Download - TẠO TRẢI PHỔ_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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THUC TNH QUAN TRNG CACHUI m
(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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THUC TNH QUAN TRNG CACHUI m
( )
( )
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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THUC TNH QUAN TRNG CACHUI m
( ) ( ) ( )
( )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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THUC TNH QUAN TRNG CACHUI m
(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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THUC TNH QUAN TRNG CACHUI m
(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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THUC TNH QUAN TRNG CACHUI m
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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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