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MINISTRY OF EDUCATION ANDTRAINING
HANOIUNIVERSITY OF SC IENC EANDTECH NOLOGY

NGUYENHO NG AN H

LOCATION-AWAREMULTIPATHBASEDCHANNELPREDICTIONFORNEXTGE
NERATION WIRELESSCOMMUNICATION SYS
TEMS

DOCTORALDISSERTATIONOFTELECO
MMUNICATIONSENGINEERING

Hanoi−202
2


MINISTRYOFEDUCATION
ANDTRAININGHANOIUNIVERSITYOF SC IENC E
ANDTECH NOLOGY

NGUYENHO NG AN H

LOCATION-AWAREMULTIPATHBASEDCHANNELPREDICTIONFORNEXTGE
NERATION WIRELESSCOMMUNICATION SYS
TEMS
Major:TelecommunicationEngineeri
ngCode:9 5 2 0 2 0 8

DOCTORALDISSERTATIONOFTELECO
MMUNICATIONSENGINEERING
SUPERVISORS:


1.Assoc.Prof.Nguyen
VanKhang2.Assoc.P r o f . K l a u s
Witrisal


DECLARATIONOFAUTHORSHIP
I declare that I have authored this thesis independently, that I have not used
otherthan the declared sources/resources, and that I have explicitly indicated all
materialwhichhavebeenquotedeitherliterallyorbycontentfromthesourcesused.
Hanoi,//
2022PhDStude
nt

NguyenHongAnh

SUPERVISORS

Assoc.Prof.NguyenV a n K h a n g

i


ACKNOWLEDGEMENT
Thisd i s s e r t a t i o n w a s w r i t t e n d u r i n g m y d o c t o r a l c o u r s e a t S c h o o l o f E l e
c t r o n i c s andTelecommunications(SET),HanoiUniversityofScienceandTechnology(HUST).I
wasalsoreceivedtremendoussupportsfromtheSignalProcessingandSpeechCom-munication Laboratory (SPSC),
Graz
University
of
Technology

(TUGraz),
Austria.
Iamsogratefulforallpeoplewhoalwayssupportandencouragemeforcompletingthisstudy.
First, I would like to express my sincere gratitude to my advisors for their
effectiveguidance, their patience, continuous support and encouragement, and their
immenseknowledge.
I would like to thank all members of SPSC, TUGraz.They have been very kind
andsupportived u r i n g m y v i s i t s t o G r a z . They h e l p e d m e a l o t w i t h t h e i r d e e p u n d e
r s t a n d - ing of the group’s topics and researches.I also would like to thank all my
colleagues inSET, HUST. They have always helped me with the research process and
given helpfuladviceformetoovercomemyowndifficulties.
DuringmyPh.Dcourse,IhavereceivedmanysupportsfromtheManagementBoardof School of
Electronics and Telecommunications. Thanks to my employer, HUST forall necessary support and
encouragement during my Ph.D journey. I am also gratefulto Vietnam’s Program
911,
for
their
generous
financial
support.Last
but
not
least,
IwouldliketothankOeADandSPSCforgivingfundsformyresearchvisitstoGraz.
Special thanks to my family and relatives for their never-ending support and sacrifice.
Hanoi,2 0 2 2
Ph.D.Student

2



CONTENTS

DECLARATIONO F A U T H O R S H I P ...........................................................i
ACKNOWLEDGEMENT............................................................................................ii
CONTENTS............................................................................................................vi
SYMBOLS........................................................................................................................vi
SYMBOLS........................................................................................................................ix
LISTOFTABLES...............................................................................................xiii
LISTO F F I G U R E S ................................................................................................xiv
CHAPTER1 . INTRODUCTION ANDMOTIVATION......................1
1.1. Literaturereview.................................................................................................1
1.1.1. Location-awarenessinmmWavebeamforming..................................................2
1.1.2. Location-awarenessinvehicularcommunications............................................3
1.1.3. Location-awarenessinadaptivemobilecommunications,scheduling androuting
4
1.1.4. Channelqualitymetric(CQM)...................................................................5
1.2. Challengesandmotivations................................................................................6
1.3. Purposesandobjectives.....................................................................................6
1.4. Researchhypotheses............................................................................................7
1.4.1. Towards a site-specificradio propagation modeling......................................7
1.4.2. Towardsa l a r g e - s c a l e p r e d i c t i n g o f r a d i o c h a n n e l s t a t i s t i c s ......7
1.4.3. Towardsasideinformation-aidedsingle-anchormultipath-basedlocalization7
1.5. Contributionsa n d o u t l i n e ..................................................................................8
CHAPTER2 . S I G N A L A N D S Y S T E M M O D E L S ..............................9
2.1. Introduction.........................................................................................................9
2.2. Systemm o d e l .........................................................................................................10
2.2.1. Representationofreflectorsusingvirtualanchors(VAs)...............................10
2.2.2. Floorplan/environmentinformationforlocation-awareapplications. .13
2.3. Hybridgeometric/stochasticsignalmodel.....................................................13

2.4. Channelqualityindicators..............................................................................15
2.4.1. SMCamplitude..........................................................................................15
2.4.2. Signal-to-interference-plus-noiseratio(SINR)...............................................16
2.4.3. ChannelC a p a c i t y .....................................................................................17


2.4.4. Positione r r o r b o u n d ( P E B ) ....................................................................19
2.5. Discussion.................................................................................................................20
2.5.1. Energyc a p t u r e .........................................................................................20
2.5.2. ContributionofindividualSMCsintheoverallchannelcapacity.................21
2.6. Chapterc o n c l u s i o n s ................................................................................27
CHAPTER3.G A U S S I A N P R O C E S S R E G R E S S I O N F O R S M C A M P L I T
U D E S 28
3.1. RelatedWork.....................................................................................................28
3.2. SMCpropagationmodel....................................................................................29
3.3. GPModeling(GPM)oftheSMCAmplitudes...................................................30
3.4. GPR...................................................................................................................31
3.4.1. GPM o d e l .......................................................................................................31
3.4.2. Prediction....................................................................................................32
3.4.3. Learning.............................................................................................................32
3.4.4. Evaluatethequalityofprediction..............................................................33
3.5. Experimenta n d r e s u l t .....................................................................................34
3.5.1. Experiment..................................................................................................34
3.5.2. Measurementp r e - p r o c e s s i n g ...................................................34
3.5.3. GPRofSMCAmplitudes............................................................................35
3.5.4. GPRo f S M C P h a s e s .....................................................................................41
3.6. Chapterc o n c l u s i o n s ................................................................................44
CHAPTER

4.R A D I O E N V I R O N M E N T M A P F O R S I T E -


S P E C I F I C PROPAGATIONMODELING
45
4.1. Relatedwork......................................................................................................45
4.2. Radioenvironmentmap(REM)usingGaussianProcessregression(GPR)

47

4.3. SMCamplitudes...............................................................................................47
4.4. SINR..........................................................................................................................50
4.5. Positione rrorbo un d........................................................................................52
4.6. Chapterc o n c l u s i o n s ................................................................................55
CHAPTER5 . APPLICATIONOFGPRENABLEDREMSTOROBUSTPOSITIONING
.......................................................................................................................................
57
5.1. Relatedwork......................................................................................................57


5.2. Problemformulation.........................................................................................59
5.3. Proposeda l g o r i t h m .........................................................................................59
5.4. Result................................................................................................................ 61
5.5. Chapterconclusions................................................................................................64
PUBLICATIONS.........................................................................................................67
BIBLIOGRAPHY........................................................................................................68
APPENDICES..............................................................................................................81
A. Descriptionofchannelmeasurementcampaigns...............................................81
A.1. Measurementcampaign1.............................................................................81
A.2. Measurementcampaign2.............................................................................82
B. Varianceofν k....................................................................................................... 88
C. PredictedVariance.............................................................................................89



ABBREVIATIONS

No. Abbreviatio Meaning
n
1
ACF
AutoCorrelationF unction
2

ADC

Analog-to-DigitalConverter

3

AOA

Angle-Of-Arrival

4

AOD

Angle-Of-Departure

5

AWGN


AdditiveWhiteGaussianNoise

6

BER

BitErrorRate

7

BF

BeamForming

8

BS

BaseStation

9

CDF

CumulativeD istributionF unction

10

CIR


ChannelImpulseResponse

11

CRLB

CramerRaoLowerBound

12

CQM

ChannelQualityMetric

13

CSI

ChannelStateInformation

14

DM

DiffuseMultipath

15

DMC


DiffuseMultipathComponent

16

EC

EnergyCapture

17

ECC

EuropeanCommunicationsCommittee

18

EFIM

EquivalentFisherInformationMatrix

19

EPB

EastPlasterBoard

20

FCC


FederalCommunicationsCommission

21

FIM

FisherInformationMatrix

22

GNSS

GlobalNavigationSatelliteSystem

23

GP

GaussianProcess

24

GPM

GaussianProcessModel

25

GPR


GaussianProcessRegression

26

GPS

GlobalPositioningSystem

27

GSCM

Geometry-basedStochasticChannelModel

28

IoT

Internet-of-Thing

29

LIDAR

LightDetectionAndRanging


30
31


LLHF
M2M

LogL ikeliHoodF unction
Machine-to-Machine

32

MAC

MediaAccessControl

33

MIMO

MassiveInputMassiveOutput

34

MINT

Multipath-assistedIndoorNavigationandTracking

35

ML

MaximumLikelihood


36

MMSE

MinimumMeanSquareError

37

MPC

MultiPathComponent

38

MRC

MaximalRatioCombining

39

MSLL

MeanSquareLogLoss

40

NLOS

Non-Line-Of-Sight


41

NGW

NorthGlassWindow

42

LOS

Line-Of-Sight

43

OFDM

OrthogonalFrequencyDivisionMultiplexing

44

PA

PhysicalAnchor

45

PAM

PulseAmplitudeModulation


46

PDF

ProbabilityD istributionF unction

47

PDP

PowerDelayProfile

48

PHY

PHYsicalLayerProtocol

49

PEB

PositionErrorBound

50

QAM

QuadratureAmplitudeModulation


51

REM

RadioEnvironmentMap

52

RF

RadioFrequency

53

RFID

RadioFrequencyIDentification

54

RRC

RootRaisedCosine

55

RSS

ReceivedSignalStrength


56

RX

Receiver

57

RV

RandomVariable

58

SALMA

Single-AnchorLocalizationsystemusingMultipathAssistance

59

SEP

SymbolErrorProbability

60

SIMO

Single-Input-Multiple-Output


61

SINR

Signal-to-Interference-plus-NoiseR atio

62

SLAM

SimultaneousLocalizationAndMapping

63

SMC

SpecularMultipathComponent

64

SMSE

StandardMeanSquareError


65
66

SNR

SW

Signal-to-NoiseRatio
SouthWall

67

ToF

Time-of-Flight

68

TX

Transmitter

69

UE

UserEquipment

70

URLLC

Ultra-ReliableLow-LatencyCommunication

71


UWB

UltraWideBand

72

VA

VirtualAnchor

73

WW

WestWall


SYMBOLS

No. Symbol

Meaning

1

a1

PositionofthePA


2

ak

Positionofthek-thVA

3

a

GPcorrelationangle

4

c

Speedo f l i g h t

5

C0,Ck,Call

6

cGP

Capacitíeo f t h e w h o l e c h a n n e l , o f i n d i v i d u a l l i n k a n d o f a l
lthe
SMClinkstogether
GPcovariance


7
8

C


CovarianceofthenoisevectortakesintoaccounttheeffectofDM

9

dk

Distancetothek-thVA

10

d0

Referencedistance

11

d

Transmittedsymbol

12

D



Covarianceofnoisevector

Database

13

D

Databasefor t e st points

14

Es

Energyofthetransmittedsymbol

15

fc

Carrierfrequency

16

GP

GaussianProcessmodel


17

Channelimpulseresponse

18

h(t)


19

hk

Averagechannelgainafterprojectionontothepulseshiftedbyτ k

20

h

Vectorcontaining channel gainsfrom projecting ontodeterministic
shiftedpulses

21

i

sampletimeindex

22


I

Identitymatrix

23



FisherInformationMatrix

24

Jp

EquivalentFisherInformationMatrix

25

Jr

Rangingdirectionmatrix

26

Kν(t)

Autocorrelationfunction ofν(t)

27


k

VAorSMCindex

28

K

TotalnumberofSMCs

Vectorsampledfromthefilteredimpulseresponse


29

K,k

Covariancematrix,vector

30

L

Likelihoodfunction

31

Noisepower

32


N0
p,p′

33

P

PEB

34

p∗

PositionoftestpointEst

35

p

imatedlocation

36

ˆ

CIRatagentpositionpafterfilteringatthereceiverFilteredC

37


r(t;p)

IRinvectornotation

38

rS ν(τ

PDP

39

)

TransmittedUWBpulseEstimatedP

40

s(t)Sˆ

DP

41

k

Agentposition

SINRofthek-thMPCs


ν(.)SI

42

NRk

Shiftedpulseinvectorform

43

s(τk(p))
T sT p

Pulse

44

trw

durationEffective pulse

45

(t)

durationTraceofamatrix

46

wk


Noisesignal

47

x

Noisecomponentafterprojectionontothepulseshiftedbyτ k

48

x

Abscissao f S M C a m p l i t u d e

49

x

Vectorofabscissasof SMCamplitudes

50

˜

VectoroftheresidualofabscissasofSMCamplitudesaccounting
fortheSMCvarianceandtheuncertaintyofphases

51


ak,b k

Realandimaginarypartsofe jφk

52

z

Decisionvariable

53

αk

Amplitudeofthek-thMPC

54

αˆ

EstimatedSMCcomplexamplitude

55

β

56

βabs,β ph


Effectivebandwidthoftheenergy-normalizedtransmitpulse

k

GPmeanfortheabsolutevalueandphaseofthek-thSMCampli-tude
Diracdeltafunction

δ(t)
57

δi,j,δ(∥p−p ∥)Kroneckerdeltafunction

58
59

ϵ

Measurementnoise

60

Γ(.)

Reflectioncoefficien
t




61


γ(.)

Thec o m b i n e d a n g l e dependenceoftheantennapatternandthe
reflectioncoefficient,a.k.a.the normalized SMCamplitude

62

λk

Langrangemultiplier

63

Λ

SMCamplitude’svariancediagonalmatrix

64

µGP

GPmean

65

µ

VectorofSMCamplitudeexpectedmeanobtainedvia.G P R


66

νˆ

EstimatedDM

67

νk

DMafterprojectionontothepulseshiftedbyτ k

68

ν(t)

Impulser e s p o n s e o f D M

69



Setofmeasuredagentpositions

70

ϕk

Directionanglew.r.tthek-thVA


71

Π⊥S(τ)

Orthogonalcomplementprojectiononthesubspacespannedbythecolu
mnofS(τ)

72

ψ

AbscissaofthenormalizedMPCamplitude

73

Φ

SMCamplitude’sphasediagonalmatrix

74

σ

StandarddeviationoftheabscissaofthenormalizedMPCampl
itude

ν

75


ph

StandarddeviationofthephaseofthenormalizedMPCamplitude

76

σ
σ

77

σn

Standarddeviationofnoise

78

σν

StandarddeviationaccountingforDMC

79

σϵ

Standarddeviationofmeasurementnoise

80

τk


Timearrival/delayforthek-thMPC

81

τ

Delay

82

τˆk

Estimateddelayw.r.tthek-thVA

83

θ

GPhyper-parameters

85

φk

Phaseofthek-thSMCamplitude

86

ζ


PhaseofthenormalizedMPCamplitude

87

E{.}

Expectationoperator

88

V{.}

Varianceoperator

StandarddeviationoftheGPcorrelationkernel

89



(1)

w.r.t.PA1

90

∗(2)

w.r.t.PA2


91
92

(.)∗


Complexconjugateoperator
Convolutionoperator


93

∥.∥

Frobeniusnorm

94

⟨.⟩

Innerp r o d u c t

95

∗abs

*oftheabscissaofthenormalizedMPCamplitude

96


∗ph

*ofthephaseofthenormalizedMPCamplitude

97

∗H

Hermitiantranspose


LISTOFTABLES

2.1 EC,Goodness-of-Fit,SINRforexampleMPCs...................................................23
3.1 Experiments e t u p ............................................................................................34
3.2 ParametersoftheGPmodelfortheabsolutevalueoftheSMCamplitudes.363.3
Predictionq u a l i t y ............................................................................................38
3.4 ErrorpercentageofthepowerpredictionofSMCs...............................................40


LISTOFFIGURES

2.1 IllustrationofmultipathgeometryusingVAsfortransmissionbetween
aPAandamobileagentwithexactfloorplaninformation, a sseen in
[50,Fig.1 ] . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

2.2 IllustrationoftheVAsforthePAandanagentwithPDFp(VA)and

p(agent),respectively,asseenin[51,Figure1.1].T h e VAfalserepresents
afalsedetectionofVA. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3
Floorplanoftheevaluationscenario .. . . . . . . . . . . . . . . . . . . .
2.4
ECofindividualSMC .. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5
ECvs.n u m b e r ofvisibleVAs. . . . . . . . . . . . . . . . . . . . . . . . .
2.6
CDFofchannelcapacityofdifferentchannelcomponents. . . . . . . . . .

12
14
21
22
24

3.1
GPregressionforSMCamplitude. . . . . . . . . . . . . . . . . . . . . . .
3.2
GPpredictionforSMCamplitude. . . . . . . . . . . . . . . . . . . . . . .
3.3 EstimatedSMC am plit ud e c om p ar ed t omea sure men tand G Pst at isti cs .
.
3.4
GPregressionforSMCphases. . . . . . . . . . . . . . . . . . . . . . . . .
3.5
GPpredictionforSMCphases. . . . . . . . . . . . . . . . . . . . . . . . .

37
39

41
42
43

4.1
4.1
4.1
4.2
4.2
4.3
4.3
4.3
4.4

GPRonSMCamplitudes .. . . . . . . . . . . . . . . . . . . . . . . . . .
GPRonSMCamplitudes (cont.) .. . . . . . . . . . . . . . . . . . . . . .
GPRonSMCamplitudes (cont.) .. . . . . . . . . . . . . . . . . . . . . .
PredictedSMCamplitudes.. . . . . . . . . . . . . . . . . . . . . . . . . .
PredictedSMCamplitudes(cont.).. . . . . . . . . . . . . . . . . . . . . .
GPpredictionofSINRforthewholeFP. . . . . . . . . . . . . . . . . . .
GPpredictionofSINRforthewholeFP(cont.).. . . . . . . . . . . . . .
GPpredictionofSINRforthewholeFP(cont.).. . . . . . . . . . . . . .
GPpredictedPEB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48
49
50
51
52
53

54
55
56

5.1
5.2
5.3
A.1
A.2
A.3
A.4
A.5

CDFoflocalizationerrors.. . . . . . . . . . . . . . . . . . . . . . . . . .
LLHFvaluesatevaluationpoints. . . . . . . . . . . . . . . . . . . . . . .
CDFoflocalizationerrors.. . . . . . . . . . . . . . . . . . . . . . . . . .
MINTmeasurementscenario.. . . . . . . . . . . . . . . . . . . . . . . . .
Photoofcorridorscenario.. . . . . . . . . . . . . . . . . . . . . . . . . .
Floorplanoftheevaluationscenario .. . . . . . . . . . . . . . . . . . . .
Equipmentusedformeasurements.. . . . . . . . . . . . . . . . . . . . . .
Calibrationsetupfortimedomainmeasurements .. . . . . . . . . . . . .

62
63
63
83
84
85
86
87



CHAPTER1INTRODUCT
IONANDMOTIVATION
1.1. Literaturereview
5G and beyond-5G will be characterized by a wide variety of use cases, as well
asorders-of-magnitude increases in mobile data volume per area, number of
connecteddevices, and typical user data rate, all compared to current mobile
communicationsystems [1]. It is visioned that context information in general and
location informationin particular can complement both traditional and disruptive
technologies in addressingseveralofthechallengesin5Gandbeyond-5Gnetworks.
A majority of 5G devices will be able to rely on ubiquitous location
awareness,supported through several technological developments: a multitude of
global naviga-tion satellite systems (GNSS) are being rolled out, complementing the
current globalpositioning system (GPS). Combined with ground support systems and
multiband op-eration, these systems aim to offer location accuracies around 1 m in
open sky.Inscenarios where GNSS is weak or unavailable (in urban canyons or
indoors), otherlocal radio-based technologies such as ultrawideband (UWB),
Bluetooth, ZigBee, andradio frequency identification (RFID), will complement
current
Wi-Fi-based
positioning.T o g e t h e r , theywillalsoresultinsubmeteraccuracy.
Accuratelocationinformationcanbeutilizedacrossalllayersofthecommunicationprotocol stack
[2] to improve the network performance.At higher layers, locationinformation is often employed
directly in natural applications, such as location-awareinformation delivery [3], or
location-aware traffic-related services [4]. At lower layers,i.e., PHY, MAC, network and transport
layers,
a
channel
quality

metric
(CQM)
mapsbetweenachannelperformanceindicatorandthepositionisoftenused.T h e n atti
met, when the user position is predicted, from the CQM, channel qualities at new
positioncanb e e s t i m a t e d b e f or e t h e u se r a c t u a l l y g oe st h e r e . Certains y st em p a r a m e
t e r s uc h asp o w e r , m o d u l a t i o n t y p e , e t c c a n b e a d j u s t e d t o t a i l o r t o t h e c h a n n
e l c o n d i t i o n a t thenewposition.
In this section, we will start by investigating certain researches in various applications, followed by discussing about CQM and a few predictive engines that
facilitatethe mapping of channel quality throughout the environment.Firstly, locationawaremmWave beamforming will be considered, because mmWave is one of the five
disruptivetechnologies that enable 5G network [1] and mmWave beamforming is a
challenge.Sec1


ondly,vehicularcommunication,inwhichsensordatabutnotlimitedtoareexchanged,isdiscusse
d,becausefullyautonomousvehicleisalsoavisionof5Gandbeyond-5G

2


systems.Thirdly,previousresearchesonwirelesscommunicationlocationawarenessareexplored.

1.1.1.Location-awarenessinmmWavebeamforming
Multiple-Input Multiple-Output (MIMO) system has the advantage of beamsteering/beamforming, which becomes necessary for mmWave signal to compensate for
thechannelattenuation.Fortunately,thesmallwavelengthatthisfrequencybandallowsmany antenna elements to be
packed and their radiation patterns to be combined.Nevertheless, that beamforming
gain cannot be easily exploited because the discoveryprocess is complex, particularly
in systems that use one RF front per side.The one-look limitation of analog
beamforming
forces
both

the
base
station
and
user
equipmenttosteertheirantennabeamsindifferentdirectionstoestablishtheantenn
alock-on.
Digital beamforming, on the other hand, would offer more flexibility in
directionalcell search methods where users "has access to digital samples from all
antenna ele-ments" [5]; nevertheless, the number of RF front ends required becomes
costly, and itwouldnotbepracticalfortheuserequipment.
In contrast, analog beamforming, although limited due to its inherent ‘one-look direction’, offers advantages because it uses a single RF front-end with reduced
cost,complexity, and power consumption. Thus, there is increasing interest in analog
beam-forming in mmW wireless systems used alone or in combination with digital precodinginahybridsolution[6],
[7].
One approach not yet fully explored utilizes the site-specific propagation characteristics in which the system is deployed.This knowledge can be exploited at the
basestation in the form of a database linked to the position of the user equipment [8].
Thedatabase measured at a large number of points in the area is given can be used
tosimulate the channels generated via. ray-tracing. From the predicted channel, the
bestorientationofbasestationandtheuserequipmentarethendeduced.
In [9], a ray-tracing tool is used, in which not only direct and reflected rays but
alsoscattered rays are simulated. Moreover, the authors proposed a simpler
beamformingschemei n w h i c h t h e a n t e n n a s a r e d i r e c t e d t o w a r d a f e w d o m i n a
n t p a t h s . B e c a u s e , it is observed that the mmWave channel is much simpler than the usual radio
signalchannelwhere"aLine-Of-Sight(LOS)orquasi-LOSchannelwithafewdominantpathclusters and
arelativelylowdensemulitpathcomponent"[9](MPC)arepresented.Forexamplethebeamcouldbesteeredtowardthefourstrongest
paths simulatenously toexploit the intrinsic space diversity of the multipath channel. In the
case with abruptchannel changes,e.g.,human blockage, from the stored database, the
beam(s)
couldberearrangedquicklybyrecruitingothernonblockeddominantpaths.



Nevertheless, in [10], a low-complexity beamforming for moving vehicle with the
helpoflocationinformationis proposed.Theuser(train)is assumedto bemoved inat
rack,



×