Elektronik Öğretmenliği Bölümü EBB 326 Haberleşme Sistemleri-II 2012-2013 Bahar Yarıyılı Öğretim Üyesi Prof. Dr. Yunus E. Erdemli Ofis: TEF-1011 Tel: 303-2238 E-posta: yunusee@kocaeli.edu.tr Ders Programı Pz.tesi: 12:00-15:00 (Teo) 15:00-16:50 (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
Ders İçeriği Örnekleme ve Darbe Kod Modülasyonu (PCM) Sayısal Veri İletimi ve Temel Prensipleri Gürültü Etkisinde Analog ve Sayısal Haberleşme Sistemlerinin Performansı Değerlendirme: Ara Sınav (%25) + Lab (%15) + Final (%60) Devam zorunluluğu: Teorik Ders (%70) Lab/Problem Saati (%80)
Neden Sayısal Haberleşme? 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.
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 Digital Modulation input: digital signal output: analog signal Digital signal FSK Frequency Shift Keying ASK Amplitude Shift Keying 2-ASK 0: A1cos(2πfct) 1: A2cos(2πfct) ASK modulated signal PSK Phase Shift Keying 4-PSK 00: Acos(2πfct+ 0 ) 01: Acos(2πfct+ π/2) 10: Acos(2πfct+ π) 11: Acos(2πfct+ 3π/2) PSK modulated signal 0 0 1 0 1 0 1 1
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. t min =1/2B 2B Birim zamanda birbirleriyle örtüşmeyecek biçimde iletilebilecek darbelerin maksimum sayısı yaklaşık olarak 1/t min =2B olmalıdır. Örnek: B=3 khz max 6000 darbe/sn & t min =1/6000=0.1667 msn
1 T n 2B 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 Intersymbol Interference Average Signal Power Average Noise Power = probability of bit error # of quantization levels 6-dB Law: Depends on: input waveshapes quantification characteristics
A-law Characteristics (Europe: A=87.6) m-law Characteristics (US, Canada, Japan: m=255)
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 x rms : the rms value of the input analog signal V/x rms : loading factor
Analog voice signal: 300-3400 Hz f s 2 3.4 khz=6.8 khz & peak percentage error: 10
DARBE KOD MODÜLASYONU (PCM)
Düzgün Kuantalama Uniform Quantization Boş kanal gürültüsünü önleyici düzgün kuantalama eğrisi Giriş a adımından küçükse, daima 0 çıkışı elde edilir.
Düzgün Olmayan Kuantalama Nonuniform Quantization Sıkıştırma (compression) ve genleştirme (expansion) eğrileri. A/D çeviricide sıkıştırma yapılmışsa, D/A çeviricide genleştirme işlemi yapılmalıdır. Düzgün Kuantalayıcı W 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 III II I Lokal kuantalama seviye (adım) sayısı: M IV V VI VIII VII Amaç; giriş genliğinin herhangi bir değeri için belirli sınırlar içinde kalan bir kuantalama hatası elde etmektir.
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: B T = n B hertz Information / Hz
Transmission Bandwidth Binary systems M (# of levels) = 2 n or n=log 2 M Signal m(t), bandlimited to B m Hz requires at least 2B m samples/sec (Nyquist). For reconstruction, we need 2nB m bits/sec or 2nB m pieces of information. 0 1 0 0 1 0 0 T 2T 3T 4T 5T 6T t Maximum Signal Rate: D Encoder Transmission System/Channel Bandwidth=B Decoder Nyquist Theorem (1920): For a system/channel bandwidth B, T min =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/2log 2 M (Hz)
Relationship between Transmission Speed and Noise 0 1 0 0 1 0 t t Encoder Transmission System/Channel Bandwidth=B s(t) + Decoder Maximum Signal Rate Channel Capacity Noise n(t) 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
Channel Capacity Shannon theorem C = Blog2(1+S/N) shows that the maximum rate or channel Capacity of a system/channel depends on bandwidth, signal energy and noise intensity. 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 Kbps If B is fixed, we have to increase signal-to-noise ratio for increasing transmission rate.
DIFFERENTIAL PULSE CODE MODULATION (DPCM) Goal: Reduce the quantization error by transmitting a difference signal which is the original signal the predicted signal. Taylor Series Expansion: Discretized Expression: Prediction Formula:
Linear Predictor
DPCM System Transmitter Receiver SNR improvement due to prediction G p =P m / P d
Delta Modulation (DM) A special case of DPCM d[k] Delta Modulator < m q [k] - Delta Demodulator
Delta Modulation (DM) DM transmits the derivative of the signal Delta Modulator Delta Demodulator
DM transmits the derivative of the signal
Slope Overload No overload occurs if ( )
SNR Performance Voice Signals Single Integration (DM) Double Integration (DM) PCM
Properties of Line Codes Transmission Bandwidth Power Efficiency Error Detection and Correction Favorable power spectral density (PSD) Timing content (synchronization) M L-Level, M-Mark, S-Space RZ-Return-to-Zero, NRZ-NoReturn-to-Zero 010010110 Digital Encoder Digital System Channel
Pulse Shaping 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
Line Codes On/Off (unipolar) 1 send p(t), 0 nothing Return to zero (RZ) Non-Return to Zero (NRZ) Polar (bipolar) 1 1 1 0 0 1 1 1 1 1 0 0 1 1 RZ NRZ t t 1 send p(t), 0 send -p(t) 1 1 1 0 0 1 1 1 1 1 0 0 1 1 RZ t NRZ t
Line Codes Alternate Mark Inversion 1 changes the sign of the waveform p(t) 0 has no pulse 1 1 1 0 0 1 1 RZ t Bi-phase Codes 1 1 1 0 0 1 1 1 1 1 0 0 1 1 NRZ t 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
P(0)=0 Example:
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
p(t) P(w) /2 /2 f Transmitted pulse spectrum Channel transfer function Received pulse spectrum
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.
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previously (HDB3). Scrambler Shift Registers Descrambler modulo 2 sum
( )
:
: : & SNR PM Example:
SNRFM
: Probability of Bit Error
SNR for Digital Systems SNR, average signal power to average noise power is important for measuring performance in analog systems In DCS, the ratio is the bit energy (E b ) per noise power (N 0 ), a normalized version of SNR Allows comparison when M-ary systems are used Bit Energy Noise Power Spectral Density Bit Time Eb S Tb S / Rb S W N0 N / W N / W N Rb Bandwidth Bit Rate Signal Power Noise Power
Why E b / N 0? 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, T b, so this allows comparison between different M-ary signals