TẠO TRẢI PHỔ_Multi-Access_Dam2 (PN)

7/30/2019 TO TRI PH_Multi-Access_Dam2 (PN)

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Ni dung

Mu Cc chui PN

Cc thuc tnh cachui PN

Cc chui Gold

Cc chuitrc giao

ng dng cc chui m trong cc h thng

CDMA


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Gii thiu

1


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PN Sequences

PN generator produces periodic sequence thatappears to be random

PN SequencesGenerated by an algorithm using initial seed Sequence isnt statistically random but will pass

many test of randomness

Sequences referred to as pseudorandom numbersor pseudonoise sequencesUnless algorithm and seed are known, the

sequence is impractical to predict


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Thuc tnh gi ngu nhin(Important PN Properties)

Tnh ngu nhin (Randomness) Phn b u (Uniform distribution)

Thuc tnh cn bng (Balance property)Thuc tnh chy (Run property) Tnh c lp (Independence)

Thuc tnh tng quan (Correlation property) Tnh khng d on trc

(Unpredictability)


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1

1 1 0

2 2 11 2 1 1

:10

( ) ...

1 ...k

i

m m

m m

m m mm m

x

g

g x g x g x g x g

g x g x g x g x x

modm 0t g(x)=0; g =g =1; do -1=1 (2)

Thhin n vtrKha ng

Kha m

M

chthan

hghidch

tochuiPN

( )

,

ii

S j l j i

i 1 i-1 2 i-2 m-1 i-m+1 i-m

i i i i

Tr ng th i ca thanh ghi dch t i xung nhp gi trphn t nh th t i xung nhp

C = g C + g C +... + g C + C Mod2 v i i >0

S = s (1),s (2),...,s (m)-; i m ii m

m

c chu k cc i N = 2 -1 = s trng th i khc 0 cc i

u ra xung nhp th C = S ( )

Si(1) Si(2) Si(3) Si(m)

x0 x1

x2

x3

xm-1

xm

g1 g2 g 3 g m-1

ci ci-m 0 1

1 1 n biu ch


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Xung ng h i Trng thi

1 01111

2 10111

3 01011

0 11111

5 00010

6 100017 01000

4 00101

9 10010

10 01001

11 10100

8 00100

13 10101

14 11010

15 01101

12 01010

Xung ng h i

17 00011

18 00001

19 10000

16 00110

21 11100

22 0111023 00111

20 11000

25 11001

26 01100

27 10110

24 10011

29 11101

30 11110

31 11111

28 11011

Trng thi

32 01111

33 Lp li

m bit u tin ca chui ra = cc bit c np vo thanh ghi dch S0Vi cc np ban u khc S0, chui ra l dch phi (2

m-1)- i ca chui vi S0.

Mt n-AND

0 0 01 1

i i(c) =S (5)

7

iT c

Si(1) Si(2) Si(3) Si(4) Si(5)

5 4 3( ) 1g x x x x x

i i-1 i-3 i-4 i-5C = C + C + C + C Mod2

B to m c a thc

0,0,0,0,0 ,0

Chui ra u r

V i mi trng th i khi u khc khng S

trng th i ca thanh ghi dch thay i theo iu kin hi quy

- c x c nh bi a thc t o m g(x).- ( )

1 31

0

i m ii m

S

m 5a nhp th C =S

c chu k cc i ca chui ra N= 2 -1=2

1

2

1 1 1 1 1, u ra C = 1111101000100101011000011100110...

0 0 0 0 1 u ra C = 10000111001101111101-N i

2 1C l dch sang phi ( =31-18=13) n vca chui C

00010010101...


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T TNG QUAN

( )( ):

1

( ) ( ) ( )lim

T

T

x

x tx t

R x t x t dtT

nh gi mc ging nhau giatn hiu x(t) v

phin bn dch thi ca n trong l tn hiu kiu cng sut

Hm t t- ng quan ca

i

chui m l hiu scc bit ging nhau v cc bt khc nhauchui v chui dch th

gii ca

a

c nT c

gia

0

1

0 1

0 1

0 1

::

S bt ging nhauS bt kh c nhau

T t- ng quan v gia hai chui m:

= ;

chun ha

R(i)

khng chun ha


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TNG QUAN CHO

1

( ) lim ( ) ( )

T

xy TR x t y t dtT

T- ng quan cho gia hai tn hiu kiu cng sut


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THUC TNH QUAN TRNG CACHUI m

(1)Thuc tnh ca s: Nu mt ca s rng mtrtdcchui m trong tp Sm, midy trong s2m-1dy m bit khc khng ny sc nhn thyngmtln. (Chnghn xt cas di 4 chochui 000100110101111. Tngtngrngchuiny cvit thnh vng)

(2) S s 1 nhiu hn s s 0:Mi chui m trong tpSm cha 2m-1s s 1 v 2m-1-1 s s 0.


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(3) Hm t tng quan dng u inh:

1,

0,

c

i

N

i c

i=10 t T

p(t) nu khc1 i v i xung l- ng cc

c =

0/1 i v i xung n cc

c(t)= c p(t-iT )

( ) ( )i ii

Php nhn i v i chui l- ng cc - c thay bng pho XOR i v i xung n cc v ng- c l i

Hm t t- ng quan tun hon chun ha ca chui m l hm: chn; tun hon dng u inh

v i c 2 -1mN hu k


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( )

( )

j i j

N 1c c

j 0

Nu m c dng n cc:

1R(i) ( 1)

N

v i i=0 modN

v i i 0 modN

1

1

N

+

-

=

= -

= -

1444444444444444444442 444444444444444444443

( )

( )

N 1

j 0

Nu chui m c dng l- ng cc

1R(i)N

v i i=0 modN

v i i 0 modN

j i j1c c

1

N

-

=

+=

= -

1444444444444444444442 444444444444444444443

(3)Hmt

t

ngquandngu

inh:


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( ) ( ) ( )

( )c c

1N

NT l chu k m; T l rng chipNu N= ( =0), thm ngu nhin hon ton

nu khc

c

c

NT

c T

c 0

c

cTc

1 , 0 TT

0 ,

1 1 1R c t c t dt 1 ( )

NT N N

t - t L =

t = + t = + L t -1444444444444444444442 444444444444444444443

cR (i)

0-N N

-1/N

1

cR ( )

0-NT NT

-1/N

1

c c

i

a) Hm t tng quan cho chui m

b) Hm t tng quan chui PN

(3)Hmt

t

ngquandngu

inh:


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(4) Cc onchy (Runs):Mtonchy l mtxu cc s "1" lin tip hay mt xu cc s "0"lin tip. Trong michui m, mtnasonny c chiu di 1, mtphnt c chiu di 2,

mtphn tm c chiu di 3 chng no ccphn s ny cn cho mts nguyn cc onchy. Chnghn c mton chy di m

s"1", mt on chy di m-1 s "0" v ivi on chy di k, 0


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(5) Ly mu (Decimation): Ly mu 1 t n>0 ca

mt chui- m c (ngha l ly mu c c n bit m

mt ln), c biu th c[n], c chu k bngN/gcd(N,n) nu khng phi l chui ton

khng; a thc to m g'(x) ca n c gc l

m n ca cc gc ca a thc to m g(x).


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Tnh cht ca chui(Properties of M-Sequences)

Tnh cht 1: C 2n-1 s "1" v 2n-1-1 s "0"

Tnh cht 2: For a window of length n slid along output forN(=2n-1)

shifts, each n-tuple appears once, except for the allzeros sequence

Property 3: Sequence contains one run of ones, length n

One run of zeros, length n-1 One run of ones and one run of zeros, length n-2 Two runs of ones and two runs of zeros, length n-3 2n-3 runs of ones and 2n-3 runs of zeros, length 1


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Properties of M-Sequences

Property 4:The periodic autocorrelation of a 1 m-

sequence is

otherwise

...2N,N,0,

11

N

R


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Definitions

Correlation The concept of determining how much similarity one set of

data has with another

Range between1 and 1 1 The second sequence matches the first sequence 0 There is no relation at all between the two sequences -1 The two sequences are mirror images

Cross correlation

The comparison between two sequences from differentsources rather than a shifted copy of a sequence with itself


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Advantages of Cross Correlation

The cross correlation between an m-sequenceand noise is low

This property is useful to the receiver in filteringout noise

The cross correlation between two different m-sequences is low

This property is useful for CDMA applicationsEnables a receiver to discriminate among spread

spectrum signals generated by different m-

sequences


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Gold Sequences

Gold sequences constructed by the XOR of two m-sequences with the same clocking

Codes have well-defined cross correlation properties

Only simple circuitry needed to generate largenumber of unique codes In following example (Figure 7.16a) two shift

registers generate the two m-sequences and these are

then bitwise XORed


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Gold Sequences


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Orthogonal Codes

Orthogonal codes All pairwise cross correlations are zero Fixed- and variable-length codes used in CDMA systems For CDMA application, each mobile user uses one

sequence in the set as a spreading code

Provides zero cross correlation among all users

Types Walsh codes

Variable-Length Orthogonal codes


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Walsh Codes

Set of Walsh codes of length n consists of the nrows of an n x n Walsh matrix:

W1 = (0)

n = dimension of the matrix

Every row is orthogonal to every other row and tothe logical NOT of every other row

Requires tight synchronization Cross correlation between different shifts of Walsh

sequences is not zero

nn

nnn

WWWWW2


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,1,0(1)

chC

,2,0(1,1)

chC

,2,1(1, 1)

chC

,4,1(1,1, 1, 1)

chC

,4,0(1,1,1,1)

chC

,4,2(1, 1,1, 1)

chC

,4,3(1, 1, 1,1)

chC

c

( , )c c

( , )c c

SF=1 SF =2 SF =4


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Typical Multiple Spreading Approach

Spread data rate by an orthogonal code(channelization code)

Provides mutual orthogonality among all users inthe same cell

Further spread result by a PN sequence(scrambling code)

Provides mutual randomness (low crosscorrelation) between users in different cells

C d A i iti M th d


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Code Acquisition Methods

Coarse Sychronization

Need to search for the correct

code phase in a region of

uncertainty

Bank of Correlators

Sliding Correlator

RASE

Mean time to acquire

Detection and False AlarmProbabilities

x 0lTc

dt

p(t)

v0

x 0lTc

dt

p(t-Tc/2)

v1

x 0lTc

dt

p(t-(2Nc-1) Tc)

v2Nc-1

Incoming

DS Signal

DS Acquisition using 2Nc correlators

x 0lTc

dt

AND

+

Threshold

Comp.

-

Psp(t-jTc) +n(t)

p(t-kTc)

VI=SI+NI

VT(l)resetSliding

Correlator

clock pulses

PN

Generator


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Code Tracking

After Code Phase

Acquisition, need fine

synchronization in the

presence of data

Adapt to time variations &

maintain lock

Delay Locked Loop Tau Dither Loop

x

x

xbandpass

filter

envelope

detector

envelope

detector

bandpass

filter

loop

filter

clock

VCO

PN

generator S

-

+

p(t+)

to data demod

p(t+Tc/2+)

p(t-Tc/2+)

Y

E1

E2

Delay Locked Loop

Y

Tc-Tc

-Rp(+ Tc/2)

Rp(- Tc/2)

Variation of Y with

O ti l h t i i l th


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Optimal noncoherent receiver: single path

Equiprobable, equi-

energy signals

AWGN

M Orthogonal DSSSwaveforms; W=1/Tc

Known path strength

& delay

Matched Filter & non-

coherent detection(q0 ignored)

Filter

matched

to s1(t)

Envelope

detector

| |

Filter

matched

to sj(t)

Envelope

detector

| |

Filter

matched

to sM(t)

Envelope

detector

| |

Sample

att=kT

and

decide

on

index

oflargest

sample

r(t)

0 T 2T

0 T 2T

0 T 2T

1/Wbits

x1

xM

xj

Di it i RAKE i


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Diversity via RAKE receiver

Exploit sharp peaks to resolve

multipath

Channel sounding produces

estimates of path strengths

Linear combination of delay linesamples with weights

proportional to the path strength

Optimal: Filter matched to

estimated channel impulse

response Square law combining (optimal for

Rayleigh case) suppresses paths

with weaker mean square strengths

0 T T+t1 T+t2 T+t3 2T

.... .. ..

Delay Line

Input

from jth

detector

Summing Bus

a0 a1 a2 a3

Delay line voltage profile at time t=T+Tm

(moves to left with time, along delay line)

1/W

Xj(t)

t

output sampled @ t = nT+Tm

RAKE

S d S t M lti l A


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Spread Spectrum Multiple Access:

Orthogonal Waveforms

Separation of individual user

signals done by Matched

Filter or Correlation Receiver

In a Synchronized system,

there is zero inter-userinterference or noise

contribution

In a single cell system,

capacity is limited by number

of orthogonal waveformspossible = W/R (same as

TDMA & FDMA)

X

900

Signal i

X X

Signal kSignal j


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TẠO TRẢI PHỔ_Multi-Access_Dam2 (PN)