Modul 11 Siskom1 Base Band Transmission · Review Probabilitas dan Statistik Gi/N l ... Modul 11 -...
Transcript of Modul 11 Siskom1 Base Band Transmission · Review Probabilitas dan Statistik Gi/N l ... Modul 11 -...
Modul #11
TE3113 TE3113 SISTEM KOMUNIKASI 1SISTEM KOMUNIKASI 1
TRANSMISIBASE-BAND
Program Studi S1 Teknik TelekomunikasiDepartemen Teknik Elektro - Sekolah Tinggi Teknologi Telkomp gg g
Bandung – 2007
Review Probabilitas dan StatistikG i /N l
Normal Distribution: Completely characterized by mean (μ) and variance (σ2)
Gaussian/Normal
⎤⎡ 21(μ) ( )
0.8
pN(y)( ) ⎥
⎦
⎤⎢⎣
⎡−= 2
2
2exp
21
σπσyypN
0.6
0.7 N1(μ=0,σ1)
0.3
0.4
0.5
σ2 > σ1
0.1
0.2
N2(μ=0,σ2)
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-3 -2 -1 0 1 2 30 y
Gaussian: Rapidly Dropping Tail Probability!
P
R
dyyP ∫∞
⎥⎦
⎤⎢⎣
⎡ −−=
ση
πσ 2
2
2)(exp
21
+ ⎦⎣ση σπσ 22
dyyR ∫∞
+⎥⎦
⎤⎢⎣
⎡ −−=
ση ση
πσ 22
2
2)(exp
21
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+ ⎦⎣σηπσ 22
Review Probabilitas dan StatistikG i /N l
pN(y)0.4
Normal Distribution: Completely characterized by mean (μ=0) and
i ( 2 1)
Gaussian/Normal
0.25
0.3
0.35
N(μ=0,σ=1)
variance (σ2=1)
Q-function: one-sided tail of normal pdf 0 05
0.1
0.15
0.2
pdf-4 -3 -2 -1 0 1 2 3 4
0
0.05
z
p ( y > z ) =
erfc(): two-sided tail. So:
4Modul 11 - Siskom I - Base Band Transmission
Standardize the Normal Distribution
Z X=
− μNormal DistributionNormal Distribution
Z =σ Standardized Normal
DistributionStandardized Normal
Distribution
σ σ = 1
Xμ
One table!One table!
μ = 0 ZOne table!One table!
5Modul 11 - Siskom I - Base Band Transmission
Example P(X ≥ 8)N lN l St d di d N lSt d di d N lSt d di d N lSt d di d N lX 8 5
10
Normal DistributionNormal Distribution
Standardized Normal Standardized Normal DistributionDistribution
Standardized Normal Standardized Normal DistributionDistributionZ X
=−
=−
=μ
σ8 510
30.
1σ = 10 σ = 1
.5000.50003821382138213821
Z0 30
.1179.1179.1179.1179
.5000.5000.3821.3821.3821.3821
Xμ = 5 8 Zμ = 0 .30Shaded area exaggeratedShaded area exaggeratedShaded area exaggeratedShaded area exaggerated
PERTANYAAN ! Luas daerah yang diarsir = 0.3821 = Q(??); ?? = 0.3
6Modul 11 - Siskom I - Base Band Transmission
Q function:Q-function: Tail of Normal DistributionDistribution
Q(z) = P(Z > z) = 1 – P[Z < z]
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Baseband Digital Transmission Link
8Modul 11 - Siskom I - Base Band Transmission
Sinyal Terima + AWGN
original messageoriginal messaged(t)
received wave y(t)=d(t)+n(t)
Modul 11 - Siskom I - Base Band Transmission 9
AWGN
n(t) = gaussian noise dengan zero-mean
σ
)(vpN
( ) ⎥⎤
⎢⎡−=
2
exp1 vvp
σ = standar deviasi = tegangan effektive noise
( ) ⎥⎦
⎢⎣−= 22
exp2 σπσ
vpN
σ standar deviasi tegangan effektive noise
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Gangguan Noise Terhadap Sinyal Digital
2 Si l ki i
2
3
1
1.5
Signal kirim
Sinyal dengan AWGN
1
-0.5
0
0.5
0
-1.5
-1 -1
0 1 2 3 4 5 6 7 8 9 10-2
-3
-2
Modul 11 - Siskom I - Base Band Transmission 11
-30 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Determining Decision Threshold
)()/(,0:
0
0
AypHypnAYaH
NY
k
+=
+−==
1
1
: 1,( | ) ( )
= = += −
k
Y N
H a Y A np y H p y A
Choose Ho (ak=0) if Y<VChoose H1 (ak=1) if Y>V
The comparator implements decision rule:
( | ) ( | )Vp P Y V H p y H dy∫≡ < =
-A V =Theshold
( k )1 1 1
0 0
( | ) ( | )( | ) ( | )
e Y
Veo Y
p P Y V H p y H dyp P Y V H p y H dy
−∞
∞
∫
∫
≡ < =
≡ > =
Average error error probability: = +P PP PP Transmitted ‘0’Average error error probability: 0 0 1 1+e e eP PP PP1
20 1 0 11/ 2 ( )= = ⇒ = +e e eP P P P P
Ch l i i G i ith th df
Transmitted 0but detected as ‘1’
( ) ⎥⎤
⎢⎡ 2
exp1 yypChannel noise is Gaussian with the pdf:
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( ) ⎥⎦
⎢⎣−= 22
exp2 σπσ
yypN
Error rate and Q-function
120 1 0 11/ 2 ( )= = ⇒ = +e e eP P P P P
0 ( )∞
∫= Ve Np p y dy-A V =Theshold
V threshold = 0
dyAyppV
ee ∫∞
=⎥⎦
⎤⎢⎣
⎡ +−==
02
2
0 2)(exp
21
σπσThis can be expressed by using the Q-function
( ) Vd Q∞
∫⎛ ⎞⎜ ⎟
by⎟⎞
⎜⎛
⎟⎞
⎜⎛ 2AQAQ
0 ( )Ve Np p y dy Qσ
∞
∫⎛ ⎞= = ⎜ ⎟⎝ ⎠
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⎟⎟⎠
⎜⎜⎝
=⎟⎠⎞
⎜⎝⎛= 2σσ
QQpe
Baseband Binary Error Rate in Terms of Pulse Shape and S/Np
12 0 1 0 1( ) Ap p p p p p Q⎛ ⎞= + = = ⇒ = ⎜ ⎟
⎝ ⎠
setting V=0 yields then
⎟⎟⎞
⎜⎜⎛
=⎟⎟⎞
⎜⎜⎛
=⎟⎟⎞
⎜⎜⎛
=⎟⎠⎞
⎜⎝⎛= 2
2 2EQSQAQAQp be2 0 1 0 1( )
2e e e e e ep p p p p p Qσ
⇒ ⎜ ⎟⎝ ⎠
for polar, rectangular NRZ [-A,A] bits
Si lProbability of occurrence
⎟⎠
⎜⎝
⎟⎠
⎜⎝⎟
⎠⎜⎝
⎟⎠
⎜⎝ 0
2 NQ
NQQQpe σσ
( ) 222 11 AAASSignal power: ( ) 222
21
21 AAAS =−+=
Noise power: bN T
NRNBWN21.
2.. 00
2 ==== ησb
N T22 00η
Energy Bit to Noise Spectral Density Ratio
NS
TNTSR
NTS
RbN
TS
BWN
TSNE
b
bbbb
N
bb .21
.21..
2..
2
..
0
=====
Note that (BW pulse shapping filter)14Modul 11 - Siskom I - Base Band Transmission
2b
NRBW =
When p0 = p1 =1/2, the value of V that minimizes the probability of error is V = 0.
⎞⎛⎞⎛⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟
⎟⎠
⎞⎜⎜⎝
⎛=
NSQ
NEQp b
e0
2
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TabelQ-functionQ function
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