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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. XX, NO. X, XXX 2023 1
Vehicle to Vehicle Path Loss Modeling
at Millimeter Wave Band for Crossing Cars
Anirban Ghosh ID , Aniruddha Chandra ID , Tomas Mikulasek ID , Ales Prokes ID ,
Jaroslaw Wojtun ID , Jan M. Kelner ID and Cezary Ziolkowski ID
Abstract—Fifth generation new radio (5G NR) is now offering
sidelink capability, which allows direct vehicle-to-vehicle (V2V)
communication. Millimeter wave (mmWave) enables low-latency
mission-critical V2V communications, such as forward crash
warning, between two vehicles crossing on a road without
dividers. In this article, we present a measurement-based path
loss (PL) model for V2V links operating at 59.6GHz mmWave
when two vehicles approach from opposite sides and cross each
other. Our model outperforms other existing PL models and can
reliably model both approaching and departing vehicle scenarios.
Index Terms—Millimeter waves, vehicle-to-vehicle (V2V) chan-
nel, path loss, 3GPP model, mean absolute percentage error.
I. INTRODUCTION
Owing to its wideband low-latency requirements,
millimeter-wave (mmWave) based fifth generation (5G)
networks will be playing a significant role in vehicle-to-
vehicle (V2V) communication [1] in the coming years. In
keeping with the advancement, 3GPP, in its release 16,
introduced the standards for 5G New Radio (NR) V2X
with sidelink (SL) aspect; where sidelink refers to direct
communication between user equipment (UEs) without
the data traveling the entire span of the network [2]. In a
V2V scenario, UEs are vehicles, and direct communication
between them can ensure a faster exchange of information for
vehicle platooning, extended sensor data exchange, advanced
driving, remote driving, and intent sharing. For example,
the NR cellular-V2X sidelink would improve reliability in
autonomous driving through services such as forward crash
warning [3].
When two cars are approaching each other from the opposite
direction, there are multiple applications that require data
exchange between them. This includes sharing information
about the road condition, traffic situation, or diversion, as
well as emergency warnings like collision avoidance between
approaching vehicles. Communication can start between vehi-
cles moving in opposite directions only when they are within
communication range. As the cars are speeding from opposite
This work was developed within a framework of the research grants: project
no. 23-04304L sponsored by the Czech Science Foundation, MubaMilWave
no. 2021/43/I/ST7/03294 funded by National Science Centre, Poland under the
OPUS call in the Weave programme, and grant no. UGB/22-863/2023/WAT
sponsored by the Military University of Technology.
A. Ghosh is with ECE Department, SRM University AP, 522240 India.
A. Chandra is with ECE Department, NIT Durgapur, 713209 WB, India
(e-mail: aniruddha.chandra@ieee.org).
T. Mikulasek and A. Prokes are with UREL, BUT, 616 00 Brno, Czechia.
J. Wojtun, J. M. Kelner and C. Ziolkowski are with ICS, MUT, 00908
Warsaw, Poland.
sides, the relative velocity is additive, and there is a very
small window for communication. Thus, we require a high
bandwidth link to effectively transfer data between them and
take actions as deemed fit.
V2V channel sounding campaigns in various scenarios
(urban, suburban, parking garage, highway, intersections) were
primarily restricted to frequencies below 6 GHz [4]–[8]. In [9]
the authors performed a measurement campaign using direc-
tional antennas both at the transmitter and the receiver, and
fixed them at a low elevation position on the car bumpers for
V2V communications at 38 GHz and 60 GHz frequency bands.
In most practical applications, it makes more sense to place
the antennas on the roof of the vehicles to reduce attenuation
and path loss (PL). In addition, the measurement was carried
out in a convoy configuration. In [10], the measurement was
carried out at 60 GHz, but here the transmitter and receiver
were placed on a fixed tripod emulating a rooftop antenna
of a stranded vehicle. Besides, here also the configuration
explored was vehicles moving away from one another and not
approaching. As an interesting study, it was pointed out in [11]
that PL can be different for varying antenna positions, even
at 28 GHz. However, there was no study on the PL model to
see if the PL, when cars are approaching, should be different
from the case when the vehicles are moving away, and if this
changes with relative speeds.
Thus to address the aforementioned gap, we performed a
measurement campaign at 59.6GHz in a V2V communication
scenario [12], [13]. The current paper focuses on the PL values
obtained from the field tests; specifically:
•Based on real-world data, a PL model is proposed for
a typical mmWave band (59.6GHz) V2V link where
vehicles approach each other, cross, and move away.
•To quantize the goodness of fit of our introduced model
we compare it with four other existing PL models in
terms of root mean square error (RMSE), Grey relational
grade-mean absolute percentage error (GRG-MAPE), and
Pearson correlation coefficient-mean absolute percentage
error (PCC-MAPE). Our model showed a better fit to
experimental data with respect to other standard PL
models.
•The proposed model is parameterized to best fit the
measurement data. The parameterized model confirms our
intuition that the same model with a different parameter
set is required for defining each scenario (moving in and
moving away) at a different relative speed.
2 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. XX, NO. X, XXX 2023
Rx
Car Tx
Car
Meeting
Point
Tx
Car
Rx
Car
Meeting Point
Antenna Assembly
Test Track
Fig. 1. (left) The aerial view of the test site [courtesy: Google Maps], (middle) the 3D site layout and measurement tracks [courtesy: Mapy.cz], and (right)
photograph showing the vehicles under test and antenna hardware assembly.
II. MEASUREMENT CAMPAIGN
The transmitter (Tx) of the time-domain channel sounder
as described in [12], comprises of Anritsu MP1800A signal
quality analyzer that supplies the seamlessly repeating Golay
complementary sequence at baseband (BB) with a bandwidth
of 4GHz. The BB signal is passed through an optional
low pass filter (LPF) to maintain bandwidth integrity before
being upconverted into the center frequency of 59.6GHz
using a SiversIma FC1005V/00 V-band up/down converter.
To compensate for phase noise, the reference signal for up-
conversion is applied from an Agilent E8257B frequency-
stable, low-phase noise generator. The output signal from the
converter passes through a band pass filter (BPF) for image
frequency rejection and a power amplifier (PA) of gain 35
dB to indemnify for propagation loss. The amplified signal is
then transmitted using an omnidirectional substrate-integrated
waveguide (SIW) antenna.
At the receiver (Rx), a similar antenna is used for the
reception of the transmitted signal. The received signal ini-
tially passed through a low noise amplifier of gain 33 dB
for loss compensation before being mixed with the signal
from a carrier generator Agilent 83752A inside SiversIma
FC1003V/01 V-band up/down converter to obtain the base-
band signal [12]. The obtained baseband signal is stored
using Tektronix 72004C (20 GHz, 50 GS/s) mixed signal
oscilloscope (MSO). Downloading data from the oscilloscope
and subsequent basic processing are facilitated by LabView
software. The synchronization between the Tx and Rx module
is established through back-to-back (B2B) calibration. Post
calibration, the synchronization is maintained with the help of
rubidium (Rb) oscillators. The transmitted Golay sequence is
generated at a data rate of RDR = 12.5Gbps and contains
N= 2048 bits, and hence the maximum observable time
is Tmax =N/RDR = 163.8ns. With a memory depth of
the MSO at MD= 31.25 MSample/channel, the sampling
rate at RS= 50 GSample/s, and the sampling interval at
Tint = 5 ms, the number of samples per channel impulse
response (CIR), Nsam/CIR =N×RS/RDR, the number CIRs
per measurement, NCIR/meas =MD/(8×Nsam/CIR )and total
time for each measurement, Tmeas =NCIR/meas ×Tint are
respectively 8192,468 and 2.34 ms.
The V2V measurement campaign [13] was conducted on the
campus of the Brno University of Technology in Brno, Czech
Republic. In Fig. 1 we provide a bird’s eye view of the test
site. No other cars except for the participating ones, nor any
notable moving objects were present during the measurements.
There are no buildings around the immediate perimeter of the
driven two-lane road except for the ones as shown in 1. The
location and controlled traffic ensure the availability of a non-
obstructed line-of-sight (LOS) throughout the measurement
campaign. A white Volkswagen Passat CC 2.0 TDI car houses
the antenna assembly for the Tx, and a black Ford Fusion 1.4i
contains the Rx antenna and associated circuitry. While the
uninterrupted power supply (UPS) was enough to power the
sequence generator in the Tx section, the MSO drained the
UPS within minutes. This is why a trailer (not seen in the
photograph) is attached at the back of the Rx car with an
additional power supply.
t= 1s
t= 0.5s
t= 0s
t= -0.5s
d= 0m
d= -10m
d= 10m
d= 20m
Tx
Tx
Tx
Tx Rx
Rx
Rx
Rx
Fig. 2. Typical variation of PL values with the relative distance between
the cars, when cars cross along the test track. Zero distance means the cars
are at the meeting point, a positive value of relative distance denotes cars
are departing and a negative value denotes they are approaching each other.
Relative speed is 70 km/h (∼20 m/s).
The Tx and Rx antennas of the sounder were placed using
suction caps on the driver’s side of the respective vehicles. The
measurement is carried out for six passes of the vehicles at two
different relative speeds - 4passes at 50 km/h (13.89 m/s), and
2passes at 70 km/h (19.44 m/s). The separation between Tx
and Rx at the beginning of each pass is approximately 35 m.
As is expected, due to varying relative speeds the rendezvous
point of the Tx and Rx keeps varying with respect to the
starting point of the Tx. A typical crossing on the measurement
track generates a PL profile as shown in Fig. 2.
III. PL MODELS
Next, we introduce four standard PL models developed for
different urban scenarios such as Urban Microcell (UMi) and
Urban Macrocell (UMa) [14] which will be used as the basis
for comparison.
GHOSH et al.WHEN CARS CROSS: MODELLING 60 GHZ MMWAVE PATH LOSS 3
Floating intercept (FI): FI PL model [15] is defined as
P L(d) = α+ 10βlog10(d) + Xσ(1)
where αis the floating intercept, βis the PL exponent (PLE),
and Xσis a zero mean Gaussian random variable representing
the large scale shadow fading with standard deviation σ(in
dB). In [15], for UMi with different directional antennas the
PLE and σwere in the range 0.4−4.5and 5.78 −8.52
dB respectively depending on the Tx height when the Tx-Rx
separation was varied over 30 −200 m. The frequencies of
interest in the work were 28 and 38 GHz.
Close-in (CI): The CI PL model [16] is given as
P L(f, d) = F S P L(f, d0) + 10βlog10 d
d0+Xσ(2)
where d0= 1 m, fis the center frequency in Hz, and
free space PL (FSPL) is a frequency-dependent parameter,
F SP L(f , d0) = 20 log10 (4πf/c), where cis the speed of
light. FSPL can be calculated as 67.95 dB for our measurement
center frequency of 59.6GHz. In [16] it was observed that for
frequencies upto 100 GHz the βand σvalues varied between
1.85 −1.98 and 3.1−4.2dB respectively for UMi and were
2and 4.1dB respectively for UMa.
alpha-beta-gamma (ABG): The third model is the alpha-
beta-gamma PL model [17]
P L(d) = α+ 10βlog10 d
d0+ 10γlog10 fc
f0+Xσ(3)
where f0= 1 GHz and γdenotes a frequency dependent PLE.
The PL model parameters, α= 2.1,β= 31.7dB, γ= 2
and σ= 3.9dB were obtained in [17] from the extensive
campaign at different frequencies below 60 GHz with varying
Tx-Rx separation in UMa.
3GPP: The fourth model is the PL model proposed for V2V
communication by 3GPP in its release 15 for LOS commu-
nication in an urban setting [18]. The model is described as
follows
P Lurban
LOS (d) = 38.77+16.7 log10 (d)+18.2 log10(fc)+Xa(4)
where the shadowing, i.e. the effect of signal power fluctu-
ations due to surrounding objects is modeled as lognormal
distribution with standard deviation Xσ= 3 dB.
In this context, it is to be noted that the parameters delin-
eated from the cited references of each model in this section
are only for LOS scenarios which is the scenario of interest
in the current campaign.
IV. PROPOSED PL MODEL AND COMPARISON WITH
OTH ER P L MODELS
The measurement sets for different relative velocities are
segregated into two scenarios - one, when the Tx is moving
towards the Rx, termed as moving in scenario and the one
when they are moving away from one another from the
meeting point.
We propose a PL model for both cases in line with the 3GPP
model with a few adaptations as follows
P L(d) = η1+ 18.2 log10(fc) + η2log10(d) + Xσ(5)
The modeled parameters - constant term, η1, and log dis-
tance dependent coefficient, η2are obtained by fitting our
model with the measured data set for various runs. For the
shadowing term, Xσ, the standard deviation (σ)varies with
relative speed and direction of motion and can be derived as,
σ=rPN
i=1 |xi−¯x|2/(N−1) [19], where xiare the
sample values, ¯xis the mean of the samples and Nis the
total number of samples.
(b)
(d)(c)
(a)
Moving in [50km/h]
TxRx
Moving in [70km/h]
TxRx
Moving away [50km/h]
Tx Rx
Moving away [70km/h]
Tx Rx
Fig. 3. Comparison of PL models for different relative velocities: [a,b] 50
km/h, [c,d] 70 km/h.
For a visual comparison, the measured data, along with the
proposed model and the four standard PL models described
in the previous section, are plotted in Fig. 3 when the relative
speed is 50 km/h and 70 km/h. The parameters used for the
standard models are chosen so as to obtain the best goodness
of fit (GoF) with the measurement data. While the cumulative
distance span for moving in and moving away scenarios in Fig.
3 remains the same (∼35 m), the rendezvous point varies with
relative speed. This can be verified from the difference in the
span of Tx-Rx separation, i.e., the horizontal axis in Fig. 3. On
the other hand, a similar trend in measurement data for moving
in (Fig. 3 (a) and 3 (c)) or moving away (Fig. 3 (b) and 3 (d))
confirms the stationarity of the measurement environment. The
figures clearly demonstrate that the proposed model is a better
fit compared to the standard models.
Table I shows how closely the various PL models fit our
measurement dataset in terms of root mean square error
(RMSE), Grey Relational Grade-mean absolute percentage
error (GRG-MAPE), and Pearson correlation coefficient-mean
absolute percentage error (PCC-MAPE) [20]. According to
Grey system theory the GRG ranges from 0to 1which
estimates the matching degree between the measured data and
that estimated from a typical model. MAPE on the other hand
differs from GRG and can provide another dimension in model
selection to match the measured data. When both the methods
are combined the accuracy of the model selection method can
be improved and is given as
ρgrg−mape =|α.ρgrg +β.ρmape|(6)
where ρgrg gives the similarity measure using solely the GRG
4 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. XX, NO. X, XXX 2023
TABLE I
GOFMEASURE OF PL MODELS FOR DIFFERENT RELATIVE SPEEDS AND
DIRECTION OF MOTION
Direction Relative PL RMSE GRG PCC
of motion Speed Model MAPE MAPE
Moving in
70 km/h
19.44 m/s
FI 5.36 0.93 0.95
CI 3.92 0.96 0.96
ABG 4.70 0.94 0.95
3GPP 3.02 0.96 0.97
Proposed 1.22 0.98 0.98
50 km/h
13.89 m/s
FI 5.23 0.94 0.95
CI 3.45 0.96 0.97
ABG 4.44 0.95 0.96
3GPP 3.18 0.96 0.96
Proposed 1.36 0.98 0.98
Moving
away
70 km/h
19.44 m/s
FI 7.64 0.94 0.94
CI 3.48 0.98 0.97
ABG 9.43 0.91 0.91
3GPP 7.38 0.93 0.92
Proposed 1.96 0.99 0.98
50 km/h
13.89 m/s
FI 8.84 0.93 0.93
CI 3.77 0.97 0.96
ABG 8.28 0.92 0.92
3GPP 6.64 0.94 0.93
Proposed 2.05 0.98 0.97
algorithm proposed in [20]. The parameters, αand β, are
the respective weighting factors for GRG and MAPE whereas
ρmape is given as
ρmape =|1−P ere|=|1−1
n
n
X
k=1 |xi(k)−x0(k)|
x0(k)|(7)
where in our case x0denotes measurement data, xidenotes
predicted value using a PL model and nrepresents the total
number of data points. PCC on the other hand as proposed
by K. Pearson can evaluate the correlation between two data
sets and produces a value in the range of −1to 1depending
on negative or positive correlation respectively. The algorithm,
however, can be modified to produce values in the range 0to
1for the ease of comparison with other similarity measures
such as GRG. For the same reason as GRG - MAPE, PCC
can be combined with MAPE to improve the accuracy of the
algorithm producing
ρpcc−mape =|α.ρpcc +β.ρmape |(8)
In each case, the PL value obtained from the model under
consideration is compared with the measurement dataset to
calculate the RMSE value and also GRG - MAPE and PCC -
MAPE values with a weighting factor, αof 0.1for GRG or
PCC and a weighting factor, βof 0.9for MAPE (or error’s
effect). The different PL model selection methods for channel
modeling as seen from Table I unanimously point to the fact
that the FI model fits the worst for the dataset being considered
while our proposed model quite closely captures the PL pattern
of the dataset. The poor performance of the FI model, in
this case, can be attributed to the lack of presence of any
frequency-dependent term in the model unlike in the proposed
or other considered models.
V. PL M ODELS FOR MOVI NG IN/ M OVING AWAY
The proposed models are also compared for the two scenar-
ios of interest to us, i.e moving in and moving away as can be
seen in Fig. 4. The extrapolation refers to the region predicted
by the proposed model only (no measured data available for
verification).
(a) (b)
Fig. 4. Comparison of proposed PL model for moving in and moving away
scenarios: (a) Relative speed = 50 km/h, (b) Relative speed = 70 km/h.
It is seen that irrespective of the relative speed, the PL
is more for departing vehicles when the separation between
Tx and Rx is less than ∼5m and the trend reverses as the
separation increases. The crossover in the trajectory happens
at a separation of approximately 4.12 m when the relative
speed is 70 km/h and at a separation of around 5.2m when
the relative speed is 50 km/h. The maximum difference in PL
in the two scenarios, however, never exceeds 2dB irrespective
of the relative speed.
Parameters for the proposed model for different directions
of motion and varying relative speed are summarised in Table
II. The values indicate that the effect of the direction of motion
TABLE II
PROPOSED MODEL PARAMETERS FOR DIFFERENT DIRECTIONS OF MOTION
AN D VARYIN G REL ATIV E SPE ED
Direction Relative η1η2σ
of motion Speed (in dB)
Moving
in
50 km/h 40.42 10.59 6.34
70 km/h 41.51 9.92 5.98
Moving
away
50 km/h 42.31 7.99 5.99
70 km/h 42.53 8.26 6.13
is more prominent than the relative speed. In fact, with a little
loss of accuracy, it is possible to derive an average model for
two scenarios irrespective of speed. The moving in conditions
can be characterized with η1≈41, η2≈10, and for moving
away, the parameters would be η1≈42, η2≈8. The standard
deviation of shadow fading can be considered fixed at 6dB
for all cases.
VI. CONCLUSIONS
The current study presents a measurement-validated PL
model for V2V scenarios - approaching and departing vehicles.
The scenarios under investigation assume great importance in
implementing automated collision avoidance and facilitating
V2X with SL. The performance of the proposed model is
assessed with other standard PL models and is found to
outperform them in terms of various metrics. Furthermore, in
the context of vehicles approaching, crossing, and eventually
departing, the model is found to be dependent more on the
scenario than the relative speed.
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