Digital Communications - Overview - Abrar Hashmi's Blog · · 2016-03-01Digital Communications -...

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Digital Communications - Overview

Lecturer: Assoc. Prof. Dr Noor M Khan

Department of Electronic Engineering,

Muhammad Ali Jinnah University,

Islamabad Campus, Islamabad, PAKISTAN

Ph: +92 (51) 111-878787, Ext. 129

Email: [email protected], [email protected]

EE5713 : Advanced Digital Communications

mailto:[email protected]

mailto:[email protected]

Week 1

This Lecture would be covered on Board and the

following concepts would be delivered:

Thermal Noise / AWGN

Signal to Noise Ratio (SNR)

Channel Bandwidth and Data Rate

Fourier Transformation and Time/Frequency Domains

Basic Diagram of A Communication System

Modulation

Baseband and Bandpass Modulation

Advanced Digital Communications -Spring-2011-Week-1-2 2

2/25/2013 Muhammad Ali Jinnah University, Islamabad Digital Communications EE3723 3

EE 4723: Digital Communications II

Instructor: Dr. Noor Muhammad Khan

Text book

– Bernard Sklar, Digital Communications: Fundamentals

and Applications, Prentice Hall, 2nded, 2001.

References/Additional readings:

– J. G. Proakis, Digital Communications, 2001

– T. S. Rappaport, Wireless Communications: Principles and Practice,

Prentice Hall, 1999

– Marvin Kenneth Simon, Mohamed-Slim Alouini, Digital Communication

over Fading Channels, John Wiley & Sons, 2004

– Lecture slides, Handouts uploaded on the class folder.


Grading Policy

Midterm: 20%

1st Major Quiz: 15%

2nd Major Quiz: 15%

Project/Assignments: 10%

Final: 40%


Communication System

Main purpose of communication is to transfer

information from a source to a recipient via a channel or

medium.

Basic block diagram of a communication system:

Source Transmitter Channel Receiver Recipient


Analog and digital communication systems

Communication system converts information into

electrical electromagnetic/optical signals appropriate for

the transmission medium.

Analog systems convert analog message into signals that

can propagate through the channel.

Digital systems convert bits (digits, symbols) into signals

– Computers naturally generate information as

characters/bits

– Most information can be converted into bits

– Analog signals converted to bits by sampling and

quantizing (A/D conversion)


Why digital communication?

Digital techniques need to distinguish between discrete

symbols allowing regeneration versus amplification

Good processing techniques are available for digital

signals, such as medium.

– Data compression (or source coding)

– Error Correction (or channel coding)

– Equalization

– Security

Easy to mix signals and data using digital techniques

2006-01-24 Lecture 1 8

Digital vs Analog

Advantages of digital communications:

– Regenerator receiver

Different kinds of digital signal are treated identically.

Data

Voice

Media

Propagation distance

Original

pulse

Regenerated

pulse

A bit is a bit!


Analog communication system example

Message signals Modulated signals


Digital Communication: Transmitter


Digital Communication: Receiver


Digital communications: Main Points

Transmitters modulate analog messages or bits in case of

a DCS for transmission over a channel.

Receivers recreate signals or bits from received signal

(mitigate channel effects)

Performance metric for analog systems is fidelity, for

digital it is the bit rate and error probability.


Performance Metrics

Analog Communication Systems

– Metric is fidelity: want

– SNR typically used as performance metric

Digital Communication Systems

– Metrics are data rate (R bps) and probability of bit error

– Symbols already known at the receiver

– Without noise/distortion/sync. problem, we will never

make bit errors

)()(ˆ tmtm

)ˆ( bbpPb


Digital communication blocks


Processes Involved


EE5713 : Advanced Digital Communications

Week 2-3: Digital Communications - Overview

Detection

Matched Filter and Correlator Filter

Error Probability

Signal Space

Orthogonal Signal Space


Detection

Matched filter reduces the received signal to a single variable

z(T), after which the detection of symbol is carried out

The concept of maximum likelihood detector is based on

Statistical Decision Theory

It allows us to

– formulate the decision rule that operates on the data

– optimize the detection criterion

1

2

0( )

H

H

z T


Detection of Binary Signal in Gaussian Noise

The output of the filtered sampled at T is a Gaussian random process


Hence

where z is the minimum error criterion and 0 is optimum

threshold

For antipodal signal, s1(t) = - s2 (t) a1 = - a2

1

1 20

2

( )

2

H

a az

H

1

2

0

H

z

H

Baye’s Decision Criterion and Maximum Likelihood Detector


Probability of Error

Error will occur if

– s1 is sent s2 is received

– s2 is sent s1 is received

The total probability of error is the sum of the errors

0

2 1 1

1 1

( | ) ( | )

( | ) ( | )

P H s P e s

P e s p z s dz

0

1 2 2

2 2

( | ) ( | )

( | ) ( | )

P H s P e s

P e s p z s dz

2

1 1 2 2

1

2 1 1 1 2 2

( , ) ( | ) ( ) ( | ) ( )

( | ) ( ) ( | ) ( )

B i

i

P P e s P e s P s P e s P s

P H s P s P H s P s


If signals are equally probable

Numerically, PB is the area under the tail of either of the

conditional distributions p(z|s1) or p(z|s2) and is given by:

2 1 1 1 2 2

2 1 1 2

( | ) ( ) ( | ) ( )

1( | ) ( | )

2

BP P H s P s P H s P s

P H s P H s

2 1 1 2 1 2

1( | ) ( | ) ( | )

2

by Symmetry

BP P H s P H s P H s

0 0

0

1 2 2

2

2

00

( | ) ( | )

1 1exp

22

BP P H s dz p z s dz

z adz


The above equation cannot be evaluated in closed form (Q-

function)

Hence,

0

1 2

0

2

2

00

2

0

2

( )

2

1 1exp

22

( )

1exp

22

B

a a

z aP dz

z au

udu

1 2

0

.182

B

a aP Q equation B

21

( ) exp22

zQ z

z


Error probability for binary signals

Recall:

Where we have replaced a2 by a0.

To minimize PB, we need to maximize:

or

We have

Therefore,

02

2

01 )(

aa

0

01

aa

2

1 0

2

0 0 0

( ) 2

/ 2

d da a E E

N N

2

1 0 1 0

2

0 0 0 0

( ) 21 1

2 2 2 2

d da a a a E E

N N

18.2 0

01 Bequationaa

QPB


Table for computing of Q-Functions


Signals vs vectors

Representation of a vector by basis vectors

Orthogonality of vectors

Orthogonality of signals


Signal space

What is a signal space?

– Vector representations of signals in an N-dimensional orthogonal

space

Why do we need a signal space?

– It is a means to convert signals to vectors and vice versa.

– It is a means to calculate signals energy and Euclidean distances

between signals.

Why are we interested in Euclidean distances between signals?

– For detection purposes: The received signal is transformed to a

received vectors. The signal which has the minimum distance to the

received signal is estimated as the transmitted signal.


Orthogonal signal space

N-dimensional orthogonal signal space is characterized by N

linearly independent functions called basis functions.

The basis functions must satisfy the orthogonality condition

where

If all Ki= 1, the signal space is orthonormal.

Njj t

1)(

jiij

T

iji Kdttttt )()()(),( *

0

Tt 0

Nij ,...,1,

ji

jiij

0

1


Example of an orthonormal bases

• Example: 2-dimensional orthonormal signal space

• Example: 1-dimensional orthonornal signal space

1)()(

0)()()(),(

0)/2sin(2

)(

0)/2cos(2

)(

21

2

0

121

2

1

tt

dttttt

TtTtT

t

TtTtT

t

T

T t

)(1 t

T

1

0

)(1 t

)(2 t

0

1)(1 t

)(1 t0


Signal space …

Any arbitrary finite set of waveforms

where each member of the set is of duration T, can be expressed

as a linear combination of N orthonogal waveforms

where .

where

M

ii ts1

)(

Njj t

1)(

MN

N

j

jiji tats1

)()( Mi ,...,1

MN

dtttsK

ttsK

a

T

ji

j

ji

j

ij )()(1

)(),(1

0

*

Tt 0Mi ,...,1

Nj ,...,1

),...,,( 21 iNiii aaas2

1

ij

N

j

ji aKE

Vector representation of waveform Waveform energy (Parseval’s theorem)


Signal space …

N

j

jiji tats1

)()(

),...,,( 21 iNiim aaas

iN

i

a

a

1

)(1 t

)(tN

1ia

iNa

)(tsi

T

0

)(1 t

T

0

)(tN

iN

i

a

a

1

ms)(tsi

1ia

iNa

ms

Waveform to vector conversion Vector to waveform conversion

dtttsK

a

T

ji

j

ij )()(1

0

*


Example: Baseband Antipodal Signals


Example: BPSK


Example QPSK


Synthesis Equation = Modulation


Example: Baseband Antipodal Signals


Example: BPSK


Correlation

Measure of similarity between two signals

Cross correlation

Autocorrelation

.)()(1

dttztgEE

czg

n

.)()()(

dttztggz

.)()()(

dttgtgg


Analysis Equation = Detection


Correlation Detector


Correlation Detector: Examples


Correlation Detector Example: QPSK


TTT

T

d

tstsdttsdtts

dttstsE

001

2

00

2

01

2

001

)()(2)()(

)()(

)63.3(2 0

N

EQP d

B

The probability of bit error is given by:


The probability of bit error for antipodal signals:

The probability of bit error for orthogonal signals:

The probability of bit error for unipolar signals:

0

2

N

EQP b

B

02N

EQP b

B

0N

EQP b

B


Bipolar signals require a factor of 2 increase in energy compared to

orthogonal signals

Since 10log102 = 3 dB, we say that bipolar signaling offers a 3 dB better

performance than orthogonal


Comparing BER Performance

For the same received signal to noise ratio, antipodal provides

lower bit error rate than orthogonal

4

,

2

,

0

10x8.7

10x2.9

10/

antipodalB

orthogonalB

b

P

P

dBNEFor


In analog communication the figure of merit used is the

average signal power to average noise power ration or SNR.

In the previous few slides we have used the term Eb/N0 in the

bit error calculations. How are the two related?

Eb can be written as STb and N0 is N/W. So we have:

Thus Eb/N0 can be thought of as normalized SNR.

Makes more sense when we have multi-level signaling.

Reading: Page 117 and 118.

2 0

0 / 2

b b

b

E ST NS Wwhere

N N W N R

Relation Between SNR (S/N) and Eb/N0

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Digital Communications - Overview - Abrar Hashmi's Blog · · 2016-03-01Digital Communications -...

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