1. TRANSMISI BASE-BAND oleh :Budi Prasetya
Modul #11
TT SISTEM KOMUNIKASI 1
TRANSMISI BASE-BAND
oleh :Budi Prasetya
Program Studi S1 Teknik Telekomunikasi
Departemen Teknik Elektro - Sekolah Tinggi Teknologi Telkom
Bandung – 2008

2. Review Probabilitas dan Statistik
Gaussian/Normal
Normal Distribution: Completely characterized by mean () and variance (2)
pN(y)
N1(=0,1)
N2(=0,2)
2 > 1
Modul 11 - Siskom I - Base Band Transmission

3. Gaussian: Rapidly Dropping Tail Probability!
Modul 11 - Siskom I - Base Band Transmission

4. Review Probabilitas dan Statistik
pN(y)
Gaussian/Normal
Normal Distribution: Completely characterized by mean (=0) and variance (2=1)
Q-function: one-sided tail of normal pdf
erfc(): two-sided tail.
So:
N(=0,=1)
p(y>z)= z
Modul 11 - Siskom I - Base Band Transmission

5. Standardize the Normal Distribution
Standardized Normal Distribution
One table!
Modul 11 - Siskom I - Base Band Transmission

6. Modul 11 - Siskom I - Base Band Transmission
Example P(X  8)
Normal Distribution
Standardized Normal Distribution
.1179
.5000
.3821
Shaded area exaggerated
PERTANYAAN ! Luas daerah yang diarsir = = Q(??); ?? = 0.3
Modul 11 - Siskom I - Base Band Transmission

7. Q-function: Tail of Normal Distribution
Q(z) = P(Z > z) = 1 – P[Z < z]
Modul 11 - Siskom I - Base Band Transmission

8. Modul 11 - Siskom I - Base Band Transmission
Tabel
Q-function
Modul 11 - Siskom I - Base Band Transmission

9. Baseband Digital Transmission Link
Modul 11 - Siskom I - Base Band Transmission

10. Modul 11 - Siskom I - Base Band Transmission
Sinyal Terima + AWGN
original message
d(t)
received wave
y(t)=d(t)+n(t)
Modul 11 - Siskom I - Base Band Transmission

11. Modul 11 - Siskom I - Base Band Transmission
AWGN
n(t) = gaussian noise dengan zero-mean
σ = standar deviasi = tegangan effektive noise
Modul 11 - Siskom I - Base Band Transmission

12. Gangguan Noise Terhadap Sinyal Digital
Modul 11 - Siskom I - Base Band Transmission

13. Determining Decision Threshold-A
V =Theshold
The comparator implements decision rule:
Choose Ho (ak=0) if Y<V
Choose H1 (ak=1) if Y>V
Average error error probability:
Transmitted ‘0’
but detected as ‘1’
Channel noise is Gaussian with the pdf:
Modul 11 - Siskom I - Base Band Transmission

14. Error rate and Q-function
V =Theshold
V threshold = 0
This can be expressed by using the Q-function by
Modul 11 - Siskom I - Base Band Transmission

15. Baseband Binary Error Rate in Terms of Pulse Shape and S/N
setting V=0 yields then
for polar, rectangular NRZ [-A,A] bits
Probability of occurrence
Signal power:
Noise power:
Energy Bit to Noise Spectral Density Ratio
Note that
(BW pulse shapping filter)
Modul 11 - Siskom I - Base Band Transmission

16. Modul 11 - Siskom I - Base Band Transmission
When p0 = p1 =1/2, the value of V that minimizes the probability of error is V = 0.
Modul 11 - Siskom I - Base Band Transmission