CH 7. Synchronization Techniques for OFDM Systems

Transcription

1 CH 7. Synchronization Tchnius for OFDM Systms 1

2 Contnts [1] Introduction Snsitivity to Phas Nois Snsitivity to Fruncy Offst Snsitivity to Timing Error Synchronization Using th Cyclic Extnsion l Tim synchronization l Fruncy synchronization Synchronization Using Spcial Training Symbols 2

3 Introduction [1] An OFDM rcivr has to prform two synchronization tasks: l l Tim synchronization to find out OFDM symbol boundary Fruncy synchronization to stimat and corrct for th fruncy offst of a rcivd signal Ø Ø Th sub-carrirs ar prfctly orthogonal only in th cas whr th transmittr and th rcivr both us xactly th sam fruncy. Thrfor, in an OFDM rcivr, any fruncy offst causs ICI as wll as SNR dgradation. Th phas nois of an oscillator also dgrads th prformanc of a rcivr. l Th phas nois causs ICI as wll as SNR dgradation in an OFDM rcivr, whil in a singl carrir systm it only givs a dgradation in th SNR. Th snsitivity to th fruncy offst and phas nois is on of th main disadvantags of OFDM. 3

4 Snsitivity to Phas Nois [1] Phas Nois: Distortion in th phas of th carrir gnratd by a local oscillator du mainly to th thrmal nois of a transistor Th powr spctral dnsity of th phas nois is somtims modld by Lorntzian spctrum whos singl-sidd spctrum S s (f) is S s 2 /( p f ) ( f ) = 1 + f / l 2 2 fl and th doubl-sidd spctrum S d (f) is givn by S d ( f ) = 1/( p f ) l 2 2 c l 1 + f - f / f f l : -3dB linwidth of th oscillator signal f c : carrir fruncy Phas nois causs two rror componnts in OFDM; th common phas rror which is common to all sub-carrirs and th random phas rror. Th common phas rror causs ICI, whil th random phas rror simply plays as th nois componnt. 4

5 Snsitivity to Phas Nois (cont.) Fig. 7.1 Exampl of phas nois powr spctral dnsity (PSD) with -3dB linwidth of 1Hz and a -100dB c /Hz dnsity at 100 khz offst. 5

6 Snsitivity to Phas Nois (cont.) Dgradation in th SNR causd by phas nois is givn by [1] f l D phas : -3dB linwidth of th powr spctral dnsity T: FFT intrval 11 4 p flt 6ln10 N Th SNR dgradation du to phas nois is proportional to f l T. s o Fig. 7.2 SNR dgradation vs. -3dB linwidth for (a) 64QAM (E s /N o = 19dB) (b) 16QAM (E s /N o = 14.5dB) (c) QPSK (E s /N o = 10.5dB). 6

7 Snsitivity to Fruncy Offst [1] If thr is a fruncy offst in OFDM systms, th numbr of cycls in th FFT intrval is no mor intgr, thrby rsulting in ICI. Dgradation in SNR causd by th fruncy offst is approximatd as [1] D f 10 3ln10 ( p f T ) 2 : fruncy offst E N s o Fig. 7.3 SNR dgradation vs. fruncy offst for (a) 64QAM (E s /N o = 19dB) (b) 16QAM (E s /N o = 14.5dB) (c) QPSK (E s /N o = 10.5dB). 7

8 Snsitivity to Timing Error [1] OFDM is rlativly robust to th timing rror; That is, if thr is no multipath, th symbol timing offst can vary ovr a guard tim without causing any ICI or ISI. Howvr, thr xists an optimal timing instant for th bst possibl multipath rsistanc in multipath nvironmnts. Fig. 7.4 Exampl of an OFDM signal showing th arlist and latst possibl timing instants for FFT. 8

9 Tim Synchronization Using th Cyclic Extnsion [1] Bcaus of th cyclic prfix, th first T G sconds part of ach OFDM symbol is idntical to th last part. This proprty can b xploitd for both tim and fruncy synchronization, as shown blow. r( t) y( t) Fig. 7.5 Synchronization using th cyclic prfix. Th corrlation output can b writtn as T G y( t) = ò r( t + t ) r ( t + T + t ) dt 0 * 9

10 Tim Synchronization Using th Cyclic Extnsion (cont.) (a) (b) Fig 7.6 Exampl of corrlation outputs for ight OFDM symbols with 192 sub-carrirs for Fig. 7.6(a) and 48 sub-carrirs for Fig. 7.6(b) both having a 20% guard tim. 10

11 Tim Synchronization Using th Cyclic Extnsion (cont.) Both figurs clarly show ight paks for th ight diffrnt symbols. Howvr, thr ar diffrnt lvls of undsird corrlation sid-lobs: l Th corrlation of two indpndnt random data suncs is random and its standard dviation is rlatd to th numbr of sampls. l Bcaus th numbr of indpndnt sampls is proportional to th numbr of sub-carrirs, Fig. 7.6(a) shows th bttr corrlation charactristic. Thrfor, th cyclic xtnsion corrlation tchniu is only ffctiv whn a larg numbr of sub-carrirs ar usd, prfrably mor than 100. In ordr to nhanc th corrlation charactristic, spcially dsignd training symbols can b usd. 11

12 Fruncy Synchronization Using th Cyclic Extnsion [1] Aftr complting tim synchronization, th fruncy offst is stimatd. Th input signal r(t) consists of an OFDM signal and additiv Gaussian nois such that r( t) = s( t)xp( j2 p f t) + n( t) f whr is th fruncy offst, th signal powr is P and th nois spctral dnsity is N o. Th sampls at th guard tim ar first multiplid by its dlayd and conjugatd sampls such that { p }{ p } * y t r t r t T s t j f t n t s t T j f t T n t T * ( ) = ( ) ( + ) = ( )xp( 2 ) + ( ) ( + )xp( 2 ( + )) + ( + ) = s t - j f T + n t s t + T - j f t + T 2 * ( ) xp( 2 p ) ( ) ( )xp( 2 p ( )) + ( + ) ( )xp( 2 ) + ( ) ( + ), * * n t T s t j p f t n t n t T 0 t T G. Th first trm is th dsird output componnt with th phas ual to th phas drift ovr a T scond intrval and th last trm can b ignord compard with th scond and th third trms if th SNR is rasonably high. Th fruncy offst is stimatd by using th avrag of y( t) ovr an intrval and th maximum-liklihood stimat of th fruncy offst is T G 12

13 Fruncy Synchronization Using th Cyclic Extnsion (cont.) 1 æ - Im y( t) ç ö 2pT è R y( t) ø ˆ 1 f = tan -. Sinc th SNR of y( t) is approximatd as SNR o 2 P PT» = 2 PN / T 2N G o G o th vctor rprsntation of th phas stimation can b rprsntd as follow. Assuming th nois componnts ar small compard with P, w hav æ n n - ç ö è P + ni ø P ˆ 1 = tan». 13

14 Fruncy Synchronization Using th Cyclic Extnsion (cont.) Thrfor, th standard dviation of th fruncy rror is givn by E s whr is th OFDM symbol nrgy and is th symbol duration. s pt E / N T / T s o G s By furthr avraging y( t) ovr K OFDM symbols, th prformanc of th fruncy offst stimation is improvd such that T s s pt K( E / N ) T / T s o G s. 14

15 Fruncy Synchronization: Prformanc Analysis (STD) Fig. 7.7 Fruncy stimation rror normalizd to th sub-carrir spacing whn K=1. Solid lins ar calculatd and dottd lins ar simulatd. (a) T G /T s =1 (b) T G /T s = 0.2 (c) T G /T s =

16 Synchronization Using Spcial Training Symbols [1] Th synchronization tchniu basd on th cyclic xtnsion is particularly suitd to tracking in a circuit-switchd mod, whr no spcial training symbols ar availabl. This cyclic prfix basd tchniu normally nds an avraging ovr a larg numbr (>10) of OFDM symbols for accurat synchronization. Howvr, for high rat packt transmission, th synchronization tim nds to b as short as possibl, prfrably a fw OFDM symbols only. To achiv a fast synchronization, spcial OFDM training symbols can b usd for which data contnt is known to th rcivr. Fig. 7.8 shows a block diagram of a matchd filtr that can b usd to corrlat th input signal with th known OFDM training symbols. From th corrlation paks in th matchd filtr output, both symbol timing and fruncy offst can b stimatd. Not that th matchd filtr corrlats with th OFDM signal in th tim domain bfor prforming an FFT at th rcivr. 16

17 Synchronization Using Spcial Training Symbols (cont.) T c T c T c cn - 1 cn - 2 c 0 T c : sampling intrval, c i : matchd filtr cofficints Fig. 7.8 Matchd filtr for a spcial OFDM training symbol. 17

18 Synchronization Using Spcial Training Symbols (cont.)

19 Rfrncs 1. R. V. N and R. Prasad, OFDM for Wirss Multimdia Communications, Artch Hous Publishrs, L. Hanjo, M. Munstr, B. J. Choi, T. Kllr, OFDM and MC-CDMA for Broadband Multi-Usr Communications, WLANs, and Broadcasting, John and Wily,