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Millimeter-Wave Channel Modeling and Coverage
Analysis for Indoor Dense Spaces
Ozan Alp Topal, Zhenyu Li, Mustafa Ozger, Dominic Schupke, Emil Bj¨
ornson, and Cicek Cavdar
Abstract—Millimeter-wave channel modeling for airplanes,
trains, and other in-vehicle environments can be considered
jointly as different variations of a general site, namely an indoor
dense space (IDS). In this work, by using ray-tracing simulations,
we compare the effect of frame material, user density, and
geometry on the channel characteristics at 28,39, and 60 GHz
bands. We observe that temporal and spatial parameters in IDS
have unique distributions some depending on the transmitter
(TX)-receiver (RX) separation in comparison to the indoor office
(IO) channel model. The frame material is the main determining
factor of the channel characteristics, with different bands and
geometries show minor effects. We extend our channel modeling
effort to MIMO deployment analysis to compare the validity of
the proposed model in terms of coverage and spectral efficiency
with the IO model. Several dominant angular intervals in the
channel cause five times higher spectral efficiency gained by
digital beamforming in comparison to analog beamforming. We
observe that the path loss in IDS is more severe compared with
IO, resulting in at least a 50% reduction in the coverage area.
Index Terms—5G, 6G, in-cabin, intra-wagon, millimeter-wave,
channel modeling, ray-tracing
I. INTRODUCTION
FIFTH generation (5G) subscriptions surpassed 1 billion
by now and are expected to surpass 5 billion by the
end of 2028 [1]. Operators can deploy 5G networks in three
different frequency bands: low, mid, and the high band. High-
band spans from 24 GHz to 100 GHz for the 5G networks,
where mainly the carrier is millimeter-wave (mmWave). As
of 2022, high-band 5G deployments are already available in
over 90 cities in the United States, and they are expected to
be widely deployed starting in 2023. The main benefit of the
mmWave bands is a large accumulated frequency spectrum,
allowing for high data rates (over 3Gbps) and low latency.
One of the limiting factors for mmWave bands is the scaled-
down coverage area compared to the low and mid bands.
These features make mmWave bands an ideal match for indoor
usage, where the data rate expectation is much higher due
to emerging indoor applications such as ultra-high definition
video streaming, wireless cognition, and augmented reality
(AR).
O. A. Topal, Z. Li, M. Ozger, E. Bj¨
ornson and C. Cavdar are with
the School of Electrical Engineering and Computer Science, KTH Royal
Institute of Technology, Stockholm, Sweden (e-mail: {oatopal, zhenyuli,
ozger, emilbjo, cavdar}@kth.se).
D. Schupke is with Airbus, Central Research and Technology, Munich,
Germany (e-mail:dominic.schupke@airbus.com).
Results incorporated in this paper received funding from the ECSEL Joint
Undertaking (JU) under grant agreement No 876124. The JU receives support
from the EU Horizon 2020 research and innovation programme and Vinnova
in Sweden.
One evident limiting factor of mmWave coverage is higher
free-space path loss, which results in approximately 10 dB
power loss at the receiver comparing 28 GHz to 2.4GHz. Fur-
thermore, mmWave signals are shown to be going under sparse
reflections and diffuse scattering with negligible diffractions.
This results in sensitivity to the blockage, where a human body
creates approximately 15 dB loss at the received signal power.
Therefore, for the last decade, mmWave propagation has been
analyzed under various outdoor and indoor scenarios both
experimentally and analytically [2]. In addition to conven-
tional environments, e.g. urban, rural and indoor office, site-
specific environments have been characterized by the standard
documents such as IEEE 802.11 ad/ay and 3GPP TR 38.901
[3], [4]. Factories, shopping malls, airports, and stadiums
can be given as examples of these environments, where the
channel characteristics are different than the conventional
indoor/outdoor scenarios. The modeling of these channels
generally starts with several on-site measurements in exem-
plary environments. Later, the measurement results converge
to a channel model that can be generalized for the considered
environment. However, due to the geometry dependency of
the mmWave propagation, the site-specific environments can
also show a range of characteristics. For example, the channel
characteristics in light and heavy machinery factories suggest
almost two unique environments [5], where the path loss
exponent in the light factory is approximately half of the heavy
factory. This suggests that one should not directly rely on past
measurement studies for a given environment, and needs to
account for the objects, geometry, and human mobility within.
mmWave communication is also suitable for more densely
populated indoor environments, such as high-speed trains,
airplanes, and (more recently) hyperloops, in addition to
the site-specific environments mentioned above. There are
several works on modeling the mmWave signal propagation
in airplanes [6], high-speed trains [7], and metro cabins [8].
Several more works also exist in the literature, which we detail
in the following section.
There are two main characteristics of these environments
that necessitate modeling them under a single umbrella term.
The first distinguishing feature is that the considered space
is smaller than other site-specific indoor environments, such
as indoor offices, malls, or factories, and thus radio node
distances are shorter. Second, many blocking objects and hu-
mans populate these environments, which are generally static
during several signaling intervals. In our prior work [9] and
throughout this paper, we refer to this environment as indoor
dense spaces (IDS). Similar to the light and heavy factory
examples given above, IDS can show different characteristics
2
TABLE I
REL ATED WO RK O N IDS CHANNEL MODELING.
E Ref. Method F (GHz) LS SS MC PE D
IW
[12] RT, M 25 −40 ✓ ✗ ✗ ✗ ✗
[10] RT, M 60,300 ✓ ✗ ✗ ✗ ✗
[13] RT, M 26.5−40 ✓ ✗ ✗ ✗ ✗
[14] RT *1 18 −40 ✗ ✗ ✓ ✗ ✗
[15] RT, M 25 −40 ✗ ✗ ✗ ✗ ✓
[16] RT, M 28 −37 ✗ ✗ ✗ ✗ ✓
[17] RT 60 ✗ ✗ ✗ ✓ ✗
[18] RT 60 ✗ ✗ ✗ ✓ ✗
AC
[19] M 300 ✓ ✗ ✗ ✗ ✗
[20] M 60 ✗ ✗ ✓ ✗ ✗
[21] M 60 ✗ ✗ ✗ ✗ ✓
[22] M 60 ✗ ✗ ✗ ✗ ✓
[6] M 60 ✓ ✗ ✗ ✗ ✗
IW, AC [9] RT 28 ✓ ✗ ✓ ✓ ✗
IW, AC Our RT 28,39,60 ✗ ✓ ✓ ✓ ✓
E: Environment, M: Measurement, F: Frequency band, LS: Large-scale
analysis, SS: Small-scale analysis, MC: Material comparison, PE: Passenger
existence, D: Deployment and coverage analysis
even among the same class of transportation vehicles.
One difference is the geometry of the environment, mainly
the seats, the size of the frame, and the additional objects in
the environment. For example, an airplane frame has roughly
the shape of a cylindrical tunnel, while a high-speed train
can have the shape of a rectangular prism [10]. Another
difference is the material of the frame and the objects inside
the environment. Airplane manufacturers adapt their interior
design by targeting fully sustainable recycled materials. This
also results in differences even among the same model of
airplanes. By considering these differences, we have defined
different material, geometry, and passenger ray-tracing (RT)
scenarios for IDS. The main contributions of this paper can
be listed as the following.
•We analyze the IDS channel at 28 GHz, 39 GHz, and
60 GHz considering different geometry, material, and
passenger scenarios. By using RT, we show and com-
pare individual path powers resulting from reflections,
diffractions, and diffuse scattering.
•We model temporal and spatial parameters for any IDS
environment for the first-time in the literature. We pro-
vide the probability distributions of number of time
and spatial clusters, inter-cluster and intra-cluster excess
delays, cluster powers, subpath power, mean and offset
values of spatial lobes. We compare the results with IO
model as in [11] since it is the most similar environment
modeled with the temporal and spatial parameters.
•We provide a clustering-based channel impulse response
(CIR) generation methodology for IDS, and provide a
multi-input-multi-output (MIMO)- orthogonal frequency
division multiplexing (OFDM) channel generation pro-
cedure from the obtained CIRs.
•We compare the coverage and spectral efficiency per-
formance of the available IO model with our model to
emphasize the main differences of IDS compared to IO
model.
A. Related Work
Channel characterization is constituted either by direct
RT or RT with supporting measurements. Measurements are
generally used to fix the ray-tracing simulation to correctly
capture the material characteristics as in [14]. In this way, the
proposed channel parameters model the fixed measurement
environment. In this work, we consider airplane cabins (AC)
and intra-wagon (IW) environments as main examples of
IDS. Therefore, as in Table I, we provide a comparison on
mmWave channel modeling for AC and IW examples. LS
denotes the large-scale parameters such as path loss, received
power, root mean square (RMS) delay spread, and RMS
angular spread, whereas SS denotes small-scale parameters
such as the number of clusters, inter-cluster delay, and subpath
power. MC denotes a comparison on different materials that
exists in the paper. For example, in [14], the authors measure
several train material characteristics and later compare them
in terms of power loss. In [10], the authors provide statistical
channel parameters of intra-wagon (IW) channels in high-
speed trains considering the 60 and 300 GHz frequency
bands. For the aircraft channel modeling, [23] conduct Ray-
Tracing (RT) simulations, and provide received signal strength
and coverage analysis. In [6], the authors provide channel-
sounding measurements at 60 GHz. By providing lower path
loss and functioning well in multipath environments, the 28
GHz mmWave band has propagation advantages in compari-
son to the 60 GHz mmWave bands [24]. However, the wireless
channel characterization for an in-cabin airplane environment
at 28 GHz and 39 GHz has not been considered in the
literature. In IW environment, path loss and shadowing are
modeled based on a measurement campaign [12], [13], [15]–
[17], but small-scale fading characteristics are not provided.
As differently from these works, we consider AC and IW as
different geometry and material cases of the IDS, and model
the differences and similarities at 28,39 and 60 GHz bands
in this paper. Since the previous work in IW and AC does
not provide SS parameters and distributions, we choose to
compare our model with two different well-modeled indoor
office (IO) channel models used by 3GPP and NYUSIM,
respectively, given in [4], [11]. We also provide coverage
and spectral efficiency analysis, where the coverage area
is redefined for the IDS due to the specific environment
geometry.
B. Organization
We first explain RT simulations and the implementation
of the considered scenarios in Section II. We explain the
considered geometry, materials, and link-budget parameters
for the simulations. In Section III, we use the RT results
to analyze the temporal and spatial characteristics of the
IDS channel. In Section IV, we provide an omnidirectional
clustering-based channel generation procedure for the IDS and
extend this model to MIMO-OFDM analysis. By using the
procedure defined in Section IV with the parameters given
in Section III, we generate channel coefficients for a BS
deployment setup in IDS and compare with the RT simulation
and channel coefficients generated by IO model in Section V.
3
TABLE II
RT SIMULATION SCENA RI OS .
Scenario Material Geometry Passenger
Baseline (BL) Metal Cylindrical Full
Dielectric variation (DV) ABS Cylindrical Full
Rectangular variation (RV) Metal Rectangular Full
Empty variation (EV) Metal Cylindrical Empty
We mainly compare delay spread, coverage area, and spectral
efficiency. In Section VI, we conclude the paper and provide
future research directions.
II. RAY TRACING (RT) MODELING
RT provides precise channel characteristics for a given
transmitter (TX) - receiver (RX) link in an environment. Pre-
cise modeling of the environment is critical for the mmWave
channel since the signal propagation is sensitive to geometrical
factors and materials. We use a commercial RT software
program, Wireless Insite for our simulations1, which is based
on the shooting and bouncing rays mechanism [5]. The RT
configurations are limited to three reflections, one diffraction
and diffuse scattering to model the mmWave propagation
since the mmWave propagation in IDS is measured and
approximated by RT simulations with these settings in [15].
A. Simulation Scenarios
The main factors affecting the mmWave propagation in
IDS can be boiled down into three categories: the selected
cabin material, the geometry of the cabin, and the presence
of the passengers. To investigate the impact of each category,
we have built a baseline scenario and three scenarios with
different selection in each category as summarized in Table II.
In the Baseline (BL) scenario, metal cylindrical body creates
favorable reflections. The environment can be imagined as the
hyperloop cabin, which is envisioned to have similar charac-
teristics [25]. In Dielectric Variation (DV) case, the material of
the cabin is Acrylonitrile Butadiene Styrene (ABS), which is
a popular material among aircraft bodies [26]. In Rectangular
Variation (RV) case, we investigate the effect of the geometry
on the reflections and the diffractions from the cabin body.
This case is similar to the cabin wagon geometry, and several
RT works have been conducted considering metallic rectan-
gular body [10]2. Since passengers are generally static during
their journey (especially when the data requirement is high by
the users), we can count them as part of the environment as in
[17]. Therefore, in BL, DV, and RV, we consider all seats are
occupied by the passengers, which we described in Table II
as full. By comparing Empty Variation (EV) and BL, we can
analyze the effect of integrating humans into the environment.
B. IDS RT Environment and Geometry
We consider two different setups as given in Fig. 1(a) and
Fig. 1(b). Setup-1 is used for obtaining the channel charac-
1Wireless InSite, available at: http://www.remcom.com/wireless-insite
2Each aircraft, train or hyperloop can have different materials, and unifying
all models using a single material is not the main goal of this work.
Instead, this study chooses one common example to emphasize that mmWave
propagation depends on the materials in the environment.
(a)
26.4 m
24 rows
RX-1
RX-2
4
4
(b)
Fig. 1. The overview of TX and RX locations for (a) Setup-1, (b) Setup-2.
(a) (b)
(c) (d)
Fig. 2. Illustration of the IDS RT environment and geometry (a) Detailed
IDS geometry from front, (b) Detailed IDS geometry from side, (c) Overview
from outside (left RV, right BL, DV, EV cases), (d) An illustration on the
grouping step for the RXs. An RX group is composed of four consequent
RX positions.
teristics for IDS for the aforementioned different scenarios.
Setup-2 is later used to analyze the performance of a possible
TX deployment in IDS. In both setups, the environment is
envisioned as the mid-size airplane cabin or high-speed train
wagon. The detailed geometry of the IDS environment is given
in Fig. 2. To have a fair comparison between the different
scenarios, we consider the same transmitter and receiver
locations, and equal total area of the simulation environment.
In Setup-1, we consider a mid-sized cabin of 44 rows
with 6 seats each. TX is located in front of the first row to
measure the path characteristics throughout the cabin length.
The details of the geometry given in Fig. 2(a) and 2(b),
such as seat, corridor or crown sizes follow the available
4
Tx
Rx
ZOD
ZOA
AOD
AOA
Azimuth Plane φ
Zenith Plane θ
Fig. 3. Angular coordinates for the simulations and the results. The azimuth
and zenith angles on the planes are defined between respectively 0to 360
degrees and 0to 180 degrees.
commercial passenger airplane models in [6]. In order to
provide cabling for the access points (APs), the locations
of the TXs are selected in the crown region of the aircraft
(on top of the corridor). Prior to the channel characterization,
several possible heights for the TX (1.8-2.2m) are compared
in terms of the path loss values observed at the RX points,
and the best performing TX height is selected. The RX points
are distributed as two parallel horizontal lines along the rows
with different heights, and the lines span the width of the cabin
as illustrated in Fig. 2(d). Each RX point on a line is 1cm
away from the other points, constituting 352 RX points per
line. The dimensions are selected based on the minimum and
the maximum heights of the possible hand movements of a
human sitting on a seat. Seats, humans, and object geometries
are preserved in different simulation cases.
In Setup-2, as a reference for the comparison, we consider
an airplane cabin scenario (corresponding to DV case), where
each UE is located in a single passenger seat, and one BS is
deployed in the center of the environment. In this case, we
position a single RX point located at 0.7 m above the floor per
passenger seat of 24 rows, and the locations are determined to
match the hand of a sitting passenger in a mid-size airplane
cabin.
C. EM Characteristics of Materials
The dielectric parameters of the materials are given in Table
III. In the table, ϵdenotes the real part of the permittivity,
and σrepresents the conductivity. The material characteristics
are obtained from several different measurement works as
given in Table III, considering the given frequency bands
in their analyses. Due to the lack of measurements of the
airplane windows, we assume regular glass for the window
material. The passenger seats are modeled by nylons, and the
passengers are modeled based on the human skin model in
[23]. While in BL, RV, and EV, the perfect electrical conductor
(PEC) material is considered for the frame, in DV, one of
the popular materials in an airplane fuselage, acrylonitrile
butadiene styrene (ABS) is considered as the frame material.
TABLE III
DIELECTRIC PROP ERT IES O F MATER IA LS CO NS IDE RE D IN T HE
SIM ULAT ION S AT 28,39,A ND 60 GH Z.
Material 28 GHz 39 GHz 60 GHz Thickn.
(cm)ϵ σ ϵ σ ϵ σ
Metal (PEC) 1 ∞1∞1∞n/a
Skin [27] 19.30 30.40 13.8 37.60 8.90 43.71 0.1
ABS [26] 2.40 0.028 2.40 0.028 2.40 0.028 0.3
Nylon [28] 3.01 0.03 3.05 0.05 3.00 0.08 0.25
Glass [29] 6.27 0.15 6.27 0.40 6.27 0.57 0.3
Note that various dielectric materials (wood, carbon-glass
composite) can be selected as the IDS frame, but this work
focuses on the comparison of the full reflective frame with a
dielectric material.
D. Simulation Parameters and Post-Processing
The simulation parameters considering Setup-1 and Setup-
2 are given in Table IV. The transmit power is limited to
27 dBm which is in line with the regulations for human
health considering the mmWave bands [30]. Considering each
scenario and the frequency band, 12 simulation setups are
generated and run in the Wireless Insite RT environment.
After the channel impulse responses (CIRs) are obtained from
each simulation, an RX-grouping post-processing is utilized.
In real-life measurements, the RX is shifted with wavelength
differences, and the measurement observations are collected
under a single RX entity to capture small-scale fading ef-
fects around the desired measurement location. Similarly, we
grouped four consecutive RX points into a single RX group
for the channel characterization as illustrated in Fig. 2(d). The
angular coordinates are given in Fig. 3. The results of the
simulations are discussed in the following sections.
TABLE IV
SIMULATION PARA ME TE RS FO R TH E SE TU PS.
Parameter Setup-1 Setup-2
TX array 1antenna 64 antennas ULA
RX array 1antenna 1antenna
Antenna separation n.a. λ/2
Carrier frequency 28,39,60 GHz 39 GHz
Bandwidth 1GHz 800 MHz
Subcarrier bandwidth n.a. 100 kHz
Antenna type Isotropic Isotropic
Antenna polarization V-V V-V
TX power 27 dBm 27 dBm
Noise figure 10 dB 10 dB
III. IDS WIDEBAND CHAN NEL CHARACTERISTICS
A mmWave transmitted signal has a limited number of
multipath components (MPC) due to the blockage sensitivity.
Therefore, in literature, the mmWave propagation is modeled
by an extended S-V channel model, where the received signal
is a summation of several copies of the transmitted signal
with different delays and angles [31]. In recent works, two
different clustered channel modeling are investigated based
on indoor and outdoor mmWave channel measurements to
group MPCs based on their delays and angular properties.
One is the 3GPP model, where a group of MPCs depart
5
and arrive from a unique AoD-AoA combination within the
mean propagation delay [4]. On the other hand, [11], [24],
[32] suggest that MPCs arriving at similar time delays have
potentially traveled from disparate directions. Similarly, the
MPCs coming or departing from similar directions also have
different delay values. Therefore, the time delay and the
angular spread characteristics of the MPCs are decoupled,
and they can form independent clusters in time delay and
angle spread domains [11]. The decoupling operation makes
the second model a more generalized approach in clustering,
where the first method corresponds to a case of paths in a
cluster being in the same temporal and spatial lobe.
In this work, we adopted the more general approach as in
[11] because the MPCs traveling close in time can have dif-
ferent spatial directions in IDS. For example, for an RX point
centered in the direction of the TX can receive reflections from
the frame around the same time interval but from opposite
angles. Therefore, decoupling provides a better understanding
of the IDS environment. The CIR generation strategy is the
same as [11]. However, due to the differences between the IDS
and indoor office environments, distributions of parameters are
different. The clustering-based wideband omnidirectional CIR
is given by
h(t, ΨAOA,ΨAO D) =
N
X
n=1
Mn
X
m=1
αm,nej φm,n ·δ(t−τm,n)
·δΨAOA −ψAOA
m,n ·δΨAOD −ψAOD
m,n ,
(1)
where τm,n is the absolute time delay of an MPC. ψAOD
m,n =
(ϕAOD
m,n , θAOD
m,n )is the AOD vector of the mth MPC of cluster
n, where ϕAOD
m,n and θAOD
m,n denotes the azimuth AOD and
zenith AOD, respectively. ψAOA
m,n = (ϕAOA
m,n , θAOA
m,n )is the AOA
vector of the mth MPC of cluster n, where ϕAOA
m,n and θAOA
m,n
denotes the azimuth AOA and zenith AOA, respectively. Nis
the number of time clusters (TCs), and Mnis the number of
MPC in the cluster n, for n= 1, . . . , N .am,n is the square-
root of the MPC power as αm,n =pΠm,n.
A. Power Distribution of MPCs
In RT simulations, we can record the interaction of each
individual MPC within the environment. Thus, we can observe
the number of reflections and diffractions of each MPC within
how much power each MPC holds. Fig. 4 shows the empirical
cumulative distribution function (CDF) of each MPC power,
|αm,n|2, for the different simulation cases. R and D represent
the received MPCs created by reflections and diffractions,
respectively. The direct path is excluded from the graph since
it is only influenced by the free space path loss (FSPL), and
the simulation cases do not influence the direct path power.
In the DV case, 20 dB less power from the reflections is
observed compared to the BL, RV, and EV cases, while 10
dB higher power from the diffractions are observed. This
result indicates that the dielectric frame material results in less
powerful reflections, leading to less powerful received signals.
Overall, reflections have higher power than diffractions. In EV,
slightly less power is observed in the reflections, indicating
Fig. 4. MPC power at 39 GHz considering different simulation cases. (R:
reflection, D: diffraction, LOS: direct path.)
Fig. 5. MPC power distribution at 39 GHz considering different frequency
bands. (R: reflection, D: diffraction, LOS: direct path.)
that the passenger presence in the cabin provides slightly more
reflections to the RX points.
Fig. 5 provides a comparison of the path power in different
frequency bands considering BL. Two consecutive frequency
bands have approximately 2dB power difference in each path
power case. The received power by the reflected MPCs is
almost as strong as the direct paths, showing the advantage of
the perfect reflective frame material. Diffractions hold almost
50 dB less power than reflections and direct paths, showing
that the diffractions have negligible effect in IDS mmWave
communications.
B. Path Loss and Shadowing
In the path loss analysis, we consider an A-Bmodel as in
3GPP modeling approaches [4]. The path loss in this model
is described by
PL [dB] = A + 10B log10 d
d0+χ, (2)
6
TABLE V
CHA NNE L PAR AME TE RS O F IDS WITH DIFFERENT CASES AND 28, 39 AND 60 G HZ B AND F RE QU EN CIE S.
Parameter BL-RV-EV DV 3GPP-IO1IO [11] IW-28 [7] IW2-60 [10] AC3[6]
LOS NLOS LOS NLOS LOS NLOS LOS NLOS LOS NLOS LOS NLOS LOS NLOS4
A[dB]
28 GHz 59.1 61.6 61.5 70.1 61.3 53.3 60 60 59.1 52.2n/a n/a n/a n/a
39 GHz 62 65.2 64.23 72.6 64.2 56.9n/a n/a n/a n/a n/a n/a n/a n/a
60 GHz 65.3 70.3 68.75 75 67.9 61.5n/a n/a n/a n/a 65.9 58.1 68.2n/a
B 1.6 4.1 1.9 4.3 1.7 3.8 1.2 2.7 7.3 3.5 1.9 2.8 1.65 -
σSF [dB] 5.4 8.3 4.4 8.2 3 8.0 1.8 9.7 1.4 7.3 5.4 7.7- -
1IO: Indoor office, 2IW: Intra-Wagon, 3AC: Airplane cabin. 4NLOS cases resulted from a human blockage on corridor.
1 5 10 50
Distance (m)
60
80
100
120
140
160
Path Loss (dB)
BL NLOS RT
BL LOS RT
BL LOS fit
BL NLOS fit
DV NLOS RT
DV LOS RT
DV LOS fit
DV NLOS fit
Fig. 6. Path loss fitting considering 39 GHz BL and DV scenarios for LOS
and NLOS conditions.
where Adenotes the expected path loss at the reference
distance, d0= 1 m for the chosen frequency band. χ∼
N(0, σ2
SF)denotes the log-normal shadowing factor. The RT
tool provides path loss results for the specific measurement
locations. The RT received power values are fitted to the line
with the smallest MSE. Fig. 6 shows path loss data and the
fitted A-Bpath loss model considering BL and DV cases for
39 GHz. The higher loss in DV compared to BL highlights
the effect of the cabin material.
The parameters of all cases and frequency bands are given
in Table V. The results presented for the reference works are
obtained by measurements for the considered frequency band.
Since BL, RV and EV cases have similar parameter values,
the average value of these cases are presented for the sake of
simplicity. In the BL, RV and EV cases, Ais less than the
FSPL at the reference distance, while considering DV-LOS
case, Atakes a similar value to the FSPL at the reference
distance, which equals to 61.2 dB, 63.7 dB, and 68.1 dB for
28 GHz, 39 GHz, and 60 GHz, respectively. In DV-NLOS,
Ais approximately 10 dB higher than in the other cases,
and in [6]. These differences highlight the contribution of
the reflections in mmWave channels. The similarity between
the BL, RV, and EV cases with the IW results in varying
frequencies demonstrates that the wagon environments can be
modeled by these cases. Similarly, the resemblance between
the DV results and AC results verify our DV case as an
airplane cabin model. Band σSF are similar in all cases and
in the reference works, showing that the path loss exponent
and shadowing scales similarly with the indoor environments
as the TX-RX separation increases as expected.
C. Temporal Characteristics
In this part, we detail the temporal characteristics of the IDS
channel considering different scenarios and frequency cases.
The statistical parameters of BL, RV, and EV are modeled
jointly since the difference in the parameters is negligible.
The temporal parameters are similar among the considered
frequency bands, and thus their parameters are also modeled
jointly.
1) The Number of Time Clusters: The number of TCs
partitioned from the power delay profile (PDP) under the 1
ns minimum inter-cluster time void interval (MTI) is denoted
as N. Our analysis shows that in IDS, the number of TCs, N,
can be fitted by a shifted Poisson distribution, which3
Pr [N′=x] = λx
Ne−λN
x!,(3)
and the number of TCs is obtained by N=N′+1, and λNis
the expectation of the number of TCs. However, the simulation
scenario and the LOS/NLOS condition create discrepancies in
the distribution parameters.
Fig. 7(a) illustrates the empirical probability mass function
(PMF) of Nin the BL LOS scenario, where the distribution
depends on the distance from the transmitter. When the TX-
RX separation is longer, a higher number of TCs is observed
due to the LOS availability. On the other hand, at longer
distances, the number of clusters is lower, which results in two
distinct components in the empirical PMF. The TCs obtained
from the first row and the second row (categorized as front
cabin, FC) contribute to forming the second PMF component,
whereas the TCs obtained from the rows behind the second
row (categorized as back cabin, BC) contribute to forming the
first PMF component. Therefore for BL LOS, λNdepends
on the TX-RX separation. In BL NLOS condition, Nis not
influenced by the distance and follows similar characteristics
throughout the environment. Thus, only one PMF component
is fitted with the shifted Poisson distribution. The results for
EV and RV are similar to BL. Hence, in Table VI, we model
them with the same parameters.
Fig. 7(b) illustrates the empricial PMF of Nin LOS DV
scenarios. The figure suggests that Nfollows the shifted
Poisson distribution regardless of the TX-RX separation due to
power attenuation brought about by the material. As listed in
Table VI, the average λNis 3.3and 4.1in LOS and NLOS DV
3In each RX location, there will be at least one TC. Therefore, we shift
the Poisson distribution by one unit.
7
(a) (b)
Fig. 7. Empirical PDF and shifted Poisson distribution fittings of the number
of TCs considering (a) 39 GHz, BL (FC includes the 1st and the 2nd row,
BC includes the rows behind 2nd row), (b) 39 GHz, DV.
0 10 20 30 40 50 60 70 80 90
Number of subpaths
0
0.05
0.1
0.15
0.2
PMF
(a)
RT data
f(x; r, p)
0 10 20 30 40 50 60 70 80 90 100
Number of subpaths
0
0.05
0.1
0.15
0.2
PMF
(b)
RT data
1f1(x1; r1, p1)
2f2(x2; r2, p2)
Fig. 8. Histogram and mixture negative binomial distribution fitting of the
number of subpaths in LOS area, 28 GHz. (a) BL, (b) DV
scenarios, respectively, which is close to the same parameter
from [24] under 28 GHz carrier frequency.
2) The Number of Subpaths: The number of subpaths of
the nth TC in the PDP is denoted as Mn. Fig. 8 shows the
number of subpaths in the LOS area considering BL and
DV scenarios. In the DV scenario, two PDF components can
be observed. Contrary to the previous case, here in all TX-
RX separations, two PMF components can be observed, so
the distribution is not distance dependent. This trend can
be explained as in the following. The corridor area in the
middle is always able to receive direct MPCs regardless of
the distance to the transmitter. Besides the direct MPCs, there
will also be MPCs reflected or scattered on the back part of
the cabin and arrive at the same location. Compared to the
direct MPCs, these MPCs hold multiple times MTI longer
propagation duration than direct MPCs. In the corridor area
of the DV scenario, the majority of the MPCs interact with the
nearby environment, arriving with a delay similar to the direct
MPCs. When portioning the TCs, the majority of the MPCs,
including the direct MPCs, form the second PMF component,
while those with longer travel time form the first component.
In the BL scenario, MPCs interacting with the frame are not
attenuated, thus MPCs with a more complex propagation path
will still be able to be received, which further leads to a larger
delay spread in a PDP. Statistically, the probability that a TC
contains a large number of subpaths will be smaller as a result.
0 2 4 6 8 10 12 14 16 18 20
Intra-cluster excess delays (ns)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cumulative probability
RT data LOS
RT data NLOS
LOS exponential fit
NLOS exponential fit
Fig. 9. Empirical CDF and the exponential distribution fitting of the intra-
cluster excess delay considering 39 GHz, DV.
In DV LOS, the expectation maximization (EM) algorithm
is used to fit the data to a mixture of negative binomial
distributions. EM is a widely used iterative method to find
the maximum likelihood estimates of the mixture parameters
[33]. The PDF of a single component can be described by
f(x;k, ξ) = 1
Γ(k)ξkxk−1e−x
ξ,(4)
where ξis the scale parameter, and kdenotes the shape
parameter of the Gamma distribution. Γ(·)is the Gamma
function. The mixture distribution in this case becomes
Pr [Mn=x] = α1f(x;k1, ξ1) + α2f(x;k2, ξ2),(5)
where α1and α2are the mixture proportions.
In the BL scenario, a single PDF component would result
in α1= 1 and α2= 0. The impact brought by the different
frequencies and changes in the geometric environment is
negligible compared to BL. As listed in the Table VI, in the BL
scenario, the shaping factor kis close to one which indicates
a good agreement with the exponential distribution.
3) Intra-Cluster Excess Delay: Intra-cluster excess delay
ρm,n is defined as the delay difference between the first arrived
subpath and the mth arrived subpath within the nth TC. Fig. 9
illustrates the empirical CDF of the intra-cluster excess delay.
ρm,n is fitted by exponential distribution
Pr [ρm,n =x] = 1
µρ
e−x
µρ.(6)
The mean value of the distribution, µρ, is positively correlated
to the distribution variance. Thus, smaller µρindicates a
smaller delay spread within a TC. The difference in the
frequency bands does not show an obvious impact on µρ.
The change of the geometric environment due to the change
of the cabin shape and the human body affects the µρin a
small range in the LOS area, while does not show a similar
impact in the NLOS area. Compared to [24], µρin IDS is
much smaller, which is a result of the confined size of the
IDS compared to IO.
8
0 100 200 300 400 500 600 700
Inter-cluster excess delays (ns)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cumulative probability
RT data LOS
RT data NLOS
LOS lognormal fit
NLOS lognormal fit
Fig. 10. Empirical CDF and the lognormal distribution fitting of the inter-
cluster excess delay considering the 39 GHz DV.
4) Inter-Cluster Excess Delay: Inter-cluster excess delay,
τn, is defined as the delay difference between the first arrived
TC in the PDP and the nth TC arrived after. Based on the
definition of the TC and the inter-cluster excess delay, τncan
be obtained from the derivation procedure as
τn=(0n= 0
τn−1+ ∆τn+ρMn−1,n−1+MTI n= 0 (7)
where ρMn−1,n−1is the maximum intra-cluster delay within
the previous TC [24]. ∆τnis the inter-cluster excess delay
without MTI, and it is fitted by a lognormal distribution as
Pr [τ′′
n=x] = 1
xστ√2πexp −(ln(x)−µτ)2
2σ2
τ,(8)
∆τn=sort(τ′′
n)−min(τ′′
n).(9)
The difference in the distribution means, µτ, between the DV
and the BL is more pronounced under LOS condition. For
39 GHz LOS area, µτfor BL is −18.9 ln(s)and −19.7
ln(s)for DV. This suggests that MPC attenuation due to
interaction with the environment is the main factor affecting
the propagation. Severe attenuation will lead to the MPCs
that have more reflections and diffractions being even harder
to capture when arrived at receivers, which further leads
to a smaller value of µτ. The similarity between BL and
EV indicates that the attenuation mainly happens due to the
interaction with the frame and the seats instead of with the
human skin.
5) Cluster Power: The power of the nth arrived TC in
the PDP, Pn, is defined as the summation of all the subpath
power belonging to a TC. Similar to normalized subpath
power, the normalized cluster power over the PDP, P′
n, can
be expressed by an exponentially decaying function with a
lognormal distributed shadowing term
P′
n=¯
P0e−τn
Γ10Zn
10 ,(10)
where ¯
P0is the mean value of the normalized first arrived
TC power in every PDP. Γis the cluster decay time constant,
and the shadowing term obeys normal distribution Zn∼
0 20 40 60 80 100 120 140 160 180
Inter-cluster excess delay (ns)
0
0.5
1
Normalized cluster power
(a)
RT data
Exponential fit
0 20 40 60 80 100 120 140 160 180
Inter-cluster excess delay (ns)
0
0.5
1
Normalized cluster power
(b)
RT data
Exponential fit
Fig. 11. Scatter plot and fitted plot of the normalized cluster power in LOS
at 39 GHz of (a) BL, (b) DV.
N(0, σZ).Pncan be obtained from P′
nand the received power
of the PDP, Pr, as
Pn=P′
n
PN
k=1 P′
n·Pr[mW].(11)
¯
P0indicates the percentage of the power held in the earliest
arriving TC. Γindicates how fast the cluster power decay with
the intra-cluster excess delay. With higher carrier frequency,
both parameters get slightly larger. Under LOS condition,
the parameters are also influenced by the frame material. As
shown in Fig. 11, considering 39 GHz LOS condition, 98.12%
of the received power is in the first arrived TC under the DV
scenario and 57.97%under the BL scenario. Γis 6.3ns in the
DV scenario compared to 13.2ns under the BL scenario. Also
from the same figure, some isolated points can be observed
in the BL scenario, these are the consequence of the corridor
area as discussed previously. Compared to the IO as in Table
VI, IDS has smaller Γand smaller ¯
P0which indicates a faster
decay of cluster power in time.
6) Subpath Power: The power of the mth arrived subpath
within the nth TC in the whole PDP is denoted by Πm,n. The
normalized subpath power over the total received power of
the belonged TC Π′
m,n can be expressed by an exponentially
decaying function with a lognormal distributed shadowing
term
Π′
m,n =¯
Π0e−ρm,n
γ10Um,n
10 ,(12)
where ¯
Π0is the mean value of the normalized first arrived
subpath power in every TC. γis the subpath decay time
constant, and the shadowing term obeys normal distribution
Um,n ∼ N(0, σU). Subpath power Πm,n can be obtained from
the normalized subpath power Π′
m,n and the power of the
belonging TC Pnas
Πm,n =Π′
m,n
PMn
k=1 Π′
k,n ·Pn[mW].(13)
As shown in Fig. 12, for 39 GHz with LOS condition, 20%
of the subpath power is in the first arrived subpath in DV
9
Fig. 12. Scatter plot and fitted plot of the normalized subpath power in LOS
at 39 GHz of (a) BL, (b) DV.
Fig. 13. Histogram and Poisson fit number of SLs in LOS at 39 GHz for
DV of (a) ZOA, (b) ZOD, (c) AOA, (d) AOD.
scenario and 16% in BL scenario. γis 0.6ns for the former
and 1.0ns for the latter. In comparison to the IO case, IDS
has smaller γas well as smaller Π′
0. This points out that the
received subpath power decays faster in IDS and the majority
of the received power is captured in a smaller time slot.
D. Spatial Characteristics
1) Number of Spatial Lobes: The number of spatial lobes
(SLs) partitioned from MPCs under the 20 dB spatial lobe
threshold (SLT) is denoted by L. Fig. 13 shows the empirical
PMF of Lin LOS condition. Similar to the number of TCs,
the distribution of Lin LOS conditions appears to be distance
related. The distance threshold to separate the cabin into FC
and BC is found to be different in the different scenarios.
Under BL, in the zenith plane, Lis obtained from the first
two rows form the second PDF component in the PMF, and the
rest form the second PMF component. In azimuth plane, the
threshold for determining FC and BC is the 11th row. Under
Fig. 14. Histogram and Poisson fit number of SLs in NLOS at 39 GHz for
DV of (a) ZOA, (b) ZOD, (c) AOA, (d) AOD.
DL, the thresholds for both azimuth and zenith plane are the
6th row. A shifted Poisson distribution can be used to fit the
two peaks individually
Pr [L=x] = λx
Le−λL
x!+min(L).(14)
Fig. 14 shows the PMF of Lin NLOS area. Due to the
similar geometric environment in NLOS area, the distribution
of Lis not distance related, and can be fitted by a single
distribution model in all scenarios. Lin AOA can be well
fitted by a shifted Poisson distribution, and Lin AOD shows
great agreement to the discrete exponential distribution
Pr [L=k] = floor(λLe−λLx) + min(L).(15)
The number of SLs is very different from [24]. Due to the
wave-guide effect brought by the frame, IDS is similar to the
corridor environments mentioned in [24], and the probability
of SL formation at some angles would be higher than the
others, thus uniform distribution does not model the angular
characteristics well.
2) Mean Direction of Spatial Lobes: The mean direction
of the lth spatial lobe is denoted as θlin zenith plane and
ϕlin azimuth plane. Fig. 15 shows the CDF of the mean
angle. The mean direction can be fitted either by a uniform
distribution or lognormal distribution. The former indicates the
probability of an MPC being blocked by the environment at
similar angles. The latter indicates there will be a certain range
of angles where MPCs have a higher chance to be blocked. In
the azimuth plane, both arrived and departed ϕlin the LOS
condition fit the uniform distribution since the majority of
the LOS area is located in the front part of the cabin where
no obstacles block the propagation. In the NLOS area, the
arrived ϕlfits the lognormal distribution due to the blockage.
Because of the reflection and scattering, MPCs departure at
similar angles may arrive at very different angles, in the zenith
plane, the arrived θlfits uniform distribution, while departure
θlfits lognormal distribution.
10
Fig. 15. Empirical CDF and fitting of the mean direction at 39 GHz for BL
of (a) ZOA, (b) ZOD, (c) AOA, (d) AOD.
0 10 20 30 40 50
Subpath angular offset
0
0.5
1
Cumulative probability
(a)
0 10 20 30 40 50
Subpath angular offset
0
0.5
1
Cumulative probability
(b)
0 10 20 30 40 50
Subpath angular offset
0
0.5
1
Cumulative probability
(c)
0 10 20 30 40 50
Subpath angular offset
0
0.5
1
Cumulative probability
(d)
RT data, LOS RT data, NLOS
Fitted data, LOS Fitted data, NLOS
Fig. 16. Empirical CDF and fitting of the subpath angular offset at 39 GHz
for DV of (a) ZOA, (b) ZOD, (c) AOA, (d) AOD.
3) Subpath Angular Offset: The subpath angular offset of
the lth subpath is denoted as ∆θland ∆ϕlin azimuth and
zenith plane, respectively. The subpath angular offset can be
fitted with zero mean normal distribution. Fig. 16 shows the
CDF of the subpath angular offset. All four angular planes
fit zero mean normal distribution. The same conclusion can
be observed in all other scenarios. In comparison to IO of
[24], the distribution variance σ∆ϕand σ∆θare both smaller
in IDS. This is due to the spatial limitations of the IDS.
IV. WIDEBAND CLUSTERING-BA SE D CIR GEN ER ATION
FO R IDS
The presented results in the previous section can be utilized
to generate channel coefficients statistically. We modify a
well-known 3D cluster-based CIR generation procedure which
is experimentally verified in [32]. The same model is also
utilized in [11] for modeling the mmWave propagation of
indoor office environments. One difference in our model is
Distance
Carrier
frequency
Generate PL
Transmit power
Generate
by using Eq.
(7)
Generate ,
Generate
by Eq. (X)
Generate by
Eq. (X)
Generate by
Eq. (X)
Generate by
Eq. (X)
Generate
by Eq. (X)
Generate
phases
Recover
absolute time
Generate mean
AoA and AoD
Generate CIR
Generate
and
Generate AoA
and AoD for all
paths
Calculate
Generate
by using Eq.
(7)
Generate
phases
Generate
by Eq. (X)
Generate by
Eq. (X)
Generate
by Eq. (X)
Generate by
Eq. (X)
Recover
absolute time
Generate by
Eq. (X)
Generate mean
AoA and AoD
Generate by
Eq. (X)
Generate
by Eq. (X)
Generate by
Eq. (X)
Generate
by Eq. (X)
Generate
Generate
phases
Generate by
Eq. (X)
Recover
absolute time
Generate CIR
Generate AoA
and AoD for
all paths
Generate mean
AoA and AoD
Generate
and
Generate
Generate Generate Generate
Recover
absolute time
Generate
Generate
phases
Bandwidth
Modified blocks
CIR output
Input parameters
Fig. 17. Wideband clustering-based channel generation procedure.
that we consider that the LOS or NLOS condition is a given
parameter in the simulator instead of using the probability
of LOS. Since IDS is a confined and static environment, a
user will stay in LOS or NLOS condition throughout the
signal reception/transmission, and LOS/NLOS condition can
be obtained from the given geometry. The other difference is
the blockage by the human body, where in our model it is
integrated into the IDS instead of being modeled as a random
shadowing effect. Our modified version can be described
as a block diagram in Fig. 17. First, temporal and spatial
parameters are generated separately. Then, while generating
AoA and AoD of all paths, we randomly assign the possible
angles to the incoming paths as detailed in [24]. As a final
output, we generate the CIR expression given in (1).
A. MIMO-OFDM Channel Generation for IDS
As outlined in [34], the SISO clustered channel fading
model can be extended to MIMO channel if the RX is in
the far field of the TX. Considering this, wideband MIMO
CIR can be obtained by
H[t] =
N
X
n=1
Mn
X
m=1
Hm,nδ(t−τm,n ),(16)
where Hm,n is the Lr×Ltchannel matrix of the mth subpath
of the nth cluster. Using a parametric methodology, Hm,n can
be obtained by
Hm,n =αm,nej φm,n ar(Φm,n)aH
t(Θm,n),(17)
where ar(Φm,n)∈CLr×1and at(Θm,n )∈CLt×1are
respectively the receiver and the transmitter antenna array
responses. Considering ULAs with λ/2antenna separation,
the array responses for the transmitter and the receiver are
described by
at(Θm,n) = 1
√Lth1, . . . , e−jπ(Lt−1) sin ϕAOA sin θAOA iT
,
(18)
11
TABLE VI
TEMPORAL CHANNEL CHARACTERISTICS.
Parameters BL, RV, EV DV 28 GHz all [11]
LOS NLOS LOS NLOS LOS NLOS
Number of TC (N)
λN(FC)13.54.2 3.3 4.1 3.6 5.1
(BC)21.5
Nmin 3.01.0 1.0 1.0 1.0 1.0
2.0
Nmax 11.013.0 7.0 13.0- -
9.0
Number of Subpaths (M)
k1.1 0.7 1.4 0.7n/a n/a
θ17.3 24.0 5.8 31.0n/a n/a
α1.0 1.0 0.6 1.0n/a n/a
Mmin 1.0 1.0 1.0 1.0 1.0 1.0
Mmax 90.0 100.0 100.0 100.0n/a n/a
Inter-cluster delay (τ)µτ[ln(s)]−18.9−18.8−19.7−18.9n/a3n/a
στ1.2 1.1 1.4 1.1n/a n/a
Intra-cluster delay (ρ)µρ0.8 1.6 1.1 1.6 3.4 22.7
Cluster Power (P)
¯
P00.6 0.3 1.0 0.4-40.7
Γ[ns] 13.4 10.6 5.5 7.2 20.7 23.6
σZ[dB] 0.9 1.3 1.6 1.4 15.4 9.6
Subpath power (Π)
¯
Π00.2 0.3 0.2 0.3- -
γ[ns] 1.0 1.1 0.6 1.0 2.0 9.2
σU[dB] 0.6 1.0 0.9 1.0 5.2 6.0
1FC: Front Cabin, 2BC: Back Cabin.
ar(Φm,n) = 1
√Lrh1, . . . , e−jπ(Lr−1) sin ϕAOD sin θAOD iT
.
(19)
The frequency response of the channel can be represented by
H[f] =
N
X
n=1
Mn
X
m=1
Hm,ne−j2πf τm,n ,(20)
where frepresents the selected subcarrier frequency due to
the narrow-band flat fading assumption for subcarriers.
As our aforementioned analysis of the spatial characteristics
indicates, mmWave in IDS has a narrow dispersion in the
angular domain. Before selecting a mmWave transmission
scheme, channel characteristics in frequency/angular domain
plays a critical role to determine the precoding/combining
and the power allocation. To obtain channel gains in the
angular domain, we can multiply the channel coefficients
in frequency with the antenna array directing the beam to-
wards the relative angle, and similarly combining the sig-
nal from a specific angle. We define the transmitted and
the received unit spatial signatures along the direction Ω
respectively as et(Ω) = 1
√Lt1, . . . , e−jπ(Lt−1)Ω T, and
er(Ω) = 1
√Lr1, . . . , e−jπ(Lr−1)Ω T. If the angular domain
is separated between Ω∈(−π/2, π/2), the channel gain in
the direction of the selected angle and at the frequency f
would become
Gf=eT
r(Ω)H[f]et(Ω)
2.(21)
To analyze the channel gain in the frequency-angular domain,
we consider an ULA TX of 1024 antennas, and single antenna
RX points. The channel responses are generated by using RT
Setup-1 CIR. Since RT Setup-1 considers SISO scenario, we
extend to MIMO channel by using (16)-(21). In this case, er=
1, and the channel gain can be given as Gf=|H[f]et(Ω)|2.
Fig. 18. Frequency angular domain channel response when RX is at (a) RX1
(b) RX2. The locations of the RXs are given in Fig. 1(b).
We consider 1024 angular directions in between −90◦and
90◦, where
St={et(−π/2),et(−π/2 + π/1024),...,et(π/2)}.(22)
Fig. 18 depicts an illustration of the channel gains on the
frequency-angular domains of two different RX positions.
To keep our results concise, we choose RX-1 and RX-2
(their positions are depicted in Fig. 2(a)) to represent LOS
and NLOS cases, respectively, although we observe similar
trends in LOS and NLOS cases. In Fig. 18(a), channel gain
is dispersed between 0◦to 45◦and also contains strong
component in 90◦. This supports our previous observations
that RX positions in LOS experience reflections as strong as
the direct path components. On the other hand, we observe
12
TABLE VII
SL PAR AM ET ERS
Parameters
BL DV
LOS NLOS LOS NLOS
Arrival Departure Arrival Departure Arrival Departure Arrival Departure
Number of SL (L)
Azimuth
λF C
L2.6 3.4- - 5.0 3.9
λBC
L0.3 0.1 1.4 1.0
µL4.5 3.4 4.2 3.1
Lmin 3.0 4.01.0 1.01.0 3.01.0 1.0
1.0 1.0 1.0 1.0
Lmax 13.0 12.019.0 16.014.0 18.021.0 14.0
4.0 7.0 12.0 13.0
Zenith
λF C
L3.1 3.97.4 3.35.1 4.37.5 3.2
λBC
L1.1 0.7 1.2 0.6
µL
Lmin 4.0 3.01.0 1.01.0 1.01.0 1.0
1.0 1.0 1.0 1.0
Lmax 14.0 12.021.0 14.020.0 18.021.0 15.0
7.0 6.0 16.0 11.0
Mean direction of SL
(θ/ϕ)
Azimuth
θmin 2.5 1.9 3.9 3.1
θmax 178.3 177.5 178.4 175.6
µθ4.1 4.5 4.0 4.5
σθ0.54 0.23 0.46 0.15
Zenith
ϕmin 1.1 0.2 0.8 0.1
ϕmax 357.3 359.9 357.9 359.9
µϕ4.7 4.5 4.7 4.5
σϕ0.7 0.4 0.6 0.4
Subpath Angular Offset
(∆θ/∆ϕ)
Azimuth σ∆θ3.5 3.6 5.2 3.4 2.1 2.4 5.5 2.9
Zenith σ∆ϕ2.7 2.4 3.6 5.0 1.8 1.6 4.1 5.3
in Fig. 18(b) that channel gains are concentrated between
−90◦to −45◦, which indicates reflection-dominated channel
condition. The lack of frequency selectivity in both figures
indicates that power allocation in the frequency domain is
not necessary. The dispersion in the angular domain shows
that analog beamforming (which uses a single beam) cannot
utilize all multipaths), but hybrid and digital beamforming can
do that by using several angular directions simultaneously.
V. IDS P ERFORMANCE COMPARISON
In this section, we compare the correctness of the proposed
IDS model with the available IO models given by [4] and
[11]. To generate the IO channel model in [11], we utilize
the NYUSIM channel simulator [35]. In an IDS environment,
passengers use data-consuming applications while they are
in their seats instead of walking in the corridor. Since the
environment has a fixed and generally symmetric design, the
possible RX positions would have a grid structure, where
each row of IDS would have some distinct distance from the
following rows. To model that, similar to RT simulations, in
our channel simulator and IO channel models, we generate 104
RX positions per row such that they are uniformly distributed
in a rectangular prism. We let Ri= [Rx
i,Ry
i,Rz
i]define
the range in terms of Cartesian coordinates of the RX points
at row i∈ {1,2, . . . , I}, where Iis the number of rows.
Due to the symmetry of the airplane cabin, Rx
i=Rxand
Rz
i=Rzfor all i, where Rx= [0,1.47] S[2.1,3.52], and
Rz= [0.6,0.9].Ry
i= [0.35 + 1.1(i−1),0.35 + 1.1(i)] for
all i. The corner points of the prisms are determined by the
possible locations of user equipment devices when a sitting
passenger is using it. We neglect the RX positions in the
corridor since the data requirement is generated by the sitting
passengers. We consider 120 rows in total in the simulators to
0 5 10 15 20 25 30 35 40
Delay [ns]
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cumulative Probability
BL-IDS model
BL-RT
DV-IDS model
DV-RT
NYU-IO
Fig. 19. RMS delay spread comparison of RT simulations of Setup-2, our
channel model, and the IO model generated by NYUSIM.
show the modeling discrepancies in the IO models, although
a commercial airplane cabin is much smaller.
A. Delay Spread
The average and variance of RMS-DS of the IO and IDS
are already compared in [9]. Fig. 19 provides a comparison
of empirical CDF of RMS delay spreads considering RT
simulations with Setup-2, the proposed channel model, and
the NYU-IO model. The mmWave signal cannot travel long
distances due to the severe blockage in IDS, and thus the
delays experienced at RX is 50% less compared to the NYU-
IO model. The results indicate approximately two times higher
coherence bandwidth in comparison to the IO models.
13
1 5 9 13 17 21 25 29 33 37 41 45 49
Row index
0.85
0.9
0.95
1
Coverage probability
Nt=1, IO
Nt=16, IO
Nt=64, IO
Nt=1, IDS-DV
Nt=16, IDS-DV
Nt=64, IDS-DV
Nt=1, RT
Nt=16, RT
Nt=64, RT
Fig. 20. Row coverage probability comparison for our model, 3GPP-IO model
and RT simulations.
Number of TX antennas
Number of covered rows
Our model-DV
3GPP-IO
Fig. 21. Coverage distance in terms of the number of rows covered, 3GPP-IO
model and our model.
B. Coverage Area
Since the potential RX locations in the IDS is modeled
with a grid structure, traditional coverage area analysis as in
outdoor and indoor area works [24] cannot be utilized here.
Instead, we define the coverage probability per row for the
IDS. We let Pc,i = Pr [SNRri>SNRth]as the coverage
probability of the row i, where the RX point is located on the
grid ias ri∈ Ri. SNRth denotes the threshold SNR, where
we set 5 dB in this study. We can use the relation between
the measured PL for riand the SNR values as
SNRri[dB] =Pt+ 10 log10 (Lt) + Gt−N0−PLri,(23)
where Ptis the transmit power in dBm, Gtis the transmit
antenna gain in dBi, and 10 log10(Lt)is the boresight array
gain, and the array gain for directions other than the boresight
is smaller than this value, dependent on the array factor of the
particular antenna pattern. By generating the locations of RX
points in grids as described above, we can estimate the path
loss values by the different channel generation procedures.
By using the path loss values, we calculate the coverage
probability for each row and compare the results of different
channel generation procedures in Fig. 20. While the dotted and
dashed lines show the performance of stochastic simulations
0 5 10 15 20 25
Spectral efficiency [bits/s/Hz]
0
0.2
0.4
0.6
0.8
1
Cumulative probability
Analog BF-RT
Digital BF-RT
Analog BF-IO
Digital BF-IO
Analog BF-IDS
Digital BF-IDS
Fig. 22. Empirical CDF of spectral efficiency of the users in a cell of 24
rows with OFDM SU-MIMO system.
with our IDS model and 3GPP-IO model respectively, the
single dots illustrate the deterministic RT performance of the
Setup-1 due to the high number of RX points per row. RT
simulations are illustrated with dots, and they are only visible
on a subset of rows because they are only carried on the rows
described in Fig. 1(a). From the Fig. 20, we can observe that
the IO model provides more optimistic channel conditions
compared to the RT simulations, while our IDS-DV model
correctly captures the RT simulations. For a 95% coverage
probability, we can see that using an array of 64 antennas can
increase the coverage from 6rows to 15 rows compared to
the single-antenna case.
Fig. 21 provides a coverage comparison of our IDS model
with 3GPP-IO model for different number of transmit an-
tennas. We consider 5dB SNR threshold and 95% coverage
probability of the row. The over-optimistic modeling of the IO
model can be observed much more effectively in this figure.
Due to the heavy blockage of the dense objects, IDS shows
more pessimistic characteristics compared to the indoor office
model.
C. Spectral Efficiency
The analysis in the previous part indicates approximately
13.2m away of coverage (total of 24 rows) when the TX is
equipped with 64 antennas. By assuming 24 rows as the cell
area of mmWave IDS when the TX is at the center, we analyze
the spectral efficiency distributions in the cell considering
analog and digital beamforming in Fig. 22. For the RT, we
consider the MISO channel results from Setup-2. Similar to
the coverage analysis, we observe poorer performance in IDS
compared to the IO. Digital beamforming provides three times
higher spectral efficiency compared to analog beamforming
similar to the indoor and outdoor results given in [24]. The
mismatch between IO model and RT simulations indicates that
IDS is a distinctive indoor environment with low achievable
data rates.
14
VI. CONCLUSION
Indoor dense spaces (IDS) can be viewed as a specific
indoor site, which by varying the material and geometry we
can model airplanes, trains, and other in-vehicle environments.
In this work, we characterize mmWave signal propagation for
IDS at 28,39, and 60 GHz bands by using RT simulations.
We compare the effect of frame material, user density, and
geometry, and we observe that the frame material determines
the number of reflections in IDS, and influences the distribu-
tion of the channel characteristics. Dense object and passenger
existence in IDS results in severe attenuation and at least
50% shrunken coverage area and lower spectral efficiency
compared with IO. This mismatch indicates that our model
captures different IDS environments, and IO model is not
suitable to use for simulating IDS. Another observation is
that digital beamforming provides five times higher gains
compared to analog beamforming due to the large angular
dispersion. In future work, the effect of passenger mobility
in the corridor can be modeled as an additional shadowing
effect.
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