APWiMob 2014, Bali 28-30 Augustus 2014

Design and Performance of a 24 GHz Band FM-CW
Radar System and Its Application
Kazuhiro Yamaguchi∗ , Mitsumasa Saito† , Kohei Miyasaka∗ and Hideaki Matsue∗∗ Tokyo University of Science, Suwa
‡ CQ-S net Inc., Japan

Email: yamaguchi@rs.tus.ac.jp, matsue@rs.suwa.tus.ac.jp, saitoh@kpe.biglobe.ne.jp

I.

I NTRODUCTION

Radar systems with 24 GHz band is based on ARIB
standard T73 [1] as sensors for detecting or measuring mobile
objects for specified low power radio station. And the 24 GHz
band radar system can be applied in various field such as
security, medical imaging and so on under indoor and outdoor
environments. There are various radar systems have been
proposed [2], [3], [4], [5]. The pulsed radar system measures
the period between the signal is transmitted and received. The
pulsed radar can detect the distance in far field, however, thetarget in near field can not be detected correctly. The Doppler
radar system measures the frequency difference between thereflected and transmitted signals. The Doppler radar can detect
the moving velocity of the target, however, the distance of thetarget can not be detected. The FM-CW (Frequency-Modulated
Continuous-Wave) radar system [6], [7] is the most widelyused for detecting the distance of the target object in nearfield and the small displacement of the target.
In this paper, we used and developed the 24 GHz FM-CW
radar system for measuring the distance and displacement ofan object when the object is static or moves very slowly. The
basic performance of the 24 GHz FM-CW radar system formeasuring a target object is analyzed by using the computer
simulation. Moreover, we proposed the differential detection
method for signal processing in the FM-CW radar system inorder to detect only the target object under the environments
which multiple objects are located. Furthermore, an example
of application with the 24 GHz FM-CW radar system is shownin experiment.

978-1-4799-3711-0/14/$31.00 ©2014 IEEE

226

݂

݂଴ ൅

݂௪
ʹ

݂଴ െ

݂௪
ʹ

Frequency

Abstract—This paper describes a design and performance of a
FM-CW (Frequency Modulated Continuous Wave) radar systemusing 24 GHz band. The principle for measuring the distanceand the small displacement of target object is described, andthe differential detection method for detecting the only target
is proposed under the environments which multiple objects arelocated. In computer simulation, the basic performance of FMCW radar system is analyzed about the distance resolution anderror value according to the various sampling time and sweep
bandwidth. Furthermore, the FM-CW radar system with theproposed differential detection method can clearly detect only
the target object under the multiple object environment, andthe small displacement within 3.11 mm can be measured. In
experiment, the performance about measuring the distance anddisplacement is described by using the designed 24 GHz FMCW radar system. As the results, it is confirmed that 24 GHz
FM-CW radar system with the proposed differential detection
method is effective for measuring target under the environments
which multiple objects are located.

Transmitted signal

Received signal

݂଴ ݂௪
‫ݐ‬௪

‫ݐ‬

Time

Fig. 1.

Sawtooth frequency modulation.

This paper consists of the following sections. Section II
describes the principle of a FM-CW radar system. Section III
describes and analyses the basic performance and the proposed
differential detection method in computer simulation. Section
IV shows the experimental results with 24 GHz FM-CW radarsystem. Finally, Section V concludes this paper.
II.

P RINCIPLE FOR FMCW RADAR

FM-CW (Frequency-Modulated Continuous-Wave) radaris a radar transmitting a continuous carrier modulated by aperiodic function such as a sawtooth wave to provide range
data shown in Fig. 1. Fig. 2 shows the block diagram of a
FM-CW radar system [8].
In the FM-CW radar system, frequency modulated signal
at the VCO is transmitted from the transmitter Tx, then signals
reflected from the targets are received at the receiver Rx.
Transmitted and received signals are multiplied by a mixer, andbeat signals are generated as multiplying the two signals. Thebeat signal pass through a low pass filter, then an output signal
is obtained. In this process, the frequency of the input signal
is varied with time at the VCO. The modulation waveformwith a linear sawtooth pattern [9] as shown in Fig. 1. This
figure illustrates frequency-time relation in the FM-CW radar,and the red line denotes the transmitted signal and the blueline denotes the received signal. Here, f0 denotes the center
frequency, fw denotes the frequency bandwidth for sweep, andtw denotes the period for sweep.
We define that the transmitting signal VT (f, x) at thetransmitter Tx in Fig. 2 is represented as
2πf

VT (f, x) = Aej c x ,(1)

APWiMob 2014, Bali 28-30 Augustus 2014

Signal

D/A

VCO

A/D

FFT

BPF

ܸ୭୳୲

Signal processing

Fig. 2.

Target 1

ܸ୘

BPF

Tx

‫ݔ‬ଵ

‫ݔ‬௞

Rx

ܸୖ

Target ݇

Target ‫ܭ‬

‫ݔ‬௄

‫ݔ‬

Block diagram of a FM-CW radar system.

where f denotes a frequency at a time, x denotes a distance
between a target and the transmitter, A denotes an amplitude
value and c denotes the speed of light.
The reflected signal VR (f, x) at the receiver Rx in Fig. 2
is represented as
VR (f, x) =K∑

The amplitude value of the distance spectrum |P (x)| in Eq. (5)is given as
{
}
k −x)
K
sin 2πfw (d∑4πf0 (dk −x)ccαk γk ejφk ej|P (x)| = A2fw
2πf (d −x)
w

k=1
2πf

Aαk γk ejφk ej c (2dk −x) ,(2)≤ A fw2

k=1

where γk and φk are the reflectivity coefficients for amplitude
and phase on kth target, respectively. αk , denotes amplitude
coefficient for transmission loss from kth target, and dk is the
distance between the transmitter and the kth target.
Here, at the receiver whose position is x = 0, Eq. (2) isrewritten as
VR (f, 0) =

K
∑

2πf

Aαk γk ejφk ej c (2dk ) .

(3)

k=1

sin
αk γk

k=1

K
∑

A2 αk γk ejφk ej

4πf dkc.

(4)

f0 − f2w∫

f0 − f2w

= A2

K
∑

K
∑

A2 αk γk ejφk ej

k=1

αk γk ejφk

∫ f0 + f2w

= A2

K
∑
k=1

4πf dkcej

e−j

4πf0 (dk −x)jcαk γk ejφk e

4πf x
c

4πf (dk −x)cf0 − f2w

k=1(6)Here, we assumed that the number of target is 1. The
distance spectrum in Eq. (5) is rewritten as
{
}
1 −x)
sin 2πfw (d4πf0 (d1 −x)cc
P (x) = A2 α1 γ1 ejφ1 ejfw,
2πf (d −x)
1

c

(7)

and the amplitude value of distance spectrum is given as
}
{
1 −x)
sin 2πfw (dc|P (x)| = A2 α1 γ1 fw.
(8)
2πf (d −x)w

1c

By using signal processing, a distance and a displacement
for the target are given from the generated output signal in
Eq. (4). By using the Fourier transform, the distance spectrumof the output signal P (x) is calculated as follow.
∫ f0 + f2w
4πf
P (x) =
Vout e−j c df=,

2πfw (dk −x)cand we have equality if and only if the phase components
ϕk + 4πf0 (dc k −x) about all of k are equal.

k=1

f0 + f2w

2πfw (dk −x)
c

k

c

}

w

The beat signal are generated as multiplying the transmitted
signal in Eq. (1) and the received signal in Eq. (3) at theposition x = 0. After LPF, the output signal Vout (f, 0) is
generated by
Vout (f, 0) =

K
∑

{

{
sin
fw

̸

P (x) = φ1 +−df

2πfw (dk −x)c

The phase value of distance spectrum ̸ P (x) is represented
as
4πf0 (d1 − x)
= θ1 (x) .
c(9)Here, θ1 (x) satisfy −π ≤ θ1 (x) ≤ π, then the displacement
for the target isdf

2πfw (dk −x)cThis equation indicates that the distance for the target isgenerated by the amplitude value of distance spectrum.

}
.
(5)

227

c (π − φ1 )c (−π − φ1 )≤ d1 ≤
.
4πf0
4πf0

(10)

If the phase value satisfies ϕ1 = 0, Eq. (10) is rewritten as−3.11 [mm] ≤ d1 ≤ +3.11 [mm] with f0 = 24.15 [GHz].
That is, the small displacement of the target within ±3.11[mm] is generated by the phase value of distance spectrum.

APWiMob 2014, Bali 28-30 Augustus 2014
PARAMETERS IN COMPUTER SIMULATIONSParameters

Value

Center frequency
Bandwidth
Sweep time
Sampling time of sweep
Number of FFT points
Window function

24.15 GHz50, 100, 200, 400 MHz
1024 µs
0.1, 1, 10 µs
4096
hamming݂௪ ൌ ʹͲͲ MHzͲǤͳ ߤ‫ݏ‬ǡ ͳ ߤ‫ݏ‬ͳͲ ߤ‫ݏ‬ܲ ‫ݔ‬TABLE I.

‫ݐ‬௦ ൌ ͳ ߤ‫ݏ‬ܲ ‫ݔ‬50 MHz
100 MHz

Measured distance [m]Fig. 4.

200 MHz

Error value for distance spectrum according to sampling interval.

400 MHz

Measured distance [m]Fig. 3.

Resolution for distance spectrum according to sweep bandwidth.

On the other hands, the maximum distance for measuringdmax isfw[Hz] ,
tw /tsc
dmax =
[m] ,
4∆f
∆f =

Measured distance [m](11)(a): 3D view.

where tw denotes the sweep time, ts denotes the interval time
for sampling. For example, in the case with tw = 1024 [µs]and ts = 1 [µs], the maximum distance is dmax = 384 [m].
C OMPUTER S IMULATION

A. Basic Performance
At first, we describes the basic performance about the
FM-CW radar with 24 GHz band. Parameters for computer
simulation are listed in Table I. Center frequency is 24.15
GHz, bandwidth are 50, 100, 200, and 400 MHz. Note that the
400 MHz bandwidth is only used for the computer simulation
because of standards in the Radio Law in Japan. Sweep timeis 1024 µs, sampling times of sweep are 0.1, 1, 10 µs, numberof FFT points is 4096, and the hamming windows is adapted
as the window function in signal processing.
We assumed that a static target is located at 10 m fromthe transmitter and receiver, and the distance spectrums are
outputted with various parameters. Fig. 3 shows the amplitude
value for distance spectrum versus measured distance withvarious sweep bandwidth. The result shows that the sweep
bandwidth influences the distance resolutions and widely bandwidth can improve the resolution. In the case with ts = 1µs, the distance resolutions with fw = 50, 100, 200, 400
MHz are ±5, ±1.5, ±1, ±0.5 m, respectively. Fig. 4 shows
the amplitude value for distance spectrum versus measured
distance with various sampling time. The result shows that228

݂௪ ൌ ʹͲͲ MHz, ‫ݐ‬௦ ൌ ͳ ߤ‫ݏ‬

Measured distance [m]III.

Target distance [m]Target distance [m](b): 2D view.
Fig. 5.

Distance spectrum for measuring moving target.

the sampling interval influences the error about the measured
distance and shortly sampling interval can reduce the error
value for distance. In the case with fw = 200 MHz, the error
values about the measured distance with ts = 10 µs is about
0.5 m.
Fig. 5 shows the result for measuring a slowly moving
target with fw = 200 MHz and ts = 1 µs. The target moved
from 10 m to 20 m at intervals of 0.5 m. Fig. 5(a) shows

APWiMob 2014, Bali 28-30 Augustus 2014݂௪ ൌ ʹͲͲ MHz, ‫ݐ‬௦ ൌ ͳ ߤ‫ݏ‬

Measured distance [m]Measured displacement [mm]݂௪ ൌ ʹͲͲ MHz, ‫ݐ‬௦ ൌ ͳ ߤ‫ݏ‬Spectrums of the other objects: ܲ଴Spectrum of the target object
Target displacement [mm]Fig. 6.

All of spectrums: ܲ

Measured displacement.

Target distance [m](a): without differential detection.

Fig. 6 shows the result for measuring a target with small
displacement, and the measured displacement versus target
displacement is outputted. The object is located at 10 mfrom the receiver, and the object moved from -5 mm to
5 mm at intervals of 0.1 mm. The small displacement canbe measured by the phase value of distance spectrum, andthe measured displacement is corresponding to the target
displacement. Note that the measured displacement denotes therelative displacement and it is not corresponding to the absolute
distance between the receiver and the target object. The small
displacement within ± 3.11 mm is correctly measured with theparameters of the FM-CW radar system in this paper, however,the displacement more than ±3.11 mm has uncertainty.
B. Proposed target detection
As mentioned in the above section, the FM-CW radarsystem can measure the distance and the small displacementfor 1 target object. However, it is a special case that only thereflected signal on a target can be received at the receiver.
In general, the receiver may receive the reflected signals
from many objects. Therefore, when there is some objects formeasuring the target distance, signal processing for detecting
the distance spectrum from the only target is required.
The proposed method removes the signals from the otherobjects by using the differential detection of distance spectrum.
Fig. 7 shows the distance spectrum when the target object
moves from 10 m to 20 m and the other objects are located at
15 m and 20 m. The transmitted signal is reflected on the target
and the other objects, the receiver receives several reflectedsignals. Therefore, the distance spectrum of the other objects
are also generated by the FM-CW radar system in Fig. 7(a),and the distance spectrum of the target can not be detected
clearly. In particular, when the reflection coefficient of thetarget is lower than that of the other objects, the distancespectrum of the other object has higher amplitude value thanthat of the target.

229

݂௪ ൌ ʹͲͲ MHz, ‫ݐ‬௦ ൌ ͳ ߤ‫ݏ‬

Measured distance [m]the amplitude value versus measured distance versus target
distance with 3-dimensional viewing, and Fig. 5(b) shows
measured distance versus target distance with 2-dimensionalviewing. The color in (b) is corresponding to the strength of
the amplitude value in (a). From these figures, it is confirmedthat the distance can be measured correctly according to thepositions of the moving target.

Spectrum of the target object

Target distance [m](b): with differential detection (Proposed).
Fig. 7. Distance spectrum for measuring moving target distance with / without
the differential detection under the environments which multiple objects arelocated.

In the proposed differential detection, at first, the distancespectrum of the other objects P0 is generated beforehand in
Fig. 7(a). Then, the distance spectrum of the target and theother object P is subtracted by P0 . By using the differential
detection, distance spectrum removed the distance spectrum of
the other targets is generated as P −P0 . Therefore, the distancespectrum of the desired target is only detected. Fig. 7(b)shows the distance spectrum by using the proposed differential
detection method, and the distance spectrum of the target iscorrectly measured. As compared with the measured distancespectrums in Fig. 7(a) and (b), it is clearly confirmed thatthe proposed method can detect target distance by using thedifference detection. The proposed differential detection caneffectively detect the moving or static target distance frommultiple reflections of the background static objects.
IV.

E XPERIMENTS

In order to evaluate the effectiveness of the proposed
method for detecting the target distance and displacement, wedevelop a FM-CW radar system and carried out the experiments with the radar system in actual environment. Table IIlists the parameters, and the developed FM-CW radar system
get a certificate of conformity with technical regulations inAPWiMob 2014, Bali 28-30 Augustus 2014
PARAMETERS IN EXPERIMENTS
Value

Center frequency f0
Sweep bandwidth fw
Sweep time tw
Sampling time of sweep ts
Transmitter power output
Antenna gain
Range of distanceRange of relative displacement

24.15 GHz
200 MHz1024 µs
1 µs0.007 W
11 dBi0 – 100 m±3.11 mm

5 sec.
Time [s]Measured distance [m]Parameters

Measured small
displacement [mm]TABLE II.

Fig. 9.

Displacement for measuring the movement of human breathing.

Fig. 10.

Setup of FM-CW Radar for detecting human breathing.

1. Without any person

2. Reflection on the human bodyTime [s](a): without differential detection.

Measured small
displacement [mm]Measured distance [m]Measured distance [m]3. Breathing detection

Time

Time

Fig. 11.

Time [s](b): with differential detection (Proposed).
Fig. 8. Distance spectrum for measuring moving target distance with / without
the differential detection.

Example of application.

detection method, the distance spectrum without the person ismeasured beforehand. By generating the distance spectrum of
the background objects beforehand, the distance spectrum of
the moving person is correctly detected in Fig. 8(b) with theproposed differential detection. Therefore, the FM-CW radarsystem can measure movement of the target person effectively.

Article 38-6 Paragraph 1 of the Radio Law in Japan, anddeveloped FM-CW radar system is accommodate to ARIB
standard T73 in Japan [1].

Fig. 9 shows the result of measuring the small displacement for human breathing. The human’s chest movement ismeasured within the range of relative small displacement. In
Fig. 9, it is detected that the period of breathing is about 4 [s]and the breathing movement is about within ±2 [mm].

A. Distance Spectrum

B. Example for application

Fig. 8 shows the distance spectrum of a moving target.
A person walked away from the FM-CW radar and thencame close between 2 [m] to 10 [m]. In Fig. 8(a), several
distance spectrums of the person and the background objects
are outputted. The distance spectrum of the moving person
is not clearly detected in Fig. 8(a). In order to detect the
distance spectrum of the moving person with the differential

Finally, we show an example of application with 24 GHz
FM-CW radar system. Fig. 10 shows a setup of the FMCW radar system for detecting human breathing in actual
environments. The FM-CW radar satisfies the safety guideline,
and the details of the safety guideline is described in Appendix.

230

Fig. 11 shows the example for detecting human breathing.

APWiMob 2014, Bali 28-30 Augustus 2014

The distance spectrum in this example is measured as following flow.
1)
2)
3)

Measuring distance spectrum without any person.
A person comes to the bed. The radar received signals
from human’s body.
The person lies asleep on the bed. The radar detects
the person’s breathing movement.

By generating the distance spectrum of the background objects
without the person, the distance spectrum of the person is only
detected. When the person comes within the range of radar,the radar system can detect reflected signals from the person,
and the distance spectrums of the human’s body are detected.
After the person lies on the bed, the radar system can detect
the small displacement for the person’s breathing movement.
By using the differential detection method, the distance andsmall displacement of the moving object is clearly detected.
V.

C ONCLUSION

In this paper, design and performance of a FM-CW radarsystem with 24 GHz band is described. In computer simulations, basic performances of FM-CW radar system is analyzed
about the distance resolution and error value according to thesweep time and the sampling interval, respectively. Moreover,the differential detection method for detecting only the target
object is proposed for measuring the distance and the displacement of the target under the environments which multiple
objects are located. In experiments, the distance spectrum of
the target object is clearly detected by using the differential detection method under the environments which multiple
objects are located. Furthermore, an example of application
for detecting human’s breathing movement is shown. As theresult, the 24 GHz FM-CW radar with the proposed differential
detection method effectively detect the distance and the small
displacement under the environments which multiple objects
are located.
ACKNOWLEDGMENT

A part of this work was supported by “Ashita wo Ninau
Kanagawa Venture Project” of Kanagawa in Japan.
The authors appreciate Prof. Toshio Nojima at Hokkaido
University in Japan getting the valuable advices for analyzing
the safety properties of the developed FM-CW radar system
according to the safety guideline.
R EFERENCES[1] ARIB STD-T73 Rev. 1.1, Sensors for Detecting or Measureing Mobile
Objects for Specified Low Power Radio Station, Association of Radio
Industries and Businesses Std.
[2] S. MIYAKE and Y. MAKINO, “Application of millimeter-wave heating to materials processing(¡special issue¿recent trends on microwave
and millimeter wave application technology),” IEICE transactions onelectronics, vol. 86, no. 12, pp. 2365–2370, dec 2003.
[3] M. Skolnik, Introduction to Radar Systems. McGraw Hill, 2003.
[4] S. Fujimori, T. Uebo, and T. Iritani, “Short-range high-resolution radar
utilizing standing wave for measuring of distance and velocity of amoving target,” ELECTRONICS AND COMMUNICATIONS IN JAPANPART I-COMMUNICATIONS, vol. 89, no. 5, pp. 52–60, 2006.
[5] T. Uebo, Y. Okubo, and T. Iritani, “Standing wave radar capable ofmeasuring distances down to zero meters,” IEICE TRANSACTIONS ON
COMMUNICATIONS, vol. 88, no. 6, pp. 2609–2615, jun 2005.

231

[6]

[7]

[8]
[9]

[10]

[11]

T. SAITO, T. NINOMIYA, O. ISAJI, T. WATANABE, H. SUZUKI,
and N. OKUBO, “Automotive fm-cw radar with heterodyne receiver,”
IEICE transactions on communications, vol. 79, no. 12, pp. 1806–1812,dec 1996.
W. Butler, P. Poitevin, and J. Bjomholt, “Benefits of wide area intrusion
detection systems using fmcw radar,” in Security Technology, 2007 41st
Annual IEEE International Carnahan Conference on, Oct 2007, pp.
176–182.
M. Skolnik, Radar Handbook, Third Edition. McGraw-Hill Education,
2008.
W. Sediono and A. Lestari, “2d image reconstruction of radar indera,”in Mechatronics (ICOM), 2011 4th International Conference On, May
2011, pp. 1–4.
C95.1-2005, IEEE Standard for Safety Levels with Respect to Human
Exposure to Radio Frequency Electromagnetic Fields, 3 kHz to 300
GHz, IEEE Std.
Ministry of Internal Affairs and Communications. [Online]. Available:
http://www.tele.soumu.go.jp/resource/j/material/dwn/guide38.pdf

A PPENDIX
In general, electromagnetic wave must be satisfied theguidelines on human exposure to electromagnetic fields, where
it have been instituted in various organizations. IEEE C95.1 in
USA [10] and ICNIRP in Europe are the guidelines, and MIC
also have instituted the guideline in Japan [11].
Developed 24 GHz FM-CW radar in this paper have theproperties as follow. The power of the transmitter is 7 [mW],
the transmitting antenna gain is 11 [dBi], the effective radiatedpower is 88 [mW], the radiation angle of the transmitting wave
is about 50 [degree], and the distance between the transmitterand the human is 2.5 [m]. According to the radar equation,
the electric field strength E and the power density P on thehuman body is calculated as√
30 × 0.088
E== 0.65 [V/m] ,
2.5
E2
0.652
P =
=
= 1.12 × 10−4 [mW/cm2 ] .
z0120π
According to the guideline [11], these parameters must be
satisfied asE ≤ 61.4 [V/m] ,P ≤ 1 [mW/cm2 ] .
Therefore, the developed 24 GHz FM-CW radar system in thispaper sufficiently satisfies the conditions in the guideline.