S Post-graduate Course in Radio Communications Spread Spectrum Principles and Methods

Transcription

1 S Pos-grdue Course Rdo Couos - Sred Seru Prles d Mehods Jro Os El: jro.os@o.o De:..

2 . BASIC PRICIPLES OF SPREAD SPECTRUM...3. DIRECT SEQUECE DS SPREAD SPECTRUM Colex sredg Dul hel querry sredg Bled querry sredg Sle bry sredg...9. FREQUECY HOP FH SPREAD SPECTRUM.... SPREADIG SEQUECES.... SPREADIG WAVEFORMS...5. M-SEQUECES GOLD SEQUECES KASAMI SEQUECES BARKER SEQUECES....6 WALSH-HADAMARD SEQUECES POWER SPECTRAL DESITY OF SPREAD SPECTRUM SIGALS... REFERECES...3

3 . BASIC PRICIPLES OF SPREAD SPECTRUM Se 94's sred seru syses were develoed for j d low robbly of ere LPI los [] by sredg he sgl over lrge frequey bd d rsg wh low ower er u bdwdh. I he j syses serl sredg seures he sgl gs rrowbd erferers Fgure [4] d he LPI syses o es he deeo s dfful s ossble for uwed ereor by hdg he sgl he ose. Fgure : rrowbd erferee rejeo [4] : Fgure 5.7 I he sred seru syses sed of llog dsjo frequey hels or e slos for dffere users he suleous users re o he se frequey bd. The fudel roble of sred seru ulle ess ouo lo ode dvso ulle ess CDMA s h eh user uses ulle ess erferee MAI ffeg ll he oher users. Whe he serl effey of he dffere ulle ess ehods ws luled by g o ou he orgl sgl bdwdh he gurd bds for FDMA gurd e for TDMA d MAI for CDMA bu o he hel roeres he followg resuls were obed : Tble [4]. 3

4 Tble : Sury of ulle ess ehologes [4] Dxo Sred Syses wh Coerl Alos : Tble. Lower level of serl effey ws obed for CDMA. I he erly ulle ess syses CDMA dd o gve ler dvge over TDMA/FDMA. The rrowbd ehods FDMA d TDMA re ore sesve o hel res bu uless hey re serous eough MAI s he dog soure of errors. Error robbly lulos bsed o MAI odeled s AWG be foud [] d [3]. However reely sred seru ehology hs beoe vble lerve for ellulr syses. The dvges of usg sred seru for ellulr los lude: here ulh dversy lrge bdwdh llows usg y ulh ooes he RAKE reever sof y by exlog he y whou rellog hels sof hd off bly roved serl effey o eed for he frequey reuse dse bewee ells d gurd bds of dje frequees rrow bd erferee rejeo Fgure [4] d here essge rvy.[] The dsdvge of sred seru s used by MAI: he deeed sgls us be orolled o hve equl ower o vod he er-fr effe. I sred seru syse he d sybols x {x } re oduled oo rrer by usg sredg sequee sgure sequee sredg ode { } h s dffere for eh user. Ths sequee sreds he rsed sgl bdwdh o be uh lrger h he d sgl bdwdh. The sred seru syse os he followg oeros : d odulo of bs o sybols sredg bdwdh exso d rrer odulo [5] : 4

5 Trser : Reever : Sredg be erfored eher o he bsebd or o he rrer frequey: D bs D odulo D sybol sequee x Sredg Pssbd sgl : Re{ x e jπf } Desredg D sybol sequee x D deodulo D bs Sredg sequee Sredg sequee Possble les for rrer odulo d deodulo Fgure Beuse geerl he d d sredg sequees re olex he rsed sgl be odeled s he rel r of he rodu of hree olex sgls : { e j π f x } s Re where he r x h s used o odule he rrer s lled he olex eveloe The olexy s leeed by he hse-shfed I- d Q-rrers. The sgls wh rel d gry rs re drw by double les Fgure. 5

6 Whe sredg s erfored e do.e. he hs of he sgure sequee re led dffere h erods T he sred seru ehod s :. Dre sequee CDMA DS-CDMA whe eh sybol x s sred o sequee of hs o sgle rrer. The sredgwvefor A re used o odule sglerrer f where h T d d wvefor x A x u T wh hebsebdolex eveloe s~ x h d u re he rel hd b ludeshgfuos T D sybol Srdg sequee : Frequey hog CDMA FH-CDMA whe eh d sybol x s sred o sequee of hs o dffere frequee shfs f of he erl rrer frequey f. I s oduled by he olex eveloe ~ j f s π x h T e D sybol Sredg sequee : f f f 3 f 4 f 4 f 5 f Te hog CDMA TH-CDMA whe he hs re used o odule sgle rrer by lg oe h sde he sybol fre T dffere e slo T for eh sequel sybol. D sybols Sredg sequee : Whe he sredg odulo s erfored he frequey do he hs of he sgure sequee re used o odule suleously dffere orhogol subrrers. Ths seru ehod s lled ulrrer CDMA MC-CDMA. Ised of odulg eh sequel sybol o dffere subrrer ylly OFDM he se sybol x s MC-CDMA used o odule ll he subrrers f f by usg dffere h vlues for eh subrrer. 6

7 However OFDM be used ogeher wh MC-CDMA by overg blo of serl d sybols o blo of rllel d sybols d odulg eh rllel sybol o dffere se orhogol subrrers. D sequee x x Serl Prllel Coverer x Sredg odulor x e jπ f x K e jπk f X x Fgure 3 [6]. DIRECT SEQUECE DS SPREAD SPECTRUM I DS sred seru syse D oduled rrer s oduled drely by ode sequee he ro of he sybol d h erods s lled he roessg g G T / T The eorl legh of oe ode erod of shor ode sequee s equl o he sybol erod G T T. The ode erod of log ode sequee os severl sybol erods G<< T << T. Shor odes re used by uluser deeo syses beuse hey use he b erod roery of he shor odes for MAI elg. Oherwse he log odes re referred beuse he erferee fro ll users beoes del o he verge. [9] D sybols Sredg sequee Sequee erod of log ode.. Colex sredg : Whe he sredg d d x sequees re olex QPSK sequees : I +j Q olex sequee xx I +j x Q olex sequee { : {±±j}} x{x :x {±/ ±j / } he olex eveloe bsebd sgl h s used o odule he I- d Q- rrers s [] : s~ x x I I Q [ I + j Q ] [ xi + j xq ] xq + j [ I xq + Q xi ] ~ si j ~ + sq Ths be leeed wh he olex sredg ru : 7

8 Fgure 4 : Colex sredg [] : Fgure 9... Dul hel querry sredg : Whe he sredg sequee s rel he I- d Q-hels hve deede sredg sequees I d Q. The d sequee x be QPSK oduled or oss of deede BPSK oduled d sequees x I or x Q. Whe BPSK d odulo s used x s rel d x I d x Q re deede d sequees I d Q rel sequee x x I +j x Q or x x I d x Q olex or rel sequees IQ { : {±}} x IQ {x :x {±/ ±j / } Ths be leeed by he dul hel querry sredg ru : Fgure 5 : Dul hel querry sredg [] : Fgure Bled querry sredg : Whe he sredg sequee s rel hvg deede sequees I d Q for he I- d Q-rrer d oly oe rel BPSK d sequee x s used I d Q rel sequees x oe rel d sequee IQ { : {±}} x{x :x {±} 8

9 Ths be leeed by he bled querry sredg ru : Fgure 6 :Bled querry sredg [] : Fgure 9.4b..4. Sle bry sredg : Oe rel BPSK oduled d sequee be lso sred o sgle rrer by he sle bry sredg : oe rel sredg sequee x oe rel d sequee { : {±}} x{x :x {±}: Fgure 7 : Sle bry sredg [] : Fgure 9.4 The DS sred seru reever erfors he followg fuos: ode syhrozo wh he og sequee hse syhrozo wh he og hse he se of ohere deeo desredg d flerg he sgl d deeg he d. Code d hse syhrozo oss of quso d rg oeros. The reeved sgl be desred by usg hed fler or orrelor. Mhed flers re used wh ohere deeo d for ode quso wh he ohere deeo. 9

10 Fgure 8 : Slfed DS/QPSK syse [] : Fgure 9. The b error robbly of DS/QPSK wh Gry odg gve by ML reever AWG hel s del o QPSK []: P e E / Q whh s del o oveol ohere QPSK. b Sredg d desredg do o rove P e AWG-hel beuse bdwdh exso s deede of d d sredg does o ffe he serl d robbly desy fuos of AWG-ose [] [7]. DS sred seru syse wh seudoose sequees s vergg ye syse. Mulle ess erferee fro oher users s redued by vergg.. FREQUECY HOP FH SPREAD SPECTRUM I frequey hog sred seru syses he rrer frequey hos hroughou fe se of frequees durg he ode erod. FH sred seru syse s vode ye syse whh erferee s redued by vodg se frequees. There re wo bs yes of FH sred seru: slow frequey hog SFH d fs frequey hog FFH. SFH syses rs oe or ore d sybols er ho. FFH syses rs he se d sybol o ulle sequel ho frequees.

11 Fgure 9 : Slfed FH syse oerg o AWG hel [] : Fgure 9.5 Whe M-ry frequey shf eyg MFSK s used s d odulo f s he frequey sero bewee sybols x. The hog frequees f h re frequey shfs relve o he eer frequey deered by he sybol x. The olex eveloe for slow frequey hog s []: 9.7 : ~ L jx π f + π f L+ s A e u L + T The olex eveloe for fs frequey hog s []: 9.8 : ~ L jx π f + π f + L s A e u L + T / L T T The er su dexes for SFH he d sybols d for FFH he hog frequees. The FH sred seru syse y use ohere or ohere deeo bu eselly for FFH he ohere frequey syheszer s dfful o lee.

12 . SPREADIG SEQUECES The sredg sequees be lssfed s orhogol sequees d seudoose P sequees. The ross orrelo of he orhogol sequees s zero d so MAI fro oher users s elled. Orhogol sequees re used syhroous CDMA syses beuse he ross orrelo fuo vres rerbly s fuo of he e shf of he sequees. The seudoose P sequees hve uo-orrelo fuo h s slr o whe Guss ose. The reeved sequees fro oher users re lso ose-le sgls. MAI fro oher users s dsrbued evely e d bewee he erferg users. Ths llows syhroous oero. They re hose o hve hree desrble rbues []: Eh elee of he sequee or +- ours wh equl frequey The uo-orrelo hs sll off-e vlues o llow rd sequee quso d 3 Cross-orrelo s sll ll delys. However he rbues d 3 re dfful o heve suleously. Desgg he sequees o hve low ross orrelo redues he rdoess of he sequees d reses he off-e vlues of he uo-orrelo fuo. [8] Sredg sequees re ofe hrerzed ers of her dsree-e orrelo roeres wh he e shf. Whe shor odes re used he uo- d ross-orrelo re luled over full sequee erod. Whe hey re luled erodlly he vlues of sequel d sybols re gored. The erod uo-orrelo of he -h olex sredg sequee over full erod s [] * + d he erod ross-orrelo over full erod bewee he -h d -h sequees d s [] + * The erod uo-orrelo over he full erod of he sequee lules oly he overlg r of he sequees [].

13 * * Slr equos re obed for he erod ross-orrelo of sequees d over full erod. T +T : : Perod ross-orrelo over full erod : Aerod ross-orrelo over full erod: T +T Fgure : Perod d erod full erod uo- d ross-orrelos : : T > [] + By usg he erod uo-orrelo he effe of dffere oseque sybols be e o ou []: - sybols re oseque d + + b b b b b b Whe log odes re used he rl erod uo- d ross-orrelos re luled over he b erod TG T sed of he whole sequee erod []. + * G G + * G G

14 4 T +T : : Perod orrelo over rl erod: Aerod orrelo over rl erod: Fgure : Perod d erod rl erod uo- d ross-orrelos : : Sybol erod Sequee erod The rl erod orrelos re o oly fuo of he dely bu lso deed uo he o he sequee where he suo ully srs. They re dfful o derve lylly. Therefore ssl uo- d ross-orrelos re used ssug h he sequees wh elees {±±j} re rdoly geered. The e d vre of he rl erod uoorrelo erod re [] [ ] [ ] + E G E G. * δ µ G G E /. δ µ σ The e d vre of he rl erod ross-orrelo erod re [] [ ] E µ G E / µ σ

15 . SPREADIG WAVEFORMS I syhroous syses he uo- d ross-orrelo for he ouous-e wvefors deed lso o he ou of overlg δ of he h wvefors : h T ' ' δ l Fgure : Ch overlg The ouous-e erod ross-orrelo over full erod bewee he sredg wvefors d deeds boh o he e shf bewee he sequees l erler d he h overlg e shf δ [] : R T τ + τ d T R δ + + Rˆ h h δ For regulr h wvefor h u T : δ R + + T T τ T R h δ Rˆ + δ δ τ τ T + δ h δ : h wvefor orrelos The xu uo- d ross-orrelos re obed by he h-syhroous roxo δ : R τ R τ The rl erod uo- d ross orrelos re ssl fuos.. M-SEQUECES A wdely used ye of P sequees re he xu-legh shf-regser sequees LFSR -sequees. Eh sequee s geered by sere LFSR h hs sges. The erod of he sequee sequee legh s. They re he loges sequees h be geered by LFSR for gve. [] 5

16 Fgure 3 : -sequee geeror [] : Fgure 9.6 The ullers {} d deoes odulo ddo. The elees hs of he sequee {} re ed o {+-} for bolr odg. The sequee hs - oes d - zeros. The feedb olyol s rve olyol of degree over GF [] : Px x x 3 x 3 - x - x A -sequee hs los del full erod uoorrelo : / The full erod uo-orrelo fuo for ouous e sequee wvefors whe he regulr h shg fuo h u T s used s : R δ δ τ + + τ T + δ T T Fgure 4 : Tyl full erod uoorrelo fuo of -sequee sredg wvefor [] : Fgure 9.7 6

17 However oly for er vlues of here exs soe rs of -sequees wh low full erod ross-orrelo. Whe he verge full erod ross-orrelo bewee sequees d s luled for dffere shfs of he sequees: θ he vlue of θ vres uh deedg o he rulr r of -sequees h re seleed d he wors θ-vlues re gre. Tbel : Bes d wors se verge ross-orrelos for -sequees []: Tble 9. Fgure 5 : Cross-orrelo fuo of yl - sequees [4] 7

18 .3 GOLD SEQUECES A se Gold sequees oss of + sequees hvg he erod h re geered by referred r of -sequees. Ths se os boh he referred r d he - ew geered sequees. The sequees re geered by g odulo- su of wh he - yllly shfed versos of or ve vers. Fgure 6 : A Gold sequee geeror wh x +x +x 5 d x +x+x +x 4 +x 5 Ths sequee geeror rodue 3 Gold sequees of legh 3. []: Fgure 9.8 Beuse he Gold sequees re o xl legh sequees exe d he uo-orrelo fuo s o -vlued. Boh he ross-orrelo d off-e uoorrelo fuos re 3-vlued : {- - -} where + / + + / + whe whe s odd s eve So boh he ross orrelo d off-e uo-orrelo fuos re uer bouded by : 8

19 Tble 3 : Pe ross orrelo of -sequees d Gold-sequees [] : Tble 9..4 KASAMI SEQUECES The sll se of Ks sequees osss / sequees hvg he erod. Ths se s geered wy slr o he Gold sequees by usg r of log sequee d shor sequee h re -sequees. Ths se os boh he log sequee d he / - ew geered sequees. The sequees re geered by g odulo- su of wh ll he / - yl shfs of. Fgure 7 : A Ks sequee geeror wh x +x+x 6 d x +x+x 3. Ths sequee geeror rodue 8 Ks sequees of legh 63. []: Fgure 9.9 9

20 Le for Gold sequees he ross-orrelo d off-e uo-orrelo fuos re 3-vlued. The ossble vlues re : {- -s s-} where / + The uer boud s for he ross orrelo d off-e uo-orrelo fuos s redued o hlf ored wh he Gold sequees of he se legh. The lrge se of Ks sequees os lso Gold sequees d hee he rossorrelo d off-e uoorrelo vlues re o he verge hgher h he sll se of Ks sequees..5 BARKER SEQUECES The Brer sequees re erod sequees fe legh sequees. Ther rossorrelo d off-e uo-orrelo vlues re led by / bu hey re ow oly for ode leghs Beuse he Brer sequees re shor d her uber s led hey re used for sel urose syses s for l syhrozo d wreless LAs. or.6 WALSH-HADAMARD SEQUECES The Wlsh-Hdrd sequees re orhogol sequees. They re he rows of he Hdrd rx h s obed by he reurso : H M H M H M srg fro H H M H M The Wlsh-Hdrd sequees be used eher o sred orhogolly orhogol CDMA he sgls of he dffere users or for M-ry orhogol odg he dffere sybols. If orhogol sequees re used for dffere users ure syhrozo s eeded beuse he orhogol sequees hve for o-zero e shfs lrge ross-orrelo d off-e uo-orrelo vlues. If orhogol sybols re used log M bs re used o eode oe of he orhogol sybols. The user sgls re sred by dffere seudoose sequees.

21 3. POWER SPECTRAL DESITY OF DS SPREAD SPECTRUM SIGALS For uorreled zero-e d sybols he ower serl desy of he bsebd olex eveloe s [] : 4.6 A S~ s~ s f σ x H f T [] : 9.58 where h s he lude shg wvefor deered by he sredg sequee d he h ulse wvefor h h H h T [] : 9.59 f H f Φ f [] : 9.6 where Φ f s he dsree Fourer rsfor of he erod uoorrelo fuo of he sredg sequee. The ower serl desy deeds o he serl rodu of he h ulse wvefor h d sredg sequee : A S~ s~ s f σx H f Φ f T [] : 9.64 For exle for he regulr h ulse wvefor h d del erod uoorrelo fuo: S f A T ~ s ~ s s ft The effe of he devo fro he del erod uo-orrelo fuo s luled for he legh- Brer sequee : d for he legh-5 -sequee : Beuse he -Brer sequee hs he erod uo-orrelo fuo h s loser o he del oe hs sooher ower serl desy. For hs reso he legh- Brer sequee hs bee hose for he IEEE 8. wreless LA sefo.

22 Fgure 8 []: Fgure 9. Aerod uoorrelo fuo for he legh- Brer sequee Fgure 9 []: Fgure 9. Aerod uoorrelo fuo for he legh-5 -sequee Fgure []: Fgure 9.3 PSD wh he legh- Brer sequee Fgure []: Fgure 9.4 PSD wh he legh- Brer sequee

23 REFERECES [] Gordo L. Suber : Prles of oble ouo d edo Kluwer Ade Publshers [] Mhel B. Pursley : Perfore Evluo for Phse-Coded Sred-Seru Mulle-Aess Couo Pr I : Syse Alyss. Mhel B. Pursley Phl V. Srwe: Pr II : Code Sequee Alyss IEEE Trsos o Couos Vol.Co-5 o. 8 Augus 977 [3] Mhel B. Pursley Phl V. Srwe Wye E. Sr : Error Probbly for Dre-Sequee Sred-Seru Mulle-Aess Couos Pr I: Error Probbly for Dre-Sequee Sred-Seru Mulle-Aess Couos :Uer d Lower Bouds Evggelos A. Geros Mhel B. Pursley : Pr II: Aroxos IEEE Trsos o Couos Vol.Co.-3 o. 5 My 98 [4] Rober C. Dxo : Sred Seru Syses wh Coerl Alos 3 d edo 994 Joh Wley & Sos [5] Rober A. Sholz : The Sred Seru Coe IEEE Trsos o Couos Vol.Co-5 o. 8 Augus 977 [6] Rjee Prsd : Persol Moble Couos 995 MGrw-Hll Seres Elerl Egeerg [7] Klo Feher : Wreless Dgl Couos Pree Hll [8] Tero Ojerä Rjee Prsd : Wdebd CDMA for Thrd Geero Moble Couos Areh House 998 [9] Sef Prvll : Vrbly of User Perfore Cellulr DS-CDMA Log versus Shor Sredg Sequees IEEE Trsos o Couos Vol. 48 o. 7 July [] Rober A. Sholz : The Orgs of Sred-Seru Couos IEEE Trsos o Couos Vol.Co.-3 o. 5 My 98 3