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o a T , y ti s r e v i n U g n u G g n a h C g n i r e e n i g n E l a c i r t c e l E f o t n e m t r a p e
D -yuan,Taiwan,ROC
: s d r o w y e
K OFDM, Channe lesitmaiton, Residua ltimingerror.
t c a r t s b
A . Aftercompleting thetiming synchronization in thereceiver ,thereisstil ltheproblem of . r o r r e g n i m i t l a u d i s e
r Mos tofpapers do no tdiscuss theeffec tofresidua ltiming error on channe l . n o i t a m i t s
e So,t hispaperfocusontheeffectsofsevera lcommonchanne lestimationmethodswhen . m e t s y s M D F O n i d e t s i x e r o r r e g n i m it l a u d i s e r e h t n o it c u d o r t n I , n o i s s i m s n a r t s s e l e r i w e h t n
I thet ransmittedsignalsarei nfluencedbychannels ,resulitngi nsigna l I . n o i t r o t s i
d t’s importan t to have an accurate channe l estimation to determine the equalizer n o i s i v i d y c n e u q e r f l a n o g o h t r o n i s l a n g i s d e t r o t s i d e h t e t a s n e p m o c o t d n a s t n e i c i f f e o c i t l u
m plexing(OFDM)system. Except et h problemofchanne lestimaiton, ti alsoexists theproblem f
o timing synchronization a tthe receiver .However ,when the timing synchronization isdone ,the n a m r o f r e p e h t t c e f f a l l i w t i d n a s t s i x e l li t s r o r r e g n i m i t l a u d i s e
r ceofchanne lestimation.
y l e t a m i x o r p p a s i l o b m y s M D F O e n o n i l e n n a h c e h t t a h t s e m u s s a t i , l e n n a h c t n a i r a v e m i t e h t n I o w t s e r i u q e r y l l a r e n e g t o l i p e h t g n i s u e s n o p s e r y c n e u q e r f l e n n a h c e h t f o n o i t a m it s e e h T . t n a t s n o c n a h c e h t s n i a t b o n e t f o t i , t s r i F . s p e t
s ne lfrequency response on thepilo tsubcarriers .Generally ,the a t a d n o e s n o p s e r y c n e u q e r f l e n n a h c e l o h w e h t , d n o c e S . n o it a l u c l a c n i d e t p o d a s i d o h t e m S L n o m m o c e h t , p e t s s i h t n I . s r e i r r a c b u s t o l i p n o s e s n o p s e r l e n n a h c e h t y b d e n i a t b o e b n a c s r e i r r a c b u s e
m thodsareshownasbelow :one-dimensionall ineari nterpolation[ 1] ,DFT-based[ 2,3,4] ,LSmethod [ 65, ] ,andothermethods[7] .Int hispaper,t hecomb-typearrangementi sused .Int hesecondchapter ,
n a h c t n e r e f f i d n o r o r r e g n i m i t l a u d i s e r f o e c n e u l f n i e h
t ne lestimation wil lbe discussed. The third . n o i s u l c n o c e h t s i t i , y l l a n i F . t l u s e r n o i t a l u m i s s i r e t p a h c l a u d is e
R Timing ErrorIn lfuenceo fChanne lEs itma iton e
R isdua lTi Eme rror
Figure1 .Principleoft het imingsynchronization. o w t n o i t n e m l l i w t
I aspects oftimingsynchronization. Two situationsareshown in figure1 .Ifthe e h t f o n o i t i s o p t r a t
s frameisbehindtheCParea .TheISIwould occursand theorthogonalityofthe r e p a p s i h t n i n o it a u ti s s i h t s s u c s i d t ’ n o d e w , o S . d e b r u t s i d e b l l i w m e t s y
s .In this paper ,we only
s t c e f f e e h t r e d i s n o c y l n o e w , n o i t c e s t x e n n I . a e r a P C e h t n i h t i w e m a r f f o n o i t i s o p t r a t s e h t r e d i s n o c y c n e u q e r f r e i r r a c d n a e s i o n s a h c u s , s t c e f f e r e h t o f o s s e l d r a g e r , r o r r e g n i m i t l a u d i s e r d n a l e n n a h c f o .t e s f f
o Assumedi nOFDMsystem,t heFFTpointsi sN,t heGuardbandareahasNvcsubcarriers .So ,
s n i a t n o c a t a d e c i t c a r p d e tt i m s n a r t e h
t N-Nv csubcarriers .Npisthe tota lnumberof pilo tsubcarriers
d n a , ) s r e i r r a c b u s t o l i p l a u t r i v e h t g n i d u l c n i
e h t r e d i s n o c y l n o d n a t n a t s n o c y l e t a m i x o r p p a s i l o b m y s M D F O e n o n i l e n n a h c e h t t a h t e m u s s a
e m i t n i l a n g i s d e v i e c e r e h t , P C g n i v o m e r r e t f A . r o r r e g n i m i t l a u d i s e r e h t t u o h t i w t c e f f e l e n n a h c
: s a n e t t i r w e b n a c n i a m o d
y[n]=x[n]⊗h[n]�n=0,1,2,3,…,N-1 , ( 1)
e r e h
w x[n] and h[n]aretransmitted signa land channe limpulseresponsein timedomain .⊗ isthe .
n o i t a r e p o n o i t u l o v n o
c Considering the residua l itming error effect ,the received signa lcan be :
d e s s e r p x e
n ( ( [ y = ] n [ d
y -nd))N], ( 2)
( ( e r e h
w n-nd))Nistheremainderofthe(n-nd)divided byN. Andndisthepositiveintegerwhichis
r o f T F F e h t g n i o d r e t f A . s t n i o p r o r r e e m i t l a u d i s e
r y[n]andyd[n] .Therelationshipbetweeny[n]and
yd[n]areasfollows:
] [ ] [ ]
[ ] [ ]
[ ]
[k Y k e 2 / X k H k e 2 / H k H k
Yd = −j πkn N = −j πknd N = d , )( 3
e r e h
w X[k] and H[k] are the transmtited signa land channe lfrequency response in the frequency .
n i a m o
d Hd[k]canbeexpressedas :
N k n j
d k H k e d
H [ ]= [ ] − 2π /
, ( 4)
, ) 4 ( m o r
F Hd[k] is thephase effec tof the channe land residua ltiming errormixed together .After
, T F F I g n i o
d hd[n]=h[((n-nd))N]=h[n-nd]isobtained .It’sshowedt ha thd[n]i st heh[n]whichdelaysnd
s i y a l e d m u m i x a m l e n n a h c e h t , m e t s y s M D F O n i r o r r e g n i m i t l a u d i s e r s t s i x e e r e h t f i , o S . s t n i o p
.r e v i e c e r e h t r o f y a l e d m u m i x a m l e n n a h c e c it c a r p e h t n a h t r e t a e r g
g n i m i T l a u d is e R f o e c n e u lf n
I Errorf orCommonChanne lEsitma iton
e m u s s
A tha tthechanne lfrequency response on the pilo tsubcarriers can be represented as Hp[k] .
Afterobtainingt hechanne lfrequencyresponseont hepilo tsubcarriers ,wecanuseone-dimensiona l T
F D , n o i t a l o p r e t n i r a e n i
l -based ,LStogett hewholechanne lfrequencyresponsefordatasubcarrier . . d o h t e m n o i t a m it s e l e n n a h c e h t n o r o r r e g n i m i t l a u d i s e r f o e c n e u l f n i e h t s s u c s i d l li w e w , n o i t c e s s i h t n I
e n
O -dimensionall ineari nterpolation[1]ist hemos tcommonchanne lestimationmethod .Therefore , o
d e
w no texplaint hemethodinthissection .Generally ,thelargerchanne lmaximumdelayexisting e
n o f o e c n a m r o f r e p e s r o w e h t , m e t s y s s i h t n
i -dimension linearinterpolation.From thesigh tof(4) , o
p s e r y c n e u q e r f l e n n a h c e h t n i d e t s i x e s i e s a h p l a n o i t i d d a e h
t nse .Theaddiitona lphaseisrelatedto r
o r r e g n i m i t l a u d i s e
r nd .Thelargernd ,thehigheristherateofosclilaiton inthechanne lfrequency
e n o f o e c n a m r o f r e p e h t e c u d e r l l i w t I . e s n o p s e
r -dimensionall ineari nterpolation . T
F
D -basedmethod method isdiscussedinmanypapers ,wecanreferto[2] .Therefore ,wedon’ t .r
e h ti e , n o i t c e s s i h t n i n i a l p x
e If the channe lmaximum exceeds the limi tpoints of DFT ,the T
F D f o e c n a m r o f r e
p -basedwil lbeaffected .I twil lprovei nt hesimulationresul.t
s s u c s i d , t x e
N theeffec tofresidua litmingerroronLSmethod.Afterobtainingt hechanne l e
s n o p s e r y c n e u q e r
f ont hepilo tsubcarriers ,theerrorfunctioncanbewrittenas:
2 1
/ 2 ] [ ] [ ˆ
∑
−∑
− −= H k L hne j kn N
p p p
p S
L F ) F I F ) H
hˆ =(( H +α )−1( H ˆ
, ( 7)
S L
hˆ i s the channe limpulse response which we wan tto estimate and Fp is the Np×Np partia lof r
e i r u o
F matrix .αist heconstan twhichi scloset ozero . Iist heNp×Npuni tmatrix. Hˆpist hechanne l
. d o h t e m S L y b d e n i a t b o y l l a u s u s i t a h t s r e i r r a c b u s e h t n o e s n o p s e r y c n e u q e r
f Inshort ,ifthesumof
m u m i x a m l e n n a h
c delayand residua ltimingerrorndislessthan thenumberofpilots ,theresidua l
. d o h t e m S L e h t t c e f f a t o n l l i w r o r r e g n i m i t
n o it a l u m i
S Resu tl
An OFDM systemwith symbolsmodulated byQPSK isused .TheFFTpointsN=2048 and theCP 9
4 8 m o r f s i a e r a d n a b d r a u G e h T . 8 2 1 s i h t g n e
l thtot he1199thsubcarriers .Thespacingofpilo t∆p=16 ,
r e i r r a c b u s t o l i p f o r e b m u n l a t o t e h t o
s Np=128 .Thenumberofpilo toutsidetheguard band areais
l e n n a h c m u m i x a m e h t t a h t e m u s s A . 1 2 s i a e r a d n a b d r a u g e h t e d i s n i t o li p f o r e b m u n e h t d n a 7 0 1
f y a l e
d orLSmethodi s107 .Thebandwidthoft hissystemi s10MHz ,andt hecarrierfrequencyi sse t z
H G 2 o
t .Thecost-207t ypica lurbansix-pathchanne lmodeli susedforoursimulaiton .Thechanne l .
1 e l b a t n i s w o h s r e t e m a r a p
e l b a
T 1 .Cos t207TU6. h
t a P
( . o
n l) Pdreolpaayg(ati'on 'l
τ ) powPeart(hlin.) powPeart(hdB) PSD 0 0.0μs 0 .5 -3 Jakes 1 0.2μs 1 0 Jakes 2 0.5μs 0.63 2 Jakes 3 1.6μs 0.25 -6 GaussI 4 2.3μs 0.16 -8 GaussII 5 5.0μs 0 .1 -1 0 GaussII
t u o h t i w R N S t n e r e f f i d a i v R E B . 2 e r u g i F
r o r r e g n i m i t l a u d i s e
r .
h t i w R N S t n e r e f f i d a i v R E B . 3 e r u g i F
r o r r e g n i m i t l a u d i s e
e r u g i
F 4 .BERwithdifferen tresidualt imingerrorwhenSNR=40. e
h
T figure2showstheBERperformanceoft heone-dimensiona lilneari nterpolaiton ,DFTandLS n
e h w R N S a i
v thereisnoresidualt imingerrorandt hevehiclespeedi s15km/h.Wecanobservet he e
n o f o e c n a m r o f r e
p -dimensiona llinear interpolation is wors tbecause this method wil laffec tby e
h T . y a l e d m u m i x a m l e n n a h
c figure3 showsthe BER performance of the one-dimensiona llinear n
e h w R N S a i v S L d n a T F D , n o i t a l o p r e t n
i residua litmingerrorpointsare40samplesandt hevehicle e
n o f o e c n a m r o f r e p e h t e v r e s b o n a c e W . h / m k 5 1 s i d e e p
s -dimensiona l ilnearinterpolaiton iswors t e c n a m r o f r e p e h t d n A . r o r r e g n i m i t l a u d i s e r e h t y b s e s a e r c n i y a l e d m u m i x a m l e n n a h c e h t f o e s u a c e b
T F D f
o -basedi salsoaffectedbyt hei ncreasingchanne lmaximumdelay .Thefigure4showst heBER e
n o e h t f o e c n a m r o f r e
p -dimensiona llinear interpolation ,DFT and LS when the SNR=40 ,with r a e n i l f o e c n a m r o f r e p e h t s w o h s n o it a l u m i s e h T . s t n i o p r o r r e g n i m i t l a u d i s e r g n i e b s i x a l a t n o z i r o h
f o m u s e h t n e h W . g n i s a e r c n i s i r o r r e g n i m it l a u d i s e r e h t n e h w g n i s a e r c e d s i n o i t a l o p r e t n
i channe l
r o r r e g n i m i t l a u d i s e r d n a m u m i x a
m ndisl argert hant henumberofpilots ,LSandDFTwil lbeaffected .
n o is u l c n o C
e h t n I . n o i t a l u m i s e h t n i n w o h s s i s n o i t a m it s e l e n n a h c t n e r e f f i d n o r o r r e g n i m i t l a u d i s e r f o t c e f f e e h T
b m o
c -typearrangement ,thesum ofchanne lmaximum delay and residua ltiming errornd which is
d n a S L e h t t c e f f a t o n l l i w s t o l i p f o r e b m u n e h t n a h t s s e
l DFT .Bu,tt het oleranceofDFTisworset han .
d o h t e m S
L Duetotheimpac tofresidua l itming error ,thechanne lmaximumdelaywhichislarger r a e n i l f o e c n a m r o f r e p e h t , o S . m e t s y s M D F O n i y a l e d m u m i x a m l e n n a h c l a n i g i r o e h t n a h t
h w e c u d e r l l i w n o i t a l o p r e t n
i ent heresidualt imingerrorexists.
s e c n e r e f e R
] 1
[ X .Dong ,W.S .Lu ,and C.K .Anthony ,“Linearinterpolation in pilo tsymbo lassisted channe l ”
, M D F O r o f n o i t a m i t s
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[ D .Li ,F .Guo ,G .L iand L .Cai ,“Enhanced DFT interpolation-based channe lesitmation for 6
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[ J.C .Lin ,“Least-Squareschanne lesitmationformobileOFDMcommunicationon itme-varying y
c n e u q e r
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V D r o f s t n e m e v o r p m
