시분할다중접속방식의위성통신시스템을위한주파수추정

Transcription

1 논문 C-08 한국통신학회논문지 '06-4 Vl.3.4C 시분할다중접속방식의위성통신시스템을위한주파수추정 정회원김종문, 종신회원이용환 Estimatin f Frequency Offset in TDA-Based Satellite Systems Jng-n Kim Regular ember, Yng-Hwan Lee Lifelng ember 요 약 TDA 시스템에서신호를수신하기위해서는정확한주파수및시간동기가필요하다. 본논문에서는 QPSK 신호를전송하는 TDA 방식의위성통신시스템에서훈련신호없이주파수편이를추정하는방법을제안한다. 제안된방법은수신신호의두부분에서정확도가높게위상을추정하고, 이위상차이로부터주파수편이를추정함으로써기존의주파수편이추정방법과비슷한성능을보이면서적은연산량이요구된다. 제안된방법을 GS을기반으로확장된 GR 위성통신시스템에적용하고시뮬레이션을통해성능을검증한다. Key Wrds:GR, satellite system, TDA, carrier recvery, frequency ffset ABSTRACT It is required fr crrect signal detectin t accurately maintain the synchrnizatin f frequency and timing in a TDA system. In this paper, we cnsider nndecisin-aided estimatin f frequency ffset fr the transmissin f QPSK signal in a TDA-based satellite system. The prpsed scheme estimates the phases f tw parts in the burst and then estimates the frequency ffset based n the difference between the tw estimated phases. Thus, it can prvides perfrmance cmparable t that f cnventinal schemes, while significantly reducing the implementatin cmplexity. The perfrmance f the prpsed scheme is analyzed and verified by cmputer simulatin, when applied t a GS based gestatinary earth rbit mbile radi(gr) system. Ⅰ. Intrductin Time divisin multiple access techniques have widely been applied t satellite links and wireless cmmunicatins []. Reliable data detectin in time divisin multiplexing access(tda) cmmunicatin systems strictly requires the synchrnizatin f carrier frequency/phase and symbl timing. TDA systems such as GS r gestatinary earth rbit mbile radi(gr) impse stringent requirements n the frequency stability f receive scillatr because the frequency and timing f the received signal are used as the reference fr the transmissin f signal [,3]. A number f wrks have been prpsed fr the carrier recvery [4-7]. st f the previus wrks cnsidered t the transmissin f linearly mdulated, burst-mde signal ver additive white LG 전자 DTV 연구소 (jmn3@lge.cm), 서울대학교전기공학부송수신기술연구실 (ylee@snu.ac.kr) 논문번호 :KICS , 접수일자 :005 년 0 월 일, 최종논문접수일자 :006 년 3 월 8 일 364

2 논문 / 시분할다중접속방식의위성통신시스템을위한주파수추정 gaussian nise (AWG) channel with/withut the use f training signal. The frmer schemes are called data-aided (DA) estimatin [5,6] and the latter schemes are called nndecisin-aided (DA) estimatin [7,8]. A maximum-likelihd (L) scheme was prpsed fr PSK signals [4], whereby a peridic training sequence is recursively passed thrugh a bank f bandpass filters implemented in a frm f discrete Furier transfrm. It adjusts the frequency spacing s as t accurately estimate the frequency f spectrum peaks f the input signal, but it requires a large implementatin cmplexity. T alleviate the implementatin prblem, simplified schemes were prpsed by apprximating the weight f the autcrrelatin functin in the likelihd equatin [5,6]. As an DA scheme, a sequence f samples is btained using differential symbl estimates that cancel ut the QPSK data mdulatin frm the received signal [7]. The average phase slpe f this sequence is prprtinal t the frequency ffset in QPSK signal. The cited phase slpe is evaluated and analyzed by a means f fitting technique [8]. In a TDA cmmunicatin system, a unique cdewrd is ften inserted in the burst fr the detectin f lgical channel, timing synchrnizatin and frequency synchrnizatin. It wuld be desirable t avid the use f a lng cdewrd particularly when the transmissin rate is lw. The GR specificatin suggests the insertin f a shrt cdewrd in each 5ms length burst fr spectral efficiency. It is required t use an DA frequency ffset estimatin scheme fr frequency synchrnizatin in the GR system. The perfrmance f DA frequency ffset estimatin schemes can be imprved using a mdified DA technique, but it requires a large implementatin cmplexity. Thus, t alleviate the implementatin prblem, we prpse an DA scheme fr the estimatin f frequency ffset while prviding errr perfrmance cmparable t that f the imprved DA schemes. Fllwing Intrductin, Sectin II describes the prpsed frequency ffset estimatin scheme and analyzes the perfrmance. The perfrmance f the prpsed scheme is evaluated when applied t the GR system in Sectin III. Finally, cnclusins are summarized in Sectin IV. Ⅱ. Frequency ffset estimatin We cnsider the transmissin f QPSK signal ver an additive white Gaussian nise(awg) channel. Then, the utput f the matched filter can be represented as ri = ciexp{ j( π fti+ φ) } + ni 0 i< L () where c i is QPSK symbl whse abslute value is the unit, f dentes the frequency ffset, T is the symbl duratin, φ is the carrier phase, L is the burst length represented in terms f symbls, and n i is circular symmetric zer- mean cmplex Gaussian nise. The variance f the real and imaginary part f n i is σ and the signal-t-nise rati (SR) is defined as ρ = σ.. Cnventinal frequency ffset estimatin schemes The frequency ffset can be estimated in an DA scheme using a 4-th rder pwer functin as [7] L ˆ 4 4 arg ( ) f = rm rm 4 πt () where arg{z} dentes the argument f a cmplex z taken in the interval [-π,π]. This scheme estimates the frequency ffset by accumulating the phase difference between the symbls in the burst. It can prvide a large perating range f f < [ 8T ], but it may nt prvide gd perfrmance. Assuming that the frequency ffset is unchanged within the burst, the frequency ffset can be estimated by a linear increment f symbl phase as [8] ˆ f = iαi+ 8πT i = 3 iαi+ πtl( L ) (3) where = ( L ) and αi = 4arg( ri)mdπ. The variance f the estimatin errr is given by 365

3 한국통신학회논문지 '06-4 Vl.3.4C ( ) σ 3 π T L L σ f. (4) This scheme smewhat imprves the estimatin but it still needs further imprvement. DA frequency ffset estimatin techniques can be applied t DA frequency ffset estimatin schemes. Assuming that r k is the received training signals, the frequency ffset can be estimated by apprximating the weight f the autcrrelatin functin in the likelihd equatin [5] fˆ = { Rˆ m } arg ( ) πt m (5) Lm where Rˆ ( ) ( ) m = r k k r = km. If r k is a QPSK mdulated, (5) can be mdified fr DA estimatin as fˆ = Lm % k = k km { R% m } arg ( ) 4 4 where R ( m) r ( r ) 4 πt m (6) =. Here, a 4-th rder apprximatin is emplyed fr the calculatin f autcrrelatin functin while eliminating QPSK mdulatin. Thus, the phase difference in the autcrrelatin functin crrespnds t fur times f the actual phase difference. Anther DA estimatin scheme was prpsed t reduce the implementatin cmplexity [6]. The frequency ffset can be estimated by using a rectangular windwing functin instead a parablic ne fr the autcrrelatin functin in the likelihd equatin as [6] ˆ f = arg Rk ( ) πt( + ) k = (7) L where R( k) r ( ) ( ). i k i ri k L k If r = + k QPSK mdulated, (7) can be mdified fr DA estimatin as ˆ ) f = arg Rk ( ) 4πT( ) + k = (8) ) ( ). L 4 4 where R k ri ( ri k) ( L k) k+ These mdified DA schemes fr the DA estimatin can prvide gd errr perfrmance at the expense f large implementatin cmplexity fr the calculatin f autcrrelatin functin... Prpsed frequency ffset estimatin scheme The frequency ffset can be estimated frm the difference f tw phases as ˆ K+ K+ 4 4 f = arg rm+ D rm 4 π DT K K (9) where K represents the start pint f the symbls used fr the estimatin, D dentes the distance between the tw part f the burst, dentes the summatin length fr each part and L= K + + D (0) The variable K can be set zer t maximally use the symbls fr the estimatin. It can be seen frm (9) that the perating range f the prpsed scheme is f < [ 8DT ]. Fr the analysis f perfrmance, the received signal can be represented using a 4-th rder functin as where i i i i i i i i 4 4 j( π fti+ φ) ri = ce i + ni = s + 4sn+ 6sn + 4sn + n () s j( π fti+ θ ) i = ce i () 4 Here, s i is the desired term fr the estimatin f frequency ffset and the remaining terms are nise. Defining the nise term as it can be shwn that w 4s n + 6s n + 4sn + n (3) i i i i i i i i E{ wi } = 0 E{ Re{ wi} Im{ wi} } = E{ Re{ wi} } E{ Im{ wi} } = σw = var [ wi] = 3σ + 88σ + 768σ + 384σ var[ Re{ w} ] = var [ Im{ w} ] = σ (4) i i wi 366

4 논문 / 시분할다중접속방식의위성통신시스템을위한주파수추정 Thus, w i is a circular symmetric zer-mean cmplex randm variable with variance σ w. The { } errr variance E ( f f ) f the estimatr (9) can be calculated when ρ and 8π ft. Since high SR assumed, wi+ Dwj terms can be neglected. If D, randm variable w i are independent identically distributed (i.i.d) with characteristics (4). Thus, it can be shwn that E { ε } σ ( ) wsin ω sin ( ω ) + ( m)cs( mω ) () Burst Burst K D K D K = 0 Fig.. Structure f the prpsed estimatin scheme Letting ξ j 8 ftd e π (5) On the ther hand, if D <, the ( D) j( ) ω j( ) ω terms f e w i and e w i+ D in (0) are verlapped as shwn in Fig. Because each f verlapped temrs is cmplex cnjugate, it has zer imaginary part. Since the remaining { w i } terms are i.i.d., it can be shwn that (9) can be written as where $ j8π ftd 4 4 ξ e = rm+ L rm (6) ( ) ε 8π f f TD (7) {( ) } = ( 8π TD) E f f E { ε } $ 4 4 ε = arg{ ξξ } = arg rm+ D rm ξ (8) (9) Letting ω 4 π ft and φ 4 π ftd, it can be shwn that j φ j( ω+ φ) j( ω( ) + φ) arg{( e wd+ e wd+ L e wd+ ) j ( ) ( 0 jω jω j φ e w e w L e w ) e } ε = j( ) ω sin ( ω ) = arg + ( m)cs( mω ) + e wi sin ( ω ) j( ) ω sin ( ω ) + e wi+ D+ wi+ Dwj sin ( ω ) j= j( ) ω sin ( ω ) Im e w i sin ( ω ) i ( m)cs( mω ) = + j( ) ω sin ( ω ) + e wi+ D+ wi+ Dwj sin ( ω ) j= (0) E { ε } Dσ ( ) wsin ω sin ( ω ) + ( m)cs( mω ) () Frm (8), () and (), we get {( ) } ( 8π TD) E f f min(, D) σ sin ( 8π ft ) sin ( 8π ft ) w + ( m)cs(8 π ftm) (3) where min(a,b) dentes the minimum f A and B. It can be seen that the errr variance is related t the frequency ffset f. On the ther hand, when 8π ft. we have Thus, [ sin ( 8π ft ) sin ( 8π ft ) ] (4) {( ) } ( 8π TD) E f f min(, D) σ w min(, D) 9 3 = ( πtd) ρ ρ ρ ρ (5) Fig. depicts the nrmalized errr variance ( σ ) ets as a functin f ρ when L =, K = 0, and f = 0. Slid lines represent the errr variance (5), while the symbls dente the simulatin results. It can be seen that the analysis and simulatin result agree well unless the SR 367

5 한국통신학회논문지 '06-4 Vl.3.4C is very lw. Fig. 3 depicts the nrmalized errr variance as a functin f fr three different values f Cmplex Input Signal + + Cmplex Output Faded Signal SR. By differentiating (5) with respect t, the ptimum values f are L /3 and L /3. The use f = L/3 prvides an perating range X X ise Generatr at given E b / 0 wider than the use f = L/3 at the expense f cmputatinal cmplexity. In what fllws. we cnsider the use f = L/3 unless stated explicitly. 0 -K/0 Jake's Rayleigh Flat Fade Generatr K = Rician Fade Factr in db rmalized Errr Variance ( σ e T ) SR (db) : =0 : =56 : =80 Fig.. Perfrmance f the prpsed estimatin scheme rmalized Errr Variance (σ e T) x0-5 L= a b c a : SR=5dB b : SR=0dB c : SR=5dB Fig. 4. GR channel mdel where a i and θ i respectively represents the magnitude and phase f Rician fading, and the ther terms are the same as in (). The perfrmance f the estimatr is perfrmed in a lgical channel TCH3 (3-timeslt traffic channel) f the GR system, where T = 4.7µ s and L = symbls [9]. Fig. 5 and 6 cmpare the perfrmance f the prpsed estimatr with thers at an SR f 0dB in an AWG channel. It can be seen that the Chuang s scheme () and the s scheme (3) prvide a wide perating range, but suffer frm pr perfrmance. It can als be seen that the scheme (6) and the L&R scheme (8) prvide gd perfrmance. Hwever, the scheme has sme weakness cmpared t the L&R scheme at sme frequency ffset range mainly due t the effect f phase ambiguity in the arg{z} functin. The perfrmance f the prpsed scheme is similar t that f the scheme. Bth the estimatr and the L&R schemes use L 3 fr. It can be seen that the prpsed Summatin Length Fig. 3. Dependence n f the estimatr perfrmance Ⅲ. Perfrmance evaluatin Fig. 4 shws a Rician channel mdel given by the GR specificatin. Then, the utput f the matched filter can be represented as ri = ca i iexp{ j( π fti+ φ + θi) } + ni 0 i< L (6) scheme prvides an perating range narrwer than the Chuang and schemes. Hwever, it prvides a sufficient perating range fr the maintenance f frequency synchrnizatin because the frequency ffset is reduced t a few Hz after initial synchrnizatin. Fig. 7 and Fig. 8 depicts the perfrmance f the prpsed estimatr as a functin f SR in the presence f 0Hz frequency ffset in AWG and Rician channel with K = db and 00 Hz 368

6 논문 / 시분할다중접속방식의위성통신시스템을위한주파수추정 Dppler frequency. It can be seen that the prpsed scheme prvides perfrmance similar t that f the and the L&R scheme. Hwever, when the phase difference between the tw part f the rm. ean Estim. Freq. Offset Chuang Prpsed Eb/=0dB RS freq. errr (Hz) Rician db 00Hz / freq.ffset = 0Hz Prpsed SR (db) Fig. 8. RS estimatin errr in a fading channel rmalized Frequency Offset ( ft) Fig. 5. Averaged perfrmance f the prpsed estimatin scheme RS Freq. Estimatin Errr (σ e T) Eb/=0dB rmalized Frequency Offset ( ft) Chuang Prpsed Fig. 6. RS estimatin errr f the prpsed estimatin scheme burst is large due t the fading, the prpsed scheme may result in a large estimatin errr. On the ther hand, since bth the and the L&R schemes use all the phase difference between the symbls frm the autcrrelatin functin, they can prvide perfrmance smewhat rbust t frequency ffset due t the fading. Table and Fig. 9 cmpare the cmputatinal cmplexity f the estimatin schemes in cnsid- Table. Cmparisn f the implementatin cmplexity Opt. value Real mult. Real add. Chuang L- 0L-8 = L/ L L- = L/3 6L/9-4L/3 8L/9-L/3 = L/3 4L/3+L 4L/3+0L-4 Prpsed = L/3 8L+4 3L/4-3 RS freq. errr (Hz) AGW / freq.ffset = 0Hz Prpsed ult. number Chuang Prpsed SR (db) Fig. 7. RS estimatin errr in an AWG channel L Fig. 9. The cmparisn f multiplicatin cmplexity 369

7 한국통신학회논문지 '06-4 Vl.3.4C eratin, where the cmplexity fr the angle calculatin f cmplex symbl with arg( ) is nt included. It can be seen that the prpsed scheme significantly reduces the cmputatinal cmplexity cmpared t ther schemes. Ⅳ. Cnclusin In this paper, we have cnsiderd the estimatin f frequency ffset in a TDA-based satellite system. We have prpsed a new nn-data aided estimatin scheme that estimates the frequency ffset based n the difference between the phases f the tw parts in the burst. The prpsed scheme requires cmplexity in prprtin t the burst length while cnventinal schemes require cmplexity in prprtin t the square f the burst length. Thus, it can significantly reduce cmputatinal cmplexity, while prviding perfrmance similar t cnventinal schemes. Finally, the perfrmance f the prpsed scheme has been analyzed and verified by cmputer simulatin when applied t a GR system. REFERECES [] D.J.Gdman, Trends in Cellular and Crdless cmmunicatins, IEEE Cmmun. agazine, vl. 9, pp. 3-40, June 99. [] GS Recmmendatin.0, Part II.3, V , ar [3] GEO-bile Radi Interface Specificatin, Part V.5, V..., April 00. [4] C. Heegard, J. A. Heller and A. J. Viterbi, A icrprcessr-based PSK dem fr Packet Transmissin ver Satellite Channels, IEEE Trans. Cmmun., vl. CO-6, pp , ay 978. [5]. P., Planar Filtered Techniques fr Burst de Carrier Synchrnizatin, IEEE GLOBECO 9, Phenix, AZ, paper., Dec. 99. [6]. and R. Reggiannini, Carrier Frequency Recvery in All-Digital dems fr Burst-de Transmissins, IEEE Trans. Cmmun., vl. 43, n. 3, pp , ar [7] J. C.-I. Chuang and. R. Sllenberger, Burst Cherent Demdulatin with Cmbined Symbl Timing, Frequency Offset Estimatin, and Diversity Selectin, IEEE Trans. Cmmun., vl. CO-39, pp , July 99. [8] S., C. linari and G. Tartara, Digital Frequency Estimatin in Burst de QPSK Transmissin, IEEE Trans. Cmmun., vl. 38, pp , July 990. [9] GEO-bile Radi Interface Specificatin, Part V., V..., Apr. 00. 김종문 (Jng-n Kim) 정회원 00년 8월서울대학교전기공학부학사 004년 8월서울대학교전기컴퓨터공학부석사 004년 9월 ~ 현재 LG전자 DTV 연구소주임연구원 < 관심분야 > VSB 시스템, OFD 시스템, 차세대통신용신호처리이용환 (Yng-Hwan Lee) 종신회원 977년서울대학교전기공학과학사 980년한국과학기술원전기전자공학과석사 989년 University f assachusetts, Amherest, 박사 980년 ~985년국방과학연구소선임연구원 989년 ~994년 Principal engineer in trla Inc. 994년 ~ 현재서울대학교전기공학부교수 < 관심분야 > 유 / 무선송수신기설계, 차세대통신용신호처리 370