Fen Chen

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Dec 6, 2000 EE 521 Dept. of ECprE

IOWA STATE UNIVERSITY

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Pseudonoise Sequenc esPseudonoise Sequenc es

in DSSS Tec hn iquein DSSS Tec hn ique

Feng CHENFeng CHENFeng CHENFeng CHENFeng CHENFeng CHENFeng CHENFeng CHEN

Inst ruc t or : Dr. St eve F. Russel lInst ruc t or : Dr. St eve F. Russel l

Dept . of ECprEDept . of ECprE

II OWAOWA SSTATETATE UU NIVERSITYNIVERSITY

Fal l , 2000Fal l , 2000

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OUTLINEOUTLINE

In t roduc t ionIn t roduc t ion

Theory of PN Sequenc esTheory of PN Sequenc es

Appl ic at ion o f PN Sequenc es in ISAppl ic at ion o f PN Sequenc es in IS--9595

Sim ulat ion o f PN Sequenc esSim ulat ion of PN Sequenc es

SummarySummary

Fut ure WorkFut ure Work ReferenceReference

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I n t roduc t ionIn t roduc t ion

Mul t ip le Ac c ess Tec hn iquesMul t ip le Ac c ess Tec hn iques FDMA: AMPSFDMA: AMPS

TDMA: ISTDMA: IS--5454

CDMA: ISCDMA: IS--9595

Frequency

PowerTime

Frequency

PowerTime

PowerTime

FrequencyFDMA TDMA CDMA

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I n t roduc t ionIn t roduc t ion

Spread Spec t rum Tec hniquesSpread Spec t rum Tec hniques Frequenc y Hopp ing S.S.Frequenc y Hopp ing S.S.

Direc t Sequenc e S.S.Direc t Sequenc e S.S. Advant ages us ing PN Sequenc esAdvant ages us ing PN Sequenc es

Ant i jamming:Ant i jamming: J/S=(BW/RJ/S=(BW/Rbb )/(E)/(Ebb /N/N 00 ))

Mul t ipa th Pro tec t ion :Mul t ipa th Pro tec t ion : t h roughout BWt hroughout BW

Mul t ip le Acc ess:Mul t ip le Acc ess: Or thogonal i tyOr thogonal i ty

Message Pr ivac y:Message Pr ivac y: PseudorandomPseudorandom

Selec t ive Cal l ingSelec t ive Cal l ing Ident i f i ca t ionIdent i f i ca t ion

Nav igat ionNav igat ion

Low Radia ted F lux Densi tyLow Radia ted Flux Densi ty

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App lic a t ions in ISApplic a t ions in IS--95 sys t em95 sys t em Dat a Sc ram bl ingDat a Sc ram bl ing

SpreadSpread --spec t rum Modu lat ionspec t rum Modu la t ion

Necess i t iesNecess i t ies

Suf f ic ient Random nessSuf f ic ient Random ness

Changing Bac kChanging Bac k

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Generat ion of PN Sequenc esGenerat ion of PN Sequenc es Linea r Feedbac k Shif t Regist er (LFSR)Linea r Feedbac k Shif t Regist er (LFSR)

N s tagesN s t ages

Peri od: 2Peri od: 2nn

--11 Max im al length sequence:Max im al length sequence:

0 0 01 0

Clock

Pulses

Modulo-2

Adder

Output

0000101011101100011111001101001

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Pseudonoise Sequenc esPseudonoise Sequenc es Balanc e Proper t yBalanc e Proper t y

Num ber of 1s d i f fers f rom t he num ber Num ber of 1s d i f fers f rom t he num ber

o f 0s by at m ost 1o f 0s by a t m ost 1 Run Proper t yRun Proper t y

22 nn --11 runs o f c onsecut ive 1s or 0sruns o f c onsecut ive 1s or 0s

Corre lat ion Proper t yCorre lat ion Proper t y

Sc a led Aut oc orre la t ion: 1Sc aled Aut oc orre la t ion: 1

Sc aled CrossSc aled Cross --c or re la t ion: 0c orre la t ion: 0

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0000101011101100011111001100100001010111011000111110011001

Balanc e: 15 0s ; 16 1sBalanc e: 15 0s ; 16 1s

Run: 2 runs of lengt h 3; 4 runs of Run: 2 runs of lengt h 3; 4 runs of leng t h 2 ; e t c .leng t h 2 ; e t c .

Corre lat ion:Corre lat ion:

Aut o ~ 1=31/31Aut o ~ 1=31/31 Cross ~ 0Cross ~ 0 --1/311/31

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Mat hem at i c a l Bac k groundMat hem at i c a l Bac k ground Fini t e Fie ldsFini t e Fie lds

A f in it e set o f elements w i th t w o operat i ons :A f in i te set o f e lements w i th t w o opera t i ons :

addi t ionaddi t ionandand mul t i p l i ca t i on mu l t i p l i ca t i on

Galois Field of q:Galois Field o f q: a f in it e f ield o f e lem ent q a f in it e f ie ld o f e lem ent q

Ex am ple: GF(2)={0,1}Ex am ple: GF(2)={0,1}

001111

110000

1100

110011

000000

1100

Addition Multiplication

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Ex t ension Galo is Fie ldsEx t ension Galo is Fie lds GF(q)=GF(pGF(q)=GF(p mm ): P ~ pr im e; m ~ any in t eger): P ~ pr im e; m ~ any in t eger

GF(p): pr im e f ie l dGF(p): pr im e f ie l d

Pr im i t ive Polynom ia lsPr im i t ive Polynom ia ls

)2()( 012

2

2

2

1

1 GFaxxaxaxaxaxxf in

n

n

n

n++++++=

!

01)( 12

2

2

2

1

1 =++++++=

aaaafn

n

n

n

n

!

112

2

2

2

1

1 +++++=

aaaa nn

n

n

n!

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Mu l t ip l i ca t ionMul t ip l i ca t ion

Add i t ionAddi t ion

tktk +=

ntkcc

cc

n

i

i

itik

n

i

i

it

n

i

i

ik

tk

=

+=+

=

=

=

,)(1

0

,,

1

0

,

1

0

,

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An ex am ple of GF(2An ex am ple of GF(2 33 )=GF(8))=GF(8)generat ed f romgenerat ed f rom 11)( 2332 +=++= xxxf

1 1 01 1 022 ++ 66==

0 1 10 1 1 +1+1 55==

1 1 11 1 122 ++ +1+1 44==1 0 11 0 1

22

+1+133

==

0 1 00 1 0 22==

0 0 10 0 111 11==

0 0 00 0 0000=0=Sequenc e over GF(2)Sequenc e over GF(2)Polynom ials over GF(2)Polynom ials over GF(2)0 and Pow ers o f 0 and Pow ers o f

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Mec hanizat ion of LFSR for Mec hanizat ion o f LFSR for B inary Pr im i t ive Polynom ia lsB inary Pr im i t ive Polynom ia ls

Sim ple Shi f t Regis t er Generat or Sim ple Shi f t Regis t er Generat or

Modular Shi f t Regis t er Generat or Modular Shi f t Regis t er Generat or

Clock

Pulses

R1

c1

R2

c2

Rn

SSRGSSRG

Clock

Pulses

R1

c1

R2

c2

Rn

MSRGMSRG

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Appl ic a t ion o f PNAppl ic at ion o f PN

Sequenc e in ISSequenc e in IS--9595

Overv iew of ISOverv iew of IS--95 Syst em95 Syst em Forw ard L inkForw ard L ink

Pi lot ChannelPi lot Channel

Sync hronizat ion ChannelSync hronizat ion Channel Paging Channel sPaging Channels

Traf f ic ChannelsTraf f ic Channels

Reverse LinkReverse Link

Ac c ess ChannelAc c ess Channel

Traf f ic ChannelTraf f ic Channel

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Appl ic a t ion o f PNAppl ic at ion o f PN

Sequenc e in ISSequenc e in IS--9595

Role of PN Sequenc es in ISRole of PN Sequenc es in IS--9595

Mul t ip leMul t ip le

accessaccessMul t ip leMul t ip le

accessaccessShort PNShort PN

n=15n=15

N/AN/AScramblesScrambles

user dat auser dat a

Long PNLong PN

n=42n=42

ReverseReverse

LinkLinkForwardForward

LinkLink

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Sim ulat ion of PNSim ulat ion of PN

SequencesSequences

Long Code Seed

Modulo-2 additionn

1 2 3 4 N

OUTPUT

.

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Sim ulat ion of PNSim ulat ion of PN

SequencesSequences

Start

iInput initial status of LFSR

Input Polynomial Parameters

The output bit is the modulo-

2 addition of all the bits in the

registers of the generator.

Shift the bits circularly to get

the next state

Output the sequence formed

by the output bits at every

state of the registers.

End

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SummarySummary

DSSS is t he c ore o f CDMADSSS is t he c ore o f CDMAtechn iquestechn iques

PN sequenc e is c ruc ia l t o DSSSPN sequenc e is c ruc ia l t o DSSS

PN sequenc e real izesPN sequenc e real izes Mult ip le Ac c essMult ip le Ac c ess

Message Pr ivac yMessage Pr ivac y

Sui t ab le t o rea lSui t ab le t o rea l --wo r l dwo r l dc omm unica t ion c hanne lsc omm unica t ion c hanne ls

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Fut ure WorkFut ure Work

Sim ula t ion o f Spread ing w i t hSim ula t ion o f Spread ing w i t h

Walsh c odesWalsh c odes

Sim u lat ion o f Transm i t t e r Sim u lat ion o f Transm i t t e r Sim ulat ion o f Rec eiver Sim ulat ion o f Rec eiver

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ReferenceReference

[1][1] C.Y. Sam uel ,C.Y. Sam uel , CDMA RF System Engineer ingCDMA RF Syste m Engineer ing, Ar t ec h House, Ar tec h House

Publ ishers, Boston , 1998.Publ is hers, Boston, 1998.

[2][2] S.L. J hong,S.L. J hong, CDMA Syst em s Enginee r ing HandbookCDMA Syst em s Enginee r ing Handboo k , Ar tec h House, Ar tec h House

Publ ishers, Boston , 1998.Publ is hers, Boston, 1998.

[3][3] CDMA Develop m ent Group,CDMA Develo pm ent Group, cdmaOne,cdmaOne, Avai la ble HTTP:Avai lab le HTTP:

ht tp: / /www.cdg.org/ f rame_cdma1.htmlht tp: / /www.cdg.org/ f rame_cdma1.html , Nov. 2000., Nov . 2000 .

[4][4] CDMA Develop m ent Group,CDMA Develo pm ent Group, CDMA Developm ent Group Whit e Paper:CDMA Develop m ent Group Whit e Paper:

Third Generat ion Syst ems,Third Generat ion System s, Avai lable HTTP:Avai lab le HTTP:

ht tp: / /www.cdg.org/ f rame_cdma1.htmlht tp: / /www.cdg.org/ f rame_cdma1.html : 3G/Int ernet & IS: 3G Pavi l i on: Det ai led: 3G/Int ernet & IS: 3G Pavi l i on: Det ai led

Inform at ion, Nov. 1998.Inform at i on, Nov. 1998.

[5][5] V. Garg and J . Wilk es,V. Garg and J . Wilk es, Wire less and Personal Com m unic at ionsWire less and Personal Comm unic at ions

SystemsSystems, Prent ic e Hal l , Upper Saddle River, NJ, 1996., Prent ic e Hal l , Upper Saddle River, NJ, 1996.

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