Pilot-assisted Channel Estimation for OFDM/TDM with Frequency-domain Equalization

Transcription

1 Pio-assised Channe Esimaion for OFDM/TDM wih Frequeny-domain Equaizaion Haris GACAI * Shinsuke TAKAOKA * and Fumiyuki ADACHI ** Eeria and Communiaion Engineering, Graduae Shoo of Engineering, Tohoku Universiy Aza-Aoba, Aramaki, Aoba-ku, Sendai, Japan E-mai: * (haris, akaoka)@mobie.eei.ohoku.a.jp, ** adahi@eei.ohoku.a.jp Absra: Orhogona frequeny division muipexing ombined wih ime division muipexing (TDM), aed OFDM/TDM, an overome he high peak-o-average-power raio (PAPR) probem of he onveniona OFDM. Is bi error rae (BER) performane in a frequeny-seeive fading hanne an be signifiany improved by he use of frequeny-domain equaizaion (FDE) based on minimum mean square error (MMSE) rierion. However, requires aurae hanne esimaion. In his paper, a pio-assised hanne esimaion sheme suiabe for OFDM/TDM wih is presened and he ahievabe BER performane is evauaed by ompuer simuaion. Keyword: OFDM/TDM, frequeny-domain equaizaion, pioassised hanne esimaion I. ITRODUCTIO Orhogona frequeny division muipexing has been araing onsiderabe aenion beause of is robusness agains frequeny-seeive fading []. However, OFDM signas have he probem of high peak-o-average power raio (PAPR) [2]. Reeny, we have shown [3] ha OFDM ombined wih TDM [4], aed OFDM/TDM, an overome he PAPR probem of he onveniona OFDM whie signifiany improving he BER performane by he use of simpe one-ap frequeny-domain equaizaion (FDE) based on minimum mean square (MMSE) rierion. We have aso shown [3] ha OFDM/TDM wih bridges OFDM and singe arrier ransmissions. requires aurae hanne esimaion (CE). In [3] and [4], an idea CE is assumed. In [5], pio-assised CE ehniques for OFDM are presened. Having in mind ha OFDM/TDM bridges onveniona OFDM and SC ransmissions, a seeion of pio sequene is very imporan. If a known pio sequene wih he onsan ampiude in he frequeny-domain is used, arge ampiude variaions may appear in he ime-domain and signa may be disored due o non-inear power ampifiaion. This is no desirabe for SC ransmission, whih is a speia ase of OFDM/TDM, where he ransmied signa ampiude in he ime-domain is onsan and he PAPR probem is no presen. In his paper, we onsider a pio-assised CE wih deayime domain windowing [5] for OFDM/TDM. oise on hanne esimaes is signifiany redued by deay-ime domain windowing, whih repaes he esimaed hanne impuse response wih zeros beyond he guard inerva (). I is neessary for pio sequene o have as muh as possibe sma ampiude variaions in he ime-domain when OFDM/TDM signa ges ose o SC. Reeny, a design of he pio sequene wih onsan ampiude in he frequenydomain and sma ampiude variaions in he ime-domain was proposed [6]. We a he pio sequene having his propery as onsan ampiude (CA) pio sequene. The average BER performane of OFDM/TDM wih pio-assised CE using CA pio sequene is evauaed by ompuer simuaion and ompared wih pio sequene having onsan ampiude in he frequeny-domain (aed frequeny-domain (FD) pio sequene), pio sequene having onsan ampiude in he ime-domain (aed ime-domain (TD) pio sequene) and Chu pio sequene [7]. The res of he paper is organized as foows. Seion II briefy desribes OFDM/TDM ransmission mode. In Se. III, he pio-assised CE is presened. Se. IV evauaes, by ompuer simuaion, he BER performane of he OFDM/TDM using pio-assised CE in a frequeny-seeive Rayeigh fading hanne. Se. V provides onusions. II. OFDM/TDM TRASMISSIO MODEL Throughou his paper, T -spaed disree ime represenaion is used, where T represens he fas Fourier ransform () samping period. An OFDM/TDM frame sruure is iusraed and ompared wih he onveniona OFDM in Fig.. Assume ha he onveniona OFDM has subarriers. The ime inerva of daa symbos (aed OFDM/TDM frame) of he onveniona OFDM is divided ino K sos as iusraed in Fig.(b); an OFDM signa wih redued number of subarriers ( m /K) is ransmied during eah ime so. The OFDM/TDM beomes SC when K whie i beomes onveniona OFDM when K. Figure 2 iusraes he OFDM/TDM ransmier and reeiver sruures. We onsider a ransmission of daamoduaed symbos {d(i); i -}. The daa-moduaed symbo sequene is divided ino K daa boks, eah having m daa symbos. Then, m -poin inverse () is appied on eah bok o generae a sequene of K OFDM signas wih m ( /K) subarriers eah. The OFDM/TDM signa an be expressed using he equivaen owpass represenaion as K k k s ( ) s ( k ) u( k ) () for -, where u()() for m - (esewhere) and s k () is he k-h OFDM signa wih m subarriers, given by m m /5/$2. () 25 IEEE

2 m m i k 2Es i s ( ) d( km + i)exp j2π (2) T m for m -, where E s represens he symbo energy. Finay, g sampe is insered a he beginning of he frame and he -insered OFDM/TDM signa is ransmied over he frequeny-seeive fading hanne. Sine he is no insered beween onseuive sos, bu ony a he beginning of OFDM/TDM frame, he iner-symbo inerferene (ISI) arises due o frequeny-seeive fading and degrades he BER performane. To overome his probem whie improving he BER performane, we appy one-ap. I shoud be noed ha FDE is no appied o eah OFDM signa wih m subarriers as in onveniona OFDM, bu o OFDM/TDM signa over he enire frame. We assume ha he hanne is omposed of L disin propagaion pahs having differen ime deays. The reeived signa an be expressed as L r( ) h s( τ ) + η( ) for - g -, where h and τ denoe he pah gain and ime deay of he h pah, respeivey, and η() is he addiive whie Gaussian noise (AWG) proess wih zero mean and variane 2 /T wih being he singe-sided power sperum densiy. Afer he is removed, he reeived ime-domain signa {r(); -} is deomposed ino frequeny omponens by -poin. The kh frequeny omponen R( is represened as R( r( ) exp j2 k π S( H ( + ( for k -, where S(, H( and ( are, respeivey, he ransmied OFDM/TDM signa omponen, he hanne gain and he noise omponen a he kh frequeny given by S( H ( ( L s( ) exp j2πk η( ) exp j2πk τ h exp j2πk Then, is appied as (3) (4). (5) R ˆ( w( R(, (6) where w( is he MMSE equaizaion weigh given by [] H ( w (. (7) 2 2 H ( + 2σ In Eq. (7), H(, E s and σ 2 (2 / T ) represen he hanne gain a he kh frequeny, he symbo energy and he noise power, respeivey, and * denoes he ompex onjugae operaion. Afer performing, -poin is appied o obain an equaized OFDM/TDM signa. Finay, he OFDM/TDM demoduaion is performed o reover he ransmied daa symbo sequene. As seen from Eq. (7), esimaion of he hanne gain and he noise power is neessary o ompue he weigh. AWG g g k K- m (b) OFDM/TDM signa * (a) Conveniona OFDM OFDM signa wih m subarriers Figure. OFDM/TDM frame sruure. Info daa Remova of Daa mod. {R(k )}.. -poin m -poin per fra me Pio seq. (a) Transmier Channe esimaion {w(k )} -poin s() M U X p() OFDM /TDM demod. Reovered daa Daademod. (b) Reeiver Figure 2. OFDM/TDM ransmission sysem mode. III. PILOT-ASSISTED CHAEL ESTIMATIO A. Channe Esimaion Using Deay-ime Domain Windowing For pio-assised CE, he pio frame is ransmied foowed by d OFDM/TDM daa frames, as shown in Fig. 3. Figure 4 iusraes he bok diagram for pio-assised CE. Firsy, by reverse moduaion, he insananeous hanne gain esimae a he kh frequeny is obained as

3 R( H ( (8) P( for k -, where P( is he kh frequeny omponen of he ime-domain pio sequene p(). Subsiuing Eq. (4) wih S(P( ino Eq. (8), H ( k ) an be expressed as ( H ( H ( +. (9) P( If P( a some frequenies, arge noise enhanemen is produed, hereby degrading he hanne esimaion auray. To avoid his noise enhanemen, i is neessary ha P( ons for a k. -poin is performed on { H ( ; k -} o obain he insananeous hanne impuse response { h ( ) ; -}. Assuming ha he aua hanne impuse response is presen ony wihin he, he esimaed hanne impuse response beyond he is repaed wih zero s o redue he noise [5]. Then, -poin is appied o obain he improved hanne gain esimaes {H e (; k - }: g H e ( h ( )exp( j2πk g ). () The noise omponen a he kh frequeny an be esimaed by removing he reeived pio omponen H e (P( from R( as e (R(-H e (P(. () The noise power esimae an be obained as {R(} k 2 2 σ e(. (2) 2 g + sampes g + sampes {P(} Pio Daa Daa Pio frame OFDM/TDM daa frame Figure 3. OFDM/TDM pio bok inserion. Reverse mod. { H ( k { h ( )} { ( k )} )} -poin Windowing Figure 4. Pio-assised CE. -poin B. Pio Sequene Generaion To avoid noise enhanemen, i is desirabe ha P( has onsan ampiude for a k. However, if P( ons for a k, arge ampiude variaions may appear in p(); his is no desirabe for SC ransmission. Therefore, we aow sma ampiude variaions in p() in order o keep he onsan ampiude in P(. In his paper, we use he CA pio sequene H e proposed in [6] and for omparison, we onsider FD pio, TD pio, and Chu pio sequene. The Chu pio sequene is given by p()os(π 2 / )+jsin(π 2 / ) for - [7]. The CA pio generaion proedure presened in [6] is shown in Fig. 5. The ime-domain represenaion of he generaed pio sequene afer i ieraions is denoed as ( ) ( ) P i p i ( ) and he frequeny-domain represenaion by (. The iniia frequeny-domain sequene () { P ( ; k } is generaed by randomy seeing he QPSK onseaion poins. The pio sequene p (i) () in he ime-domain is generaed as foows: ( ) p i ( ) is inpu o an idea hard-imier, produing a modified sequene p ( ) exp( j arg( p ( ) ) HL -poin is performed on { p ( ); } o obain HL { P HL ( ; k } ( P i ) HL ( is inpu o he idea hard-imier, produing a modified sequene P ( exp( j arg( PHL ( ) -poin is performed on { P ( ; k } o obain { p ( ) ; } Repea his proedure a suffiien number of imes The ampiude of CA pio sequene is aways onsan in he frequeny-domain. The generaed CA pio sequene in ime-domain is shown in Fig. 6. I an be seen ha, afer ieraions, he generaed CA pio sequene has amos he onsan ampiude in he ime-domain, whie he ampiude in he frequeny-domain is kep onsan. This is aso onfirmed by he probabiiy densiy funion (PDF) of he normaized ampiude of he CA pio sequene (see Fig. 7). In our simuaions in Se. 4, he number of ieraions is se o. Hard imier (HL) ( ) phl i ( ) ( ) P i ( ) HL ( k ) P i ( -poin Hard imier (HL) i -poin ( ) p i ( ) { P ( k )} Figure 5. Ieraive generaion proedure of CA pio sequene. Imaginary p () ( ) Rea (a) p () () ()

4 Imaginary p () ( ) Rea (b) p () () Figure 6. Ampiude of CA pio sequene in ime-domain. PDF p (i ) ( ) ii ii ormaized ampiude Figure 7. Ampiude PDF of he CA pio sequene in ime-domain. IV. PERFORMACE EVALUATIO Simuaion ondiions are shown in Tabe I. We assume QPSK daa-moduaion wih 256 and g 32. The propagaion hanne is a T -spaed L6-pah frequenyseeive bok Rayeigh fading hanne having uniform power deay profie. Bok fading means ha he pah gains say onsan over one OFDM/TDM frame bu varies frameby-frame. Transmier Channe Reeiver TABLE I. SIMULATIO CODITIOS. Daa moduaion QPSK umber of poins m 256/K umber of sos per frame K256 Frame engh 256 g 32 L6-pah frequeny-seeive bok Rayeigh fading umber of poins 256 FDE MMSE Figure 8 shows he average BER performanes of OFDM/TDM wih pio-assised CE using CA pio, FD pio, TD pio, and Chu pio as a funion of he reeived bi energy-o-awg power sperum densiy raio E b /.5(E s / ) (+ g / ) (+/ d ) for he normaized Dopper frequeny f D T s.4, where /T s /[T (+ g / )] is he ransmission symbo rae (f D T s.4 orresponds o a mobie ermina moving speed of 8km/h for 5GHz arrier frequeny and ransmission daa rae of /T s M symbos/se). Deay-ime domain windowing is assumed for pio-assised CE. The average BER performane wih TD pio severey degrades due o arge noise enhanemen. The average BER performanes of CA pio, FD pio, and Chu pio are amos idenia. However, he FD pio has PAPR probem and i is no appropriae for SC (K256) ase. The average BER performane of OFDM/TDM wih pio-assised CE using CA pio wih and wihou deay-ime domain windowing is poed in Fig. 9, as a funion of he average E b /. The BER performane wih idea CE is aso poed for omparison. Idea CE refers o he ase wihou he effe of noise (e.g., ony raking error agains he hanne ime variaions is presen). When deay-ime domain windowing is used, he signa-o-noise raio (SR) of he hanne esimaes is improved by a faor of / g, eading o an improved BER performane. Wihou deay-ime domain windowing, E b / degradaion for an average BER -4 from he idea CE ase is abou 4.3 (4.) db for K and abou 4.9 (4) db for K256 when d 3 (5). However, when he deay ime-domain windowing is used, he E b / degradaion redues o.8 (.6) db for K and.7 (.9) db for K256 when d 3 (5). In he foowing, we ony onsider pioassised CE wih deay-ime domain windowing and CA pio. How he fading rae impas he ahievabe BER performane is disussed beow. Figure pos he average BER as a funion of f D T s for d 3 and 5 when E b / 2 db. For omparison, he BER wih idea CE is aso poed. For d 3 (5), he average BER remains onsan uni f D T s reahes. (.),.2 (.2) and.4 (.5) for K256, 6 and, respeivey, and sars o degrade due o raking error as f D T s vaue inreases..e-.e-2.e-3.e-4.e-5 K 256 K, 6 and 256 K 6 f D T s.4 TD pio FD, Chu and CA pios K Average E b / (db) (a) d 3

5 .E-.E-2.E-3.E-4.E-5 Figure 8..E-.E-2.E-3.E-4.E-5.E-.E-2.E-3.E-4.E-5 K 256 K, 6 and 256 K 6 MMSE f D T s.4 TD pio FD, Chu and CA pios K Average E b / (db) K 256 (b) d 5 Comparison of various pio sequenes. f D T s.4 CA pio Idea CE wih windowing w/o windowing K 6 K Average E b / (db) K 256 (a) d 3 f D T s.4 CA pio Idea CE wih windowing w/o windowing K 6 K Average E b / (db) (b) d 5 Figure 9. BER performane wih pio-assised CE..E-.E-2.E-3.E-4.E-5 CA pio Pio CE Idea CE d 5.E f D T s d 3 E b / 2 db K K K K6 K K256 Figure. Impa of Dopper frequeny. V. COCLUSIOS In his paper, we presened pio-assised CE wih deay-ime domain windowing for OFDM/TDM wih MMSE- FDE. The insananeous hanne ransfer funion is esimaed by reverse moduaion using periodiay insered pio bok. Sine OFDM/TDM hanges beween OFDM and SC ransmission by varying he parameer K, a pio sequene having as muh as possibe onsan ampiude in he imedomain is desirabe. The BER performane using he CA pio sequene wih onsan ampiude in he frequeny-domain and sma ampiude variaions in he ime-domain was evauaed by ompuer simuaion and ompared wih TD pio, FD pio, and Chu pio sequenes. I was shown ha pioassised CE wih deay-ime domain windowing using CA pio ahieves an E b / degradaion of ess han db from he idea CE ase when CA pio bok is insered afer every 5 OFDM/TDM daa boks. Chu pio sequene ahieves he same BER performane as he CA pio sequene. REFERECES [] S. Hara and R. Prasad, Muiarrier Tehniques for 4G Mobie Communiaions, Areh House, June 23. [2] R. D.J. van ee, R. Prasad and R. van ee, OFDM for wireess muimedia ommuniaions, Areh House, Jan. 2. [3] H. Gaanin, e a., Generaized OFDM for bridging beween OFDM and singe-arrier ransmission, Pro. 9 h Inern. Conf. on Comm. Sys., Singapore, Sep. 24. [4] C. V. Sinn, e. a., Common arhieures for TD-CDMA and OFDM based mobie radio sysems wihou he neessiy of a yi prefix, MS-SS Workshop, Oberpfaffenhofen, Germany, Sep. 2. [5] S. Coeri, M. Ergen, A. Puri, and A. Bahai, Channe esimaion ehniques based on pio arrangemen in OFDM sysems, IEEE Trans. Broad., Vo. 48, o. 3, pp , Sep. 22. [6] R. Dinis, e a., Channe esimaion for MIMO sysems empoying singe-arrier moduaions wih ieraive frequeny-domain equaizaion, 6 h IEEE VTC, LA, USA, Sep. 24. [7] D. C. Chu, Poyphase odes wih good periodi orreaion properies, IEEE Trans. Inf. Theory, Vo. 5, o. 7, pp , Juy 972.