Abstract-In this paper, 60 GHz millimeter-wave indoor propagation characteristics are simulated and analyzed using the method of SBR/IM (shooting and bounding ray tracing/image). And the simulated and measured results agree well, so the correctness of the method has been validated. Some propagation parameters are obtained in the simulation, such as the indoor reception power distribution, distribution of phase angle of received power, root mean square (RMS) delay spread, direction of arrival, RMS angular spread, Doppler shift, etc. The analysis of the above results provides the foundation for the indoor coverage of millimeter-wave communication system

Qin-Jian Shi

Ye-Rong Zhang

Yuan-Jian Liu

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Progress In Electromagnetics Research C, Vol. 43, 15–28, 2013
SIMULATION AND ANALYSIS OF 60 GHz MILLIMETER-
WAVE INDOOR PROPAGATION CHARACTERISTICS
BASE ON THE METHOD OF SBR/IMAGE
Yuan-Jian Liu, Qin-Jian Shi*, and Ye-Rong Zhang
College of Electronic Science and Engineering, Nanjing University of
Posts & Telecommunications, Nanjing, Jiangsu 210003, China
Abstract—In this paper, 60 GHz millimeter-wave indoor propagation
characteristics are simulated and analyzed using the method of
SBR/IM (shooting and bounding ray tracing/image). And the
simulated and measured results agree well, so the correctness of the
method has been validated. Some propagation parameters are obtained
in the simulation, such as the indoor reception power distribution,
distribution of phase angle of received power, root mean square (RMS)
delay spread, direction of arrival, RMS angular spread, Doppler shift,
etc. The analysis of the above results provides the foundation for the
indoor coverage of millimeter-wave communication system.
1. INTRODUCTION
With the continuous development of wireless communications
technology, spectrum occupancy is increasing. So it is necessary to
develop microwave high-end spectrum resources to achieve high-speed
broadband wireless communications. The most prominent advantage
of millimeter wave is frequency bandwidth, and one percent of relative
bandwidth of millimeter wave can provide available bandwidth to
hundreds of megabytes or even gigabytes. It is particularly important
to study the millimeter-wave propagation characteristics in the indoor
environment, because millimeter-wave band communication is mainly
used in office, laboratory, etc [1–3]. The models of study on the
indoor propagation characteristics can be divided into two categories:
empirical and deterministic models [4]. The empirical model is based
on simple formulas, so it only requires simple inputs, and its operation
is very fast. However, the model requires precise equipment, and some
Received 1 June 2013, Accepted 31 July 2013, Scheduled 23 August 2013
* Corresponding author: Qin-Jian Shi (ud3776034@126.com).
16 Liu, Shi, and Zhang
useful propagation parameters cannot be obtained in the measure, such
as direction of arrival, distribution of the direction angle of arrival
and angular spread. Thus this model has significant limitation on
the study of radio channel [5]. The deterministic model is based on
the theory of electromagnetic wave propagation, and two methods are
generally used: ray tracing method and finite difference time domain
method. In recent years, ray tracing method has been used to predict
the indoor propagation characteristics because of the improvement of
the calculation ability of computer.
Ray tracing method includes image method, minimum optical
path method, test-ray method, shooting and bounding ray tracing
method, deterministic ray tube method and shooting and bounding ray
tracing/image method (SBR/IM). The image method [6, 7] is a simple
ray tracing method because it does not need to do the intersection test.
But it can only be applied to a simple structure of the environment.
The minimum optical path method [8] is essentially the same as the
traditional image method. This method does not use reflection law but
the minimum optical path to determine the location of the reflection
point of wall. It cannot be applied to complex environment either.
The test ray method [9] does not need to determine the location of
the point of the receiver in advance, but it needs receiving ball. It can
be applied to the complex environment, but the prediction accuracy of
this method is affected by the radius of receiving ball. So the calculated
efficiency is not high. The shooting and bounding ray tracing method
[10] does not need receiving ball, but this method takes up a lot of
computer resources. The deterministic ray tube method [11] saves
computer resources, but it needs to create a ray tree based on the
actual environment, and it is complex. The shooting and bounding ray
tracing/image method [12, 13] can be used for any complex propagation
environment, and it can find all the radio wave propagation paths from
the transmitter to the receiver with high accuracy and computational
efficiency. So this method is a valuable method which can be used to
predict the radio wave propagation. In this paper, 60 GHz millimeter-
wave indoor propagation characteristics are simulated based on the
shooting and bounding ray tracing/image method.
2. THE REALIZATION OF SBR/IM
2.1. Indoor Structure Representation
Indoor building structure will be simplified, and the geometry data
and form data of each plane will be recorded while every face is given
a unique identifier to represent the plane. Then data are entered
Progress In Electromagnetics Research C, Vol. 43, 2013 17
into the database in accordance with the prescribed format, and the
appropriate priority list will be established.
2.2. Wavefront Generation
The radio beams radiated by the transmit antenna can be deemed
many ray tubes. The wavefront ball should be divided to generate
the ray tubes, and the shape and size of each wavefront are the same.
The shape of wavefront can be an equilateral triangle, quadrilateral
or hexagonal. In this paper, a common method is used to divide
the wavefront ball. A regular icosahedron in the interior of wavefront
ball is shown in Fig. 1, and twelve vertex coordinates of the regular
icosahedron can be calculated [14].
Figure 1. Regular icosahedron in the interior of wavefront ball.
2.3. The Establishment of the Emitted Ray Tubes
The tetrahedral ray tube with sections of equilateral triangles is shown
in Fig. 2 [14, 15].
2.4. Intersection Test
The model of intersection test is shown in Fig. 3 [14, 15].
2.5. The Determination of Reflected Ray Tubes
The image source point can be located using the image method, and
three intersection points of three rays of the emitted ray tube and plane
18 Liu, Shi, and Zhang
 
Pi
Pj Pk
T
Figure 2. Establishment of the emitted ray tube.
x
y
z
d
r1
r2
r i
n
Figure 3. The model of intersection test.
can be determined. So the reflected ray tubes will be obtained by the
four points.
2.6. The Determination of Ray Tubes Which Reach the
Received Point
Figures 4 and 5 are the schematic diagrams of the determination of
ray tubes which reach the received point [14, 15].
2.7. Calculation of Received Field
The received field is the vector sum of the ray tubes filed which can
reach the receiving point [14, 15].
Progress In Electromagnetics Research C, Vol. 43, 2013 19
T
Li
Lj
R
1
2
3
  Pi
  Pj Pk
 
    Lk 
θ
θ
θ
Figure 4. Schematic diagram of
receiving point.
1
2
3
1Γ
2
Γ
Lk
R
jL
T
Pk P
Pi
j
Li
θ
θ
θ
Figure 5. Schematic diagram of
judgment method.
(1) The calculation formula of the direct field is
−→
E =
−→
E 0 ·
e−jk|TR|
|TR| .
−→
E 0 is the electric filed value of ray tube T − PiPjPk in the
reference position ∆PiPjPk, and k is wave number. |TR| is the actual
propagation distance when the ray tube T − PiPjPk reaches received
point R.
(2) The calculation formula of the reflected field is
−→
E =
−→
E 0 ·
{ΠRi} · {ΠTi} · {Πe−γili} · SF . {ΠRi} is the dyad of the reflection
coefficient, R̄i = Ri⊥ē⊥ē⊥ + Ri‖ē‖ē‖, Ri⊥ =
cos θi−
√
ε2/ε1−sin2 θi
cos θi+
√
ε2/ε1−sin2 θi
,
Ri‖ =
(ε2/ε1) cos θi−
√
ε2/ε1−sin2 θi
(ε2/ε1) cos θi+
√
ε2/ε1−sin2 θi
.
{
ΠTi
}
is the dyad of the transmission
coefficient, Ti = Ti⊥ē⊥ē⊥ + Ti‖ē‖ē‖, Ti⊥ = Ri⊥ + 1, Ti‖ = (Ri‖ +
1) ·
√
ε1/ε2. γi is the phase change relative to the reference position
∆PiPjPk and the li is the attenuation change relative to the reference
position. SF is the diffusion factor, and the calculation formula is
SF =
√
S∆LiLjLk√
S∆PiPjPk
, S∆LiLjLk is area of triangle ∆LiLjLk, S∆pipjpk is
area of triangle ∆PiPjPk.
3. NUMERICAL RESULTS
The simulation environment in [16] is a room with dimensions 14.5 ×
9.9 × 2.6, as shown in Fig. 6. The ceiling is made of gypsum board,
and the floor is made of resin. In the simulation, vertically polarized
omnidirectional antennas with 5 dBi of gain are used, and the heights
20 Liu, Shi, and Zhang
of transmitter antenna and receiver antenna are 2.2m and 1.2 m,
respectively. The frequency of transmitted signal is 59.5 GHz, and the
transmission power is 10 dBm. The transmitter antenna is in the center
of the room, and the receiver antenna moves along a straight line. The
electromagnetic properties of all materials are given in Table 1.
14.5m(wood)
9.9m
(wood)
window(glass)
14.5m(gypsum board)
9.9m
(gypsum board)
Metal 
door
12m
window(glass)window(glass)
Figure 6. Simulation environment.
Table 1. Electromagnetic properties of different materials.
Material
Electromagnetic property
εr σ
Wood 5.0 0.001
Glass 2.4 0.001
Gypsum board 2.8 0.150
Resin 4.0 0.001
3.1. Correctness Verification
Simulated and measured results in [16] agree well as shown in Fig. 7,
so the correctness of the method has been validated. And Fig. 9 shows
the difference between the simulated and measured results at both
ends. The following is the reason for the difference. (1) There is
a difference of electromagnetic property between the simulation and
actual material. (2) It cannot be assured that the movement of receiver
Progress In Electromagnetics Research C, Vol. 43, 2013 21
is completely a straight line in the measure. (3) There is a difference in
the size of simulation room between the simulation and actual room.
(4) The number of received points in the measure is smaller than in
the simulation.
(a)
(b)
-40
-60
-80
Rx. Power
Figure 7. Received power: (a) Measured result in literature [16],
(b) simulated result.
Figure 8. The distribution of received power.
22 Liu, Shi, and Zhang
3.2. The Distribution of Received Power
As shown in Fig. 8, the received power in the intermediate position is
significantly higher than the other position, and the received power on
the edge of the room is low because the transmitter antenna is in the
center of the room. The received power of the direct path accounts
for a large part of the total received power. But the distribution of
received power is not completely inversely proportional to the distance
from the transmitter antenna. It is shown that there are reflected
paths and diffraction paths besides the direct path in the process of
propagation. Fig. 9 shows the statistical distribution of phase angle of
received power which is in uniform distribution.
Figure 9. The phase angle of received power.
Figure 10. The RMS delay spread (The solid line is the result
using omnidirectional antenna, and the dotted line is the result using
directive antenna).
Progress In Electromagnetics Research C, Vol. 43, 2013 23
3.3. The Root Mean Square (RMS) Delay Spread
Figure 10 shows the RMS delay spread of millimeter-wave in an
indoor environment. The solid line is the RMS delay spread using
omnidirectional antenna, and the dotted line is the result using
directive antenna. The RMS delay spread is the second moment of
power delay profile, and it is defined as:
σ =
√√√√√
Np∑
i=1
Pit2i
PR
− t̄ 2
t̄ is the average time of arrival and defined as t̄ =
Np∑
i=1
Piti
PR
. Pi is the
received power of the ith path and PR the total of received power. The
RMS delay spread is a better measure of the spread of multipath, and
it varies in the level of ns [14].
In this paper, the RMS delay spread of millimeter-wave varies
between 4.8 ns and 16.6 ns as shown in Fig. 10. The worst RMS delay
spread occurs at the distance of −5m and 5 m, which is close to the
(a)
24 Liu, Shi, and Zhang
(b)
Figure 11. Mean angle of arrival: (a) Mean angle of arrival θ̄,
(b) mean angle of arrival φ̄.
edge of the room, and the least RMS delay spread occurs at the distance
of 0 m which is just below the transmitter antenna. This is because
when the receiver antenna is just below the transmitter antenna, there
are almost only reflected paths from surface of the floor and ceiling
besides the direct path. And the RMS delay spread can be reduced
about 2 ns–4 ns by using a directive antenna to suppress reflections
from surface of floor and ceiling.
3.4. The Direction of Arrival and RMS Angular Spread
The direction of arrival which is defined as ā = sin(θA) cos(φA)x̄ +
sin(θA) sin(φA)ȳ + cos(φA)z̄ can be obtained.
Figure 11 shows the mean angle of arrival of all the received point.
The θ̄ is defined as θ̄ = tan−1(
√
A2x+A
2
y
Az
), and the φ̄ is defined as
φ̄ = cos−1(AyAx )(A =
N∑
i=1
Piā).
Progress In Electromagnetics Research C, Vol. 43, 2013 25
(a)
(b)
Figure 12. RMS angular spread: (a) RMS angular spread (θ̄),
(b) RMS angular spread (φ̄).
Figure 12 shows the RMS angular spread. The RMS angular
spread (θ̄) varies between 0◦–80◦. The RMS angular spread (φ̄) varies
between 10◦–90◦.
3.5. Doppler Shift
The formula of Doppler shift is ∆f = f0[ d̄·VT +ā·VRc ]. So each path
will cause the Doppler shift when the transmitter or the receiver is
moving. So the Doppler shift can be determined (Assuming that
the transmitter is fixed and that the speed of receiver is 1m/s).
The Doppler shift varies between −800Hz and 800 Hz as shown in
Fig. 13. This simulation environment is similar to indoor mobile
communication environment, so the range of Doppler shift in this
simulation provides the theoretical foundation for the indoor coverage
of millimeter-wave communication system.
26 Liu, Shi, and Zhang
Figure 13. Doppler shift.
4. CONCLUSIONS
In this paper, the 60 GHz millimeter-wave indoor propagation
characteristics are simulated and analyzed using the method of
SBR/IM. And the simulated and measured results are in good
agreement, so the correctness of the method has been validated. The
received power of the direct path accounts for a large part of the
total received power. The RMS delay spread of millimeter-wave varies
between 4.8 ns and 16.6 ns in this simulation, and the RMS delay spread
can be reduced about 2 ns–4 ns by using a directive antenna. Assuming
that the transmitter is fixed and the speed of receiver is 1m/s, the
Doppler shift will vary between −800Hz and 800 Hz. The analysis
of the above results provides a foundation for the indoor coverage of
millimeter-wave communication system. This simulation environment
is almost an empty room. However, the actual indoor environment
Progress In Electromagnetics Research C, Vol. 43, 2013 27
is not as simple as the simulation environment. Millimeter wave
propagation characteristics in complex indoor environments require
further analysis, which is our next research direction.
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SIMULATION AND ANALYSIS OF 60 GHz MILLIMETER- WAVE INDOOR PROPAGATION CHARACTERISTICS BASE ON THE METHOD OF SBR/IMAGE

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SIMULATION AND ANALYSIS OF 60 GHz MILLIMETER- WAVE INDOOR PROPAGATION CHARACTERISTICS BASE ON THE METHOD OF SBR/IMAGE

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