Elektronik Öğretmenliği Bölümü EBB 326 Haberleşme ...akademikpersonel.kocaeli.edu.tr/yunusee/poster/yunusee22.02.2012... · güvenlik ve kriptolama gibi sinyal işleme teknikleri

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 ?