# Wital: A COTS WiFi Devices Based Vital Signs Monitoring System Using NLOS
Sensing Model

Xiang Zhang, Yu Gu, Huan Yan, Yantong Wang, Mianxiong Dong, Kaoru Ota, Fuji
Ren, Yusheng Ji Xiang Zhang, Huan Yan and Yantong Wang are with the School of
Computer and Information, Hefei University of Technology, China. E-mail:
<EMAIL_ADDRESS>Yu Gu (corresponding author) and Fuji Ren are with I+ Lab,
School of Computer Science and Engineering, University of Electronic Science
and Technology of China. E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>Mianxiong Dong and Kaoru Ota are with the Dept. of Sciences and Informatics,
Muroran Institute of Technology, Japan. E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>Yusheng Ji is with the National Institute of
Informatics, Tokyo 101-8430, Japan. E-mail<EMAIL_ADDRESS>
###### Abstract

Vital sign (breathing and heartbeat) monitoring is essential for patient care
and sleep disease prevention. Most current solutions are based on wearable
sensors or cameras; however, the former could affect sleep quality, while the
latter often present privacy concerns. To address these shortcomings, we
propose Wital, a contactless vital sign monitoring system based on low-cost
and widespread commercial off-the-shelf (COTS) Wi-Fi devices. There are two
challenges that need to be overcome. First, the torso deformations caused by
breathing/heartbeats are weak. How can such deformations be effectively
captured? Second, movements such as turning over affect the accuracy of vital
sign monitoring. How can such detrimental effects be avoided? For the former,
we propose a non-line-of-sight (NLOS) sensing model for modeling the
relationship between the energy ratio of line-of-sight (LOS) to NLOS signals
and the vital sign monitoring capability using Ricean K theory and use this
model to guide the system construction to better capture the deformations
caused by breathing/heartbeats. For the latter, we propose a motion
segmentation method based on motion regularity detection that accurately
distinguishes respiration from other motions, and we remove periods that
include movements such as turning over to eliminate detrimental effects. We
have implemented and validated Wital on low-cost COTS devices. The
experimental results demonstrate the effectiveness of Wital in monitoring
vital signs.

###### Index Terms:

Wi-Fi, CSI, sleep monitoring, vital signs, wireless sensing

##  I Introduction

Respiratory rate and heart rate are key physiological indicators for assessing
the health of a human being, and some diseases can be detected or prevented by
finding abnormalities in such vital signs, e.g., sleep apnea[1], asthma[2] and
sudden infant death syndrome (SIDS) [3]. In many such diseases, patients
develop symptoms only for a short period of time, and therefore, long-term
continuous monitoring is needed. However, due to limited medical resources and
funding, long-term inpatient observation is impractical for most people.
Therefore, continuous and cost-effective monitoring of vital signs in the home
setting is highly desired.

Traditional vital sign monitoring protocols are mainly based on specialized
sensors attached to the body, such as electrodes for polysomnography (PSG) [4]
and electrocardiography (ECG) [5]. However, these special devices are not
suitable for use in the home environment since they are generally expensive
and can affect sleep quality. Other methods based on attached nonspecialized
sensors, such as pressure or acceleration sensors, also require contact with
the body, which can cause inconvenience to users. As a result, contactless
vital sign sensing has received a great deal of attention, mainly focusing on
vision- and radio frequency (RF)-based solutions. However, lighting conditions
limit computer-vision-based solutions. Meanwhile, although RF-based methods
[6, 7] can provide noninvasive vital sign monitoring without the
aforementioned drawbacks, the devices (software-defined radio or radar
systems) used in traditional RF-based solutions are typically costly and
difficult to deploy.

Therefore, Wi-Fi-based vital sign monitoring has recently received
considerable attention [8, 9, 10] due to its advantages of noncontact sensing
and reliance on widespread and low-cost Wi-Fi devices. The reason why Wi-Fi
can be used to detect vital signs is that breathing and heartbeats causes
abdominal and chest deformations, which affects the propagation of Wi-Fi
signals and WiFi Channel State Information (CSI) can record this information
[11]. In turn, we can use the recorded CSI to recover the desired vital signs.

The first challenge in Wi-Fi-based vital sign monitoring is that the torso
deformation caused by respiration/heartbeats is extremely weak and only
minimally affects Wi-Fi signal propagation. Therefore, a theoretical model is
needed to guide the implementation of such a system. Currently, most state-of-
the-art schemes are based on the Fresnel zone model [12], the Fresnel
diffraction model [8], or the CSI-ratio model [9, 13]. The Fresnel zone model
analyzes how human motion leads to effective displacement, and the Fresnel
diffraction model [8] indicates that optimal sensing performance can be
achieved at or near the line of sight (LOS). However, neither of these two
Fresnel-based models considers the effect of the energy ratio of LOS to non-
line-of-sight (NLOS) signals on NLOS sensing. The CSI-ratio model is very
useful for data processing, but it yields better results when the perception
sensitivity of the deployed hardware is higher.

The second challenge is that the effects of motions such as turning over may
be mixed with those of breathing/heartbeats, thus affecting the accuracy of
vital sign detection. If these movements are not distinguished from the
movements of interest, they can have a detrimental effect on the monitoring
results. However, current Wi-Fi-based vital sign monitoring methods all lack a
method to differentiate different kinds of motions during sleep. Moreover,
since breathing/heartbeats and turning over are all dynamic phenomena,
existing motion segmentation schemes [14] for use in other Wi-Fi-based sensing
applications are not applicable because they aim to separate dynamic and
static activities. Thus, for accurate monitoring, we need a solution that can
distinguish between different types of motions.

In this paper, we propose Wital, a contactless vital sign monitoring system
based on low-cost and widespread commercial off-the-shelf (COTS) Wi-Fi
devices. To address the first challenge identified above, we propose an NLOS
sensing model for monitoring vital signs to guide the implementation of the
system. For the second challenge, we propose a regularity-based motion
segmentation method that can accurately separate breathing/heartbeats from
other motions. We also implement a monitoring system using MATLAB that enables
easy monitoring of vital signs.

The main contributions of this paper are summarized as follows:

  1. 1.

We propose an NLOS sensing model to investigate the relationship between the
energy ratio of LOS to NLOS signals and the ability to monitor vital signs. We
theoretically prove that blocking the LOS signals during NLOS sensing is
beneficial for vital sign monitoring.

  2. 2.

We propose a motion segmentation method based on regularity detection, which
can accurately distinguish periods of motion (such as turning over and rising
from bed) that are different from vital signs.

  3. 3.

We implement a vital sign monitoring system using MATLAB. Experimental results
indicate that our method achieves 96.618% and 94.708% accuracy for breathing
and heart rate detection, respectively.

We organize the remainder of this paper as follows. In section II, we provide
an overview of related work. We describe our NLOS sensing model in section
III. We introduce our system design in section IV. Then, we evaluate our
method and analyze the experimental results in section V. Finally, we conclude
our work in section VI.

##  II Related Work

TABLE I:  Comparison of the proposed system with the latest research results. Reference |  Vital Signs |  Accuracy |  Requirements |  Model Support
---|---|---|---|---
[15] |  breathing rate (various sleep postures) |  greater than 85% |  2 transmitters and 3 receivers, 3 data streams, natural breathing |  no
[11] |  breathing rate (various sleep postures) and heart rate (only supine) |  80% of estimation errors are less than 0.5 bpm for breathing rate, 90% of estimation errors are less than 4 bpm for heart rate |  pair of transceivers, one data stream, metronome to control breathing |  no
[16] |  breathing rate (various postures) |  over 99% |  pair of transceivers, cables and splitters, two data streams, metronome to control breathing |  yes
[8] |  breathing rate (various sleep postures) |  for good positions, overall estimation accuracy is as high as 98.8%; for bad positions, accuracy decreases to 61.5% |  pair of transceivers, one data stream, natural breathing |  Fresnel diffraction model
[9] |  breathing rate (various sleep postures) |  less than 0.3 bpm for breathing rate |  pair of transceivers, two data streams, natural breathing |  CSI-ratio model
[17] |  breathing rate (various sleep postures) |  average 0.31 bpm for breathing rate |  pair of transceivers, one data stream, natural breathing |  ambient-reflected signal model
Our system |  breathing rate and heart rate (both for various sleep postures) |  accuracy of 96.887% for breathing rate and 94.708% for heart rate, average errors of 0.498 bpm for detected breathing rate and 3.531 bpm for detected heart rate |  pair of transceivers, one data stream, natural breathing |  NLOS sensing model

###  II-A Sensing with Wi-Fi

Due to the widespread deployment of Wi-Fi devices and the convenience of
wireless sensing, research on passive sensing based on Wi-Fi has received
widespread attention [18, 19, 20]. These studies are mainly based on the
received signal strength index (RSSI) or CSI. The RSSI is easy to acquire, but
its granularity of perception is crude. The CSI can only be obtained by
modifying the underlying drivers of Wi-Fi network cards, but the granularity
of sensing is better than that of the RSSI [21, 22].

With the help of Wi-Fi RSSI or CSI data, existing research has enabled human
presence detection [23], gesture recognition [24, 25, 26], cross-domain
gesture recognition [27, 28], localization [29], sleep movement detection [30]
and driving activity detection [31] by means of COTS Wi-Fi devices. In the
past two years, Wi-Fi-based perception research has further expanded into new
fields. [32] used Wi-Fi devices to image key points of the human body,
enabling human visualization without vision equipment. [33] used Wi-Fi devices
to track symbols drawn with a finger in the air. [34] achieved the stealing of
mobile phone passwords using COTS Wi-Fi devices. By extracting the
interference-independent component, PhaseAnti [21] realizes the effective
recognition of various activities in cochannel interference scenarios. SMARS
[35] utilizes CSI for sleep stage detection based on sleep breathing status
detection and an autocorrelation function (ACF).

###  II-B Breathing and Heartbeat Monitoring

The respiratory rate and heart rate are key physiological indicators for
assessing the health of the human body. In general, the current methods used
to track such vital sign information fall into three categories: contact-
sensor-based, vision-based, and RF-based methods.

Most traditional solutions use contact sensors for physiological signal
detection. For example, PSG [4] and ECG [5] involve measuring body functions
such as breathing or heartbeats by attaching multiple sensors to a patient. H.
Aly _et al._ [36] utilized the accelerometer and gyroscope in a mobile phone
to detect the breathing-induced chest motion of a person. Smart sleeping mats
[37] use pressure sensor arrays for breathing detection. However, contact-
sensor-based approaches are typically costly, complex to deploy, and obtrusive
during measurement.

Contactless vital sign sensing methods, such as vision- and RF-based schemes
are more user-friendly. However, vision-based solutions [38] are usually
susceptible to variations in lighting conditions and present privacy concerns.
As an alternative, research on the use of wireless radio signals as sensors
has recently received increasing attention. As RF signals travel from the
transmitter to the receiver, they are affected by breathing-induced chest
movement along their propagation path. However, RF-signal-based solutions
usually rely on special equipment, such as ultrawideband devices [39] or
frequency-modulated continuous wave (FMCW) radar [7, 6]. The devices used in
these solutions are costly and not suitable for everyday environments.
Compared with these solutions, Wi-Fi-based solutions are less expensive and
simpler to deploy and can be implemented using COTS equipment.

Previous Wi-Fi-based breathing monitoring studies are mostly based on the RSSI
[40, 41, 42]. The RSSI characterizes the total received power over all paths;
thus, it is a coarse-grained that is inherently incapable of capturing
multipath effects. In contrast, CSI can effectively capture fine-grained
channel and multipath information. Therefore, most of the latest related
schemes are based on CSI [15, 11, 12, 8, 43, 44, 9, 35, 45]. Liu _et al._ [15]
obtained the respiratory rate by applying the short-time Fourier transform
(STFT) to the CSI amplitude. However, this solution requires the deployment of
two routers and three computers. Liu _et al._ [11] used a pair of Wi-Fi
devices to monitor the respiratory rate in different sleeping postures.
However, they needed to leverage LOS conditions between the devices for
heartbeat detection. [16] used the CSI phase to detect the breathing rate,
using cables and splitters to connect the transmitter and receiver to
eliminate phase shifts.

[12] proposed the Fresnel zone model to relate the depth, location, and
direction of human breathing to the detectability of respiration by examining
the received signal strength in the context of the Fresnel zones. [8]
presented the Fresnel diffraction model to relate the target person’s position
to the detectability of respiration within the first Fresnel zone (FFZ) and
declared that the closer the person is to the LOS, the better the monitoring
of respiration is in the lying posture. These models have provided excellent
insight for later research. However, the Fresnel zone model and the Fresnel
diffraction model do not consider the impact of changes in the LOS-to-NLOS
signal ratio on vital sign monitoring. [9] used the CSI ratio of two receive
antennas to eliminate the phase offset and utilized complex plane projection
to achieve long-distance breathing detection. In this scheme, at least two
antennas are required at the receiver, making it incompatible with single-
antenna receivers and increasing the computational cost. Additionally, the
CSI-ratio model is a data processing model. It will yield better results when
the perception sensitivity of the deployed hardware is higher. The authors of
[17] were among the first to realize respiration monitoring with cell phones,
and they proposed an ambient-reflected signal model under the NLOS setting to
obtain the variations in the CSI amplitude at the receiver, which varies with
subtle displacements of the human chest. Their work showed that blocking the
LOS signal is beneficial for NLOS sensing, but no theoretical proof was
provided. We compare these systems with our work in Table I.

Note that this paper is an extension of our previous work that was presented
at IEEE BIBM 2021 [46]. In our previous work, we found that blocking the LOS
signal is beneficial for NLOS sensing, and in this paper, we utilize a model
based on Ricean K theory to explain why in more detail. We also propose a new
motion segmentation method based on regularity detection, which can accurately
distinguish sleep motions (such as turning over and rising from bed) that are
different from breathing/heartbeat motions.

##  III Preliminaries

In this section, we first analyze preliminary experiments. Then, we propose
our NLOS sensing model based on Ricean K theory for better monitoring of vital
signs.

###  III-A Channel State Information

The CSI of a signal describes its attenuation along its propagation paths due
to phenomena such as scattering, multipath fading or shadow fading caused by
motion, and decay in power over distance. In the frequency domain, this
attenuation can be characterized as follows [47]:

$Y=H\cdot X+N,$ (1)

where $Y$ and $X$ are the received and transmitted signal vectors,
respectively; $N$ is additive white Gaussian noise; and $H$ is the channel
matrix representing the CSI.

For Wi-Fi CSI, the received signal’s channel frequency response (CFR) can be
expressed simply as the superposition of the dynamic path CFR and static CFR:

$H(f,t)=H_{s}(f,t)+H_{d}(f,t).$ (2)

The dynamic CFR can be written as:

$H_{d}(f,t)=\sum_{k\in D}h_{k}(f,t)e^{-j2\pi f\tau_{k}(t)},$ (3)

where $f$ and $\tau_{k}(t)$ represent the carrier frequency and the
propagation delay on the $k^{th}$ path, respectively, and $D$ is the set of
dynamic paths. The received signal has a time-varying amplitude in the complex
plane [12]:

$|H(f,\theta)|^{2}=|H_{s}(f)|^{2}+|H_{d}(f)|^{2}+2|H_{s}(f)||H_{d}(f)|cos\theta,$
(4)

$\theta$ is the phase difference between the static vector and the dynamic
vector, and the term that causes the amplitude fluctuation of the CSI waveform
is $2|H_{s}(f)||H_{d}(f)|cos\theta$. In the case that the range and position
of the motion are constant, $\theta$ is also constant, and the only factors
affecting the fluctuation range are $|H_{s}(f)|$ and $|H_{d}(f)|$.

Figure 1: Fresnel zones.

(a)

(b)

(c)

Figure 2: Antenna settings for the preliminary experiments. The elliptical
region between the antennas is the first Fresnel zone (FFZ). The region
between the solid chest line and the dotted line is the range of chest
deformation induced by breathing. (a) Setting 1. T1 is the transmit antenna,
and R1, R2, and R3 are the receive antennas. The distance between T1 and R3 is
80 cm, and the distance between T1 and R1 is 120 cm. (b) Setting 2. The chest
is on the LOS of T1–R2. The distance between T1 and R3 is 20 cm, and the
distance between T1 and R2 is 120 cm. (c) Setting 3. The chest is in the FFZ
of T1–R2. The distance between T1 and R3 is 30 cm, and the distance between T1
and R2 is 120 cm.

###  III-B Preliminary Experiments and Analysis

The CSI-ratio model is focused on data processing, and it requires at least
two antennas placed close together at the receiver. The ambient-reflected
signal model focuses on ambient-reflected signals, which are inconsistent with
our objectives. Therefore, we chose to explore the effects of the Fresnel
models in our preliminary experiments. As shown in Fig. 1, the Fresnel zones
are defined as a series of concentric ellipsoids, where $P_{1}$ and $P_{2}$
are the positions of the transmit antenna and the receive antennas,
respectively, and $Tx$ and $Rx$ represent the transmitter and receiver,
respectively. For a given radio wavelength $\lambda$, we can construct the
Fresnel zones by means of the following equation [48]:

$|TxQ_{n}|+|Q_{n}Rx|-|TxRx|=n\lambda/2,$ (5)

where $Q_{n}$ is a point at the boundary of the $n$th Fresnel zone.

The Fresnel zone model analyzes how human body motion causes an effective
displacement $d(t)$, representing the change in the reflected (dynamic) path
length of the signal. The dynamic path phase shift caused by this effective
displacement can be expressed as $e^{-j2\pi f\tau_{k}(t)}=e^{-j2\pi
d(t)/\lambda}$, where $\lambda$ represents the wavelength of the Wi-Fi signal.
The larger the effective displacement is, the greater the phase shift caused
by the motion, and the more significant the effect on $|H_{d}(f)|$ and the
CSI. Previous studies [12] have shown that when the direction of human body
deformation is approximately 0 degrees, the effective displacement caused by
human body motion is the largest, and the sensing efficiency is the best. As
the angle increases, the effective displacement decreases, and the sensing
efficiency worsens [12]. Moreover, when the target moves along the boundary of
a Fresnel zone, there is no effect on the reflected path length.

Different from the Fresnel zone model, the Fresnel diffraction model [8]
focuses only on the FFZ. This mathematical model was developed to relate the
location of a human target to the detectability of respiration within the FFZ
by modeling various human targets as cylinders of varying size and then
analyzing how a cylinder within the FFZ affects the received RF signal. The
findings show that the closer to the LOS the target is, the better the
respiratory monitoring effect in the lying posture.

Based on these findings, we constructed a prototype system to carry out
preliminary experiments.

(a)

(b)

(c)

Figure 3: Vital sign monitoring performance under different settings. (a)
Performance under setting 1. (b) Performance under setting 2. (c) Performance
under setting 3. SNR denotes the signal-to-noise ratio.

[Prototype] Our prototype system consisted of two commodity mini PCs serving
as the transmitting and receiving devices. These two mini PCs were each
equipped with an Intel Network Interface Controller (NIC) 5300. The antenna
settings are shown in Fig. 2.

[Participant] One 22-year-old student participated in the preliminary
experiments.

[Environment] We conducted the experiments in a $7\times 10$ m2 office room
with furniture, including chairs, couches, computer desks, and book cabinets,
as shown in Fig. 5.

[Setting] The package sending rate was set to 1000 Hz. The participant
conducted experiments in different sleeping postures (prone, supine, left-
facing recumbent, and right-facing recumbent) under different antenna settings
(as shown in Fig. 2), and the experimental results are shown in Fig. 3.

By analyzing the preliminary results, we obtained the following key
observations [46].

_Breathing indeed affects the channel response, and the experimental setting
also affects the channel response:_ First, we confirmed that respiration-
induced signal changes were recorded under all settings. As shown in Fig. 3,
we observed significant fluctuations in the CSI amplitude induced by
respiration in all settings.

_Fresnel-diffraction-model-based sensing:_ Similar to the findings presented
in [8], we observed that proximity to the LOS resulted in excellent sensing
performance (for both supine and prone positions in setting 2). Similar to
[8], we also found that the T1–R2 antenna pair had poor perception ability
when the volunteer was lying on his side. This is because the direction of
trunk deformation in the anteroposterior dimension (breathing mainly causes
deformation in this dimension) was roughly parallel to the LOS path of T1–R2.
Accordingly, the deformation in the anteroposterior dimension could cause
little significant effective displacement when the volunteer was lying on his
side. The respiration-induced abdominal/thoracic deformation in the
mediolateral dimension is too small; hence, its effect on signal propagation
is also relatively small. Moreover, as shown in Fig. 3b and 3c, it was
difficult to observe significant fluctuations caused by breathing in various
sleeping positions during certain periods. This is because in the sleeping
state, the position of the torso differs greatly between the side-lying and
flat-lying postures, and thus, it is difficult to ensure that different users
have the torso close to the LOS in all sleeping postures. Therefore, it would
be wise to develop a system that does not rely on the FFZ for robust
monitoring of vital signs.

_Fresnel-zone-model-based sensing:_ The Fresnel zone model [12] was developed
to relate the depth, location, and direction of a person’s breathing to the
detectability of breathing by examining the received signal strength in the
context of the Fresnel zones. However, the Fresnel zone model cannot explain
some of the phenomena observed in our experiments. In setting 1, when the
human target is prone or supine, the direction of abdominal/thoracic
deformation in the anteroposterior dimension induced by breathing is nearly
parallel to T1–R3. According to the Fresnel zone model, the effective
displacement caused by the thoracic/abdominal deformation is tiny, and thus,
the sensing performance of T1–R3 should not be good, or at least should be
worse than that of T1–R1; however, in our experiments, the sensing performance
of T1–R3 was better than that of T1–R1. We believe that the reason may be that
the LOS path of the T1–R3 antenna pair was blocked by the shelf. In the
following subsection, we verify our conjecture through a Ricean-K-based
derivation and experiments.

###  III-C NLOS Sensing Model Based on Ricean K Theory

To study in depth the phenomena that occurred in the preliminary experiments
for better monitoring of vital signs, in this section, we propose our NLOS
sensing model to analyze the relationship between the power ratio of the LOS
and NLOS signals and the NLOS sensing ability based on Ricean K theory.

The Ricean K factor is defined as the ratio of the power on the LOS path to
the power on the NLOS paths. The baseband in-phase/quadrature-phase (I/Q)
representation of the received signal can be expressed as follows [49]:

$x(t)=\sqrt{\frac{K\Omega}{K+1}}e^{j(2\Pi
f_{D}cos(\theta_{0})t)+\phi_{0}}+\sqrt{\frac{\Omega}{K+1}}h(t).$ (6)

Here, $K$ is the Ricean factor; $\Omega$ denotes the total received power;
$\theta_{0}$ and $\phi_{0}$ are the LOS angle of arrival (AOA) and phase,
respectively; $f_{D}$ is the maximum Doppler frequency; and $h(t)$ is a
diffuse component representing the sum of the large number of multipath
components, constituting a complex Gaussian process.

Since the antennas do not move in the considered experimental scenario, i.e.,
$f_{D}=0$, we can simplify equation (6) to:

$x(t)=\sqrt{\frac{K\Omega}{K+1}}e^{\phi_{0}}+\sqrt{\frac{\Omega}{K+1}}h(t).$
(7)

In the case that the torso does not block the LOS signals, all LOS components
and part of the NLOS components correspond to static path conditions, and the
remainder of the NLOS components correspond to dynamic path conditions.
Considering equation (7) and ignoring the transmit power, we define $|H_{s}|$
and $|H_{d}|$ as follows:

$|H_{s}|=\frac{K}{K+1}+\frac{1}{K+1}\cdot\rho,$ (8)
$|H_{d}|=\frac{1}{K+1}\cdot(1-\rho).$ (9)

Here, $\rho$ is the proportion of the static path contribution to the NLOS
components. Combining the above with equation (4), we obtain the following
equation:

$\begin{split}|H|^{2}=|H_{s}|^{2}+|H_{d}|^{2}+2|H_{s}||H_{d}|cos\theta\\\
=\frac{(K+\rho)^{2}}{(K+1)^{2}}+\frac{(1-\rho)^{2}}{(K+1)^{2}}\\\
+\frac{2(K+\rho)(1-\rho)}{(K+1)^{2}}cos\theta.\end{split}$ (10)

The motion-induced variation in the signal amplitude can be quantified as
follows:

$f(K,\rho)=2|H_{s}||H_{d}|cos\theta=\frac{2(K+\rho)(1-\rho)}{(K+1)^{2}}cos\theta.$
(11)

The output of the above formula depends on three variables, namely, $\theta$,
$K$ and $\rho$. Considering that the change in the phase difference caused by
breathing is relatively stable, we omit $\theta$. Then, we take the derivative
of equation 11 with respect to $K$ to obtain the following formula:

$f{}^{\prime}(K)=\frac{2(1-\rho)(-K^{2}-2\rho K+1-2\rho)}{(K+1)^{4}}.$ (12)

When $K>1-2\rho$, $f(K,\rho)$ decreases as $K$ increases. Under normal
circumstances, only a small part of the signal from an omnidirectional antenna
can be reflected by the human body, which means that $\rho$ is generally
larger than 0.5. In other words, appropriately blocking the LOS path can make
the CSI more sensitive to human body motion.

_How does $\rho$ influence the Wi-Fi sensing capability?_

In some Wi-Fi-based sensing studies, directional antennas have been used to
enhance the performance of Wi-Fi sensing. A directional antenna can transmit
its signal directly toward the human body, ensuring that as much of the NLOS
component as possible will be subject to dynamic path conditions (decreasing
$\rho$). We can also use the proposed model to explain why this works and
provide guidance for subsequent research.

We first seek a formula to explain the influence of $\rho$ on Wi-Fi sensing.
We take the derivative of equation 11 with respect to $\rho$ to obtain:

$f{}^{\prime}(\rho)=\frac{2(-2\rho+K-1)}{(K+1)^{2}}.$ (13)

When $K$ is invariant, the Wi-Fi sensing capability increases as $\rho$
increases in the interval [0,$\frac{1-K}{2}$] and decreases as $\rho$
increases in the interval [$\frac{1-K}{2}$,1]. For a more intuitive
explanation, we map the CSI signal to the complex plane for further
discussion.

Figure 4: The CSI in the complex plane when $H_{s}|>=|H_{d}|$. $H_{s}$,
$H_{d}$ and $H_{f}$ represent the static and dynamic vectors and the composite
vector of $H_{s}$ and $H_{d}$, respectively.

Now, we can explain the conclusion in a more intuitive way. We will first
explain how to use the complex plane to intuitively visualize the sensing
capability [9]. As shown in Fig. 4, $H_{s}$, $H_{d}$ and $H_{f}$ represent the
static and dynamic vectors and the composite vector of $H_{s}$ and $H_{d}$,
respectively. According to [9], when the dynamic path length changes on a
short time scale, the amplitude of $H_{d}$ remains the same, but the phase
(the angle of $H_{d}$ with respect to the $I$-axis) changes. This means that
$H_{d}$ draws a circle with the end point of $H_{s}$ as its center, as shown
in Fig. 4. The amplitude and phase extracted from the CSI correspond to the
amplitude of $H_{f}$ and its angle with respect to the $I$-axis, respectively,
and the sensing capability of the CSI can be expressed as:

$AS=|H_{fmax}|-|H_{fmin}|,$ (14)

$AS$ denotes the CSI sensing ability, which is expressed as the maximum
amplitude difference in the CSI waveform caused by motion. $|H_{fmax}|$ and
$|H_{fmin}|$ are the maximum and minimum absolute values of the composite
vector $H_{f}$, respectively.

Next, we discuss how $\rho$ affects the sensing capability in two cases: $K>1$
and $0<=K<=1$. When $K>1$, $\frac{1-K}{2}<0$; according to formula 13, the
sensing capability decreases monotonically as $\rho$ increases in the interval
[0,1]. In the complex plane, it can be seen that $|H_{s}|>|H_{d}|$; when
$|H_{s}|>=|H_{d}|$, $|H_{fmax}|^{2}=|H_{s}|^{2}+|H_{d}|^{2}+2|H_{s}||H_{d}|$
and $|H_{fmin}|^{2}=|H_{s}|^{2}+|H_{d}|^{2}-2|H_{s}||H_{d}|$. The maximum
value that $AS$ can reach is $(|H_{s}+H_{d})-(|H_{s}-H_{d})=2|H_{d}|$; in
other words, the larger $H_{d}$ is, the better the sensing capability.

When $0<=K<=1$, this means that $0.5>=\frac{1-K}{2}>=0$, and according to
equation 13, the sensing capability increases as $\rho$ increases in the
interval [0,$\frac{1-K}{2}$] and decreases as $\rho$ increases in the interval
[$\frac{1-K}{2}$,1]. In the complex plane, when $\rho$ is in the interval
[$\frac{1-K}{2}$,1], according to equations 8 and 9, $|H_{s}|>|H_{d}|$, this
situation is the same as in the previous paragraph: a smaller $\rho$ is
better. When $\rho$ is in the interval [0, $\frac{1-K}{2}$], which means that
$|H_{s}|<|H_{d}|$, the maximum value of $AS$ is
$|H_{fmax}|-|H_{fmin}|=|H_{d}|+H_{s}|-(|H_{d}|-|H_{s}|)=2|H_{s}|$. In other
words, the larger $H_{s}$ is, the better the sensing capability, which means
that a larger $\rho$ is better.

In practical applications, it is difficult to achieve $|H_{s}|<|H_{d}|$ unless
$K<1$ and most of the NLOS component is subject to the dynamic path
conditions. Therefore, decreasing $\rho$ is conducive to improving the sensing
capability. Considering that directional antennas can reduce $\rho$,
directional antennas are concluded to be beneficial for Wi-Fi-based sensing.

Figure 5: System architecture.

_Does blocking the LOS make the sensing ability worse?_ Blocking the LOS path
reduces the Ricean K value, but does blocking the LOS make the sensing ability
worse? Formula 11 contains two main variables, $K$ and $\rho$. Does a
situation exist in which blocking the LOS path reduces $K$ but increases
$rho$, resulting in poorer motion perception? We believe that it is difficult
for such a scenario to occur unless the blocking causes the static signal
energy ($|H_{s}|$) that reaches the receiver to be too low. Suppose that in
the worst-case scenario, the LOS path is blocked such that the NLOS signal
energy increases by $L$, but no part of $L$ is allocated to the dynamic
vector. Then, the amplitudes of $|H_{s}|$ and $|H_{d}|$ do not change, nor
does their product, and the sensing capability is equal to that in the
original case. In an actual indoor environment, it is difficult to prevent any
of the blocked LOS signal from spreading to the human body at all. In summary,
regardless of whether $rho$ is large, small or constant, no deterioration in
the sensing capability will be caused by blocking the LOS unless the blocking
severely affects the signal received at the receiver.

##  IV System Design

###  IV-A System Overview

In this section, we present the system design of our vital sign monitoring
system, Wital. The Wital system is shown in Fig. 5 and is divided into three
modules:

Data Collection. We collect better CSI data for vital sign monitoring based on
our NLOS sensing model (blocking the LOS). Since the data collection setup is
different in different scenarios, this section describes only the general data
processing modules (data preprocessing and vital sign extraction) in detail.
The data collection setting considered in this paper is described in the
evaluation section.

Data Preprocessing. We first select the best-performing subcarrier via
subcarrier selection, and we then distinguish the vital signs from other
motions in accordance with our motion segmentation method. Finally, we denoise
the CSI data to remove outliers.

Vital Sign Extraction. The preprocessed data are divided into two parts via
frequency-domain segmentation: one mainly includes breathing, and the other
mainly contains heartbeats. Then, we extract the breathing rate and heart rate
using the Fast Fourier Transform (FFT).

###  IV-B Data Preprocessing

Subcarrier Selection. Different subcarriers have different central frequencies
and may have different sensing performances. Therefore, it is essential to
select a suitable subcarrier that can capture vital signs as effectively as
possible. Based on previous experience[50], we select the subcarrier with the
largest variance for Wital.

Figure 6: A example of the regularity calculation results. $WEP$, $TP$, and
$PAP$ represent the wave end point, turning point, and positioning activation
point, respectively.

Motion Segmentation. During vital sign monitoring, it is impossible for the
monitored person to remain quiescent at all times. Random movements such as
turning over can affect the accuracy of vital sign monitoring; therefore, it
is necessary to design a motion segmentation method to locate and filter out
motions that are different from breathing/heartbeats.

Since both breathing/heartbeats and turning over are movements, the dynamic
vs. static segmentation method used in previous studies is not applicable. To
fill this gap, we propose a motion segmentation method that can distinguish
vital signs from other movements. Our method is based on the assumption that
breathing and other activities have different regularities. We choose a data
sequence containing two instances of turning over as well as normal breathing
as an example to verify this hypothesis, as shown in Fig. 6.

To calculate the regularity of the CSI data, we first establish a variable-
length window $A$ and a fixed-length window $B$. $A$ starts at the beginning
of the CSI waveform, $B$ starts at the end of $A$, and the initial length of
both $A$ and $B$ is 2000 packets. We calculate the minimum Euclidean distance
(MED) between the CSI data contained in $B$ and the data in $A$ and record the
result. Then, we expand window $A$ forward by 100 packets, shift window $B$
forward by 100 packets, and calculate the MED again. The process is iterated
until the end of the waveform is reached.

The results are shown in Fig. 6. The MED increases sharply when the first
instance of turning over occurs and begins to decrease once this movement
ends. From the experimental results, we can observe that the regularities
differ between breathing and turning over, whereas the regularities of actions
of the same type are similar.

The key steps of our segmentation method are as follows:

  1. 1.

Initialization. Establish a variable-length window $A$ and a fixed-length
window $B$. $A$ starts at the beginning of the CSI waveform, $B$ starts at the
end of $A$, and the initial length of both $A$ and $B$ is 2000 packets. Also
establish an empty set $MA$.

  2. 2.

Activation point detection. Calculate the MED of the CSI windows as described
above. If $MED>v\cdot ave(MA)$ in the current iteration (where $ave()$ is the
averaging function), mark this point as a positioning activation point (PAP)
and go to the next step; otherwise, record the MED into $MA$ (where $v$ is the
threshold for judging whether an action occurred; $v=2.5$ in our experiments).

  3. 3.

Start-point positioning. Based on the obtained MED waveform ($MA$), construct
an auxiliary positioning waveform to accurately locate the start point of the
motion. Establish two points in front of PAP as the turning point (TP) and the
wave end point (WEP). The distance from TP to WEP is 20 packets, and the
constructed waveform is as shown in Fig. 6. Calculate the Euclidean distance
(ED) between the constructed waveform and the MED waveform and record the
result; then move TP forward by 10 packets and repeat the above process for 50
iterations. Finally, choose the TP with the minimum ED as the start point of
the motion.

  4. 4.

End-point positioning. Set the identified start point as the beginning of the
CSI waveform, initialize the parameters as described in the first step, and
calculate the MED as described above. Then, use the previously described
method to position the end point of the motion. Set the identified end point
as the beginning of the CSI waveform, and return to step 1. Repeat the entire
process until the end of the monitoring period.

Figs. 7 and 8 show the experimental results of our proposed segmentation
method. Our inspiration for designing this method is that the regularity of
respiration differs greatly from those of other activities; consequently, as
shown in Figs. 7 and 6, our method can precisely locate the time period during
which such an activity occurs. For different pairs of activities, the
difference in regularity may be smaller, and thus, the positioning of these
activities may not be very precise. We tested the performance achieved in
distinguishing between walking and jumping using the proposed method, as shown
in Fig. 8, from which it can be seen that the segmentation accuracy is still
within an acceptable range.

Figure 7: Performance of our motion segmentation method. Figure 8: Performance
of our motion segmentation method when handling different activities.

Data Denoising. The received CSI data may contain a large amount of
interference noise due to equipment and environmental factors. In the
preprocessing module, we use the Hampel filter to filter out outliers that
have markedly different values from other neighboring CSI measurements. The
goal of the Hampel filter is to identify and replace outliers in a given
series. Specifically, we calculate the median of the set consisting of the
current CSI sample and its six surrounding samples (three on each side) and
use the median absolute deviation to calculate the standard deviation of the
set. If the difference between the current sample and the median exceeds three
times the standard deviation, this sample will be replaced by the median
value.

Figure 9: Real-time system interface. The upper left part is the parameter
setting interface, which can be used to set the storage location of the
received data, the time axis scale, the receiving rate, the sender’s IP
address, whether to enable vital sign detection, etc. The bottom left shows
the time when the current packet was received and the size of the packet. The
top right is the real-time display of the CSI waveform, and the bottom right
is the real-time display of vital signs.

(a)

(b)

(c)

Figure 10: Comparison of the processed CSI and the accelerometer (ACC)
readings for heartbeats. (a) Supine. (b) Facing right. (c) Facing left.

###  IV-C Vital Sign Extraction

Frequency-Domain Segmentation. The trunk deformation caused by the heartbeat
is very small, and the changes in the CSI caused by this deformation can be
overwhelmed by the changes caused by breathing [11]. Therefore, we first need
to segment them in the frequency domain. Here, we leverage Butterworth
bandpass filters based on some prior knowledge in the frequency domain: the
frequency range associated with a normal heartbeat is 60 bpm to 120 bpm,
corresponding to 1 Hz to 2 Hz, and the frequency range associated with normal
breathing is 15 bpm to 30 bpm, corresponding to 0.25 Hz to 0.5 Hz.

Vital Sign Extraction. After segmenting the CSI in the frequency domain, we
extract the heart and respiratory rates by applying the FFT. We have used
MATLAB to implement a real-time system for the processing and display vital
signs to facilitate our experiments, as shown in Fig. 9. This system works on
the monitoring side and is connected to the data acquisition equipment via a
network.

##  V Performance Evaluation

In this section, we first evaluate the proposed vital sign monitoring system,
Wital, and then verify the effectiveness of our NLOS sensing model.

###  V-A Experimental Setup

The performance of vital sign detection varies greatly among different people
and different sleeping postures within the FFZ. Therefore, in our experiments,
we constructed our prototype system in accordance with setting 1, and we
selected the T1–R3 antenna pair to monitor vital signs. Due to the limitations
imposed by the bed, the torso is closer to R3 when the human target is lying
either face up or face down; in other words, the torso is far from the mid-
perpendicular of T1–R3. According to the Fresnel zone model, the chest
displacement caused by breathing/heartbeats in the anteroposterior dimension
still has a significant effect on T1–R3, thereby ensuring the monitoring
performance in different sleeping postures. If we were to select the T1–R1
antenna pair, however, as shown in Fig. 11, the monitoring performance would
become worse when the person’s arm is blocking the side. This is because the
main factor affecting the CSI received by R1 when the target is in the
left-/right-facing recumbent position is the torso deformation in the lateral
abdomen, and the arm sometimes blocks this area. This is why we selected T1–R3
for vital sign monitoring instead of T1–R1.

Figure 11: Obstruction of the LOS signal from T1 to R1 in setting 1. The K
factor of the T1–R1 stream decreases to 12.4, and the K factor of the T1–R3
stream increases to 5076. Figure 12: The prototype system. T1, R1, R2, and R3
represent the transmit antenna and receive antennas 1, 2 and 3, respectively.

(a)

(b)

(c)

Figure 13: System readings with no other person present and with active
interference. (a) Setup. (b) With interference from other activities. (c) With
no other person present.

In our experiments, we placed a lead plate under T1 to block the LOS path from
T1 to R3 in accordance with our NLOS sensing model. CSI data were collected
using csitool [51], and the receiver transmitted the received CSI data to the
monitoring computer for processing via the network.

We used COTS hardware devices to implement the proposed system. Specifically,
we used two mini PCs with Intel Link 5300 Wi-Fi NICs as the transmitting and
receiving devices. The mini PCs each had a 2.16 GHz Intel Celeron N2830
processor with 2 GB of RAM and Ubuntu OS version 12.04. The monitoring
computer was a desktop computer equipped with an Intel Core i5 3450 CPU (3.1G
Hz) and 2 GB of storage.

We conducted the experiments in a laboratory environment, as shown in Fig. 12,
with a total of 10 volunteers (6 male and 4 female) whose age range was 21 to
26 years. These 10 volunteers were university students who volunteered to
participate in the experiments. During the experiments, we did not restrict
the normal activities of others in the laboratory.

Each participant underwent a 30-minute actual test in different natural
sleeping positions (prone, supine, left-facing recumbent, and right-facing
recumbent). Different from previous work [11, 16], we did not use a metronome
to control the volunteers’ respiratory rate, and we did not need to use a
directional antenna to monitor the heart rate under LOS conditions. The
ground-truth respiratory rate and heart rate were measured by an accelerometer
attached to the abdomen and a fingertip pulse oximeter, respectively.

###  V-B Evaluation Results

Figure 14: Comparison of the processed CSI and the accelerometer (ACC)
readings for breathing. Figure 15: Errors of vital sign estimation for
different volunteers.

Fig. 13 shows the system readings in the presence of people performing other
activities and in an unoccupied room. Our system does not output false
respiratory/heart rate values in either of these scenarios.

Figure 16: Errors of vital sign estimation for different sleeping postures.

We compared the obtained respiratory waveforms with the data from the
accelerometer attached to the abdomen, as shown in Fig. 14. From this figure,
we can observe that the CSI waveform is highly consistent with the respiratory
waveform obtained by the accelerometer. Fig. 10 compares heartbeat waveforms
obtained in different postures with the readings from the accelerometer
attached to the chest, and we find that the heartbeat readings obtained from
the accelerometer are also consistent with the results of CSI detection. These
results indicate that the CSI obtained from Wi-Fi signals can be used to
extract fine-grained heartbeat and respiration information.

We evaluated the overall performance of breathing and heart rate estimation in
different sleeping postures. The final results indicate average errors of
0.498 bpm (beats per minute) for the detected breathing rate and 3.531 bpm for
the detected heart rate, and the corresponding accuracy is 96.887% and
94.708%, respectively.

Fig. 15 illustrates the errors of vital sign (respiration and heart rate)
monitoring for different participants; the volunteers had different body
types, which led to different final results. However, in general, our system
shows high accuracy in detecting respiration, and the error in detecting the
heart rate is also within the acceptable range for nonclinical environments.

(a)

(b)

(c)

Figure 17: Distributions of the three streams in Fig. 3a. (a) T1–R1,
$K=201.1$. (b) T1–R2, $K=17.8$. (c) T1–R3, $K=52$. PDF means probability
density function.

Fig. 16 illustrates the vital sign (respiration and heart rate) monitoring
errors in different sleeping postures. These errors are relatively small in
the supine and right-facing recumbent postures. However, the largest error in
the monitored heart rate was found for the left-facing recumbent posture,
while the largest error in the monitored respiratory rate was found for the
prone posture. This is because the effective displacements of the dynamic path
caused by these two sleeping postures are relatively small and not conducive
to vital sign monitoring. Overall, our system can accurately monitor vital
signs in different sleeping postures.

###  V-C Evaluation of the NLOS Sensing Model

To verify the NLOS sensing model proposed in section III, we first calculated
the Ricean K value of each stream in setting 1 (Fig. 2a), as shown in Fig. 17,
from which it can be found that the larger the value of $K$ is, the worse the
sensing capability. Then, we placed a lead sheet between the T1–R1 antenna
pair in setting 1 (decreasing $K$) and performed a breathing monitoring
experiment, and the results are presented in Fig. 11, showing that the motion
sensing capability of T1–R1 was significantly improved. We also show the
average breathing detection error (BDE), the variance of the CSI waveform
(VAR), and the mean amplitude difference (MAD) in Fig. 18. We can observe
improvements in both the detection accuracy and the sensitivity to motion.

Figure 18: The average breathing detection error (BDE), the variance of the
CSI waveform (VAR), and the mean amplitude difference (MAD) when T1–R1 was
blocked and unblocked.

###  V-D Comparison with Previous Approaches

In this subsection, we compare Wital with four previously reported Wi-Fi-based
vital sign monitoring approaches [52, 53, 45, 10].

TVS. Similar to our method, TVS [52] uses the CSI amplitude for respiration
sensing. First, the Hampel filter and a moving average filter are employed to
clean the collected CSI data to remove noise. Then, subcarriers with larger
variance are selected and subjected to the FFT to obtain the final results.

PhaseBeat. PhaseBeat [53] uses the phase difference between the CSI readings
of two antennas for respiration sensing. First, environment detection, data
calibration, subcarrier selection and the discrete wavelet transform are used
to preprocess the captured data. Then, peak detection is employed to estimate
the respiratory rate.

TensorBeat. TensorBeat [45] is also a phase-difference-based method. First,
the obtained CSI phase difference data are used to create tensors, and then,
canonical polyadic (CP) decomposition is employed to obtain the respiration
signals. Finally, peak detection is used to estimate the respiratory rate.

ResBeat. ResBeat [10] uses both phase difference and amplitude for respiration
monitoring. First, an adaptive signal selection module is leveraged to select
the most sensitive signal group from the CSI amplitude groups and CSI phase
difference groups. Then, peak detection is used to estimate the respiratory
rate.

Figure 19: Comparison with previous approaches.

Fig. 19 presents the results. Wital achieves better performance than the other
solutions. Although Wital’s data processing is less sophisticated than that of
the other solutions, we improve the respiration sensing ability by attenuating
the LOS signal under the guidance of the proposed NLOS sensing model.

###  V-E Limitations and Future Work

There are still some limitations to the application of our system in real-
world scenarios, and these limitations are driving our further research. In
this subsection, we describe these limitations and the solutions we propose to
explore.

The first limitation is that Wital cannot recover the exact heartbeat
waveform. Since the MATLAB-based system has difficulty handling multiple
threads, we have used a crude bandpass filter and the FFT to obtain the
heartbeats; however, this approach is not sufficient to obtain highly accurate
and timely vital signs. The difficulty in overcoming this problem is that the
trunk deformation caused by heartbeats can be overwhelmed by that caused by
breathing, and it is difficult to separate heartbeats from breaths. The second
limitation is that we are currently discarding the time periods during which
interfering sleep activities occur, but it is also important to monitor vital
signs during these periods. The challenge in solving this limitation is that
such activities can overwhelm the vital signs. The third limitation is that
for multiperson scenarios, we may be able to acquire the respiratory rates of
multiple people (with different respiratory rates) via the FFT, but recovering
the vital sign waveforms of individual people is difficult because of the
superposition of the signal changes caused by multiple persons breathing.

Fortunately, these three problems can be viewed as the same general problem of
separating signals that are superimposed on each other. Solutions based on
traditional independent component analysis (ICA) may not solve these problems
very well. However, we have reviewed some literature and believe that methods
based on big data and deep learning may have unexpected benefits. For example,
[54] developed a nonlinear generalization approach based on temporal
dependencies (e.g., autocorrelations), contrastive learning and a multilayer
perceptron (MLP) for ICA or blind source separation. Some other literature on
learning disentangled representations has focused on variational autoencoders
(VAEs) [55, 56]. The authors of these studies first encode the original input
to obtain latent variables and impose artificially specified constraints on
these latent variables to force the approximate posterior to match the prior
in the latent space (under the assumption that the latent variables obtained
by the VAE approximate the true latent variables of the input). Then, they
reconstruct the input using a decoder and the obtained latent variables.
Finally, a well-trained VAE can disentangle the factors (latent variables) of
interest from the inputs. The core of both approaches is to find a suitable
and effective model structure and constraints; these constraints should
reflect the differences in the factors that are to be separated. We are
currently experimenting with these solutions to enhance the applicability of
our system.

##  VI Conclusion

In this paper, we show the ability to use Wi-Fi signals to track breathing and
heartbeats in different sleeping postures using only one pair of Wi-Fi
devices. To achieve this, we propose an NLOS sensing model based on Ricean K
theory to help monitor the minor displacements caused by breathing and
heartbeats, and we theoretically prove that blocking the LOS signal is
beneficial for motion detection in NLOS sensing. We also propose a motion
segmentation method based on regularity detection, which can accurately
identify the time ranges corresponding to motions different from vital signs
(such as turning over and rising from bed). We have implemented a prototype
system to evaluate our method. The experimental results indicate that our
method achieves 96.618% and 94.708% accuracy for breathing and heart rate
detection, respectively.

## References

  * [1] S. D. Min, J. K. Kim, H. S. Shin, Y. H. Yun, C. K. Lee, and M. Lee, “Noncontact respiration rate measurement system using an ultrasonic proximity sensor,” _IEEE Sensors Journal_ , vol. 10, no. 11, pp. 1732–1739, 2010.
  * [2] P. X. Braun, C. F. Gmachl, and R. A. Dweik, “Bridging the collaborative gap: Realizing the clinical potential of breath analysis for disease diagnosis and monitoring–tutorial,” _IEEE Sensors Journal_ , vol. 12, no. 11, pp. 3258–3270, 2012.
  * [3] F. L. Facco, D. W. Ouyang, P. C. Zee, and W. A. Grobman, “Sleep disordered breathing in a high-risk cohort prevalence and severity across pregnancy,” _American journal of perinatology_ , vol. 31, no. 10, pp. 899–904, 2014.
  * [4] C. A. Kushida, M. R. Littner, T. Morgenthaler, C. A. Alessi, D. Bailey, J. Coleman Jr, L. Friedman, M. Hirshkowitz, S. Kapen, M. Kramer _et al._ , “Practice parameters for the indications for polysomnography and related procedures: an update for 2005,” _Sleep_ , vol. 28, no. 4, pp. 499–523, 2005.
  * [5] T. A. Nappholz, W. N. Hursta, A. K. Dawson, and B. M. Steinhaus, “Implantable ambulatory electrocardiogram monitor,” May 19 1992, uS Patent 5,113,869.
  * [6] M. Zhao, F. Adib, and D. Katabi, “Emotion recognition using wireless signals,” in _Proceedings of the 22nd Annual International Conference on Mobile Computing and Networking_ , 2016, pp. 95–108.
  * [7] S. Yue, H. He, H. Wang, H. Rahul, and D. Katabi, “Extracting multi-person respiration from entangled rf signals,” _Proceedings of the ACM on Interactive, Mobile, Wearable and Ubiquitous Technologies_ , vol. 2, no. 2, pp. 1–22, 2018.
  * [8] F. Zhang, D. Zhang, J. Xiong, H. Wang, K. Niu, B. Jin, and Y. Wang, “From fresnel diffraction model to fine-grained human respiration sensing with commodity wi-fi devices,” _Proceedings of the ACM on Interactive, Mobile, Wearable and Ubiquitous Technologies_ , vol. 2, no. 1, p. 53, 2018.
  * [9] Y. Zeng, D. Wu, J. Xiong, E. Yi, R. Gao, and D. Zhang, “Farsense: Pushing the range limit of wifi-based respiration sensing with csi ratio of two antennas,” _Proceedings of the ACM on Interactive, Mobile, Wearable and Ubiquitous Technologies_ , vol. 3, no. 3, pp. 1–26, 2019.
  * [10] X. Wang, C. Yang, and S. Mao, “Resilient respiration rate monitoring with realtime bimodal csi data,” _IEEE Sensors Journal_ , vol. 20, no. 17, pp. 10 187–10 198, 2020.
  * [11] J. Liu, Y. Chen, Y. Wang, X. Chen, J. Cheng, and J. Yang, “Monitoring vital signs and postures during sleep using wifi signals,” _IEEE Internet of Things Journal_ , vol. 5, no. 3, pp. 2071–2084, 2018.
  * [12] H. Wang, D. Zhang, J. Ma, Y. Wang, Y. Wang, D. Wu, T. Gu, and B. Xie, “Human respiration detection with commodity wifi devices: do user location and body orientation matter?” in _Proceedings of the 2016 ACM International Joint Conference on Pervasive and Ubiquitous Computing_. ACM, 2016, pp. 25–36.
  * [13] Y. Zeng, D. Wu, J. Xiong, J. Liu, Z. Liu, and D. Zhang, “Multisense: Enabling multi-person respiration sensing with commodity wifi,” _Proceedings of the ACM on Interactive, Mobile, Wearable and Ubiquitous Technologies_ , vol. 4, no. 3, pp. 1–29, 2020.
  * [14] Y. Gu, J. Zhan, Y. Ji, J. Li, F. Ren, and S. Gao, “Mosense: An rf-based motion detection system via off-the-shelf wifi devices,” _IEEE Internet of Things Journal_ , vol. 4, no. 6, pp. 2326–2341, 2017.
  * [15] X. Liu, J. Cao, S. Tang, J. Wen, and P. Guo, “Contactless respiration monitoring via off-the-shelf wifi devices,” _IEEE Transactions on Mobile Computing_ , vol. 15, no. 10, pp. 2466–2479, 2016.
  * [16] D. Zhang, Y. Hu, Y. Chen, and B. Zeng, “Breathtrack: Tracking indoor human breath status via commodity wifi,” _IEEE Internet of Things Journal_ , vol. 6, no. 2, pp. 3899–3911, 2019.
  * [17] J. Liu, Y. Zeng, T. Gu, L. Wang, and D. Zhang, “Wiphone: Smartphone-based respiration monitoring using ambient reflected wifi signals,” _Proceedings of the ACM on Interactive, Mobile, Wearable and Ubiquitous Technologies_ , vol. 5, no. 1, pp. 1–19, 2021.
  * [18] Y. Ma, G. Zhou, and S. Wang, “Wifi sensing with channel state information: A survey,” _ACM Computing Surveys (CSUR)_ , vol. 52, no. 3, pp. 1–36, 2019\.
  * [19] Y. Gu, X. Zhang, Z. Liu, and F. Ren, “Besense: Leveraging wifi channel data and computational intelligence for behavior analysis,” _IEEE Computational Intelligence Magazine_ , vol. 14, no. 4, pp. 31–41, 2019.
  * [20] J. Huang, B. Liu, P. Liu, C. Chen, N. Xiao, Y. Wu, C. Zhang, and N. Yu, “Towards anti-interference wifi-based activity recognition system using interference-independent phase component,” in _IEEE INFOCOM 2020-IEEE Conference on Computer Communications_. IEEE, 2020, pp. 576–585.
  * [21] J. Huang, B. Liu, C. Miao, Y. Lu, Q. Zheng, Y. Wu, J. Liu, L. Su, and C. W. Chen, “Phaseanti: an anti-interference wifi-based activity recognition system using interference-independent phase component,” _IEEE Transactions on Mobile Computing_ , pp. 1–1, 2021.
  * [22] J. Huang, B. Liu, C. Chen, H. Jin, Z. Liu, C. Zhang, and N. Yu, “Towards anti-interference human activity recognition based on wifi subcarrier correlation selection,” _IEEE Transactions on Vehicular Technology_ , vol. 69, no. 6, pp. 6739–6754, 2020.
  * [23] H. Huang and S. Lin, “Widet: Wi-fi based device-free passive person detection with deep convolutional neural networks,” _Computer Communications_ , vol. 150, pp. 357–366, 2020.
  * [24] H. F. T. Ahmed, H. Ahmad, and C. Aravind, “Device free human gesture recognition using wi-fi csi: A survey,” _Engineering Applications of Artificial Intelligence_ , vol. 87, p. 103281, 2020.
  * [25] K. Qian, C. Wu, Z. Yang, Y. Liu, and K. Jamieson, “Widar: Decimeter-level passive tracking via velocity monitoring with commodity wi-fi,” in _Proceedings of the 18th ACM International Symposium on Mobile Ad Hoc Networking and Computing_ , 2017, pp. 1–10.
  * [26] H. Yan, Y. Zhang, Y. Wang, and K. Xu, “Wiact: A passive wifi-based human activity recognition system,” _IEEE Sensors Journal_ , vol. 20, no. 1, pp. 296–305, 2020.
  * [27] Y. Zhang, Y. Zheng, K. Qian, G. Zhang, Y. Liu, C. Wu, and Z. Yang, “Widar3.0: Zero-effort cross-domain gesture recognition with wi-fi,” _IEEE Transactions on Pattern Analysis and Machine Intelligence_ , vol. 44, no. 11, pp. 8671–8688, 2022.
  * [28] Y. Gu, X. Zhang, Y. Wang, M. Wang, H. Yan, Y. Ji, Z. Liu, J. Li, and M. Dong, “Wigrunt: Wifi-enabled gesture recognition using dual-attention network,” _IEEE Transactions on Human-Machine Systems_ , vol. 52, no. 4, pp. 736–746, 2022.
  * [29] L. Zhao, H. Huang, X. Li, S. Ding, H. Zhao, and Z. Han, “An accurate and robust approach of device-free localization with convolutional autoencoder,” _IEEE Internet of Things Journal_ , vol. 6, no. 3, pp. 5825–5840, 2019.
  * [30] Y. Cao, F. Wang, X. Lu, N. Lin, B. Zhang, Z. Liu, and S. Sigg, “Contactless body movement recognition during sleep via wifi signals,” _IEEE Internet of Things Journal_ , vol. 7, no. 3, pp. 2028–2037, 2020.
  * [31] Y. Bai, Z. Wang, K. Zheng, X. Wang, and J. Wang, “Widrive: Adaptive wifi-based recognition of driver activity for real-time and safe takeover,” in _2019 IEEE 39th International Conference on Distributed Computing Systems (ICDCS)_. IEEE, 2019, pp. 901–911.
  * [32] F. Wang, S. Zhou, S. Panev, J. Han, and D. Huang, “Person-in-wifi: Fine-grained person perception using wifi,” in _Proceedings of the IEEE International Conference on Computer Vision_ , 2019, pp. 5452–5461.
  * [33] D. Wu, R. Gao, Y. Zeng, J. Liu, L. Wang, T. Gu, and D. Zhang, “Fingerdraw: Sub-wavelength level finger motion tracking with wifi signals,” _Proceedings of the ACM on Interactive, Mobile, Wearable and Ubiquitous Technologies_ , vol. 4, no. 1, pp. 1–27, 2020.
  * [34] Y. Meng, J. Li, H. Zhu, X. Liang, Y. Liu, and N. Ruan, “Revealing your mobile password via wifi signals: Attacks and countermeasures,” _IEEE Transactions on Mobile Computing_ , vol. 19, no. 2, pp. 432–449, 2020.
  * [35] F. Zhang, C. Wu, B. Wang, M. Wu, D. Bugos, H. Zhang, and K. R. Liu, “Smars: Sleep monitoring via ambient radio signals,” _IEEE Transactions on Mobile Computing_ , vol. 20, no. 1, pp. 217–231, 2019.
  * [36] H. Aly and M. Youssef, “Zephyr: Ubiquitous accurate multi-sensor fusion-based respiratory rate estimation using smartphones,” in _IEEE INFOCOM 2016-The 35th Annual IEEE International Conference on Computer Communications_. IEEE, 2016, pp. 1–9.
  * [37] J. Paalasmaa, M. Waris, H. Toivonen, L. Leppäkorpi, and M. Partinen, “Unobtrusive online monitoring of sleep at home,” in _2012 Annual International Conference of the IEEE Engineering in Medicine and Biology Society_. IEEE, 2012, pp. 3784–3788.
  * [38] M. Kumar, A. Veeraraghavan, and A. Sabharwal, “Distanceppg: Robust non-contact vital signs monitoring using a camera,” _Biomedical optics express_ , vol. 6, no. 5, pp. 1565–1588, 2015.
  * [39] J. Salmi and A. F. Molisch, “Propagation parameter estimation, modeling and measurements for ultrawideband mimo radar,” _IEEE Transactions on Antennas and Propagation_ , vol. 59, no. 11, pp. 4257–4267, 2011.
  * [40] N. Patwari, L. Brewer, Q. Tate, O. Kaltiokallio, and M. Bocca, “Breathfinding: A wireless network that monitors and locates breathing in a home,” _IEEE Journal of Selected Topics in Signal Processing_ , vol. 8, no. 1, pp. 30–42, 2013.
  * [41] N. Patwari, J. Wilson, S. Ananthanarayanan, S. K. Kasera, and D. R. Westenskow, “Monitoring breathing via signal strength in wireless networks,” _IEEE Transactions on Mobile Computing_ , vol. 13, no. 8, pp. 1774–1786, 2013.
  * [42] H. Abdelnasser, K. A. Harras, and M. Youssef, “Ubibreathe: A ubiquitous non-invasive wifi-based breathing estimator,” in _Proceedings of the 16th ACM International Symposium on Mobile Ad Hoc Networking and Computing_. ACM, 2015, pp. 277–286.
  * [43] C. Wu, Z. Yang, Z. Zhou, X. Liu, Y. Liu, and J. Cao, “Non-invasive detection of moving and stationary human with wifi,” _IEEE Journal on Selected Areas in Communications_ , vol. 33, no. 11, pp. 2329–2342, 2015.
  * [44] C. Chen, Y. Han, Y. Chen, H.-Q. Lai, F. Zhang, B. Wang, and K. R. Liu, “Tr-breath: Time-reversal breathing rate estimation and detection,” _IEEE Transactions on Biomedical Engineering_ , vol. 65, no. 3, pp. 489–501, 2017.
  * [45] X. Wang, C. Yang, and S. Mao, “Tensorbeat: Tensor decomposition for monitoring multiperson breathing beats with commodity wifi,” _ACM Transactions on Intelligent Systems and Technology (TIST)_ , vol. 9, no. 1, pp. 1–27, 2017.
  * [46] Y. Gu, X. Zhang, H. Yan, Z. Liu, and Y. Ji, “Real-time vital signs monitoring based on cots wifi devices,” in _2021 IEEE International Conference on Bioinformatics and Biomedicine (BIBM)_. IEEE, 2021, pp. 1320–1324.
  * [47] Y. Gu, H. Yan, M. Dong, M. Wang, X. Zhang, Z. Liu, and F. Ren, “Wione: One-shot learning for environment-robust device-free user authentication via commodity wi-fi in man–machine system,” _IEEE Transactions on Computational Social Systems_ , vol. 8, no. 3, pp. 630–642, 2021.
  * [48] F. Zhang, K. Niu, J. Xiong, B. Jin, T. Gu, Y. Jiang, and D. Zhang, “Towards a diffraction-based sensing approach on human activity recognition,” _Proceedings of the ACM on Interactive, Mobile, Wearable and Ubiquitous Technologies_ , vol. 3, no. 1, pp. 1–25, 2019.
  * [49] C. Tepedelenlioglu, A. Abdi, and G. B. Giannakis, “The ricean k factor: estimation and performance analysis,” _IEEE Transactions on Wireless Communications_ , vol. 2, no. 4, pp. 799–810, 2003.
  * [50] Y. Gu, X. Zhang, Z. Liu, and F. Ren, “Wifi-based real-time breathing and heart rate monitoring during sleep,” in _2019 IEEE Global Communications Conference (GLOBECOM)_. IEEE, 2019, pp. 1–6.
  * [51] D. Halperin, W. Hu, A. Sheth, and D. Wetherall, “Tool release: Gathering 802.11n traces with channel state information,” _ACM SIGCOMM CCR_ , vol. 41, no. 1, p. 53, Jan. 2011.
  * [52] J. Liu, Y. Wang, Y. Chen, J. Yang, X. Chen, and J. Cheng, “Tracking vital signs during sleep leveraging off-the-shelf wifi,” in _Proceedings of the 16th ACM international symposium on mobile ad hoc networking and computing_ , 2015, pp. 267–276.
  * [53] X. Wang, C. Yang, and S. Mao, “Phasebeat: Exploiting csi phase data for vital sign monitoring with commodity wifi devices,” in _2017 IEEE 37th International Conference on Distributed Computing Systems (ICDCS)_ , 2017, pp. 1230–1239.
  * [54] A. Hyvarinen and H. Morioka, “Nonlinear ica of temporally dependent stationary sources,” in _Artificial Intelligence and Statistics_. PMLR, 2017, pp. 460–469.
  * [55] F. Locatello, S. Bauer, M. Lucic, G. Raetsch, S. Gelly, B. Schölkopf, and O. Bachem, “Challenging common assumptions in the unsupervised learning of disentangled representations,” in _international conference on machine learning_. PMLR, 2019, pp. 4114–4124.
  * [56] G. Mita, M. Filippone, and P. Michiardi, “An identifiable double vae for disentangled representations,” in _International Conference on Machine Learning_. PMLR, 2021, pp. 7769–7779.