Short Paper: Performance Analysis of MIMO-BasedDecode-and-Forward Relaying VANETs

Bengi Aygün⇤, Alkan Soysal†, and Alexander M. Wyglinski⇤⇤Wireless Innovation Laboratory, Department of Electrical and Computer Engineering

Worcester Polytechnic Institute, Worcester, MA 01609-2280, USA† Department of Electrical and Electronics Engineering

Bahçeşehir University, Istanbul 34353, TurkeyEmail: {baygun, alexw}@wpi.edu, alkan.soysal@bahcesehir.edu.tr

Abstract—In this paper, we present a novel transceiver ar-chitecture for vehicular ad hoc networks (VANETs) employinga combination of decode-and-forward (DF) cooperative commu-nications and multiple-input multiple-output (MIMO) transmis-sion. To assess the performance of the proposed architecture,we have developed a geometric model that is applicable to highmobility environments, where each channel element consists ofa sum of complex harmonic exponentials. To assist with theperformance assessment, we derived the lower bound on the er-godic channel capacity for the DF scenario. We perform iterativealgorithms and provide the transmit covariance matrices whichpresent the certain lower bound for given power constraints.Simulation results show that allocated power over the spatialdimension converge to their optimum value and consequentlythe exact lower bound is obtained instead of getting sub-optimalachievable rates.

I. INTRODUCTION

At the core of any current intelligent transportation system(ITS) is some form of information connectivity to an externalnetwork, whether it is with another vehicle within the vicinityor a nearby roadside access point or base station. Givenrecent substantial research activities in the area of wirelessdata transmission, there is a significant opportunity to enableeven higher data rates and more robust information exchangesbetween vehicles and with roadside infrastructure. Such activ-ities have given rise to the concept of the vehicular ad hocnetwork (VANET) [1], and more recently the introduction ofMIMO-based VANETs, where multiple input-multiple-output(MIMO) techniques are used to increase capacity, data rates,and transmission robustness [2]-[3]. Such systems, coupledwith the opportunistic access of wireless spectrum [4]-[6],have the potential to facilitate large information exchangesin both vehicle-to-vehicle (V2V) and vehicle-to-infrastructure(V2I) scenarios in real-time. Such information exchangescan be used to enhance vehicular safety, as well as enablesemi- and fully-autonomous vehicles. Although there has beensubstantial research efforts being conducted on VANETs, thereare still several significant technical challenges that need to beaddressed, including the following:

• The network topology is time-varying since the distancesbetween the vehicular nodes can potentially change overdistance and time. Unstable network architecture bringssome difficulties to the designer to have sufficiently

accurate channel model for mobile environments [7].• Theoretical quantitative analysis of the proposed network

architecture needs to incorporate the time-varying dynam-ics of the operating environment in order to obtain anaccurate performance assessment.

• Architecture analysis should be performed rapidly sincethe channel parameters change very often on VANETs.Also, the relay node needs to decode and re-code thesignal without violating time synchronization in DF sce-narios.

In this paper, we propose a novel DF MIMO vehicle-to-vehicle (V2V) VANET architecture when the receivers haveperfect channel state information (CSI) and the transmit-ters have only covariance feedback. We perform full duplexmode communications with individual power constraints at thesource and relay. For the research presented in this paper, wehave assumed traffic scenarios where the vehicles are movingrelatively slowly, thus yielding block fading scenarios. Thus,we extend the geometrical channel model, which is robustto time-varying channels, by adapting the model presentedin [7]. Next, we quantitatively analyzed the lower bound onthe channel capacity by using the technique proposed in [9].Simulation results show that the iteration algorithm presentsthe transmit covariance matrices which gives the allocatedpower to each transmit antenna which satisfies lower bound.

The primary novel research contributions of this paper arethe following:

• We propose a novel MIMO-based DF VANET architec-ture that combines broadcast and multiple access links.

• We have derived a new geometrical model for MIMOrelay transmission based on [7] that increases the channelcapacity and reliability.

• We have devised a DF strategy that has not been em-ployed previously by VANETs since it allows the sourceand the relay to form a collaborative transmit antennaarray

• Using the presented power allocation algorithms on thetransmit antennas, we achieve the exact lower bound onthe capacity instead of struggling sub-optimal achievablerates.

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Fig. 1. Network architecture of DF VANETs.

The rest of the paper is organized as follows. In SectionII, we introduce proposed architecture for MIMO-based DFVANETs. In Section III, we present a derivation for thetheoretical lower bound on the channel capacity. Finally, wepresent several simulation results in Section IV.

A. NotationsIn this paper, upper (lower) boldface letters are used to

denote matrices (column vectors). The conjugate-transposeoperation is shown as (.)† and E[.] to express expectation withrespect to all random variables within the brackets. The matrixtrace and determinant are denoted as tr(.) and |.|, respectively.

II. PROPOSED ARCHITECTUREA. Architecture Overview

In the proposed DF MIMO VANET architecture, the sourcevehicle transmits data x

s

to both the relay and destinationvehicles. In turn, the relay vehicle receives x

s

, decodes it,re-encodes it as the relay data x

r

, and sends it to destinationvehicle. The coding scheme at the relay vehicle helps to correctfor any collusion on transmitted data.

The transmission from the source to the relay, as well asthe relay to the destination, uses the same carrier frequency(Fig. 1). This frequency architecture shows DF architectureprovides more reliable transmission than single link by usingsame frequency band [8]. By allocating sufficient power toeach transmission link within the network, the lower boundof the MIMO-based relaying VANETs can be analyzed at thephysical layer.

A highly dynamic VANET topology does not lend itself tostandard channel models. The effects of Doppler spread withrespect to relative velocities between nodes need to be detectedand fixed. Furthermore, a successful implementation must takeinto account of safety application at the application layer. Thisissue causes limits on latency and reliability of packet deliverywhich are strong challenges to designer.

B. Geometrical FrameworkThe source, relay, and destination vehicles are assumed to

possess instantaneous speeds of vs

, vr

, and vd

, with anglesto x-axis labeled as ↵

s

, ↵r

, and ↵d

, respectively (Fig. 2).In this paper, we consider block fading since the car speedsare assumed to be sufficiently low, e.g.i., rush-hour trafficscenarios. Therefore, Doppler effect on fading channel is stableon a block. We extend the geometrical model, which wasproposed in [7], such that the reference model is derived underthe non-line-of-sight (NLOS) conditions. The proposed three

rings scattering model is based on only local scattering sincehigh path loss dilutes the effects of remote scatterers. Thescatterers of source (relay and destination, respectively) areS

m

s

,m = 1, ...,M (Skr

, k = 1, ...,K and Sld

, l = 1, ..., L).The random phase shift for the source (relay and destination)is ✓(m)

s

(✓(k)r

and ✓(l)d

) which is i.i.d. random variable with auniform distribution over the interval [0, 2⇡).

Distances between the mobiles are Dxy

where the subscriptx and y refer the transmitter and receiver nodes, respectively.The angle of source to relay link and x-axis is �

s

and theangle of relay to destination link and x-axis is �

d

. The radiiof the scatterers of transmitters and receivers, R

s

, Rr

, andR

d

, are significantly smaller than the distances between thecorresponding nodes. The antenna spacings for each node aredefined as �

s

, �r

, and �d

, which are less than radii of thescatterers. The angles between antenna arrays and x-axis aredefined as �

s

, �r

, and �d

.

( )msf

sd

( )msS

sa sb

sg

sR

sd

dv

sv

rd

( )krS

( )ksrf =

( )krdf

rb

rR

dd

( )krdf

db

dR

, ,sr sr sD H x

Multiple Access Channel (MAC)

Broadcast Channel (BC)

, ,rd rd rD H x

, ,sd sd sD H x

da

( )ndS

dg

rv

ra

Fig. 2. System model of DF MIMO VANET based on geometrical approach.C. Channel Model

The channel between a transmitter and a receiver is repre-sented by H

xy

[n], whose dimensions are the number of receiveantennas times the number of transmitter antennas [9]. Thereceived signals at the relay and destination nodes for vehicularMIMO relay channels are defined as:

r[n] = Hsr

[n]xs

+ nr

, y[n]=Hsd

[n]xs

+Hrd

[n]xr

+ny

(1)

where the covariance matrices of the transmitted signals areQ

s

= E[xs

x†s

] and Qr

= E[xr

x†r

]. Noise vectors at the

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TABLE ITHE PARAMETERS DEFINES CHANNEL COEFFICIENTS BASED ON ANGLES AND DISTANCES

h

(11)

sr

[n]

h

(11)

rd

[n] h

(11)

sd

[n]

g

(mk)

sr

= a

(m)

s

b

(k)

r

c

(mk)

sr

g

(kl)

rd

= a

(k)

r

b

(l)

d

c

(kl)

rd

g

(ml)

sd

= a

(m)

s

b

(l)

d

c

(ml)

sd

�

(m)

s

= (2⇡/M) (m � 1/2) + ↵s

,m = 1, ...,M

�

(k)

rd

= (2⇡/K) (k � 1/2) + ↵r

, k = 1, ..., K

�

(m)

s

=(2⇡/M) (m � 1/2) + ↵s

,m = 1, ...,M

�

(k)

sr

= (2⇡/K) (k � 1/2) + ↵r

, k = 1, ..., K

�

(l)

d

= (2⇡/L) (l � 1/2) + ↵d

, l = 1, ..., L �

(l)

d

=(2⇡/L) (l � 1/2) + ↵d

, l = 1, ..., L

a

(m)

s

= e

j(⇡/�)�

s

cos(�

(m)

s

��s

)

a

(k)

r

= e

j(⇡/�)�

r

cos(�

(k)

r

��r

)

a

(m)

s

= e

j(⇡/�)�

s

cos(�

(m)

s

��s

)

b

(k)

r

= e

j(⇡/�)�

r

cos(�

(k)

sr

��r

)

b

(l)

d

= e

j(⇡/�)�

d

cos(�

(l)

rd

��d

)

b

(l)

d

= e

j(⇡/�)�

d

cos(�

(l)

d

��d

)

c

(mk)

sr

= e

j(2⇡/�){Rs

cos(�

(m)

s

��s

)�Rr

cos(�

(k)

sr

��s

)}c

(kl)

rd

= e

j(2⇡/�){Rr

cos(�

(k)

rd

��d

)�Rd

cos(�

(l)

d

��d

)}c

(ml)

sd

= e

j(2⇡/�){Rs

cos(�

(m)

s

)�Rd

cos(�

(l)

d

)}

✓

sr

= (�2⇡/�)(Rs

+ D

sr

+ R

r

) ✓

rd

= (�2⇡/�)(Rr

+ D

rd

+ R

d

)

✓

sd

= (�2⇡/�)(Rs

+ D

sd

+ R

d

)

f

(m)

s

= f

s

max

cos(�

(m)

s

� ↵s

)

f

(k)

rd

= f

r

max

cos(�

(k)

rd

� ↵r

)

f

(m)

s

= f

s

max

cos(�

(m)

s

� ↵s

)

f

(k)

sr

= f

r

max

cos(�

(k)

sr

� ↵r

)

f

(l)

d

= f

d

max

cos(�

(l)

d

� ↵d

) f

(l)

d

= f

d

max

cos(�

(l)

d

� ↵d

)

relay, nr

, and at the destination, ny

are zero-mean identitycovariance complex Gaussian random vectors. Although a 2⇥2MIMO model is presented in this paper, the channel modelcan be extended to any number of antenna array elements.Considering a three ring MIMO model for VANETs, the firstchannel element of H

xy

[n] for the finite number of scatterersis defined as [7]:

h

(11)sr

[n] =

1pMK

M,KX

m,k=1

g

(mk)sr

e

j

[

2⇡(

f

(m)

s

+f(k)sr

)

t+(

✓

(mk)

sr

+✓sr

)] (2)

h

(11)rd

[n] =

1pKN

K,NX

k,n=1

g

(kn)rd

e

j

h2⇡

⇣f

(k)

rd

+f(n)d

⌘t+

⇣✓

(kn)

rd

+✓rd

⌘i

(3)

h

(11)sd

[n]=

1pMN

M,NX

m,n=1

g

(mn)sd

e

j

h2⇡

⇣f

(m)

s

+f(n)d

⌘t+

⇣✓

(mn)

sd

+✓sd

⌘i

(4)

where fx

max

= v

x

/� is maximum Doppler frequency and �is the carrier’s wavelength [7]. The angle of departure of themth and kth transmitted waves are �(m)

s

and �(k)sr

at the sourceand the relay. The angle of arrival of the kth and lth receivedwaves are �(k)

rd

and �(l)d

at the relay and the destination. Theparameters in these equations are defined in Table I. The otherchannel elements are obtained by replacing a(p)

x

and b(p)y

withthe complex conjugates a(p)†

x

and b(p)†y

for h(22)xy

[n], a(p)x

witha

(p)†x

for h(12)xy

[n], b(p)y

with b(p)†x

for h(21)xy

[n] where p is mfor source, k for relay, and l for destination.

III. THEORETICAL LOWER BOUND ON THE CHANNELCAPACITY

A. Lower Bound AnalysisIn this section, we analyze the lower bound on the channel

capacity of MIMO VANETs in terms of mutual informationof the link from the source to relay and mutual information ofthe multiple access channel. When there is only covariance atthe transmitter, a lower bound on low-speed vehicular MIMOVANETs is shown as [9]:

C � Clower

= max

tr(Qs

)Ps

,tr(Qr

)Pr

min(I

mac

, I

sr

) (5)

I

mac

=E

h���I+Hsd

[n]Qs

H†sd

[n] +Hrd

[n]Qr

H†rd

[n]

���i

(6)

I

sr

= E

⇥log

��I+Hsr

[n]Qs

H†sr

[n]

��⇤ (7)

where the power constraints are tr(Qs

) Ps

and tr(Qr

) Pr

.

B. Power Allocation on TransmittersLower bound on MIMO-based Relay VANET includes

a max-min type optimization problem. Therefore, we havefound the values for the Q

s

and Qr

jointly in or-der to overcome this problem [10]. Using this solu-tion, which is elaborated in [9], we can subsequentlyobtain the result of the Lagrange derivation as E1 =E

h⇢

⇤H†sd

[n]D�1mac

Hsd

[n]+(1�⇢⇤)H†sr

[n]D�1sr

Hsr

[n]

i µ

s

I

and E2 = Eh⇢

⇤H†rd

[n]D�1mac

Hrd

[n]

i µ

r

I where ⇢⇤ is[0, 1], D

mac

and Dsr

are the expressions inside the deter-minant in (6) and (7), respectively. We perform the followingiterative algorithms to find optimum covariance matrices:

Qs

(u+ 1) =

E1(u)Qs(n)

tr(E1(u)Qs(u))P

s

(8)

Qr

(u+ 1) =

E2(u)Qr(u)

tr(E2(u)Qr(u))P

r

(9)

After running this algorithm for all ⇢ values for [0, 1], aminimization over ⇢ is applied in order to find the lowerbound. Simulation results prove that the algorithm convergesregardless of the initial points [9].

IV. SIMULATION RESULTS

A. Simulation SetupWe analyze the performance of proposed model numerically

using computer simulations written in MATLAB. The expecta-tion operator is calculated using Monte Carlo-type simulations.In simulation experiments, the power of the source and relaynodes, P

s

and Pr

, are set to be equal to 10dBm. The numbersof scatterers are located within the vicinity of each nodechosen as M = N = K = 40 for each node that has2⇥ 2 MIMO antennas. The angles between antenna spacingsand x-axis are �

s

= �

r

= �

d

= ⇡/2. The speeds of carsare changing in time between 6 m/s to 20 m/s where thewavelength is � = 0.051 m. The motion angle is chosen as↵

s

= ↵

r

= ↵

d

= ⇡ which means the nodes move on negativex-axis.

B. Results AnalysisThe channel matrices are obtained by using the channel

elements. By increasing iteration index, the power allocationsto the transmit directions converge their optimum values which

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2 4 62

3

4

5

6

7

8

iteration index

eig

en

valu

e

λ1Q

s

λ2Q

s

λ1Q

r

λ2Q

r

Fig. 3. Convergence of the eigenvalues of the source and relay transmitcovariance matrices for 2⇥2⇥2 MIMO VANETs. Eigenvalues of the transmitcovariance matrices indicate the allocated power on to transmit antennas.By increasing iteration index, the eigenvalues converge their optimum valueswhich gives the exact lower bound.

200400

600800

5

10

15

208.5

8.6

8.7

8.8

8.9

Initial Distance (m)Scatterer Radius (m)

Low

er

Bound (

bit/

s/H

z)

Fig. 4. Lower bound depending on scatterer radiuses and initial distances.By increasing initial distance, the lower bound decreases. Conversely, lowerbound increases by increasing scatterer radius.

gives the exact lower bound, regardless of the initial points asshown in Fig. 3. In this figure, only the eigenvalues of thecovariance matrices of source and relay nodes are shown byusing the fact that the eigenvalues of the covariance matrix givethe transmit power in the corresponding transmit direction.

Time-varying channel model is defined by immediate chan-nel elements depending on the geometrical parameters. InFig. 4, the changes on lower bound is shown based oninitial distances (D

sr

= D

rd

= D

sd

) and scatterer radiuses(R

r

= R

s

= R

d

). Since the longer distance causes higherinterference on the channel, the lower bound decreases byincreasing initial distance. Moreover, increased scatterer ra-dius transform the channel behavior from interfered channelto multi-path channel. Therefore, lower bound increases byincreased scatterer radius.

In Fig. 5, the effects of Doppler frequency(fs

max

) andantenna spacing (�

s

) is shown. Since Doppler effect causesthe distortion on channel, lower bound decreases by increasingmaximum Doppler frequency value. Conversely, lower boundincreases when the antennas move away each other since themitigation of interference effect.

V. CONCLUSIONIn this paper, we have presented a novel full-duplex MIMO

VANET architecture employed in DF scenarios when thetransmitters have partial CSI and the receivers have perfectCSI. A geometrical channel model that is applicable for time

0.51

1.52

200300

400500

6008.5

8.6

8.7

8.8

8.9

δs/λf

smax

(Hz)

Lo

we

r B

ou

nd

(b

it/s/

Hz)

Fig. 5. Lower bound depending on antenna spacing (�s/�) and maximumDoppler frequency (fs

max

). Lower bound increases by increasing antennaspacing since the effect of interference reduces. By increasing Dopplerfrequency, lower bound decreases since the rised effect of scattering.

varying channel is used. We present the lower bound and theiterative algorithms that give the optimum power allocation onthe transmit antennas. The power allocation over the spatialdimension of the channel has a significant impact on theperformance.

For our ongoing work, we will extend our approach to fasttime-varying MIMO VANETs and explore how this proposedarchitecture will perform within an urban area scenario withobstacles and crossroads. Furthermore, vehicular dynamicspectrum access (VDSA) will be combined with the currentresults to find an approach to both power and spectrumallocation optimization.

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