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A Study of Channel Estimation in O'F'DM SystemsSinem C olerl, Mustafa Ergeu.Anuj Puri , Ahmad. .B ahai

A,'b.dra.ct- 1I'l ledt3Jnrnd esl !Imanoll l ~c=chDJiq1K;5: ID~OFIl M ; S ; Y . 5 ' -tems baSDlil.on. piltot :llI'raJnl:!l:lIIlII:lIIt al'l!: 1mtTlllfI~1Jj! > : I I ~ U~i'o\Crs~~y()ffCnlifm-

nia, Ee[~~iry" (~m!!~I: cs1iMm,.eI~:~n@~oos:_be~ky.odll)AII~j Pwlti i!;r=lIrc. ~roffl:8Sl}T11.1.II~"'i:

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Follow ing llCifT block, guasd Iilim c, w hich is chosen ItO belang:r thanthe expected dday spread; IS inserted to preventlnter-symbol interference. This gnard tiIWI: includes thecych-cally extended part ofOFDM symbol in ordcr to d imlnaM:: l Ii iM: :r -canier iliiM::rrcrcnllcc(Ie!),The transnsitred sig.-.ailx j( n} will passthrougb thefrcC!jl!.lcncy

selectiveume Yliry ing : fad~.ng channel wi th adl d~~ivc noise,Al tbe receiver, rui'terpasslliig todiserete dornallii.~ilnol!lgh A.J[)

1IIDI1iow pasa f il te r, g l !l li ro time is rem ove d 1IID I1 i{ n) is .sclii:~oDFT Il~ock,Following DFT bloek.jhe pilot slgnllals arc extracted 1IIDI1I~illeestimated chlllm.nd Ife ( k ) for thed ata s!1IIl.ci:ullllii.ndis obtainedin ehannel estimation block A flll::r tb e estjmation of the trans-mined d at a. b y:

X =Y(k). n,(k) k=O,l,_ .. N-ltlx:lbamu:y informatlon dliia es obtained bock in 'sig.-.al deraap-pd'blockUL CHANNEL EST~MATION BAS~IDON BLOCK-TYPE

P~lO'1i' ARRANGEMENTInlib lo ck -t yp e p il ot b as ed ch aa ae l e stim a tio n, OfDM chanael

estimation symbolsare t li l li isrn it tcd pcriodlcaUy; in which allsub-carriers a m : used as pilots, TIx: cSl ima tl on C1 IID I.e pcsformedby! ll l oi .n g: it hc rLS o r .MMSE 1[2],[3].If ( be t ime dorna ll ii . channel vector h is G aussian and uncorre-

lated w ith the: C hM Ud noise W, tbe frequency domain M:MSEestimate of his glvcnll by [3]1:

where RiLl' 1 li 11 dR l' yl ir cl 11 e c ro ss ccvanaacc matrixbetweenh aad Y and the al!lt~ ov:arii.ancc m atrix of Y respectively, Ri.J.i s the a l! lto-cova ri i. lI il lc>cmatrix of h . and 0-2 represents the noisevariance E{lIW(kW},Th e LS esrlmate, which mi li l. imlzcs (Y - XFh)off (y - X Fh),

is representedby-When tbechansel is slow fadling; the d i! li nn d c st in ul lt io nlnsidethe H ock C 1IID I.e : Ilpolaled!!l!.i1ing; the decision feedback

cC!j!lllalzcrlill each sub-earrier, Deci slon f,ec:ollb,ackcC!jl!.lalzc r fortb e k fl. sub-camcrcanbe described as follow s:

The ehannel response lIit.lillCkth sab-cartlesestinsated [romt he p re vi ou s .! ly rn bo l { H " ( k ) - } is used W f in dt he c st~. rn al edtransrniued signal {X", ( k)} ,

X ( . 1 1 : \ =Y(k). c = s H; (k) k=O,l,_ .. N-]. {X" ,(kH is m llp!pl:d10 Ibe b~.nary dara through "signaldemapper' an d then obtained backthroagh ' 'slgnllal rnap~per'tas {Xp"",,(kn"

~ The c stlma re dc ha aa et H e ( k) is updalcol by:k =(), l , . _.N - 1

S l li iCe : !: i. edeci s lon fcedl l1 liCk eq U l I liz .cr has ItO ass um e th li! tb e de -eisio ns a re co rrect. th e fas t :fad ~.n g:ch asn el w m cause tb e com-pletc loss of e sti m ated chanue] parameters.

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IV, CHAiNlNEL ESTIMATIOiNi AT P~lOT FREQUENCIES E N ]COMB-TYp~ PILOTARR.i\N(mM~~iT

lncomb-type pilotbased channel e:stlm ~tion, the Np pi.bt1i1igna~s1I[euniformly In se rte d ~ .n to X(k) aeeosdirrg to the fol-ilowlng: oqllllltlon:

) [ ( . 1 1 : ) =X(mL-t l)_ { :l!~(m),- '. inf.daia

{=o(=Jl,._.[.-l

where L = nli.rnlbcr oil'cani,criS/Np an d Ip(m) is the mfl pi -ilo~earner v,a1l!.1c.W e d cfi li ic {H p( k ) k = 0, I, ._.Np} as~he frc:q]lllcncy response of thechannel lIt pilos sub-carriers, Th eestimate of thechannel a l p i. ~m ~mlb -C1 l!m .c rsb as ed On llLS esti-m~rr eon e s given by :

where Y ,, ( k ) lind X" ( k } lire output and ~ . n I I !p ! 1 I t a l l : the kl/. pi.bl!.i1uib--canie:[espectively,Since LS cst~ma~ is ! .i11 i .sccp t ib lc~o no ik l' l: :1mo llCI, MMSE es[p roposed w~li lc com[pro .mi1 i1 i. ngcomp~cx i~y ,. Since .MMSE in -

clades the IlIiI atriix inversion al C1l.C~]I~ralt ion; tbe s imp l i li ic c l lin-ca r MMSE estimator is suggested en 116], In this slmpllffed ver-1i1ion.mi]c inverse i s o li i. ly needed to becalculated onllce.llIii. [41]1,thecomplexity es funiller redsced with 11 low-rank approximll.-~ io nl b" )' u s in g s ll ii ~.~~ [ v a~ Ii lO [ ;ccomposition,

(2)V..INTERPOLATION TECHNIQUES IN COME-TYPE

.PILOT ARRANGEMENT

0)

ln cornb-ctypcpilot basedchannel cstemation,an efficient in -terpol ation techa uC!jI!.lC8 1ii'CC:CS8~rylii.order 10 'I::st~rnalc dl!linudal data sub-carders by uslliig the chaenel inrorm ation~l pi.~ot!.i1uib--crriers,Th e linear inllt'cq)'DIMion method i s s hownl l~ o p cr fm i lM lbcnc r

~h~lm.hepieeewiae-constant imC:IJlQ~arion i ni l [7l TIx: ci:mnudc stim altuo n at the data-earner k; mL < k {m) + c-IH,.(m -t])

{

_ .. ( .. -U)c :u --2-'C~ =(0..- ]')(O-t 1),0 = - f r. _ ~Cu1"l)C-~. - -2-. -

(5)Thelow-pass interpojation isperform ed by inserting :lCWiS~.nto~he mi_gj .n :a1seq UCllC"C 1IIDI1ibe n a pp l YUIii.ga lo wp ass FIR fil-~c r (i1!~erp jUfK.:tkm In MATUD)thllt a~ il.ow s t he o rig in al da taItO p a:ss lb rol!.lg h u nch aa ged an d ilm l:l::[ po llilc sb etw een su eh (h althe m ea n-S lJllila r:c e rro r be tw een tile im erpo lated poin ts an d th eir~lIcal vahtes i is mi n~mi:lcol .

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P i . l io t F i :: :I t io2:5644_1 kHz,175kHz,B I "S K , .QP S IC,DQPSK J6Q A.M

Channe] Modle~'IAiElLlE ~.

The s .p~, in e cubi c i nt er po l a ti on (Sf)lin jllrlcllon irsMA HAll')prodllil,CCSa. smooth and continuous polynomial fitted to givendata points,

The lim e domain iIItcl'Jl'Dlation i s a h igh -: re sohn ian interpol a-tionbased on zero-paddjngand DFf/IDfT [8]" Af te r o bt ai ni ngtb e estimated chaanel {Hr( k), k =OJ1, Np -I} ,~'!I'efirst COII-vert it to tiene domain by ]OFT:

NJI-:UG(n) =.~ u. /~'N:~

, ~ 'I~ ] -n =, 1 , . .. N" - .U .

Then, by usi !llgl~]e basic mula-rate sig.-. a i l . processing properties[9] , ~] e oigL la~s interpolated by t r~mMo rm il li lg t he Npp oin ts i .n to.N pa lrn l: !l wi ll :J ithe oo l.bwing mel~ l IOd!:

0:5;n

8/3/2019 A Study of Channel Estimation in OFDM

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1~r-----~----~----~~----~----_r----~~--__'

H i 10~1.. ,

10~F r .. ". .= = - , " ,. . , .. , ~ -- - - ,-+. OolIElIIIHr4,..,~..::;a-,~I--4-. i r c J ; 1 i - l 1 l ' 7 l l 1 I-e-,I:!I:E~~-e-. dH:1I .b~ ~~.......LIItS

10-~~'====~10==~~1=~----~~~'-----2=~~'----~~~'----~3~~--~

Fjg_ : 1 : , QPSK Miod ulation w.iil l l l Ril':!h:ig. FiMli.~ (CI1~.rld ~.DLlJ)pl\:rrFreq, fig_ 4, DQE'SK MoolIJl~.'io. wi.1illIl.~yli:;i!:J F!IId~.~(C It'illnn!::l ~. Dop~Ii::[ Freq.7 lJE-Iz) 70E-lz )

' 1 1 1 1 " ,--------~----~----~~----~----_r----~~--_____, 1~r--------'--------'--------''--------'-----------,

-------'Ii[f'

..... U. il-I- .a-Eiam4~Pi-P'"~IIIPIH""I iI - lind::Inb-e- ~tJ,:~i:{2.+::ili:!l*--=~-".

Fjg_ .3 , J6QAM Modwtl! l i io.n.w i ! h J Ril':!leig. FaI!ling (Cbru.el J, [)o~liIer F roq"7lJE-Iz)

r .mgc. l l from tbe best to UtO wa rn ! a s r ol .~m ll' S: : l ow-pas s, s phnc ,timc-demaiu. st:conllol-ordc[ and linear, Theresult was CltpoC'~odsince tbelow-pass int,cl]Johtt ionl!Jl~riI inlIslmul Oi!I :uonocs the ~,n1-terpolation such U:mt~ho rn01l11-OCJ.UiiKrror between the iliiM::[-polml:riI points 1IIld their ideal.values i s minimized. TIx:~ resultsare ; ; i l l so con s is ton lt wi tH: !t ll 108Coli l~a il ii .ccIin [4 ]I ,md I I5] .DQiPSK rnodularrkm based ctl!tlnnd estlmation sOOW . l la~moSl

th e S1l!IIilCerformance wr al l C111l11OCI.stlmtlluonl tecbniques OJ'L-cept tile decisioa-feedbaek mot hod .. This is expected becausedividing two consecutive data s!lIb.-

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'liB" 1-----.----.-----.----.-----.----.----.,

,--+-~.~aa..1+r- llPi-P"- ' i ' - " " ' ". : I j i. . . 1 . . .z........g..bb:lit;H!4- -H-:ilbl Ht:hi:~' 1 1 0 - : . : 1 p .: :-