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7/28/2019 A New Geometrical Channel Model for Vehicle-To-Vehicle Communications
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A New Geometrical Channel Model for Vehicle-to-Vehicle Communications
Lin Cheng*(l), Fan Bai(2) and Daniel D. Stancil(3)
(1) Trinity College, Hartford, CT, 06106
(2) General Motors Research, Warren, MI, 48090
(3) Carnegie Mellon University, Pittsburgh, PA, 15213E-mail: lin.cheng@trincoll.edu
Introduction
The mobile outdoor vehicle-to-vehicle propagation channel has received much
recent attention. Dedicated Short Range Communications (DSRC) systems have
been proposed to support safety and service operations for vehicular networks. In
North America, the Federal Communications Commission has allocated 75 MHz
of spectrum at 5.9 GHz for DSRC based information exchange between vehicles
[1]. Because vehicular networks bring significant potential for a wide range of
services and applications, we have made on-road measurements to gain a detailed
understanding of various vehicle-to-vehicle (V2V) propagation channels that
cover diverse and rapidly changing environments [2].
Grounded in observations from realistic on-road data, this work provides the
foundation for a new analytical model for the V2V channel based on scattering
objects distributed along the roadside. Here we focus on the Doppler spectrum
predicted by the model and comparisons with on-road measurements.
Comparisons are also made with the predications of the double ring model for
mobile-to-mobile nodes surrounded by dense, isotropic scatterers [3].
New Geometric Model
In contrast to previous models, we propose a geometry in which the scatterers are
located along each side of the road, as shown in Figure 1. Let 8 represent theangle to a scatterer with respect to the receiving vehicle. Considering scatterers
within the differential angle d8 about 8, we define p(B) to be the probability
distribution of B. Similarly, we define f(B) to be the response from scatterers
observed at angle B, and G(B) to be the antenna gain in the direction B. If the
signals scattered from the various objects are uncorrelated, then the mean power
arriving within the differential angle dB is
dP =G(8)p(8)f(8)d8 . (1)
The received power spectral density 8(f) can be obtained by equating the power in
element dB to the power in an element of spectrum. If the scattering objects are
located symmetrically about the vehicle, then the scatterers at ±8make identicalcontributions to the spectrum, and we can write
8(f)d f =2G(8)p(8)f(8)d8 , (2)
where 0 8 1! . Using the fact thatG,p, andfare positive definite functions, the
magnitude of the scattered power spectral density can be expressed
18(f) 1= 2G(8)p(8)f(8) / 1df / d8 I·
978-1-4244-3647-7/09/$25.00 ©2009 IEEE
(3)
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(7)
(8)
L -IcILI
••••••• · · ~ ~ . ~ : ~ : ! ! · · · · ~ · · ~ · f-I dIJ···4
•••(j "t *~ •• l " " e . ~ · ' ••• ..
.. L
•••••••••••••••(a) Receiver and location of scatterers (b) Response from a single scatterer
Fig. 1: Geometry for the proposed model.
For uniformly distributed objects, we describe the scatterers on the roadside by a
density parameter p (number of scatterers per unit length). Referring to Fig. l(a),
the distance between the vehicles of interest to the rows of scattering objects is
taken to be s, L is the projected path length along the road from angle 0, and dL is
the projected path length change along the road from angle dO. From the geometry
we have L=s cotO, from which we can obtain dL. The number of scatterers in the
angular range dO can then be written
p(O)dO=-pdL =spcsc2OdO. (4)
Next, we derive the response f(O) from these scatterers. The power Pr received
from a single scattering object is given by the radar equation
~ = ~ ~ ~ ) : 2 a( :2 )(:; ). (5)
where Ptrepresents the transmitter power; Gf, Gr are the gains of the transmitting
and receiving antennas, respectively; A is the wavelength; ( j is the radar cross
section of the object (assumed to be isotropic); dtis the distance from the
transmitter to the object; and dris the distance from the object to the receiver. The
contribution to the total power arriving within the range of angles dO is given by
the power from one scatterer times the number of scatterers in the length (-dL)subtended by the angle dO
dP= ~ G t G r ) } a ( _ l )(_1) (-dL). (6)(4Jl')3 d
t
2 d; P
The radar equation assumes free space propagation where the signal power falls
off as the inverse square of the distance. However, for a 2-ray ground reflection
model, the power initially falls off inversely with distance d squared, but after
some critical distance dc' the power falls off inversely with the fourth power of d.
To describe this we introduce a dimensionless distance function D(d) such that
(
(do / d)2 , d de
D(d) =2 4
(dO / de) (de /d ) , d > de
where do is a reference distance that is much smaller than dc. In terms of this
function, the differential received power can be expressed as
dP = ~ G t G ; } , } 4 a D(dt )D(dr)spcsc2OdO.
(4Jl") do
Comparison with Eqs. (1) and (4) enables us to obtain the functionj{O).
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................d - ,., d
_ . ; 3 : : C ~ = = = - ~ t
dtr
(a) Case 1: Ahead
111 ....- - dd ~ · · - - - - " - t-----............. 8.
r __ . _ . _ . _ . ~ : : : : : : : ~d
tr
(c) Case 3: Behind
~ ~ ~ ~ ~ ~d
tr
(b) Case 2: In between
Fig. 2: Cases for analysis (a) Scatterer
ahead of both the transmitter and receiver;
(b) Scatterer in between the transmitter
and receiver; (c) Scatterer behind both the
transmitter and receiver.
To determine the contribution of a scattering object to the Doppler spectrum,
three separate cases must be considered as shown in Fig. 2. As an example, we
present the analysis of the case when the scatterer is ahead of both the transmitter
and receiver as shown in Fig. 2(a). In this case 0 8 8ai
, where ()ai is the
threshold angle between the regions "ahead" and "in-between." Based on the
geometry, we have dr =scscO and dt = ~ S 2 +(scotO-dtr )2 . For a given angle
() seen by the receiver, the corresponding angle ()t as seen by the transmitter is
~ =tan-1(s /(s cot 8 -dtr) ) •
To the scatterer, the change in frequency of the transmitted signal is Vt cos()t / A,
where Vt is the speed of the transmit vehicle. The receive vehicle traveling at
speed Vr sees an additional shift of Vr cos() / ,1. Mapping the () value to the f
representation, we have f =(vt cos8t +vr cos8) /A, and we can express the
received spectrum in terms of (). The result is
1S(f(8)) 1= 2 ~ A } ( J ' G (8)G (8)D(d )D(d ) spcsc2
8 (9)(4Jr)3 t t r t r 1df / d8 1 '
where df I dO = - (d ~ I dO)(vt sin Or +Vr sin 0) IA and
d ~ I dO=S2 csc20/[(scotO-dtr )2 +S2J.
A similar approach is used to analyze the cases depicted in Fig. 2(b) and (c).
Experiments
To illustrate the use of the above model, this section discusses an evaluation of
the generated spectra and comparison with on-road data. Fig. 3 shows twoexamples of measured spectra in the suburban environment. The transmit and
receive vehicles were both moving at approximately the same speed, with line-of
sight. We took the lane width s to be 8m and scatterer density p = 0.5 per meter in
the geometrical model, and a Lorentzian line-shape function was added to
represent the line-of-sight (LoS) components in the spectrum. The double-sided
spectra generated by the geometrical model are plotted in Fig. 3 in blue, and the
double ring model predictions in red. Since the double ring model predictions do
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not include the line-of-sight, a meaningful comparison between the models is
restricted to the shape of the pedestal, or base. The magnitudes of the theoretical
curves were scaled to match the data. As can be seen, the new geometrical model
gives reasonable agreement with the experimental spectra. Further, the new model
captures the increase in power near the edges of the spectra better than the double
ring model.
1500 2000000
10.91.. . . ---- '-_---- '--_--- '---_.1. . . . --------1. ._---- '--_--- '-------- ' 1o·91....---- '-_---- '--_......L..-_'------ '-_---- '--_......L..------- '
-2000 -1500 -1000 -500 0 500 1000 1500 2000 -2000 -1500 -1000 -500 0 500
Frequency [Hz] Frequency [Hz]
Fig. 3: Comparisons between the measured spectra (black), the double-ring model
(red), and the new model (blue). (a) Vt = Vr = 12.3 mis, (b) Vt = 8.2 mis, Vr = 8.7
mls.
Conclusion
We have presented a new analytical model of the Doppler spectrum in the V2V
environment based on scattering objects distributed along both sides of the
roadway. Comparisons with examples of measured spectra from the suburban
environment show improved agreement with the shape of the spectra compared to
the double-ring model. We believe the new model could be beneficial for bothwireless emulators and network applications. For example, the model would
improve the accuracy of wireless emulators, in turn making more accurate
hardware performance evaluations (such as BER) possible. Similarly, an accurate
physical level channel model allows the evaluation of different MAC protocols
under realistic conditions.
References
[1] "Standard specification for telecommunications and information exchange between roadside
and vehicle systems - 5GHz band dedicated short range communications (DSRC) mediumaccess control (MAC) and physical layer (PHY) specifications," ASTM E2213-03," Sept.
2003.
[2] Lin Cheng, Benjamin Henty, Daniel Stancil, Fan Bai and Priyantha Mudalige, "Mobilevehicle-to-vehicle narrow-band channel measurement and characterization of the 5.9 GHzdedicated short range communication (DSRC) frequency band," IEEE Journal on Selected
Areas in Communications, vol. 25, no. 8, pp. 1501 - 1516,2007.[3] A. S. Akki and F. Haber, "A statistical model of mobile-to-mobile land communication
channel," IEEE Trans. on Vehicle Technology, 1986.