseph Ip Distinguished Engineering Fellow from 2015 - 2018.

**Jingfu Dong** Jingfu Dong is currently pursuing the bachelor's degree in Communication Engineering at the School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, China. His research interests include ubiquitous computing, mobile computing, and wireless sensing.

**Zhaoxin Chang** Zhaoxin Chang received the bachelor's degree in computer science from Peking University, Beijing, China, in 2020, and the master's degree in computer science from Institut Polytechnique de Paris, Palaiseau, France, in 2023. He is currently working toward a PhD degree in computer science with SAMOVAR, Telecom SudParis, Institut Polytechnique de Paris, Palaiseau, France. His current research interests include wireless sensing, ubiquitous computing, and mobile computing.

**Duo Zhang** Duo Zhang received the bachelor's degree in computer science and technology from the School of Computer Science, Northwestern Polytechnical University, Xi'an, China, in 2021. He is currently pursuing the Ph.D. degree in computer science with the School of Computer Science, Peking University, Beijing, China. His research interests include ubiquitous computing, mobile computing, and wireless sensing.

**Djamal Zeghlache** (Life Member, IEEE) received the Ph.D. degree in electrical engineering from Southern Methodist University, Dallas, TX, USA, in 1987. He was an Assistant Professor with Cleveland State University from 1987 to 1991. In 1992, he joined Télécom SudParis, Institut Mines-Telecom, where he acts as a Professor and the Head of the Wireless Networks and Multimedia Services Department. His current research concerns architectures, protocols, and interfaces for future networks addressing cloud, SDN, and NFV optimization, control, and management reinforced by data-driven approaches and in network intelligence.

**Daqing Zhang** (Fellow, IEEE) received the Ph.D. degree from the University of Rome "La Sapienza," Italy, in 1996. He is currently a Chair Professor with the Key Laboratory of High Confidence Software Technologies, Ministry of Education, School of Computer Science, Peking University, China; and Telecom SudParis, IP Paris, France. He has authored more than 300 technical papers in leading conferences and journals. His research interests include context-aware computing, urban computing, mobile computing, big data analytics, and pervasive elderly care. He is the Winner of the Ten-Years CoMoRea Impact Paper Award at IEEE PerCom 2013 and the Ten-Years Most Influential Paper Award at IEEE UIC 2019, the Honorable Mention Award at ACM UbiComp 2015 and 2016, and the Distinguished Paper Award at ACM UbiComp 2021. He was the general chair or the program chair for more than 17 international conferences, giving keynote talks at more than 20 international conferences. He is an Associate Editor for the IEEE PERVASIVE COMPUTING, ACM Transactions on Intelligent Systems and Technology, and the Proceedings of the ACM on Interactive, Mobile, Wearable and Ubiquitous Technologies.