digital comm fundamentals

Digital Communications Digital Communications Digital Communications Digital Communications ---- OverviewOverviewOverviewOverview

Instructor: Prof. Engr. Dr. Noor M. Khan

Acme Center for Research in Wireless Communications (ARWiC),

Department of Electronic Engineering,

EE5713 : Advanced Digital Communications

1

Department of Electronic Engineering,

Muhammad Ali Jinnah University,

Islamabad Campus, Islamabad, PAKISTAN

Ph: +92 (51) 111-878787 Ext. (Office 116, ARWiC Lab 186)

Email: [email protected], [email protected]

Advanced Digital Communications, Spring-2015, Week-1- 6

EE 5713: Advanced Digital Communications

Instructor: Prof. Dr. Noor Muhammad Khan

Text books

Bernard Sklar, Digital Communications: Fundamentals and Applications, 2001.

J. G. Proakis, Digital Communications, 2001

09-Mar-15 Advanced Digital Communications, Spring-2015, Week-1- 6 2

J. G. Proakis, Digital Communications, 2001

References/Additional readings: 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%

Major Quizzes: 30%

Class Participation: 05%

Assignments/Surprise Quizzes: 05%

09-Mar-15 3

Assignments/Surprise Quizzes: 05%

Final: 40%


Recent Developments Internet boom in last two decades

Cellular Communications : present boom

Optical Fiber, Satellite Communications, WiFi

Job Market

Course Learning Motivations

Advanced Digital Communications, Spring-2015, Week-1- 6 4

Job Market Probably one of the most easy and high paid job recently

Intel has already changed to wireless and Micron is following

Research Potential

Multiuser Communications

MIMO and Space-Time Processing etc.

Digital Communications - Fundamentals

Week 1-2

This Lecture would be covered on Board and the following concepts would be delivered:

Thermal Noise / AWGN

Signal to Noise Ratio (SNR) 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

5Advanced Digital Communications, Spring-2015, Week-1- 6

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:

09-Mar-15 6

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.

09-Mar-15 7

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 utilize discrete symbols allowing regeneration instead of amplification offered in Analog schemes

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

Digital vs Analog

Advantages of digital communications:

Regenerator receiver

Originalpulse

Regeneratedpulse

2006-01-24 9

Different kinds of digital signal are treated identically.

DataVoice

Media

Propagation distance

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


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

)()( tmtm


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

)( bbpPb =

Digital communication blocks


Processes Involved



Week 3:

Principles of Digital Communications-Overview

PCM

Line Coding Schemes


Line Coding Schemes

Pulse Code Modulation

09-Mar-15 Muhammad Ali Jinnah University, Islamabad Digital Communications EE3723 18

Figure The basic elements of a PCM system.

Encoding


Advantages of PCM

1. Robustness to noise and interference

2. Efficient regeneration

3. Efficient SNR and bandwidth trade-off

4. Uniform format

Virtues, Limitations and Modifications of PCM


4. Uniform format

5. Ease add and drop

6. Secure

Line coding and decoding


Signal element versus data element


Synchronization

Receivers clock Setting must match the senders one

Effect of lack of synchronization


Considerations for PCM Waveforms

DC components

Transmission bandwidth

Power efficiency

Error detection and correction capability


Error detection and correction capability

Favorable power spectral density

Adequate timing content Self Synchronization

Noise and Interference Immunity

Cost and Complexity

Polar NRZ-L and NRZ-I schemes

In NRZ-L, the level of the voltage determines the value of the bit: RS232

In NRZ-I (-M or S), the inversion or the lack of inversion determines the value of the bit. USB, CD, and Fast-Ethernet

NRZ-L and NRZ-I both have an average signal rate of N/2 Bd.


NRZ-L and NRZ-I both have a DC component problem.

Example A system is using NRZ-I to transfer 1-Mbps data. What

are the average signal rate and minimum bandwidth?

Solution

The average signaling rate is S = N/2 = 500 kbaud. The minimum bandwidth for this average baud rate is Bmin = S


minimum bandwidth for this average baud rate is Bmin = S = 500 kHz.

RZ scheme

Return to zero

Self clocking


Polar biphase: Manchester and differential Manchester schemes

In Manchester and differential Manchester encoding, the transition at the middle of the bit is used for synchronization.

The minimum bandwidth of Manchester and differential Manchester is 2 times that of NRZ. 802.3 token bus and 802.4 Ethernet


Bipolar schemes: AMI and pseudoternary

In bipolar encoding, we use three levels: positive, zero, and negative.

Pseudoternary:

1 represented by absence of line signal

0 represented by alternating positive and negative


0 represented by alternating positive and negative

DS1, E1

PSD of various line codes


Coded Mark Inversion (CMI)

Another modification from AMI: Binary 0 is represented by a half period of negative voltage followed by a half period of positive voltage

Advantages:

good clock recovery and no d.c. offset

simple circuitry for encoder and decoder compared with HDB3

Disadvantages: high bandwidth


Multilevel: 2B1Q scheme

Integrated Services Digital Network ISDN


r = 2

Multitransition: MLT-3 scheme


Summary of line coding schemes

/Bipolar


/Bipolar

Delta Modulation (DM)



Week 4-6:

Principles of Digital Communications-Overview

Detection

Matched Filter and Correlator Filter


Matched Filter and Correlator Filter

Error Probability

Signal Space

Orthogonal Signal Space

Analysis and Synthesis Equations

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


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

Hence

where z is the minimum error criterion and is optimum

1

1 20

2

( )

2

H

a az

H

> +

Probability of Error Error will occur if

s1 is sent s2 is received

s2 is sent s1 is received

0

2 1 1

1 1

( | ) ( | )

( | ) ( | )

P H s P e s

P e s p z s dz

=

=

1 2 2( | ) ( | )P H s P e s=


The total probability of error is the sum of the errors0

1 2 2

2 2

( | ) ( | )

( | ) ( | )

P H s P e s

P e s p z s dz

=

=

2

1 1 2 21

2 1 1 1 2 2

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

( | ) ( ) ( | ) ( )

B ii

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

[ ]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 21 ( | ) ( | ) ( | )2by Symmetry

BP P H s P H s P H s= +


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

0 0

0

1 2 2

2

2

00

( | ) ( | )

1 1exp

22

BP P H s dz p z s d z

z adz

= =

=

0

1 2

2

2

00

2

0

2

( )

1 1exp

22

( )

1exp

22

B

a a

z aP dz

z au

udu

=

=

=


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

Hence,

0222

1 2

0

.182B

a aP Q equation B

=

21( ) exp

22

zQ z

z

Error probability for binary signals Recall:

Where we have replaced a2 by a0.

To minimize PB, we need to maximize:

18.2 0

01 Bequationaa

QPB

=


or

We have

Therefore,

02

201 )(

aa

0

01

aa

21 0

20 0 0

( ) 2

/ 2d da a E E

N N = =

21 0 1 0

20 0 0 0

( ) 21 1

2 2 2 2d da a a a E E

N N = = =

[ ]

[ ] [ ] [ ]

+=

=

TTT

T

d

tstsdttsdtts

dttstsE

22

2

0 01

)()(2)()(

)()(

)63.3(2 0

=

N

EQP dB

The probability of bit error is given by:


[ ] [ ] [ ] += tstsdttsdtts 0 010 00 1 )()(2)()(

The probability of bit error for antipodal signals:

The probability of bit error for orthogonal signals:

=

0

2

N

EQP bB

= E


The probability of bit error for unipolar signals:

=

02N

EQP bB

=

0N

EQP bB

Error probability for binary signals


Table for computing of Q-Functions

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:

E ST NS W

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


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 / 2b b

b

E ST NS Wwhere

N N W N R

= = =

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

Problem:

Consider a Binary Communication System that receives equally likely signals and plus AWGN (see the following figure).

Assume that the receiving filter is a Matched Filter (MF), and that the noise Power Spectral Density is equal to Watt/Hz. Use the

)(1 ts )(2 ts

N

Evaluating Error Performance


the noise Power Spectral Density is equal to Watt/Hz. Use the values of received signal voltage and time shown on figure to compute the Bit Error Probability.

0N

s)(millivolt)(2 ts

0 1 2 3

1

2

s)(ts)(millivolt)(1 ts

0 1 2 3

2

1

s)(t

Problem:

Consider that NRZ binary pulses are transmitted along a communication cable that attenuates the signal power by 3 dB (from transmitter to receiver). The pulses are coherently detected at the receiver, and the data rate is 56 kbits/s. Assume Gaussian noise with N0 =10-6 Watts/Hertz. What is the minimum amount of Power

Error Performance based Designing


with N0 =10 Watts/Hertz. What is the minimum amount of Power needed at the transmitter in order to maintain a bit-error probability of Pe = 10-3?

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


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 orthogonalitycondition.

{ }Njj

t1

)(=

tttK

ttK j

T

ijiji d)()(1

)(),(1 * =>

Example of an orthonormal basis

Example: 2-dimensional orthonormal signal space

0)()()(),(

0)/2sin(2

)(

0)/2cos(2

)(

2

1

=>=

Signal space

=

=N

jjiji tats

1

)()(

ia1

)(1 t

1iaT

)(1 t

ia11ia

Waveform to vector conversion Vector to waveform conversion

dtttsaT

jiij )()(0

*=


),...,,( 21 iNiim aaa=s

iN

i

a

a

M

1

)(tN

iNa

)(tsi0

T

0

)(tN

iN

i

a

a

M

1

ms=)(tsi

iNa

ms

Basis Functions: An example

A set of 8 orthogonal of basis functions


What signals can we form with this set of basis functions?

Basis Functions: An example

11[n] + 02[n] + 1/33[n] + 04[n] + 1/55[n] + 06[n] + 1/77[n] + 08[n] =

1 [n] + 0 [n] + 1/9 [n] + 0 [n] +

Linear combination of basis functions Waveforms in the span of basis functions


11[n] + 02[n] + 1/93[n] + 04[n] + 1/255[n] + 06[n] + 1/497[n] + 08[n] =

11[n] + 1/22[n] + 1/33[n] + 1/44[n] + 1/55[n] + 1/66[n] + 1/77[n] + 1/88[n] =

Representation of a signal in signal space


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

.)()(1

+

= dttztgEE

czg

n


Autocorrelation

.)()()( +

+= dttztggz

.)()()( +

+= dttgtgg

Analysis Equation = Detection


Correlation Detector


Correlation Detector: Examples


Correlation Detector Example: QPSK


MF Detector Example: QPSK


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