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Pilot patterns for channel estimation in OFDM

Article in Electronics Letters · July 2000

DOI: 10.1049/el:20000714 · Source: IEEE Xplore

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Santiago Zazo José M Paez Borrallo

Universidad Politécnica de Madrid Tecnológico de Monterrey
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Pilot patterns for channel estimation in slamlard [6] and studied in [7]. Sampling localions (or, equivii-
OFDM Icntly, pilot positions in tlic 2D grid) can hc descrihed using ilic
senipling matrix V. &ich gcoinclry is clcscribcd by dctining two
M.J. Ferniindez-Getino Ga lincarly indcpendenl vectors vI [vII 1 . ~and
~ 1v2~ = [al2 vzz]“,and tlie
J.M. Piez-Uorrallo loczitions of a doubly periodic set of samples i n llic (‘Il, r12)-planc
or (lime, frcqucncy)-plane in vccior nolalion are: d = V,,, whcrc 11
111 orlhogonid Iiaqncncy ilivisim innlliplcxing. OFDM. pilal- = [dl d?I7’; II = [nl nd” and V = [vI vz]. For tlic particular
symbol distrihulinn can hc v i e d as a 2D sampliiig ~ m h l c m gcoinelrics shown in Fig. 1, tlic snmpling matrices, V, can he wril-
rcliilcd 10 l l i c cliiiiiiicl Cvcilocncy rcip~msc.Cul-rcnl pilot piillci-as tell >IS follo\n.s:
with ti cuniinon inoliition iiic folmulalcd and B inuvcl hexi~gon;il
pilot gemictry proposed, wliicli is optiinum in terns of siimpling
eflkicncy and proviilcs bcttei pcrhbnnancc tliiin tiny otlicr
paucms.

In/rod~ici;(in:OFDM is a nietliod for llie parallel data transmis-

sion of a number of suhcliannels using frequency division multi-
plcxing [I]. It is widely acccptcd a s ii triinsinissioii Iccliniquc i n Note how rectangular siinipling (V,) is merely mi cxtcnsion ofperi-
several wireless syslems, e.g. in H P kinks, OFDM has heen shown odic ID sampling bul ii p~irliciil~iri~itioii of 2D sampling. The
to outperform single-carrier schemes [2]. Channel estimation in sampling density is proportional lo l/lrl(,fVI. Thc lower tlic pilol
cohcrcnt OFDM can bc pcrfnrincd by inscrting pilot-symbols into dcnsity, thc more cfficient is the geomeiry. lr llic 2D speclrum is
tlie two-dimensional Lime-keiequency lattice, since (lie kiding chan- circularly bandliniitcd. lhc mosl cfficient sampling strategy is the
ncl can he viewed as a two-dimensional stocliastic signal saiiiplcd hexagonal one, since il reqiiircs I3.4% Scwcr w i i p l e s thin reckiii-
at scattered pilot positions, where a noisy sample is ohtaiiicd [3, 41. gular sampling lo rcprcscnl the same sigixil [8]. l l i e signal lo bc
In the design of cliiiiincl estinliitors for OPDM, pilol information sallipled is the transform of the channel impolsc response and its
iiiusl bc distrihulcd opliinally iii ilic timc-frequency grid [5]. 2D Fourier transforni, disregiirding edge efkcis, ciiii hc approxi-
Currently, mosl of the pilol patieriis llxil llavc bccn proposed mated to fulfil this condition. Hexagonal sanipling is slill tlie most
arc dcrivcd froin pcriodic rcctangular s;inipling, with sonic modifi- cfticicnt patlcrn, as pKoVeli by the simuliiiions prcscntcd i n this
calions to obtain bcttcr perforinancc 16, 71. We proposc using hcx- Lcttcr.
agonal pilot distributions, a inicthud which lias provcn, ondcr Since lhc tiiiic-frcqucncy grid cannot he considered lo coni-
cerkiin condilions, to he lhc inns1 cfficicnl w;iy OS senipling iwa- pletely per‘lbrm lhc cstiimition, it will be divided into K x I . suh-
dimensional signals [XI and one which is currently used i n image grids; iii T of tlicse locaiions, pilols will he pkrcd, while i n tlie
processing and the design of cellular systems. Thc performancc of remaining ( K L r ) positions, channel atLenoalions niiisl be erli-
the propuscd pilol pallcrii schenic is analyrcd taking in10 accounl mtilcd will1 tlic aid of channcl kiiowlcdgc a i pilots positions.
the par;imeters OS a mullicarrier FIF link, allhough it caii bc uscd
0
for any OI’DM communications systcm

2 D pilor p ~ m n , A~ :tradc-off has to he found; pilots have Lo he lo I

placed close enough lo guarantee reliable estiiiiatioii OS llo chan-
nel frequency response and, a i l l i e siinie lime, pilot dcnsiiy must
he kepl tis IOW as possible Lo avoid reducing the d>ll>l-KatC.Thc
discrete-time cliiiiiiicl rcspoiisc to bc cslimatcd is alrcady ii kitlice
of the coniinuous signal. Sampling at piloi positions will ( I n s bc r
w
m ........
considcrcd as taking a suh-latticc.
The iuost lypical inclhod oE sampling ii 2D signal is by iiieans
of pcriodic rectangular sampling, wlicrc cacli dimclision Ihas
.... --- ---- -Q

equally spiccd samples with ii ccrlain period dcleriiiiiied by thc

CI.....
..............
..........
cohcrcncc time or cohcrcncx handwidlh of llie chiinnel. N , denotes .%..
.....
the piloi spacing in the time dimension iind N2 is tlie pilot spacing .....
in the frequency direction. However, periodic sampling can adopt
yal.ious gcomctrics, as sccn in Fig. I -3ol 10 12 14 16 16 20 22 24 2R 28 30
~~

frequency sweeping SNR. dB

“2
“2
1
hexagonal rectangular linearly-increasinq

I I I I I I i I I I Clronnd e,st;inotor: 211 Wiiwr .filler: l‘hc cstiniiition algorithm is

uscd onlv la evaliuitc tlic iliSfcrcnt nilols naitcriis. so coiiiulcxitv

’F””i””[9],” w
was cniploycd. Virsi, chaniol aitcnoations 111 piloi locations
m can he esiimaled using Llic lcasl squares (LS) critcrioii [9]. Arrang-
in O F D M i i , , , ~ , ~ / ~ ‘ , ~ si.ii1
Fig. I Piioi di.~lriI~ulim~.s /,,~,,~~ ing thc traosmiitcd ;md received symhols at the pi101 positioiis in
(7’ x I)-veclors, xI,and ya. respectively, whcrc X,, is ii di;igonal
I’ilol syiiihols arc iiiiirkcd in grcy
mairix wliose main diagonal is d i q ( X , , ) = x,,,llic csiini;ilcd chan-
nel ;ittcmi:;tions a i ilic piloi posilions arc given by eqn. 3 in a ( T x
The lirsl geoniclry (V,) is rectangolar sampling, hut wiili the l)-vccior Ill,
parlicular feature OS complete sweeping or the keqiiency dimcii-
sion. The second geometry (V,) is rectangular and tlic Ihird (VI,) is flP = x,-’y, (3)
a hexagonal pattcrn. l~inally,tlic fourth gcoiiictry pr,J is ii Torr At cvcry sub-grid, oiicc tlic clmiiiicl tittcnuarions til the pilot posi-
of rectangular modified paticrn, linearly iiicrcasing i n tlic fie- tions arc lknown, a i l csliniatioii of lhe discrete-lime Crequency
qucncy dimcnsion 7’hc l a s l pillern 1x1shcen adopled in llie DVB response of Ihe channel is calculated using the LMMSH 2D fillcr.

ELECTRONICS LETTERS 8th June 2000 Vol. 36 No. 12 1049

 ~

Denoting by 6 tlie ((KL - x I) vector that contains the ( K L - 2 ZAZO,S , I'AUZ-IH3RRAI.I.O. .I.-hl , and Vl:kNhNDrz-C;I~,TINO
I) altenuaiions t o be eslimatcd in lhc sub-grid, tlic MMSE esti- 'Iligh fi-cquency data link (HFDL) for civil iiviiilion
( ~ A R C I AM.I.:
.
mation algorithm is shown in cqn. 4 A comparison bclwren singlc aod multilonc voiccband modcms'.
Proc. IEEE Vehic. Tcchnol. Conl. VTC'99-Spring, I~Ioiiston,
fi = [ R . I , , , ( R ~ ~ ) - ~ ] ~ ; ~ (4) Tcxsis, USA. 16-19 M;iy 1999, \ I d 3, pp. 2113-2118
3 iiOiiI',st. K A I S E R . s., ; m i IWI~I:KSON. P.: "L'wa-dimensional uilot-
11..

iyliere RI,, represents the cross-covariance matrix between k kind svmhol-aidcd channel cstimiilion bv, Wiencr fillcrini.'. I'roc. iEEE
~~~~~~ I ~~~

h,, wliicli depends on llie relativc posilions beiwecn the estimated 101. Conf, i\coustics, Spccch and Sig. Pruc., ICASSP'97, 21-24
alteiiirations and the used pilol positions, and R,,,is ihe anto-COY- April 1997, Munich, Gcrm;iny, Vol. 3, pp. 1845-1848
ariance matrix of h , , depcnding on the numbcr of pilots and llicir 4 NUSSON. I<., I:DI'OIlS, O., SANIIBLL. M , ;Lnd IIOKJLSSON, PO.: ' A n
relative locations. Auto-correlalion and cross-cotrelalion matrices andysis of two-dimcnsioniil pilot-symbol assisted modulzition For
can bc calculaled assmning that the channel correlation is separa- OFDM'. PI" IliEE Ini. Conf. Universal Pcrsonal
ble in time and frequency [7]. Commonicalions, ICIJPC")7, San Iliego, CJSA, 12-16 October
1997, pp. 71-74
5 TUFVF.SSON, I., and M A S F . N ~ 1.: ~ , 'Pilol iissislcti channcl cstiminioii
Simularion ~enrlts:Voicchand data tra"ssion over HI: liiiks lias for OFDM in mobilc ccllul;il- syslcms'. I'roc. IEEE Vchic. Tcchnol.
been considered, which is widely recognised as a difticult commu- Con?. VTC'97, Arizon;,, USA, M a y 1997, pp
nication problem. In this low data-ralc cnvironment, binary data 6 IWIMIIRS. U,: 'Digiti video bro;idc;isting', I
arc mapped to a complex QPSK constellation. Thc ionospheric 1998. p p 104-110
channel prcscnts multipath amplitude Sading with up to 2112. two- 7 SANIIIILL. M.: 'Dcsign and analysis o f cstiniiilors Cor multititnricr
sided R M S Doppler spread and lwo-path Raylcigh slatislics. Otic inoduliilion and ultrasonic imaging'. PhD Thcsis, L u l c ~Univcrsity
OFDM-symbol duralion. ,,,,,,,7; is 5.71 ins, and each of the of Tcchnology, LulcS, Swcilco, Sepicmhcr 1996
O F D M symbols uses iV = 16 suhcarricrs, with Lhe samc number 8 I>lIIICI!ON. D , C , and MI(llSLREAU, 11.M.: 'MuItidirncnsiao;II digital
signal proccssing' (Prcnlicc IIall, NJ, 1984)
of samplcs in the time domain (t6Tr), whcrc 7; is thc symbol 9 SCIIAIlI'. L I,.: 'Slalistical signdl proccasing: Uctcction, cstiniation
dnratioii T, = I/?+' = 0.3568nis. Thc system bandwidth, PX is and time series analysis' (Addison-Wcslcy, 1991)
2800Hz, which leads t o an inter-carrier spacing of A / = 1 7 5 H ~ .
The one-sided Doppler. frequency spreading normalised lo tlic
inter-carrier spacing is f D,,,,,, =.f; ,,,,,,,/Af= 0.0057. The degree of
Requcncy-scleclivily is detcrmined by a maximnm delay sprcad, T
= 0.5ms. A cyclic prefix of 0.7136ms. corresponding io CP = 2
samples is tlicn added to llic O F D M symbol lo overcome tlic All-optical writehead memory for 2OGbit/s
delay spread. data packets
When dcsigning lbe pilol pallern, dimcnsions in the sampling
grid musl be normalised to the cohercncc lime (inverscly rcliiled to
the Doppler fading ratc) and lhe cohcrence bandwidth (inversely M. Kalyvas, C. Bintjas, K.Zoiros, T. Houbavlis, H.
related to [lie delay sprcad); Cor tlic cliamel correlation Sunction, A v r a m o n o u l o s . L. Occhi. L. Schares. G. Guckos. S.
the analysis given in [7] has bccii umed. Thcorctically, to fulfil
the 2D sampling theorem, pilot spacing for periodic rcclangulm. A writable till-oplicid mcmory for wl-iable length, 20 Ghitlr dalu
sampling is given by [4, 71 packcls is dcmonstrilteil. l h e mcinory iiscs an ullrafast noiili~wir
inlerreromctcr (UNI) @e atid docs not p a f i r m dala invcrling in
ciicli piiss. Rcgcncrarive sioliigc with low switching ancrgics is
verified.
Thesc cxpressions are nscd as a refercncc poinl lo delerniinc thc
pilot spacing in the time and frequency dimensions, NI and Nz, Ifrtruduction: In rccciil years the evcr incrcasing capacity dcnxmds
rcspeclively. Taking into acconnt tlicse values, thc pilot density, in opiical fibrc networks has spurred effbrls towards higher single
d,,, is kcpt constant and thc pilol symbols arc scattered according channel lint. rilles [I] and all-optical signal proccssing syslems [2 41.
to thc diflerent pattcrns. Fig. 2 shows the perlbriiiancc without One essential snbsyslem that will help in the realisation of high
channel coding for thc diferenl pilot gconietries. capaciiy, optical packei switclicd networks is a robust optical
memory wilh full writelread capahilily at the linc ratc. Regencni-
Cunclu.si~,ns:Dcsign stralegies of pilot patterns for O F D M wire- livc memories wing optical fibre as tlic shift register and all-opli-
less systcms in highly frequcncy selectivc Raylcigh fading cliimiicls cal gates for rcgeneralioii 151 offcr tlic advanlagc of low jiller
have bceii analysed. Chamicl eslimation in the O F D M time-frc- accu~nnl;ilioii during storagc. Semiconductor oplical amplifier
qnciicy grid can he vicwcd as a two-dimcnsionel inlerpolation. A (SOA) inlerseromctric g a l a liave hecn uscd increasingly, bccansc
novel hcx;igonal pilot patlern has been proposed and conipircd of their low swilchina eiicrrics and latencies Kl, A UNI-based. all-
with olher pilot distribulions currcnlly adopted in OFDM sys-
tems. With this hexagonal sampling slralegy, a certain perforin- ._
ance can bc mainlained, rcduciiig pilot dcnsily, and thus lcading inore recently a t%?I-besed regciicrativc memory lias hccn demon-
to a lower overhead of the embedded sigiialling so that morc &ala striated, capable of sloring IOGbitIs of data crror-Sree [8]. In this
can be lriinsmilied. Lelter, we rcporl tlie demonstration of ;I single-UN1 gate regeiier-
ative memory, capablc of arhilrary data packct slorage a t 20Gbilh
and ils regeneration for many circulations. This is lo our knowl-
Aclcnoivledmnent: This work h;is been narliallv suonorled hv tlic
I ~ . I
edge thc liighcstrate demonstration of arbitrary dala packel stor-
Spanish Rcsearch Council (CICYT ComisiOn Intenninistcrial dc
age without data invcrting on successive circnlations.
Cicncia Y Tecnologia), under grant TIC 98-0748.
E.xperiiiient: Fig. 1 shows tlic experimental setup, which consists
of ii programmablc optical pattern gcncration circuit, a UN1 gate
and a fcedback circnit that forms lhe shifl rcgistcr. The clock sig-
nal cniers the UNI, is swilched for the first tinic from the loading-
up dala seqneiicc and is consequently switchcd from the recirculat-
iiig stored rcpliclis of the sequcnce. The circnits arc puwcred from
28040 Madrid, Siiuiii~ two gain-switclicd DPH diode Iascrs, LDI and LD2, that provide
ilic clock and loading-up data packel Tor storage. The laser diodes
were driven a t IOGHz from a signal gcncrator and produccd 9ps
References pulscs aster libre comprcssion. The si@ from LD2 was modu-
lated in a LiNbO, modulator (MODI) driven from ii programma-
1 DINGIIAM, J.A c.: 'Mullicarries madulaiion for data tl-ammission ble pulse pciicIator to nroducc bit scuuciices. Tlic vnlse trains
An idca whose time has comc', IEEE Chnniun. Mag., 1990, 28, ( 5 )
pp. 5-14

1050 ELECTRONICS LETTERS 8th June 2000 V d 36 No. 72

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