Chapter 1_1_2008

Biomedical Telecommunication Systems Lab. Biomedical Telecommunication Systems Lab. Pusan National University Pusan National University 1

Digital Communications By Bernard Sklar

Prof. : Hyeog-soong

Kwon

E-mail: [email protected]://be.pnu.edu/~hskwon


Syllabus

Text Book : Digital Communications 2ed by Bernard Sklar Reference: Digital Communications, 4th ed. Mcgraw Hill , By Proakis

Principles of communications, 5th ed., J.Willy , By Zimemer

Topics Signals and Spectra, Random process Formatting and baseband modulation Baseband demodulation / Detection Bandpass modulation and demodulation Modulation and coding tradeoffs Synchronization ( or Spread-Spectrum Techniques)


EvaluationAttendance: 10%, Midterm : 30%, Final term : 40%, Report:5%, Quize :15 % , (subject to change if necessary)

ProjectMatlab coding, Simulink design Mid/Final Exams include the project-related problems

Office hour: Tuesday 3:00 pm ~ 6:00 pm, Room 3563

Teaching Assistance

Ik-Sung Cho (Ph.D), Hong-Gyu Jeon-. Office: room 3568-. Tel: 055-350-5688(BTS Lab.)-. E-mail: [email protected]


1.1 Digital communication signal processing1.1.1 Why digital?

Advantage Easy to regenerate original function Digital circuits are less subject to distortion & Interference than analog circuits High signal fidelity can be obtained with extremely low error rates through digital

techniques s.a. error detection & correction coding Digital circuits are more reliable, lower cost, more flexible implementation in H/W

(Micro-Processor, LSI, Digital switch, etc..) It protect against interference & Jamming and provide encryption, privacy It is simpler multiplexing (CDMA, TDMA) than the analog Easy storage & processing of Data (Digital data/image compression technology)

Disadvantage Required additional steps : sampling & A/D conversion Required a greater bandwidth than analog method Required complicated synchronization issues : Frame synch.

Symbol timing synch. Network synch.


1.1.1 Why digital?


1.1.2 Typical block diagram and transformations


Formatting Transforms the source information into digital symbols by the sampling,quantization and coding.

Source coding removes redundant or unneeded informationEncryption prevents unauthorized users from understanding messages and frominjecting false messages into the system.

Channel coding, for a given data rate, can reduce the probability of error, or reducethe signal-to-noise ratio(SNR) requirement, at the expense of bandwidth or decoder

complexity.

Modulation is the process by which the symbols are converted to waveforms that arecompatible with the transmission channel.

Frequency spreading can produce a signal that is less vulnerable to interference and can be used to enhance the privacy of the communicators.

Basic signal processing function


Multiplexing and Multiple access procedures combine signals that might have

the different characteristics or might originate from different source, so that they

can share a portion of the communications resources.

Transmitter & Receiver

Codec (Coder / Decoder)

Modem (Modulator / Demodulator)

RF(XMT / RCV) : XMT : freq up conversion stage,high power Amp Antenna

RCV : AntennaLow-Noise Amp(LAN)Down conversion stage



1.1.3 Basic digital communication nomenclature

Information source : The device producing information to be communicated.Information sources can be analog or discrete

Textual message : A sequence of characters.

Character : A member of an alphabet or a set of symbolsex) ASCII, EBCDIC etc.

HOW ARE YOU?(ex) OK

$9,567,216.73

A(ex) 9

&


Binary digit(bit) : The fundamental information unit for alldigital systems

Bit stream : A sequence of binary digits (ones and zeros)

Symbol (digital message) : A group of k bits as considered unit( The size of symbol, ) 2kM =


Data rate : This quantity is bits/sec(bps)

Digital waveform : A Voltage or current waveform (a pulse for baseband transmission, or a sinusoid for bandpasstransmission) that represents a digital symbol.

MTT

kR 2log1==

Symbol rate (baud rate) : the rate at which the signal state changes when observed in communication channel

(ex) 6bits / 6ms = 1000bits/s

, where T is the k bit symbol duration


Bandwidth efficiency -> bits/ sec/ Hz

Ex ) If a system requires 4KHz of bandwidth to continuously send8000 bps of information,

Ex ) If a system uses four frequency to convey pairs of bits through a channel & the symbol is changed every 0.5ms

symbol rate = 1/ 0.5 ms

= 2000 symbols/sec = 2000 baud

data rate = 2/ 0.5 ms = 4000 bps

Bandwidth efficiency = 8000bps / 4000Hz

= 2bits/sec/Hz


1.1.4 Digital versus analog performance criteria

analog: Signal to noise ratioPercent distortionExpected mean-square error between the transmitted and

received waveform

digital: Probability of incorrectly detected digitProbability of error


1.2 Classification of signals

Signal

Time function: f(t) Frequency function: f()

Frequency domainTime domain

Transformation

x(t) ..

h(th(t) .) .

y(ty(t) .) .

. X(f)

. . H(fH(f))

. . Y(fY(f))

Time domain Frequency domain


1.2.1 Deterministic & Random Signalsa) Deterministic Signal

- A signal which has no uncertainty w.r.t. its value at any time.- Possible to write as an explicit expression

x(t)= 5cos10t

b) Random Signal- It has some degree of uncertainty before the signal actually occurs- Not possible to write such an explicit expression- When examined long period, it has certain regularities in terms of

probability & statistical averages- Useful for characterizing signals & noise in communication system


1.2.2 Periodic & Non-periodic Signalsa) Periodic Signal (power signal)

- There exists a const T0 s.t.x(t) = x( t + T0 ) for - < t <

b) Non-periodic Signal (energy signal)- There is no value of T0

1.2.3 Analog & Discrete Signalsa) Analog Signal

- A continuous function of time. x(t)- Uniquely defined for all t

b) Discrete Signal- Exist only at discrete times. x(kT)- Sequence of numbers defined for each time, kT

Analog signal

Discrete signal

t

t t

t

e -l t l e- t 2


1.2.4 Energy Signal & Power Signal energy signal

(communication systems performance depend on the received signal energy) It has nonzero but finite energy for all time

It has finite energy but zero average power nonperiodic signal, deterministic signal

power signal It has finite but nonzero power for all time

It has finite average power but infinite energy periodic signal, random signal

===

dttxdttxE

dttxET

TTx

T

T

Tx

)()(lim

)(

22/

2/

2

2/

2/

2

=

==2/

2/

2

2/

2/

2

)(1lim

)(11

T

TTx

T

T

Tx

Tx

dttxT

P

dttxT

ET

P


1.2.5 Unit Impulse Function

Dirac-delta function, an infinitely large amplitude pulse, with zero pulse width, and unity weight,concentrated at the point where its argument is zero

U(t)

t

1

0

t

(t)

1

0

U (t)

t 01

t

(t)

===

==

)()()(

tat t valueSampling0at t unbounded is )(

0for t 0)(

1)(

00

0

txdttttx

tt

dtt


1.3.1 Energy Spectral Density( ESD : x(f) )-

Total energy of a real valued energy signal x(t)

Define as

functioneven : )(2)(

)()(

0

22

====

dffdff

dffXdttxE

xx

x

2)()( fXfx =

1.3 Spectral density

The spectral density of a signal characterizes the distribution of the signal's energy or power in the frequency domain.

This concept is important when considering filtering in communication systems.It has useful to measure the signal and noise in the output of the filter.

00 t

t


Using Parsevals theorem

== dffXdttxEx 22 )()(

== dttxdttxE TTTx )()(lim 22/ 2/ 2

[ ]

==

=

=

=

dffXdffXfX

dfdtetxfX

dtdfefXtx

dtdfefXtxE

ftj

ftj

ftx

2*

2*

2*

2

)()()(

)()(

)()(

)()(


1.3.2 Power spectral density ( PSD : )

-

Average power of a periodic signal,

=

==n

n

T

TXCdttx

TP 2

2/

2/

2

0

0

0

)(1 , where terms are the complex Fourier series coefficients of the periodic signal

)( fGx

nC

=

==

=

0

02

)(2)(

)()(

dffGdffGP

nffCfG

XXX

nnX


Ex) Find Fouriers coefficient

sol) Fourier coefficient

x(t)

-T -T T T0 0 0 04 4

tA

.. . ...

..........

......

A2

0 1 2.

nnc

ncAn

nA

n

n

AdtAeT

cT

T

tjnn

sinsin where

2sin

22

2sin

2

2sin1 4/

4/

0

0

0

=

==

==


-T 2 T 2t

A

Ex) Find Fouriers transformation

sol) Fourier transformation

1/T 2/T

AT)(sin

sin)()( 02

TfcATTn

TnATdtetxfX tfj

===


For

Correlation is a matching process ; Autocorrelation refers to the matching of a signal with a delayed() version of itself. It is useful to detect signal in the noise.

Autocorrelation of an Energy signal

+= dttxtxRx )()()( - Properties

; Symmetrical in about zero. for all ; Maximum value occurs at the origin. ; Fourier Relation. ; Value at the origin is equal

to the energy of the signal.

)()( = xx RR)0()( xx RR

)()( fR xx dttxRx = )()0( 2

1.4 Autocorrelation

1.4.1 Autocorrelation of an energy signal

0 0

X( )2tA

Rf(t)

A

T t -T T

(a) (b)


1 1 2 3 4 5

12h(t)*s(t)

t


Autocorrelation of a power signal

For

- when the power signal, x(t), is periodic with period T0 ,

For

+=2/

2/)()(1)( lim

T

TTx dttxtxT

R

+= 2/ 2/0

0

0

)()(1T

Tdttxtx

T

)cos(2)( 0 += twtX1.4.2 Autocorrelation of a power signal

)()( = xx RR)0()( xx RR

)()( fGR xx dttx

TR

T

Tx = 2/ 2/ 20

0

0

)(1)0(

- Properties

; Symmetrical in about zero. for all ; Maximum value occurs at the origin. ; Fourier Relation. ; Value at the origin is equal

to the energy of the signal.


Ex) Find the value of autocorrelation

Rx( )

1

1/fo


2T T T 2T/ 2 *

/ 2

1( ) lim ( ) ( )T

f TTR f t f t d

T = + 1t t =

/ 2 *1 1/ 2

1lim ( ) ( )T

TTf t f t dt

T

T/ 2T

( )fR 22A

2

(0)2f

AR = 02T

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Chapter 1_1_2008