Camera Ready Version FINAL Cross Junction Model v2

6
A Geometry Based Stochastic Model for MIMO V2V Channel Simulation in Cross-Junction Scenario Andreas Theodorakopoulos Panagiotis Papaioannou Taimoor Abbas * and Fredrik Tufvesson * Department of Electrical and Information Technology, Lund University Box 118, SE-22100, Lund, Sweden Emails: [wir12ath, wir12ppa]@student.lu.se , [taimoor.abbas, fredrik.tufvesson]@eit.lth.se * Abstract—In this paper a multiple-input multiple-output (MIMO) simulation model for vehicle-to-vehicle (V2V) communi- cation channels in an urban cross-junction scenario is presented. The model is an extension and modification of an existing T- junction model in the literature. Four propagation processes are considered: line-of-sight (LOS), single bounce reflections from side walls, double bounce reflections from side walls, and single bounce reflections from the corner of the building in front of the transmitter (TX) and receiver (RX). Each propagation process is linked to a cluster of scatterers, with a cluster size that varies with respect to the position of the TX and RX. The relations between angle-of-arrivals and angle-of-departures of all Multipath Components (MPCs) are derived depending on the different positions of the TX and RX. For the single bounce reflections from the corner a new method is being used where the scatterers are distributed randomly in a triangular plane, based on the assumption that corners of buildings typically have different scattering objects contributing to the reflection process. A complete expression for the time-variant transfer function is then derived by super positioning all contributions, including the LOS when this is available. The final results show that our model follows a realistic measurement based path-loss model, which subsequently makes the model a suitable candidate for analyzing MIMO V2V fading channels in cross-junction scattering environments. I. I NTRODUCTION Vehicle-to-vehicle (V2V) communications is a promising technology which will increase the efficiency of the traffic flow, reduce the number of road accidents and provide the basis for intelligent transportation systems [1]. The funda- mental difference from a radio channel point of view when compared to traditional mobile communication is that both the transmitter (TX) and the receiver (RX) are moving. There are several measurement based studies and theoretical studies dedicated to V2V communications analyzing the statistical properties of the channel and mathematical representation of it [2]–[4]. The channel conditions in V2V communication scenarios can be extremely dynamic and single-input single- output (SISO) systems may not be an appropriate choice for a reliable reception in such scenarios. For that reason multiple- input multiple-output (MIMO) technology should also be considered in order to provide increased diversity and therefore higher robustness in the whole system [5]. A large number of measurement campaigns dedicated to V2V communication have been conducted to characterize MIMO channels around the 5.9 GHz frequency [7]–[9]. More- over, several types of theoretical channel models have been proposed for analyzing V2V communications environments, like the two-ring MIMO V2V channel model described in [10]–[12], the geometrical street scattering model for a straight road in [13], the geometrical model for a corner junction in [14] and the T-junction scattering model that is presented in [15], [16]. Although these models are useful for a performance analysis of mobile-to-mobile (M2M) communication, they do not always cover all the different important scattering environments and cannot be applied to every street geometry like, e.g., a four-way cross-junction. Intersections in urban areas are quite common and usually constitute a place where frequent car accidents can happen, which justifies the need for a channel model of this scenario. Therefore, in this work we use the modeling concepts from the T-junction model and extend it for four way cross-junction. In this paper, we propose a novel geometry based stochastic channel model (GSCM) for MIMO V2V channel simulations in an urban cross-junction scattering environment. To the author’s best knowledge there is no other (GSCM) presented in the past to model a V2V cross-junction scattering environment using a similar approach. In our model both line-of-sight (LOS) and non-line-of-sight (NLOS) propagation are assumed, and both single and double bounce reflections are considered in the model. We take into account three clusters placed at realistic positions based on the experiences gained from real measurements. The first two clusters are located at the sides of the streets in which TX and RX are moving while the corner of the building located in front of the TX and RX, which is exactly on the opposite side of TX/RX streets, is considered to be the third cluster. For this third cluster we distribute the scatterers randomly in a triangular plane, with the assumption that corners of buildings typically have different scattering objects contributing to the reflection process and to add randomness needed for the channel model. The geometry of a street intersection described by the cross-junction model is depicted in Fig. 1(a)-1(c). From the geometry of the model we derive exact expressions for the angle-of-arrival (AOA) and angle-of-departure (AOD), which are crucial for the channel characteristics. Moreover, the space-time-frequency cross-correlation func- tion (STF-CCF), the spatial CCF, the temporal auto-correlation function (ACF) and the frequency-correlation function (FCF)

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Page 1: Camera Ready Version FINAL Cross Junction Model v2

A Geometry Based Stochastic Model for MIMOV2V Channel Simulation in Cross-Junction Scenario

Andreas Theodorakopoulos† Panagiotis Papaioannou†

Taimoor Abbas∗ and Fredrik Tufvesson∗

Department of Electrical and Information Technology, Lund UniversityBox 118, SE-22100, Lund, Sweden

Emails: [wir12ath, wir12ppa]@student.lu.se†, [taimoor.abbas, fredrik.tufvesson]@eit.lth.se∗

Abstract—In this paper a multiple-input multiple-output(MIMO) simulation model for vehicle-to-vehicle (V2V) communi-cation channels in an urban cross-junction scenario is presented.The model is an extension and modification of an existing T-junction model in the literature. Four propagation processes areconsidered: line-of-sight (LOS), single bounce reflections fromside walls, double bounce reflections from side walls, and singlebounce reflections from the corner of the building in frontof the transmitter (TX) and receiver (RX). Each propagationprocess is linked to a cluster of scatterers, with a cluster sizethat varies with respect to the position of the TX and RX. Therelations between angle-of-arrivals and angle-of-departures of allMultipath Components (MPCs) are derived depending on thedifferent positions of the TX and RX. For the single bouncereflections from the corner a new method is being used wherethe scatterers are distributed randomly in a triangular plane,based on the assumption that corners of buildings typicallyhave different scattering objects contributing to the reflectionprocess. A complete expression for the time-variant transferfunction is then derived by super positioning all contributions,including the LOS when this is available. The final results showthat our model follows a realistic measurement based path-lossmodel, which subsequently makes the model a suitable candidatefor analyzing MIMO V2V fading channels in cross-junctionscattering environments.

I. INTRODUCTION

Vehicle-to-vehicle (V2V) communications is a promisingtechnology which will increase the efficiency of the trafficflow, reduce the number of road accidents and provide thebasis for intelligent transportation systems [1]. The funda-mental difference from a radio channel point of view whencompared to traditional mobile communication is that boththe transmitter (TX) and the receiver (RX) are moving. Thereare several measurement based studies and theoretical studiesdedicated to V2V communications analyzing the statisticalproperties of the channel and mathematical representation ofit [2]–[4]. The channel conditions in V2V communicationscenarios can be extremely dynamic and single-input single-output (SISO) systems may not be an appropriate choice for areliable reception in such scenarios. For that reason multiple-input multiple-output (MIMO) technology should also beconsidered in order to provide increased diversity and thereforehigher robustness in the whole system [5].

A large number of measurement campaigns dedicated toV2V communication have been conducted to characterize

MIMO channels around the 5.9 GHz frequency [7]–[9]. More-over, several types of theoretical channel models have beenproposed for analyzing V2V communications environments,like the two-ring MIMO V2V channel model described in[10]–[12], the geometrical street scattering model for a straightroad in [13], the geometrical model for a corner junction in[14] and the T-junction scattering model that is presented in[15], [16]. Although these models are useful for a performanceanalysis of mobile-to-mobile (M2M) communication, theydo not always cover all the different important scatteringenvironments and cannot be applied to every street geometrylike, e.g., a four-way cross-junction. Intersections in urbanareas are quite common and usually constitute a place wherefrequent car accidents can happen, which justifies the needfor a channel model of this scenario. Therefore, in this workwe use the modeling concepts from the T-junction model andextend it for four way cross-junction.

In this paper, we propose a novel geometry based stochasticchannel model (GSCM) for MIMO V2V channel simulationsin an urban cross-junction scattering environment. To theauthor’s best knowledge there is no other (GSCM) presented inthe past to model a V2V cross-junction scattering environmentusing a similar approach. In our model both line-of-sight(LOS) and non-line-of-sight (NLOS) propagation are assumed,and both single and double bounce reflections are consideredin the model. We take into account three clusters placed atrealistic positions based on the experiences gained from realmeasurements. The first two clusters are located at the sidesof the streets in which TX and RX are moving while thecorner of the building located in front of the TX and RX,which is exactly on the opposite side of TX/RX streets, isconsidered to be the third cluster. For this third cluster wedistribute the scatterers randomly in a triangular plane, with theassumption that corners of buildings typically have differentscattering objects contributing to the reflection process and toadd randomness needed for the channel model.

The geometry of a street intersection described by thecross-junction model is depicted in Fig. 1(a)-1(c). From thegeometry of the model we derive exact expressions for theangle-of-arrival (AOA) and angle-of-departure (AOD), whichare crucial for the channel characteristics.

Moreover, the space-time-frequency cross-correlation func-tion (STF-CCF), the spatial CCF, the temporal auto-correlationfunction (ACF) and the frequency-correlation function (FCF)

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are also derived. The power-delay-profile (PDP) and the nor-malized channel gain are derived from numerical simulations.The results on correlation functions are however left for futureanalysis therefore not included in this paper.

The structure of the paper is as follows. In Section IIthe geometrical scattering model for the cross-junction isintroduced.The MIMO channel simulator is derived in sectionIII by following the methodology in [15], [16] and changingthe model appropriately for the cross-junction scattering envi-ronments. In the following section IV we present the numericalsimulation results. Finally, in Section V conclusions are given.

II. THE GEOMETRIC CROSS-JUNCTION SCATTERINGMODEL

The locations of the scatterers are of utmost importance forthe statistical properties of the fading channel, and their posi-tion around the TX and RX play a very important role. Havingsaid that, it is quite important to geometrically approach theproblem in such a way that it would be realistic and woulddescribe the environment in an appropriate way. As realitycannot be described in a totally perfect way, the geometricalapproach should be as close as possible but simple enough tobe processed.

The cross-junction propagation model is based on the pre-viously mentioned T-junction model [15] that is specificallydesigned for three-way street junctions. The four-way cross-junction model in this paper is an extension of the T-junctionmodel. In this work we do not only extend the model but alsouse realistic parameters for numerical simulations.

The geometry that is used for our study, to generalize across-junction in an urban area, is shown in Fig. 1(a)-1(c).The TX and RX vehicles are assumed to be at positionsOT (0,−hR1 −Dy) and OR(hT2 +Dx, 0) moving towards thejunction O(0, 0), which is the centre point of the referredgeometry, with velocities νT and νR, respectively. The TX andthe RX have MT and MR element antenna arrays, respectively.

In reality, scatterers exist along all sides of the streets butfor simplicity we take three main clusters that contribute mostto the received power based on experience gained from realV2V channel measurements.A first cluster comes from thescatterers close to the TX denoted by STm for m = 1, 2, ...,M ,which is used in the single bounce close to the TX (SBT).A second cluster comes from the scatterers found close tothe RX denoted by STn for n = 1, 2, ..., N , which is usedfor the single bounce close to the RX (SBR). Double bounce(DB) reflections arriving at the RX, defined as the MPCs thatbounce on the SBT cluster as well on the SBR clusters, are alsoconsidered and are shown in Fig. 1(b) (for more informationsee [18]).

Furthermore, a third cluster comes from a single bouncereflection process from the corner (SBC) that is added in themodel as shown in Fig. 1(c). The scatterers denoted by SCkfor k = 1, 2, ...,K are assumed to be uniformly randomlydistributed in a triangle at the corner located in the frontdirection of the TX and the RX vehicles. The corner is formedat each time instant with respect to the position of the vehiclesby drawing sight lines starting from the vehicles to the edges

φΤ

αmT

αnTγΤ

β nR

βmR

h1T h2

T Dx

x

y

h1R

δR

Dy

h2R

SmT

SnR

O (0,0)

PThc max

hc max

PR

SkC

OT

VT

δΤ

(MT)

(1)

φR

γR

(MR)

VR OR

(1)

D 0mT

D m0TR

(a) Single-Bounce (SB)

TR

OT

φΤ

VT

αmT

γΤ

β nRφR γR

δR

(MT)

(MR)

h1T h2

T Dx

Dy

x

y

D n0R

h1R

h2R

VR

D mn

D 0mT

SmT

SnR

O (0,0)PThc max

hc max

PR

SkC

(1)

OR

(1)

δΤ

(b) Double-Bounce (DB)

O (0,0)β k

CφR γR

δR

(MR)

Dy

y

h1R

h2R

SnR

OR

(1)

PThc max

hc max

PR

SkC

VR

x

D kTx

D kRx

SmT

OT

φΤ

VT

α kC

γΤ

(MT)

h1T h2

T Dx

(1)δΤ

(c) Single-Bounce from corner (SBC)

Fig. 1. The geometry of the Cross-junction scattering model depicting; (a)the single-bounce mechanism, (b) the double-bounce mechanism, and (c) thesingle-bounce mechanism created by the corner.

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of the side buildings to the building at the opposite corneras shown in Fig. 1(c). A threshold hcmax is set in order toassure that the reflection is coming from the actual cornerand not from scatterers very far away. From the geometry ofthe model then, the angles and the distances are calculatedusing the coordinates from both scatterer and vehicle, with areference point given by O.

III. THE STOCHASTIC MIMO V2V CHANNELSIMULATION MODEL

For the channel simulation model, finite numbers of scat-terers are chosen as in [16]. The time-variant transfer functionof the channel is composed of the superposition of five partialtransfer functions [17] given by (1) below,

Hpq (f ′, t) = HLOS (f ′, t) + HSBTpq (f ′, t)

+HSBRpq (f ′, t) + HSBC

pq (f ′, t)

+HDBpq (f ′, t) , (1)

where,

HLOS (f ′, t) =√ddecayLOS · e−j

2πλ dLOS

·e−j2πf′τ ′LOS · ej(f

TLOS+f

RLOS)t, (2)

HSBTpq (f ′, t) =

M∑m=1

√dTXmd

Tma

Tmb

Tm

·ej[θm+(fTm+fRm)t] · e−j2πf′τ ′pmnq , (3)

HSBRpq (f ′, t) =

N∑n=1

√dRXnd

Rn a

Rn b

Rn

·ej[θn+(fTn +fRn )t] · e−j2πf′τ ′pnq , (4)

HSBCpq (f ′, t) =

K∑k=1

√dCkd

Ck a

Ck b

Ck

·ej[θk+(fTk +fRk )t] · e−j2πf′τ ′pkq , (5)

HDBpq (f, t) =

M∑m=1

N∑n=1

√dDBmnd

TRmna

Tmb

Rn

·ej[θmn+(fTm+fRn )t] · e−j2πf′τ ′pmnq , (6)

and their components are,

dTm = e−j 2π

λ

(hT1

− cos(αTm)+hT1 +hT2 +Dx

− cos(βTm)

), (7)

dRn = e−j 2π

λ

(hR2

sin(βTm)+hR1 +hR2 +Dy

sin(αRn )

), (8)

dTRmn = e−j 2π

λ

(hT1

− cos(αTm)+

hR2sin(βRn )

+DTRmn

), (9)

dCk = e−j2πλ ·(D

Rxk +DTxk ), (10)

aTm = ej2πλ (MT−2p+1)

δT2 cos(αTm−γT ), (11)

aRn = ej2πλ (MT−2p+1)

δT2 cos(αRn−γT ), (12)

aCk = ej2πλ (MT−2p+1)

δT2 cos(αCk −γT ), (13)

bTm = ej2πλ (MR−2q+1)

δR2 cos(βTm−γR), (14)

bRn = ej2πλ (MR−2q+1)

δR2 cos(βRn−γR), (15)

bCk = ej2πλ (MR−2q+1)

δR2 cos(βCk −γR), (16)

fTm = 2πfTmax cos(φT − αTm

), (17)

fRm = 2πfRmax cos(φR − βTm

), (18)

fTn = 2πfTmax cos(φT − αRn

), (19)

fRn = 2πfRmax cos(φR − βRn

), (20)

fTk = 2πfTmax cos(φT − αCk

), (21)

fRk = 2πfRmax cos(φR − βCk

), (22)

DTRmn = {[Dx + hT1 + hT2 + hR2 · cot(βRn )]2

+[Dy + hR1 + hR2 + hT1 · tan(αTm)]2} 12 . (23)

The τ ′LOS , τ ′pmq , τ′pnq , τ

′pkq and τ ′pmnq are the propagation

delays of the LOS, SBT, SBR, SBC and DB components fromthe p-th transmitting element to the q-th receiving element,respectively. In the following, we give the expressions forthe propagation delays for all the cases, starting with τ ′pmq ,τ ′pmq = Dpmq/c0 where Dpmq is the distance of the pathtraveled by the wave from the antenna element ATp to theantenna element ARq through the scatterer STm. Dpmq is definedfrom the geometry of the intersection as

Dpmq = DTpm +DTR

mq , (24)

DTpm = DT

0m − (MT − 2p+ 1))δT2

cos(αTm − γT ), (25)

DTRmq = DTR

m0 − (MR − 2q + 1))δR2

cos(βTm − γR), (26)

where,

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DT0m = −hT1 / cos(αTm), (27)

DTRm0 = −(hT1 + hT2 +Dx)/ cos(βTm). (28)

Similarly the delays τ ′pnq are given by τ ′pnq = Dpnq/c0,where Dpnq is the distance of the path traveled by the wavefrom the antenna element ATp to the antenna element ARqthrough the scatterer SRn . Dpnq is given as

Dpnq = DRnq +DTR

pn , (29)

DTRpn = DTR

0n − (MT − 2p+ 1))δT2

cos(αRn − γT ), (30)

DRnq = DR

n0 − (MR − 2q + 1))δR2

cos(βRn − γR), (31)

whereDTR

0n = (hR1 + hR2 +Dy)/ sin(αRn ), (32)

DRn0 = hR2 / sin(βRn ). (33)

Likewise, the delays τ ′pkq are given by τ ′pkq = Dpkq/c0,where Dpkq is the distance of the path traveled by the wavefrom the antenna element ATp to the antenna element ARqthrough the scatterer SCk . Dpkq is given from the followingexpression as

Dpkq = DTpk +DTR

kq , (34)

DTpk = DT

0k − (MT − 2p+ 1))δT2

cos(αCk − γT ), (35)

DTRkq = DTR

k0 − (MR − 2q + 1))δR2

cos(βCk − γR), (36)

where

DT0k = DTx

k =

√(OTx − PScx)

2+ (OTy − PScy )

2 (37)

DTRk0 = DRx

k =

√(ORx − PScx)

2+ (ORy − PScy )

2, (38)

and where PScx,y are the points of the scatterers distributedin the triangle, OTx,y are the points of the Tx and OTx,y arethe points of Rx.

Finally, the propagation delays τ ′pmnq of the double bouncecomponent are calculated from τ ′pmnq = Dpmnq/c0, whereDpmnq is the total distance travelled from the ATp antennaelement to the ARq antenna element via the scatterers STm andSRn . Then Dpmnq is given by

Dpmnq = DTpm +DTR

mn +DRnq, (39)

where DTpm, DTR

mn and DRnq are given by (25), (23) and (31),

respectively.In all the partial transfer functions there is a squared multipli-cation factor [ddecayLOS , dTXm , dRXn , dCk , dDBmn ] that rep-resent the power decay of each multipath component coming

from each scatterer depending on the distance it has traveled.Moreover, the phases θn θm θk and θmn are independent andidentically distributed random variables uniformly distributedover [0, 2π). The symbols αTm, αRn and αCk indicate the AODswhile βTm, βRn and βCk indicate the AOAs. Moreover the γTand γR show the antenna tilt w.r.t. the x-axis at the TX and RX.The terms fTmax and fRmax are the maximum Doppler shiftsaffected by the movement of the TX and RX, respectively.

The calculation of the AOAs and AODs is based on theRiemann sum method (RSM) which is analyzed in [19]. Exactrelationships are derived for the AOAs and AODs that arebased on the geometry of the cross-junction model. The αTmaxand the αTmin are derived for every position of the TX and RX.The scatterers are assumed not to remain in a constant positionbetween packets transmitted, instead, they are redistributed inthe cluster following every new TX/RX position. The sameassumption applies for the αRmax and αRmin as,

αTm = αTmin +

∣∣αTmax + αTmin∣∣

M(m− 1/2) , (40)

for m = 1, . . . ,M and n = 1, . . . , N , where,

αRn = αRmin +

∣∣αRmax + αRmin∣∣

N(n− 1/2) , (41)

αTmax = π − arctan

(Dx ·Dy − hR1 ·

(hT1 + hT2

)Dx · hT1

), (42)

αTmin = π − arctan

(Dy

hT1

), (43)

αRmax = arctan

(Dy + hR1 + hR2

hT2

), (44)

αRmin = arctan

(Dy

hT2

). (45)

The AOAs for the single-bounce components can be derivedfrom the following expressions,

βTm = π + arctan(hR1 +Dy + hT1 · tan(αTm)

hT1 + hT2 +Dx), (46)

βRn =

π − arctan

(hR2 · tan(αRn )

tan(αRn ) · (Dx + hT2 )− (hR1 + hR2 +Dy)

).

(47)

For the double-bounce components, the RSM is used againto determine the αTm and βRn , with the only difference beingthe calculation of αTmin, βRmax and βRmin. The αTm and βRn aregiven by the (48) and (49) as,

αTm = αTmin +

∣∣αTmax + αTmin∣∣

M(m− 1/2) , (48)

βRn = βRmin +

∣∣βRmax + βRmin∣∣

N(n− 1/2) , (49)

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where m = 1, . . . ,M and n = 1, . . . , N . The αTmax is givenby (42) and the rest of the parameters are determined fromthe expressions below,

αTmin = π − arctan

(Dy

hT1

), (50)

βRmax = π − arctan

(hR2Dx

), (51)

βRmin = π − arctan

(Dy · hR2

Dx ·Dy − hT2 ·(hR1 + hR2

)) . (52)

Finally, we derive the exact geometry of the corner by usingcoordinates referring to the junction as point O(0, 0). PointsPT and PR are found by using straight line equations in orderto define the three points of the triangle. The front corner ofthe triangle (vertex) will always be at PCxy (−hT1 , hR2 ). Thenext two coordinates PT (x, y) and PR(x, y) are defined asthe points that can be found by the geometry using straightlines starting from the TX and the RX passing through thecorners of the side buildings, situated close to the TX andRX, and ending at the building walls at the opposite corner,respectively.

For each position a check should be made so that PT (x) <=hcmax and PR(y) <= hcmax. Each side of the triangle canhave maximum length hcmax in order to keep the cornercluster at a reasonable size. PT (y) and PR(x) are always staticand equal to hR2 and −hT1 , respectively.

Then by using PT (x, y), PR(x, y) and PC(x, y) we definea triangle in which we uniformly randomly distribute Kscatterers and together with the TX and RX we calculate theAOA and AOD that are used in the expressions mentionedbefore (13), (16), (22), (21), (35), (36) as,

αCk = π + arctan

(PSCk (y)−OT (y)

PSCk (x)−OT (x)

), (53)

and

βCk = π + arctan

(PSCk (y)−OR(y)

PSCk (x)−OR(x)

). (54)

where OTx,y and ORx,y are the points of the TX and RXposition respectively as defined in Section II and PSCk (x, y)are the points of each scatterer SCk for k = 1, 2, ...,K asaforementioned.

IV. NUMERICAL RESULTS

In the following part we present simulation results basedon parameters described below. With a carrier frequency fcof 5.9 GHz we get an approximate wavelength λ equal to50.8 mm. The TX and RX speeds are set to 10 m/s whichtranslates to 36 km/h and the directions of our moving termi-nals are φT = π/2 and φR = π.

The antenna orientations are γT = 0 and γR = π/2,respectively. Four elements were used for each antenna arrayat 1.5 m height from the ground and with a spacing of λ/2.Furthermore, the streets have a width of 20 m and distances

Fig. 2. The time variant Impulse Response H(τ ,t) for channel 1 whereelements p = q = 1

50 100 150 200−90

−80

−70

−60

−50

−40

−30

−20

−10

0

Combined distance of TX−junction−RX [m]

No

rma

lize

d C

ha

nn

el G

ain

[d

B]

Simulation

Reference Model

Fig. 3. Channel gains comparison for channel 1 where elements p = q = 1

to the left sides hT1 = hR1 = 15 m and to the right sideshT2 = hR2 = 5 m. The time sampling is set to ∆t = 2.5 msand the bandwidth was set to 240 MHz. Moreover the trianglethreshold hcmax in the corner was set to 5 m with K = 50scatterers randomly distributed inside the triangular plane. Theroad side clusters are composed of M = N = 70 scatterers.Our frequency was separated into 769 frequency samples andwe get 961 m maximum delay after the IFFT. We then simulatethe power-delay profiles (PDPs) of the simulated time-variantchannel transfer function. The PDPs are shown in Fig. 2, wherewe can clearly see the effect of LOS and can distinguish thecontribution from the corner cluster from the other MultipathComponents (MPCs) in the NLOS region, as it always comeswith a larger delay due to the geometry. It is worth mentioningthat the higher power seen at the end of the PDP (e.g., fordelays exceeding 800 m) is due to artifacts introduced by theinverse Fourier transform of the transfer functions.

The normalized channel gain of our simulation model isthen compared with the combined measurement based LOSand NLOS path-loss model from [21], which is validated in[22]. The reference power for each scatterer is then taken from[23], i.e., −5 dB for LOS and −84 + 24ηp for each scatteringcomponent, where ηp is the path-loss exponent that is assumed

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to be uniformly distributed as U [0, 3.5]dB. The comparison ofthe channel gains is presented in Fig. 3.

In this comparison, it can be seen that the simulation gainfits nicely to the validated reference model. Nevertheless, asmall difference can be spotted at the beginning of the line-of-sight, at approximately 30 m of combined distance fromTX to RX through the junction. This is due to the fact thatthe reference model does not take into account the LOS andsubsequently the diffraction that comes from the corner, whichshould make the transition smoother. Finally, after 100 metersa small difference can be noted between the two comparedgains, which is due to the second or higher order scatteringcomponents that are not present in the simulation in order toavoid the high increase in both theoretical and computationalcomplexity.

V. CONCLUSION

By starting with the T-Junction model a novel cross-junctionmodel for multiple-input multiple-output (MIMO) vehicle-to-vehicle (V2V) channel simulation has been derived. A newcluster is added at the corner of the street intersection based onthe experiences gained from the measurements that play a veryimportant role in cross-junction environments. Moreover, thewidth of each cluster varies with respect to the position of thetransmitter (TX) and receiver (RX). The power of each scatteris calculated from the measurement based model parameters.Finally, the proposed cross-junction simulation model appearsto following the measurements based reference channel model,that makes cross-junction model a very good candidate foranalyzing the V2V fading channel in four-way junctions inurban areas.

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