Bipolar Encoding Biphase Mark Code (Alternate Mark Inversion)

Home , Bipolar encoding, Eye pattern, Symbol rate

Communication Systems, 5e

Chapter 11: Baseband Digital Transmission Chapter 14: Bandpass Digital Transmission A. Bruce Carlson Paul B. Crilly

• Chapter 11: Baseband Digital Transmission – Digital signals and systems – Noise and errors – Bandlimited digital PAM systems – Synchronization Techniques • Chapter 14: Bandpass Digital Transmission – Digital CW modulation – Coherent binary systems – Noncoherent binary systems – Quadrature-carrier and M-ary systems – Orthogonal frequency division multiplexing – Trellis-coded modulation

© 2010 The McGraw-Hill Companies Why go digital? • Stability – Inherently invariant of performance. Identical clock rates result in identical results. No temperature variance or component aging effects. • Flexibility – Reprogramming allows for changes and upgrades – Apply digital signal processing to meet different needs encryption, compression, encoding • Reliable Reproduction – All circuits perform identically with identical results.

3 Digital Formatting and Transmission

4 Digital Signals and Systems

• An ordered sequence of symbols – Produced by a discrete information source – With symbols drawn from a defined alphabet • Binary symbols are one subset of symbols – Represent binary digits, 0 and 1 known as bits – Symbols may be represented by multiple bits (M-ary) • Interested in: – Symbol rate, symbols per second and bits per second (bps) – Symbol error probability or rate (bit-error-rate or BER measures) 5 Digital Pulse-Amplitude Modulation (PAM) • Also referred to as pulse-code modulation (PCM) • The amplitude of pulse take on discrete number of waveforms and/or levels within a pulse period T.

xt  a k p t  kT   k • p(t) takes on many different forms, a rect for

example 1 0  t  T pt   0 else

xmT    a k p mT    kT  a m p   a m , for 0    T k

6 Digital Signaling Rate

• For symbols of period T, the symbol rate is R=1/T

• The rate may be in bits-per-second when bits are sent. A bps rate is usually computed and defined. • The rate may be in symbols-per-second when symbols are sent. When there are a defined number of bits-per-symbol, the rate may be defined in bits-per-second as well. – If parity or other non-data bits are sent, the messaging rate and the signaling rate may differ. 7 PAM/PCM Types

NRZ RZ Manchester

AMI-Bipolar Encoding Biphase Mark Code (Alternate Mark Inversion)

8 PAM/PCM Transmission

• Pulse code modulation (PCM) is used when a binary data stream is to be sent

• In PCM the binary sequence is used to define logical signal levels for transmission. – A logical level may map to bits (e.g. 0-High, 1-Low) – A bit value may define whether a level changes or not, i.e. Mark : change whenever the bit is a one Space: change whenever the bit is a zero – Period half-cycles can take on various structures based on a bit value or the sequence of bits

9 PCM Common Waveform Types

• Marks (1’s) and Spaces (0’s)

• Non-return-to-zero (NRZ) – Level, Mark, Space • Return-to-zero (RZ) – unipolar, bipolar, AMI (alternate mark inversion) • Manchester – biphase level, biphase mark, biphase space

10 PCM Types Again

NRZ RZ Manchester

AMI-Bipolar Encoding Biphase Mark Code (Alternate Mark Inversion)

11 PCM Type Selection

• Spectral characteristics (power spectral density and bandwidth efficiency) • Bit synchronization capability • Error detection capability • Interference and noise immunity • Implementation cost and complexity – Simple to modulate and demodulate

12 Spectral Attributes of PCM If Bandwidth W=1/T, then WT=1

Note that WT=0.5 or a bandwidth equal to ½ the symbol rate can be used!

13 ABC Binary PAM formats

(a) unipolar RZ & NRZ

(b) polar RZ & NRZ

(d) split-phase Manchester

(e) polar quaternary NRZ

Figure 11.1-1

• When multiple bits per symbol are sent M  2n – The symbol rate is

R Bit R Bit R Symbol   log2 M n – “Quaternary NRZ” is a 4-ary symbol providing 2 bits- per-symbol based on 4 amplitude levels • Digital mapping of the symbols is performed • Gray Codes typically used so that the nearest neighbor only has one-bit different (improves the bit-error rate of the symbol type being used)

15 Transmission

~ yt  a k  p t  t d  kT  n t   k

16 Transmission

~ yt  a k  p t  t d  kT  n t   k • The digital signal is time delayed

t d • The pulse is “filtered” and/or distorted by the channel ~ pt  fnp t  hc t 

• Recovering or Regenerating the signal may not be trivial ˆ ~ ymT  td  am   ak  p mT  kT  n mT  td  km – Signal plus inter-symbol interference (ISI) plus noise 17 Distorted Binary Baseband Signal

• The eye pattern results after signal demodulation and filtering. The “optimal” sampling time and other measurement of signal/receiver performance can be measured (noise margin, timing jitter,

timing sensitivity, etc) 18 Symbol Periods and ISI

• For a signal with the maximum number of level transitions (typically, 01010101) • The binary signal would form a square wave of period 2T. – Fourier Series of fundamental plus odd harmonics • To minimally pass this signal, a low pass filter with cutoff frequency of B  1/2T = R/2 may be used … – This concept also comes from Nyquist – Therefore the previous comments about BT = ½

19 Symbol Periods and ISI (2)

• To minimally pass this signal, a low pass filter with cutoff frequency of R/2 may be used …

• The optimal binary symbol pulse shape would then have a band-limited spectrum …

1  f   t  Pf  rect  pt  sinc t R  sinc   R  R   T 

• Note that the value of other symbols that could cause ISI is equal to zero at the “optimal” symbol sampling time … the center of the eye diagram.

– A way to minimize ISI using the optimal filter! 20 Matlab Bipolar NRZ

• Sinc Function Waveform Sum (SincEyev2.m) • Eye Diagram

Eye Diagram For Square Wave 1 1 0.8 0.8 0.6 0.6

0.4 0.4

0.2 0.2

0 0

-0.2 -0.2

-0.4 -0.4 -0.6 -0.6 -0.8 -0.8 -1 -1 -4 -3 -2 -1 0 1 2 3 4 -8 -6 -4 -2 0 2 4 6 8

21 Matlab Bipolar NRZ (2)

• Sinc Function Waveform Sum • Power Spectral Density

Power Spectral Density 20 1

0.8 10

0.6 0 0.4 -10 0.2

0 -20

-0.2 -30 -0.4 -40 -0.6

-0.8 -50 -1 -60 -4 -3 -2 -1 0 1 2 3 4 0 1 2 3 4 5 6 7 8

22 Baseband Binary Receiver

  yt  a k p t  kT ht   nin t  h t   k 

yt k  a k  n t k  • Synchronous Time sampling of maximum filter output 23 Regeneration of a unipolar signal

24 Unipolar Binary Error Probability

• Hypothesis Testing using a voltage threshold – Hypothesis 0 • The conditional probability distribution expected if a 0 was sent

pY yk | H0  pY a k n t k | a k  0  pY n t k 

pY yk | H0  pN yk – Hypothesis 1 • The conditional probability distribution expected if a 1 was sent

pY yk | H1  pY a k n t k | a k  A  pY A  n t k 

pY yk | H1  pN yk - A

V P  PY  V  p y | H dy e1  Y 1   P  PY  V  p y | H dy e0  Y 0 V

• Use Hypothesis to establish a decision rule – Use threshold to determine the probability of correctly and incorrectly detecting the input binary value 26 Average Error Probability

• Using the two error conditions: – Detect 1 when 0 sent – Detect 0 when 1 sent

Perror  PH0 Pe0  P H1 Pe1 • For equally likely binary values 1 PH  P H  0 1 2 1 P  P  P error 2 e0 e1 • Optimal Threshold

PH0 pY Vopt | H0  PH1 pY Vopt | H1  27 Threshold regions for conditional PDFs

A V  opt 2 28 For AWGN

• The pdf is Gaussian 1  y2  p y | H  p y  exp  Y 0 N  2  22  2 

1   2  for Qx    exp d 2 x  2 

  V   A  P  PY  V  p y dy  Q  Q e0  N     V     2 

V  A  V   A  P  PY  V  p y  A dy  Q  Q e1  N          2 

29 Modification for Bipolar Signals

• Hypothesis Testing using a voltage threshold – Hypothesis 0 • The conditional probability distribution expected if a 0 was sent

pY yk | H0  pY a k n t k | a k  A  pY - A  n t k 

pY yk | H0  pN yk  A – Hypothesis 1 • The conditional probability distribution expected if a 1 was sent

pY yk | H1  pY a k n t k | a k  A  pY A  n t k 

pY yk | H1  pN yk - A

A A V    0 30 opt 2 2 Modification for Bipolar Signals (2)

• Determining the error probability

  AV   A  P  PY  V  p y  A dy  Q  Q e0  N     V     V  AV   A  P  PY  V  p y  A dy  Q  Q e1  N          • Notice that the error has been reduced – The distance between the expected signal values may be twice as large as the unipolar case (using +/- A)