A Novel Stochastic Geometrical Model for WidebandMIMO-V2V Channels

Ahmad ElMoslimany⇤, Amr El-Keyi⇤, Yahya Mohasseb†⇤Wireless Intelligent Networks Center (WINC), Nile University, Giza, Egypt 12677Email: ahmed.amr@nileu.edu.eg,aelkeyi@nileuniversity.edu.eg

†Department of Communications, The Military Technical College, Cairo, Egypt 11331.Email: mohasseb@ieee.org

Abstract—In this paper, we present a novel widebandmultiple-input multiple-output Vehicle-to-Vehicle channelmodel. The proposed channel model is derived using thegeometrical elliptical scattering approach. In order toemulate the appearance and disappearance of scatterers(vehicles, terrain, roadside units, etc.) in the environment,we associate a persistence process with each physicalscatterer in the model. The parameters of the proposedmodel can be tuned to represent a variety of vehicularenvironments. We also derive the temporal and spatialcorrelation functions of the channel coefficients. Channelmeasurements and numerical examples are presented toprovide more insight into the model and the physicalinterpretation of its parameters.

Index Terms—MIMO-V2V channel modelling, geomet-rical elliptical scattering, nonstationary channels.

I. INTRODUCTION

Vehicle-to-Vehicle (V2V) channels experience highrelative velocities between the transmitter and the re-ceiver in addition to a dynamic ambient environment.This results in a rich multipath fading environment inwhich the rapid motion of scatterers leads to continuousvariation in the power-delay profile. Due to these uniquefeatures, V2V channels do not lend themselves easilyto standard channel models, e.g., [1]. Instead, statisticalmodels are needed to represent the time varying natureof the channel impulse response (CIR).

Classical statistical channel models typically use theWide Sense Stationary Uncorrelated Scattering (WS-SUS) assumption [2]. However, for V2V channels, thisassumption is not valid for prolonged time intervals.In fact, V2V channels are statistically nonstationarybecause of the physical environment dynamics. This ismainly due to the motion of the transmitter, receiver,and significant reflectors/scatterers. For example, thepresence of a large truck on the side of the transmitteror receiver can contribute to a multipath component for

This work was supported by General Motors, USA.

a relatively short duration (until the vehicle passes thetruck). Furthermore, the omnidirectional antennas forthe transmitter and receiver are at low elevations, andhence, over moderate spatial scales reflectors/scattererswill “appear and disappear”. There are two approachesfor handling the nonstationary nature of practical V2Vchannels. The first approach is based on the concept of alocal scattering function, developed in [3] and used, e.g.,in [4], to estimate the time interval over which the WS-SUS assumption is valid. The second approach is basedon modelling the channel as a tapped delay line with thetap amplitudes following some probabilistic distributionand modulated by a birth/death (on/off) process [5]. Theon/off process for each tap was modelled by a first-orderMarkov chain with a prespecified state transition matrixin [6].

In this paper, we develop a novel model for widebandMIMO-V2V channels. The proposed channel model isderived using the geometrical elliptical scattering ap-proach [7]. However in [7], scattering is assumed tooccur uniformly on an ellipse. This assumption doesnot suit the V2V scenario where the low elevation ofantennas precludes a such a rich scattering assumption.Here, we associate a persistence process with eachphysical scatterer in the environment. The persistenceprocess models the existence and absence of the physicalscatterers, and hence, we can capture the dynamics ofthe scatterers in V2V channels. Note that, in generaleach time delay path (TDP) is due to the contributionof multiple scatterers and not a single one. Hence, theproposed model is a more accurate representation of thevehicular environment than the approach in [6] whichmodulates the tap coefficient representing a TDP by abirth/death process [6]. We will present the derivationand the characteristics of this model that make it suitablefor modelling a wide variety of vehicular environments.Also, we will analyze the temporal and spatial correla-tion functions of the channel coefficients and investigate

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the effect of the model parameters on these functions.Channel measurements are presented that illustrate thenon-stationary behavior of V2V channels. In addition,numerical simulations are provided to illustrate thespatial and temporal correlation characteristics of theproposed MIMO-V2V channel model.

II. SCATTERING MODEL

Let us consider a transmitter and a receiver equippedwith multiple antennas each where the number of trans-mit (receive) antennas is given by M

T

(M

R

). The angleof the direction of the relative velocity between thereceiver and transmitter is denoted by ↵

v

. The proposedwideband MIMO-V2V channel model is derived fromthe geometric multi-elliptical scattering model shownin Fig. 1. In this model, we assume that the centersof the transmit and receive arrays are located on thetwo foci of M ellipses. The distance between the twofocal points is 2f . The major axis half-length andminor axis half-length of the mth ellipse are denotedby a

m

and b

m

, respectively. The scatterers (vehicles,trees, buildings, etc.) that contribute to the same TDPlie on the same ellipse, where each ellipse correspondsto a different time-differentiable path (TDP) (delay bin).The mth ellipse contains N

(m)c

slots where each slotcontains a scatterer. The scattering from the mth ellipsecontributes to the mth channel coefficient whose delayis ⌧

m

= mT

s

where T

s

is the sampling interval of thebaseband-equivalent transmitted signal. The scatteringslots are distributed along the ellipses and their numberand distribution depend on the physical and vehicularenvironment, e.g., terrain type, density of vehicles on theroad, etc. We use �

(m)T

and �

(m)R

to respectively denotethe angles of departure and arrival of a ray travellingfrom the transmitter to the receiver via a scatterer locatedon the mth ellipse. The angle �

(m)T

(�(m)R

) is measuredfrom the center of the transmit (receive) array. Note thatthe model can be simply extended to include a line-of-sight component that contributes to the first TDP.

We use a multiplicative birth/death process, zn,m

[q],to account for the appearance and disappearance ofscatterers in each ellipse. However, we do not accountfor the drift of scatterers into a different delay bin. Theprocess models the persistence of the scatterer wherez

n,m

[q] = 1 if a scatterer is present in the nth slot ofthe mth ellipse at the qth time instant and z

n,m

[q] = 0

otherwise. We model zn,m

[q] using a first-order Markovmodel that assumes that the presence of the scatterer inthe slot depends only on the current state and not on howlong the slot was occupied. Although this assumption

Fig. 1. Geometric elliptical scattering model for an MT

⇥ MR

MIMO channel with local scattering clusters lying on the ellipse.

might not be very accurate in practice, it simplifiesthe analysis of the statistics of the channel coefficientsand still allows us to model a wide range of vehicularenvironments. Note that a first-order Markov process wasalso used to model the persistence of the coefficients ofthe tapped delay line representing the V2V channel in[6]. The state transition probabilities of the Markov chainreflect the degree of nonstationarity of the environment.For example, as the velocity of the vehicles increases, theprobability that the Markov chain will make a transitionfrom 0 to 1 or from 1 to 0 will increase since thescatterers will appear and disappear more frequently. Wecan write the probability transition matrix of this Markovchain as

⇤(n,m)=

1� �

(n,m)01 �

(n,m)01

�

(n,m)10 1� �

(n,m)10

!

(1)

where the i, jth entry of the matrix ⇤(n,m) denotes theprobability that the Markov chain will make a transitionto state j � 1 given that it is in state i � 1. Let ⇡(n,m)

i

denote the steady state probability that the Markov chainwill be in state i, which is also equal to the long runproportion of time that the Markov chain will be in statei. Hence, ⇡(n,m)

0 +⇡

(n,m)1 = 1, and ⇡

(n,m)1 can be written

as

⇡

(n,m)1 =

�

(n,m)01

�

(n,m)10 + �

(n,m)01

(2)

The ratio �

(n,m)01 /�

(n,m)10 determines the ratio between the

long-run proportion of time that the scatterers will bepresent in the scattering slots to that in which they willbe absent. For example in a dense urban environmentwhere vehicles move regularly and rarely change theirrelative position with respect to each other, the ratio�

(n,m)01 /�

(n,m)10 will be relatively high.

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III. CHANNEL IMPULSE RESPONSE

Let h

kl

[p, q] denote the discrete-time baseband-equivalent impulse response of the channel between thelth transmit antenna and the kth receive antenna wherethe index p is the delay index and q is the time index,i.e.,

h

kl

[p, q] =

M

X

m=0

h

(m)kl

[q]�(p�m) (3)

where �(p �m) is the Dirac delta function. Accordingto the geometrical elliptical scattering model, the mthTDP is due to the contribution of the scatterers on themth ellipse. Therefore, the mth channel coefficient canbe written as

h

(m)kl

[q] =

N

(m)cX

n=0

z

n,m

[q]

Z

�(n,m)R

g

(n,m)kl

(�

(m)R

, q)d�

(m)R

(4)

where g

(n,m)kl

(�

(m)R

, q) is the contribution of the raytransmitted from the lth transmit antenna to kth receiveelement and scattered via the nth scatterer slot in the mthellipse and received at an angle �

(m)R

at the receive array.Note that the scattering slot extends over the receiveangular interval �(n,m)

R

. We can write g

(n,m)kl

(�

(m)R

, q)

as

g

(n,m)kl

(�

(m)R

, q) = E

n,m

(�

(m)R

) exp

⇣

j✓

n,m

�

�

(m)R

�

⌘

exp

⇣

�jK0D(n,m)kl

�

�

(m)R

�

+ j2⇡F

D

�

�

(m)R

�

qT

s

⌘

(5)

where E

n,m

(�

(m)R

) is the amplitude density function ofthe scattered wave from the nth scattering slot in the mthellipse with respect to the angle �

(m)R

, ✓n,m

�

�

(m)R

�

is arandom phase shift due to the scattering process, K0 =

2⇡/� where � is the wavelength of the RF propagatingsignal, and F

D

�

�

(m)R

�

is defined as

F

D

�

�

(m)R

�

= f

D

cos

�

�

(m)R

� ↵

v

�

(6)

where f

D

is the maximum Doppler frequency. In (5),D

(n,m)kl

(�

(m)R

) is the total distance travelled by a rayemitted from lth transmit element to the kth receiveelement via a scatterer in the nth slot in the mth ellipseand received at an angle �

(m)R

. Note that we can write

D

(n,m)kl

(�

(m)R

) = D

(l,n,m)T

(�

(m)T

) +D

(n,k,m)R

(�

(m)R

) (7)

where D

(l,n,m)T

(�

(m)T

) is the distance from the lth ele-ment in the transmitter to the scatterer in the nth slotof the mth ellipse at the angle �

(m)T

and analogouslyD

(n,k,m)R

(�

(m)R

) is the distance from the same scatterer

in the nth slot of the mth ellipse to the kth elementin the receiver. For the sake of readability, in the re-mainder of this paper we will suppress the dependenceof D

(l,n,m)T

�

�

(m)T

�

, D

(n,k,m)R

�

�

(m)R

�

, g

(n,m)kl

�

�

(m)R

, q

�

,F

(m)D

�

�

(m)R

�

and ✓

n,m

�

�

(m)R

�

on the transmit and receiveangles and denote them by D

(l,n,m)T

, D(n,k,m)R

, g(n,m)kl

(q),F

(m)D

, and ✓

n,m

, respectively.We assume that the aperture of the transmit and re-

ceive arrays is much less than the distance a

m

�f for theM ellipses. Using the approximation

p1 + x ⇡ 1+x/2

for x ⌧ 1, we can approximate D

(l,n,m)T

and D

(n,k,m)R

as

D

(l,n,m)T

= D

(n,m)T

� d

Tlcos

⇣

�

(m)T

� ↵

Tl

⌘

(8)

D

(n,k,m)R

= D

(n,m)R

� d

Rkcos

⇣

�

(m)R

� ↵

Rk

⌘

(9)

where D

(n,m)T

⇣

D

(n,m)R

⌘

is the distance from the centerof the transmit (receive) array to the scatterer at thetransmit angle �

(m)T

⇣

receive angle �

(m)R

⌘

in the nth slotof the mth ellipse, d

Tl(d

Rk) is the distance between the

lth element of the transmit array (kth element of thereceive array) and the center of the transmit (receive)array, and ↵

Tl(↵

Rk) is the inclination angle of the

lth transmit element (kth receive element). Note thatD

(n,m)T

(�

(m)T

)+D

(n,m)R

(�

(m)R

) = 2a

m

is constant for themth ellipse and does not depend on the scatterer locationon the ellipse. From Fig. 1, we can write �

(m)T

as

�

(m)T

=

8

>

>

>

<

>

>

>

:

f

⇣

�

(m)R

⌘

0 < �

(m)R

�

(m)0

f

⇣

�

(m)R

⌘

+ ⇡ �

(m)0 < �

(m)R

2⇡ � �

(m)0

f

⇣

�

(m)R

⌘

+ 2⇡ 2⇡ � �

(m)0 < �

(m)R

2⇡

(10)where �

(m)0 = ⇡ � arctan(

2m�12m

), m

is the reciprocalof the eccentricity of the mth ellipse, i.e.,

m

= a

m

/f ,and

f

⇣

�

(m)R

⌘

=arctan

0

@

�

2m

� 1

�

sin

⇣

�

(m)R

⌘

2

m

+ (

2m

+ 1) cos

⇣

�

(m)R

⌘

1

A

(11)

IV. STATISTICAL PROPERTIES OF THE CHANNELCOEFFICIENTS

In order to simplify the derivation of the correlationfunctions of the channel coefficients, we assume that1) The channel coefficients that account for differentTDPs are uncorrelated as they result from interactionsfrom scatterers on different ellipses. 2) Scattering from

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different slots in the same ellipse is uncorrelated as eachslot corresponds to a distinct scatterer. 3) E

n,m

�

�

(m)R

�

=

E

n,m

is independent of �

(m)R

, i.e., the scatterers havea uniform radar cross section. Note that the scatteringslots can be occupied by a vehicle, tree, building, etc.and their radar cross-sections are different and in generalunavailable. 4) The scattering phase angles ✓

n,m

�

�

(m)R

�

are independent for different n, m, and �

(m)R

and inde-pendent of the process z

n,m

[q]. They are modelled asrandom variables uniformly distributed between 0 and2⇡.

The temporal correlation of the mth channel coeffi-cient between the lth transmit antenna and the kth receiveantenna at time instants q and q + p is given by

r

(m)

kl

[p, q]=En

N

(m)cX

n,n

0=0

z

n,m

[q]z

n

0,m

[q+p]S

(n,m)

kl

[q]S

(n

0,m)

⇤

kl

[q+p]

o

(12)where E {·} denotes the expectation operator which istaken over the random variables z

n,m

, zn

0,m

, ✓n,m

and✓

n

0,m

, and

S

(n,m)

kl

[q] =

Z

�(n,m)R

g

(n,m)

kl

(�

(m)

R

, q)d�

(m)

R

(13)

=E

n,m

Z

�(n,m)R

e

j

⇣2⇡F

(m)D qTs+✓n,m�K0D

(n,m)kl

⌘

d�

(m)

R

(14)

where (14) follows from substituting with (5) into (13)and applying the third assumption.

r

(m)

kl

[p, q]=

N

(m)cX

n=0

�

n,m

[p, q]E✓n,m

�

S

(n,m)

kl

[q]S

(n,m)

⇤

kl

[q + p]

(15)where �

n,m

[p, q] = Ezn,m{zn,m [q] z

n,m

[q + p]} is theprobability that the nth slot of the mth ellipsoid will beoccupied by a scatterer at both time instances q and (q+

p). Given the probability ⇡

(n,m)1 [q] = P {z

n,m

[q] = 1}and the probability transition matrix ⇤(n,m), we can eval-uate �

n,m

[p, q] using the Chapman-Kolmogorov equa-tion as

�

n,m

[p, q]=⇤(n,m)p

(2,2) ⇡

(n,m)1 [q] (16)

where ⇤(n,m)p

(i,j) is the i, jth entry of the p-step state tran-sition matrix ⇤(n,m)p . Using the fourth assumption, wecan write the expectation in (15) as |E

n,m

|2 I(�(n,m)R

, p)

where the integration I(�(n,m)R

, p) is given by

I(�(n,m)R

, p) =

Z

�(n,m)R

e

j2⇡F (m)D pTs

d�

(m)R

. (17)

Fig. 2. Delay-temporal contour of the measured channel.

Since both �

n,m

[p, q] and I(�(n,m)R

, p) do not dependon the index of the transmit or receive antenna, we candrop the dependence of r

(m)kl

[p, q] on the indices k andl and write the temporal correlation of the mth channelcoefficient as

r

(m)[p, q]=

N

(m)cX

n=0

|En,m

|2 ⇤(n,m)p

(2,2) ⇡

(n,m)1 [q]I(�(n,m)

R

, p).

(18)The resulting expression for the temporal correlationin (18) shows that the channel coefficients are non-stationary as it depends on the index q through theprocess z

n,m

[q].Next, we evaluate the spatial correlation function as

a function of the geometry of the transmit array Tx

and receive array Rx

. Let us consider the mth channelcoefficient of two channels at the time instant q; the firstfrom transmit antenna k to receive antenna l, and thesecond from transmit antenna k

0 to receive antenna l

0.The spatial correlation function of the mth coefficient ofthese two channels is given by

r

(m)

kl,k

0l

0(q, Tx

,Rx

)=En

N

(m)cX

n,n

0=0

z

n,m

[q]z

n

0,m

[q]S

(n,m)

kl

[q]S

(n

0,m)

⇤

k

0l

0 [q]

o

(19)Using the modelling assumptions and going through thesame steps as in the derivation of the temporal correlationfunction, we can write

r

(m)

kl,k

0l

0 (q, Tx

,Rx

)=

N

(m)cX

n=0

⇡

(n,m)

1

[q]E✓n,m

n

S

(n,m)

kl

[q]S

(n,m)

⇤

k

0l

0 [q]

o

(20)

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Fig. 3. Temporal correlation function of the channel versus timeand delay

For simplicity, we evaluate the spatial correlation func-tion at q = 0. Using equations (7) – (9), we can writeD

(n,m)kl

as

D

(n,m)kl

=2a� d

Tlcos(�

(m)T

� ↵

Tl)� d

Rkcos(�

(m)R

� ↵

Rk)

(21)Substituting with D

(n,m)kl

(�

(m)R

) in the expression forS

(n,m)kl

[0] in (14) and using the fourth assumption, wecan write the spatial correlation function at q = 0 as

r(m)kl,k

0l

0(Tx

,Rx

)=N

(m)cX

n=0

|En,m

|2⇡(n,m)1

Z

�(n,m)R

C(n,m)ll

0 (Tx

)K(n,m)kk

0 (Rx

) d�(m)R

(22)where the above integration can be evaluated numericallyusing the relationship between �

(m)T

and �

(m)R

in (10) and

C(n,m)

ll

0 (Tx

)= e

jK0

⇣dTl

cos(�

(m)T �↵Tl

)�dT 0lcos(�

(m)T �↵T 0

l)

⌘

(23)

K(n,m)

kk

0 (Rx

)= e

jK0

⇣dRk

cos(�

(m)R �↵Rk

)�dR0kcos(�

(m)R �↵R0

k)

⌘

(24)

V. EXPERIMENTAL VALIDATION

We have measured the CIR of a 2 ⇥ 2 MIMO-V2Vchannel operating at a center frequency of 5.8 GHz.The channel sounder was implemented on Rice Univer-sity’s Wireless Open-Access Research Platform (WARP)boards V1.2. The transmitted signal from each antennais a periodic 511-chip Gold sequence that provides acoding gain of 54 dB. The signals from the two transmitantennas are time-multiplexed to remove the mutualinterference. The sequences are generated at a rate of40 ⇥ 10

6 chip/sec where sampling is performed at thechip rate. Since the duration of one code cycle is 1024chips (511 chip for the m-sequence followed by 513

zeros), the CIR can be sampled once every 25.6 µsecwhich is an order of magnitude higher than the expectedcoherence time of the channel. The captured samplesare stored temporarily in an on-chip buffer and thentransferred to the SRAM. The capture cycle is repeatedevery 1 msec, and hence, the CIR can be measured overa temporal duration of 256 msec. The CIR is computedby correlating the received samples with the transmittedsequences.

In the measurement experiment, we use two vehicleswhere the antennas are mounted on the rooftops of thevehicles with a separation of 2.5 cm. The transmittedpower is given by 19 dBm. The experiment is performedin a suburban area in the campus of Nile University. Thetwo vehicles move in opposite directions at a speed of30 km/hr each. Fig. 2 shows the delay-temporal contourplot of the impulse response of the channel between thefirst receive and the first transmit antennas. The figureillustrates the non-stationary nature of the CIR as somecoefficients appear and disappear repeatedly.

VI. A NUMERICAL EXAMPLE

In this section, we will present a numerical exampleto illustrate the temporal and spatial correlation charac-teristics of the proposed model. We consider a vehicularchannel at f

c

= 5.85 GHz with bandwidth 10 MHz, andhence, the sampling frequency of the CIR is T

s

= 100

nsec. The relative speed between the two vehicles is 100km/hr and the inclination angle of the velocity vector is↵

v

= 0. We consider only one TDP corresponding toone ellipse. We set the lengths of the major and minoraxes as 20 and 12, respectively. We assume that thereare N

c

= 2 scattering slots that extend over the angularintervals �(1)

R

= [98

�, 108

�] and �(2)

R

= [110

�, 235

�].

The transition probabilities of Markov chain associatedwith the two scattering slots are identical and its pa-rameters are given by �01 = 0.005 and �10 = 0.001.Note that the selected transition probabilities indicatethat the scatterers exist in each slot for 83.33% of thetime. The parameters of the simulation correspond to ahighway environment with high mobility. Fig. 3 showsthe temporal correlation of the channel coefficient versusthe delay ⌧ = pT

s

and the time t = qT

s

. The initialprobabilities ⇡

(n)1 [q] were selected as 0.5 for n = 1, 2.

From the figure we can see that the channel coefficientis not stationary as the temporal correlation is a functionof time.

Next, we investigate the spatial correlation character-istics of the channel model. We consider a uniform lineartransmit and receive array equipped with M

T

= M

R

= 8

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Fig. 4. Spatial correlation between channel coefficients h11 and h22

elements each and their tilt angles are given by ↵

T

=

↵

R

= 0. Fig. 4 shows the spatial correlation functionbetween two channel coefficients h11 (t,⌧ ) and h22 (t,⌧ )

versus the normalized transmit antenna elements spac-ing �

T

/� and the normalized receive antenna elementsspacing �

R

/�. We can see from this figure that thechannel coefficients become almost uncorrelated whenthe spacing between the antenna elements of the transmitand receive arrays is in the order of 3�. Hence, spatialdiversity gains can be harvested with an antenna arraywith inter-element spacing in the order of 15 cm that canbe easily mounted on vehicles and roadside units.

Next, we evaluate the joint direction-of-departure/direction-of-arrival (DoD/DoA) angularpower spectrum (APS) of the channel coefficientsgenerated according to the model. We consider the sameparameters used in the last example except that wehave a horizontal circular arrays at the transmitter andreceiver sides whose elements are separated by 0.75�.The APS is calculated using the Capon beamformerfrom the sample spatial covariance matrix of thegenerated channel coefficients [8]. Fig. 5 shows theAPS of the MIMO channel. We can see from thisfigure that the highest values of the APS are in theangular directions of the two scattering slots where thefirst slot extends over the DODs �(1)

T

= [14.5

�, 17.5

�]

and DOAs �(1)R

= [98

�, 108

�] and the second slot

extends over the DODs �(2)T

= [18

�, 336

�] and DOAs

�(2)R

= [110

�, 235

�].

VII. CONCLUSION

We have derived a wideband MIMO-V2V channelmodel using the geometrical elliptical scattering ap-

Fig. 5. Angular power spectra of the simulated MIMO channel.

proach that captures some of the inherent characteris-tics of vehicular environments. The persistence of thescatterers in the channel was modelled by a birth/deathprocess. We have analyzed the statistical properties ofthe channel and derived closed-form formulas for thetemporal and spatial correlation functions. Experimentalmeasurements were presented that illustrate the non-stationary behavior of the channel. Our future workincludes improving the spatial resolution and captureduration of the measurement platform to be able toextract the model parameters corresponding to differentV2V environments.

REFERENCES

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[3] G. Matz, “On non-WSSUS wireless fading channels,” IEEE

Trans. Wireless Commun., vol. 4, pp. 2465–2478, 2005.[4] A. Paier et al., “Non-WSSUS vehicular channel characterization

in highway and urban scenarios at 5.2 GHz using the localscattering function,” in Proc. Int. Workshop Smart Antennas, Feb.2008, pp. 9–15.

[5] Q. Wu, D. Matolak, and I. Sen, “5-ghz-band vehicle-to-vehiclechannels: Models for multiple values of channel bandwidth,”IEEE Transactions on Vehicular Technology, vol. 59, no. 5, pp.2620–2625, 2010.

[6] D. W. Matolak, “Channel Modeling for Vehicle-To-Vehicle Com-munications,” IEEE Commun. Mag., vol. 46, pp. 76–83, May2008.

[7] M. Patzold and B. Hogstad, “A wideband mimo channel modelderived from the geometric elliptical scattering model,” in 3rd

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(ISWCS), 2006, pp. 138–143.[8] M. Ozcelik, N. Czink, and E. Bonek, “What makes a good

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The 3rd International Conference on Communications and Information Technology (ICCIT-2013): Wireless Communicationsand Signal Processing, Beirut

The 3rd International Conference on Communications and Information Technology (ICCIT-2013): Wireless Communicationsand Signal Processing, Beirut

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