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Elektronik Öğretmenliği Bölümü
EBB 326 Haberleşme Sistemleri-II
2011-2012 Bahar Yarıyılı
Öğretim Üyesi
Prof. Dr. Yunus E. Erdemli
Ofis: TEF-1011
Tel: 303-2238
E-posta: [email protected]
Ders Programı
I. Öğr. Pz.tesi: 12:00-15:00 (Teo)
15:00-16:50 (Lab)
II. Öğr.
Çarşamba: 17:00-20:00 (Teo)
20:00-21:50 (Lab)
Referanslar:
1) Modern Digital & Analog Communication Systems
B. P. Lathi, HRW, Inc., Chicago, 1989
2) Sayısal Haberleşme
A. H. Kayran, E. Panayırcı, Ü. Aygölü
Birsen Yayın, İstanbul
http://www.birsenyayin.com
Değerlendirme: Ara Sınav (%25) + Lab (%15) + Final (%60)
Devam zorunluluğu: Teorik Ders (%70) Lab/Problem Saati (%80)
Örnekleme ve Darbe Kod Modülasyonu (PCM)
Sayısal Veri İletimi ve Temel Prensipleri
Gürültü Etkisinde Analog ve Sayısal Haberleşme
Sistemlerinin Performansı
Ders İçeriği
• Sayısal sinyaller analog sinyallere göre gürültü ve parazit sinyallerinden
daha az etkilenirler.
• Sayısal sinyallerdeki bozulmalar tekrar ediciler (regenerative repeaters)
tarafından giderilebilir.
• Hata sezme (error detection) ve düzeltme (correction) teknikleri sayesinde az hata
oranlı sinyal iletimi yapılabilir.
• Sayısal sinyallere parazit ve karıştırıcı sinyal etkilerinden korunabilmek için
güvenlik ve kriptolama gibi sinyal işleme teknikleri uygulanabilir.
• Sayısal devreler analog devrelere göre daha esnek, daha dayanıklı, ve daha az
maliyetli olarak tasarlanabilir.
Neden
Sayısal
Haberleşme?
Sayısal Haberleşme Alıcı-Verici Birimi
Sayısal Haberleşme Çoklu-Atlama Kanalı
Sayısal Tekrarlayıcı
Analog-to-Digital Conversion
PCM modulator
Quantization
& Encoding
Transmitted
output
Telephone
Speech
Digital Modulation
ASK – Amplitude Shift Keying 2-ASK 0: A1cos(2πfct) 1: A2cos(2πfct)
PSK – Phase Shift Keying 4-PSK 00: Acos(2πfct+ 0 ) 01: Acos(2πfct+ π/2) 10: Acos(2πfct+ π) 11: Acos(2πfct+ 3π/2)
Digital Modulation input: digital signal output: analog signal
FSK – Frequency Shift Keying
0 0 1 0 1 0 1 1
Digital signal
ASK modulated signal
PSK modulated signal
Example:
Darbe Genlik Modülasyonu
Flat-Top PAM Signal Generation
Darbe Süre (Genişlik) Modülasyonu
Pulse Duration (Width) Modulation
PDM (PWM)
PDM İşaretinin Üretilmesi
PDM İşaretinin
PAM Dalgasına
Dönüştürülmesi
Darbe Yeri (Konumu) Modülasyonu - Pulse Position Modulation (PPM)
İdeal Alçak Geçiren Fitreden Darbe İletimi
X(f)=At sinc(pft)
2
İdeal Alçak Geçiren Kanalın Çıkışı
Bt >> 1 y(t) ~ x(t) : çok az bozunum
Bt << 1 y(t) ≠ x(t) : çok fazla bozunum
İzin verilebilir sınırlar içinde distorsiyon için: t ≥ 1 . tmin=1/2B
2B
Birim zamanda birbirleriyle örtüşmeyecek biçimde iletilebilecek darbelerin
maksimum sayısı yaklaşık olarak 1/tmin=2B olmalıdır.
Örnek: B=3 kHz max 6000 darbe/sn & tmin=1/6000=0.1667 msn
BTn
2
1
Bant genişliği B [Hz] olan ideal bir AGF’den eşit aralıklarla
saniyede 1/Tn=2B adet impuls biçiminde mesaj işareti iletilebilir.
Spectrum of PCM signal depends on
Bit rate:
Correlation of PCM data
PCM waveform (pulse shape)
Line encoding
For no aliasing:
Bandwidth of PCM waveform:
Quantizing noise caused by the M-step quantizer
Bit errors in the recovered PCM signal
(channel noise + improper channel filtering ISI)
Aliasing noise
# of quantization levels
probability of
bit error
6-dB Law:
Average Signal PowerAverage Noise Power
=
Depends on:
input waveshapes
quantification characteristics
“Intersymbol Interference”
m-law Characteristics
(US, Canada, Japan: m=255)
A-law Characteristics
(Europe: A=87.6)
m =255 Quantizer
Compandor (Compressor + Expandor)
SNR for Different Quantizers
Uniform quantizing:
m-law companding:
A-law companding:
n: # of bits used in the PCM word
V: the peak design level of the quantizer
xrms: the rms value of the input analog signal
V/xrms: loading factor
Analog voice signal: 300-3400 Hz fs ≥ 2×3.4 kHz=6.8 kHz
& peak percentage error:
10
DARBE KOD MODÜLASYONU (PCM)
Düzgün KuantalamaUniform Quantization
Boş kanal gürültüsünü önleyici
düzgün kuantalama eğrisi
Giriş a adımından
küçükse, daima ‘0’
çıkışı elde edilir.
Düzgün Olmayan KuantalamaNonuniform Quantization
Sıkıştırma (compression) ve
genleştirme (expansion) eğrileri.
A/D çeviricide sıkıştırma yapılmışsa,
D/A çeviricide genleştirme işlemi
yapılmalıdır.
W
Düzgün
Kuantalayıcı
Bazı haberleşme sistemlerinde, sıkıştırma işlemi
doğrudan analog ses işareti üzerinde yapılır.
Çok kanallı sistemlerde kullanılan işaret seviyesi değişimi
(düzgün olmayan sıkıştırma + düzgün kuantalama)
A-tipi sıkıştırma m-tipi sıkıştırma
A-tipi sıkıştırma eğrisinin parçalı gösterimi
Amaç; giriş genliğinin herhangi bir değeri için belirli sınırlar
içinde kalan bir kuantalama hatası elde etmektir.
Lokal kuantalama
seviye (adım) sayısı: MI
II
III
IV
V
VI
VIIVIII
Örnek 0 010 0011
işaret biti
0 (+)
1 (-)
parça numarasını
belirleyen bitler:
2 nolu parça
parça içinde işaretin kaçıncı dilime
karşı geldiğinin belirlenmesi için
kullanılan bitler: 3. dilim
0 010 0011
kodlanmış işaretin genliği:
0.25 + 3(0.25/16) = 0.296875
1 Hertz can transmit a maximum of 2
pieces of information per second
Noiseless channel of B Hz can transmit a
signal of B Hz error-free
Can reconstruct this signal with 2B samples
Thus, channel of B Hz can transmit 2B
pieces of information or 2 pieces of
information/hertz
Minimum theoretical channel bandwidth is:
BT = n B hertz
Information / Hz
Transmission Bandwidth
Binary systems
M (# of levels) = 2n or n=log2M
Signal m(t), bandlimited to Bm Hz requires at least 2Bm samples/sec (Nyquist).
For reconstruction, we need 2nBm bits/sec or 2nBm pieces of information.
Nyquist Theorem (1920):
For a system/channel bandwidth B, Tmin=1/2B maximum signal rate:
D=2B pulses/sec (baud rate, Baud) = 2Blog2M bits/sec (bit rate, bps)
To transmit data in bit rate D, the minimum bandwidth of a system/channel must be
B ≥ D/2log2M (Hz)
EncoderTransmission
System/ChannelBandwidth=B
Decoder
t2T0 5T4T3TT 6T
0 1 0 0 1 0
Maximum Signal Rate: D
EncoderTransmission
System/ChannelBandwidth=B
Decoder
t
0 1 0 0 1 0
Maximum Signal Rate
Channel Capacity
Shannon Theorem (1948):
For a system/channel bandwidth B and signal-to-noise ratio S/N, its channel capacity is,
C = Blog2(1+S/N) bits/sec (bps, bit rate)
C is the maximum number of bits that can be transmitted per second with a Pe=0.
To transmit data in bit rate D, the channel capacity of a system/channel must be
C ≥ D
+
Noise n(t)
s(t)
t
Relationship between Transmission Speed and Noise
Shannon theorem C = Blog2(1+S/N) shows that the maximum rate or channelCapacity of a system/channel depends on bandwidth, signal energy and noiseintensity. Thus, to increase the capacity, three possible ways are
1) increase bandwidth; 2) raise signal energy; 3) reduce noise.
Shannon theorem tell us that we cannot send data faster than the channel capacity, but we can send data through a channel at the rate near its capacity.
Examples
1. For an extremely noise channel S/N 0, C 0, cannot send any data regardless of bandwidth
2. If S/N=1 (signal and noise in a same level), C=B
3. The theoretical highest bit rate of a regular telephone line where B=3000Hz and S/N=35dB.10log10(S/N)=35 log2(S/N)= 3.5x log210
C= Blog2(1+S/N) =~ Blog2(S/N) =3000x3.5x log210=34.86 KbpsIf B is fixed, we have to increase signal-to-noise ratio for increasing transmission rate.
Channel Capacity
DIFFERENTIAL PULSE CODE MODULATION (DPCM)
Taylor Series Expansion:
Discretized Expression:
Prediction Formula:
Goal: Reduce the quantization error by transmitting a difference signal
which is the original signal – the predicted signal.
Linear Predictor
DPCM System
Transmitter
Receiver
SNR improvement
due to prediction
Gp=Pm / Pd
Delta Modulation (DM) A special case of DPCM
d[k]
Delta
Modulator
Delta
Demodulator
-
mq[k]
<
Delta Modulation (DM)
Delta
Modulator
Delta
Demodulator
DM transmits the derivative of the signal
DM transmits the derivative of the signal
Slope Overload
No overload occurs if
( )
SNR Performance
Single Integration (DM) Double Integration (DM)
Voice Signals
PCM
M
Properties of Line Codes
Transmission Bandwidth
Power Efficiency
Error Detection and Correction
Favorable power spectral density (PSD)
Timing content (synchronization)
DigitalEncoder
DigitalSystemChannel
…010010110
L-Level, M-Mark, S-Space
RZ-Return-to-Zero, NRZ-NoReturn-to-Zero
Choose p(t) so that
Improve the shape of the PSD (e.g. Manchester (Split-phase) Waveform (f))
Minimize interference between adjacent pulses at RX (trade-off bandwidth and PSD shape)
Make PSD=0 at DC and low frequencies
Small bandwidth, most power at small number of frequencies
Low peak power
Pulse Shaping
Line Codes
On/Off (unipolar)
“1” send p(t), “0” nothing
Return to zero (RZ)
Non-Return to Zero (NRZ)
Polar (bipolar)
“1” send p(t), “0” send -p(t)
1 1 1 0 0 1 1
tRZ
1 1 1 0 0 1 1
tNRZ
1 1 1 0 0 1 1
tRZ
1 1 1 0 0 1 1
t
NRZ
Alternate Mark Inversion
“1” changes the sign of the waveform p(t)
“0” has no pulse
Bi-phase Codes
Line Codes
1 1 1 0 0 1 1
t
RZ
1 1 1 0 0 1 1
NRZ
t
1 1 1 0 0 1 1
NRZ
t
Power Spectral Density (PSD) S(w)
Not bandwidth efficient
No error detection or
correction capability
Nonzero PSD at dc
The most power efficient
scheme
Transparent
Example:
P(0)=0
Not bandwidth efficient
No error detection or
correction capability
Nonzero PSD at dc
Not power efficient
Not transparent
Bandwidth efficient
Single-error detection
capability
Zero PSD at dc
Not power efficient
Not transparent
/2 /2 f
p(t) P(w)
Transmitted pulse
spectrum
Received pulse
spectrumChannel transfer
function
Example-1:
Example-2:
Minimum-bandwidth pulse that
satisfies the duobinary pulse criterion
Differential Coding: For the controlled ISI method, a zero-valued sample implies transition, that is,
if a digit is detected as 1, the previous digit is 0, or vice versa. This means that the digit interpreation is
based on the previous digit. If a digit were detected wrong, the error would be tend to propagate.
Differeantial coding eliminates this problem.
.
previously (HDB3).
Scrambler Descrambler
Shift
Registers
modulo 2 sum
( )
:
::
&
Example:
SNRPM
SNRFM
: Probability of Bit Error
SNR, average signal power to average noise power is important for measuring performance in analog systems
In DCS, the ratio is the bit energy (Eb) per noise power (N0), a normalized version of SNR
Allows comparison when M-ary systems are used
SNR for Digital Systems
0
/
/ /
b b b
b
E S T S R S W
N N W N W N R
Bit Energy
Noise Power
Spectral Density Bandwidth
Bit Time Bit Rate
Noise Power
Signal Power
Why not SNR? Power Signal: finite average power, infinite energy,
good model for analog signal
Energy Signal: zero average power, finite energy
Power signals are good for analog signals since they can be thought of as existing for a long time
Digital symbols exist over one symbol or bit interval, Tb, so this allows comparison between different M-ary signals
Why Eb / N0 ?