Communication Systems, 5e

Chapter 11: Baseband Digital TransmissionChapter 14: Bandpass Digital Transmission

A. Bruce CarlsonPaul B. Crilly

© 2010 The McGraw-Hill Companies

© 2010 The McGraw-Hill Companies

Chapter 11 & 14

• 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

3

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.

4

Digital Formatting and Transmission

5

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)

6

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.

• p(t) takes on many different forms, a rect for example

k

k kTtpatx

else0

Tt01tp

T0for,apakTmTpamTx mmk

k

7

Digital Signaling Rate

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

• 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.– If parity or other non-data bits are sent, the messaging

rate and the signaling rate may differ.

8

PAM/PCM Types

Biphase Mark Code

RZ

AMI-Bipolar Encoding(Alternate Mark Inversion)

ManchesterNRZ

9

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

10

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

11

PCM Types Again

Biphase Mark Code

RZ

AMI-Bipolar Encoding(Alternate Mark Inversion)

ManchesterNRZ

12

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

13

Spectral Attributes of PCMIf Bandwidth W=1/T, then WT=1

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

14

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(a) unipolar RZ & NRZ

(b) polar RZ & NRZ

(c) bipolar NRZ

(d) split-phase Manchester

(e) polar quaternary NRZ

Figure 11.1-1

ABC Binary PAM formats

15

M-ary Coded Symbols

• When multiple bits per symbol are sent

– The symbol rate is

– “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)

n2M

nR

MlogRR Bit

2

BitSymbol

16

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(a) Baseband transmission system (b) signal-plus-noise waveform: Figure 11.1-2

Transmission

tnkTttp~atyk

dk

17

Transmission

• The digital signal is time delayed

• The pulse is “filtered” and/or distorted by the channel

• Recovering or Regenerating the signal may not be trivial

– Signal plus inter-symbol interference (ISI) plus noise

tnkTttp~atyk

dk

thtpfntp c~

dt

dmk

kmd tmTnkTmTpaatmTy

~ˆ

18

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(a) Distorted polar binary signal (b) eye pattern: Figure 11.1-3

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)

19

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

20

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 …

• 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!

Rfrect

R1fP

TtsincRtsinctp

21

Matlab Bipolar NRZ

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

-4 -3 -2 -1 0 1 2 3 4

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-8 -6 -4 -2 0 2 4 6 8-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1Eye Diagram For Square Wave

22

Matlab Bipolar NRZ (2)

• Sinc Function Waveform Sum• Power Spectral Density

-4 -3 -2 -1 0 1 2 3 4

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8-60

-50

-40

-30

-20

-10

0

10

20Power Spectral Density

23

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Figure 11.2-1

Baseband Binary Receiver

• Synchronous Time sampling of maximum filter output

thtnthkTtpaty ink

k

kkk tnaty

24

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(a) signal plus noise (b) S/H output (c) comparator output: Figure 11.2-2

Regeneration of a unipolar signal

25

Unipolar Binary Error Probability

• Hypothesis Testing using a voltage threshold– Hypothesis 0

• The conditional probability distribution expected if a 0 was sent

– Hypothesis 1• The conditional probability distribution expected if a 1 was

sent

kYkkkY0kY tnp0a|tnapH|yp

kYkkkY1kY tnApAa|tnapH|yp

kN0kY ypH|yp

A-| 1 kNkY ypHyp

26

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Conditional PDFs Figure 11.2-3

Decision Threshold and Error Probabilities

• Use Hypothesis to establish a decision rule– Use threshold to determine the probability of correctly

and incorrectly detecting the input binary value

V

0Y0e dyH|ypVYPP

V

1Y1e dyH|ypVYPP

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Average Error Probability

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

• For equally likely binary values

• Optimal Threshold

1e10e0error PHPPHPP

21HPHP 10

1e0eerror PP21P

1optY10optY0 H|VpHPH|VpHP

28

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Figure 11.2-4

Threshold regions for conditional PDFs

2AVopt

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For AWGN

• The pdf is Gaussian

for

2

2

2N0Y 2yexp

21ypH|yp

x

2

d2

exp21xQ

2AQVQdyypVYPP

VN0e

2

AQVAQdyAypVYPPV

N1e

30

Modification for Bipolar Signals

• Hypothesis Testing using a voltage threshold– Hypothesis 0

• The conditional probability distribution expected if a 0 was sent

– Hypothesis 1• The conditional probability distribution expected if a 1 was

sent

kYkkkY0kY tnA-pAa|tnapH|yp

kYkkkY1kY tnApAa|tnapH|yp

AypH|yp kN0kY

A-ypH|yp kN1kY

02A

2AVopt

31

Modification for Bipolar Signals (2)

• Determining the error probability

• 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)

AQVAQdyAypVYPPV

Ne1

AQVAQdyAypVYPP

VNe0