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: [email protected]

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)



(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).



................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



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.

A New Geometrical Channel Model for Vehicle-To-Vehicle Communications

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