IEEE Circuits and Systems Magazine - Q1 2021 - 45

```using the same source in the transmission and receive,
the phase noise of the reflected signal is correlated with
the receiver local oscillator. If the time delay between
the two signals is small; which is usually the case in vital
sign detection, then the phase noise effect can be greatly reduced. This phase noise reduction is usually referred to as range correlation in coherent radar systems.
Once the received signal is down-converted by means of
multiplication with the transmitted signal and low-pass
filtered, the resulting signal can be written as [1]:
R ^ t h = 1/2 A r cos c 2r ^2d 0 + 2x ^ t hh + z c t - 2d 0 m - z ^ t hm
m
c
(11)
Since this is a coherent receiver, the phase noise difference is small and can be ignored. The output of the
baseband can be written as:
R ^ t h = 1/2 A r cos c 2r ^2d 0 + 2x ^ t hhm
m

(12)

which presents the relation between chest displacement and the phase of baseband signal [1].
To account for the Doppler effect in the phase of
the received signal, equation (9) is can be modified
as follows:
di = 4rdd
m

(13)

where di is the phase changes caused by the change
of position (motion), dd. The Doppler modulated frequency of the reflected wave can then be calculated by
integrating both sides, resulting in:
fd ^ t h =

2v ^ t h
m

(14)

where v ^ t h is the target velocity.
Typically, the received signal containing the Doppler
frequency is then channeled through a low noise amplifier (LNA). Next, this signal is down converted into baseband using a mixer and a low pass filter. The remaining
signal contains the Doppler frequency, fd, caused by the
target motion. From this, the target speed can by extracted using equation (14). Another important parameter is x, which is the total travel time taken by the signal
from the transmitter to the receiver after being reflected
by the target at a distance R from the transmitter. It can
be expressed as follow:
x=

2R
C

(15)

This parameter is usually associated with the calculation of the range profile in linear frequency modulated
continuous wave (LFMCW) radars, or commonly known
FIRST QUARTER 2021

as FMCW radars. All aforementioned principles and
equations are fundamental in the calculation and detection of respiration rate and heart rate [8].
One of the most widely used concepts in literature to
model respiration and heartbeat is the " rib cage model " .
During the respiration, the chest's anterior and lateral
diameters expand and shrinks periodically in the anterior-posterior and lateral directions. On the other hand,
the heart expands and shrinks periodically in all directions. The changes in the boundaries of the chest wall
and the heart in the " rib cage model " are described as
sinusoidal oscillations as follows [9]:
d ^ t hr = m r sin ^2rfr t h

d ^ t hh = m h sin ^2rfh t h

(16)
(17)

where d ^ t hr and d ^ t hh describes the displacement due
to respiration and heartbeat, respectively. Parameters
m r and m h represent the amplitude of the displacement
due to respiration and heartbeat, respectively, fr is the
respiratory rate, and fh is the heart rate [9], [10]. Radars
can detect these tiny displacements in the human chest
due to respiration and heartbeat, as described in by (16)
and (17). These displacements modulate the phase of
the signals transmitted by the radar, based on the Doppler principle. Thus, the target respiration and heart
rate information are embedded in the modulated phase
then be performed using a variety of algorithms.
III. Radar Types for Vital Sign Detection
Generally, vital sign detection is made more effective by
selecting the right type of radar. Besides that, practical
aspects such as technical requirements and environment in which the vital sign detection takes place determines the suitability of the radar type. These requirements may include typical detection distance, multiple
targets detection, moving targets sensing, and throughwall detection. The four potential radar types, namely
continuous wave radar (CW), linearly frequency-modulated continuous wave radar (LFMCW) or (FMCW),
ultra-wide band impulse radar (UWB-IR) and step frequency continues wave radar (SFCW) and their features,
advantages and drawbacks are summarized in Table 2.
CW radar is used in vital sign detection for its cost efficiency and design simplicity. However, CW radars do
not have range detection capability, they receive reflections from everywhere. As a result, compared to other
types of radars, they are less immune to jammers and
unwanted reflections. Consequently, their detection is
limited for used within short distances. Moreover, a CW
radar is not suitable in detecting vital signs of multiple
IEEE CIRCUITS AND SYSTEMS MAGAZINE

45

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IEEE Circuits and Systems Magazine - Q1 2021

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