Communication Systemspkalra/OLD-COURSES/siv864-2010/session-08-11.pdf · Tx Rx. IIT Delhi Nov 6,...

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Communication Systems

Monika AggarwalCARE, IIT Delhi

IIT Delhi

2CARE-IITDNov 6, 2008

Communication

� Conveying information.

� Transmission of information,

� Using symbols, signs, behavior, speech, writing, or signals

� Communication is the process of transmitting information from a sender to a

receiver with the use of a medium.

� For us, communication is a process in which the

� Source produces the information

� Transmitter, transmits information

� It is transmitted through a medium

� Receiver receives the transmitted signal

� Received signal reproduces information (may be with some errors).

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Basic Communication

� Communication to transfer information from one point to another.

� Therefore basic constituents of communication system are

� Source

� Medium

� Receiver

Sea Surface

Sea bottom

Tx

Rx

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Basic Blocks of Communication System

Source Transmitter Medium Receiver

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Source

� Source of Signal

� Something we want to transmit!!,

� Data, audio, speech, image, video…

� may be something else also…your feelings!!

� Can be 1-D, 2-D or of any dimension signal.

� Can be of any language.

� Source can be analog or digital.

� Analog signals can also be converted into digital signals before transmitting.

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Source : Information

� What we want to transmit!!,

� something meaningful.

� Meaningful information

� Something new

� Something we do not know

� Redundant information has no value,

� Can be avoided!!

� Information is the measure of meaningful data to be transmitted.

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Information

� Information is acquired through study or experience.

� Measure of the uncertainty of an outcome,

�If you have done bad in exam, than your result has more information.

� Mathematically we define the information as,

�Low probability data has high information

� Information is the measure uncertainty of one unit of signal

)(log)(

1log)( xp

xpxI −==

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Example

� Suppose we have a binary discrete source emits ‘0’ and ‘1’,

� Both ‘0’ and ‘1’ occur with equal probability,

� p(0)=0.5

� p(1)=0.5

� It emits each bit after ts second.

� Information content in the source is

I(x=0) = -log(0.5) = 1

I(x=1) = -log(0.5) = 1

Source is emitting 1 bit of information per ts second.

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Example


� Both ‘0’ and ‘1’ occur with different probability,

� p(0)=q

� p(1)=1-q


� Information content in the source is

I(x=0) = -log(q) ; I(x=1) = -log(1-q)

� Now how do we calculate the number of bits source is emitting in ts second.

� Take the average of both the outputs

= -q log(q) - (1-q) log(1-q)

� This is entropy of the source

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Entropy

� We transmit sequence of units, and each unit may have different information.

� Entropy : Average of information,

� Measure of average amount of information emitted by a source.

� Provide average number of bits required to represent the signal.

∑∑ −== )(log)()()()( xpxpxIxpxH

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Example


� Both ‘0’ and ‘1’ occur with different probability,

� p(0)=q

� p(1)=1-q


� Entropy the source is

H(x)= -q log(q) - (1-q) log(1-q)

� It is the number of bits source is emitting in ts second

� Source is having information of worth these number of bits

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Entropy and Source Coding

� Entropy gives the minimum number of average bits required to represent the

source.

� Source coding is representing the source outputs by series of bits.

� Both discrete as well as analog signal is to be converted into bits.

� Average of number of bits (R) required represent source output is lower bounded

by source entropy (H(x)).

� Source coding is said to be efficient, if average of number of bits required is equal

to source entropy.

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Source Coding

� Aim of the Source Coding is to represent source signal into bits.

� Codes should be

� Uniquely decodable

� Instantaneously decodable

� Input sequence is 001001

• Code I breaks

• Code III adds delay

• Code II is okay

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Methods of source coding

� Discrete signal

� Probability of block decoding error can be made arbitrary small if

R > H(x).

� examples

• Huffman coding

• Lempel-Ziv Algorithm etc.

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Source Coding : Signal Compression

� Codes should be “uniquely decodable”, i.e. source coding is reversible

� Completely reversible : Lossless coding.

� Partial reversible : Lossy coding

� Analog Signal take can any value

� f : Real --- > Real

� While representing the analog signal into bits, we will always have some loss,

� This loss is measured in terms of distortion ‘D’.

� Distortion is function of number of bits R required to represent the signal or vice versa.

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Some Analog Source Encoding Techniques

� Temporal waveform coding

� Pulse code modulation (PCM)

� Differential Pulse Code Modulation (DPCM)

� Delta Modulation (DM)

� Spectral waveform coding

� Sub-band Coding

� Model based waveform coding

� Linear predictive coding (LPC)

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Some Results of Analog Source encoding

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SinkSource

Decoding

Error

Control/

Channel

Decoding

Demod-

ulation

Receiver

/

Filter

Channel

SourceSource

Coding

Error

Control/

Channel

Coding

Modulation

Transmitter

/

Filter

Block Diagram of Communication System

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Channel

� Medium or Channel transfer the information from source to receiver

� Channel is a system,

� Input X, what we want to transmit

� Output Y, What we receive, noise distorted version of input X.

Receiver

YChannelTransmitter

X

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Effects of Channel

� Channel effects the communication System in many ways

� It limits its Rate of tranmission

� It adds noise in the transmitted Signal

� It adds distortion in terms of multipath

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Mutual Information

� Aim here is to extract X from received Y.

� Amount of information about X present in Y is very important.

� Because receiver extract X from Y

� This quantity is measured by I(X,Y)

� The average amount of information about X that can be provided by Y

� Average Information present in X is H(X).

� Average amount of information remaining in X, cannot be transferred to Y is

H(X/Y), called conditional entropy.

� So the information of X present in Y is

I(X,Y)=H(X)-H(X/Y)

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Binary Symmetric Channel

� Suppose we have a binary discrete source emits ‘0’ and ‘1’, with probabilities,

� p(X=0) = q

� p(X=1) = 1-q

� Channel conditional probabilities are

� p(Y=0/X=0) = 1-p p(Y=1/X=0) = p

� p(Y=0/X=1) = p p(Y=1/X=1) = 1-p

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Capacity

� I(X,Y) is called mutual information.

� Mutual information is function of the information of signal as well as channel.

� For a given channel, the maximum value of mutual information is measure of the

Capacity of the Channel.

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Binary Symmetric Channel

� Suppose we have a binary discrete source emits ‘0’ and ‘1’, with probabilities,

� p(X=0) = 0.5

� p(X=1) = 0.5

� Channel conditional probabilities are

� p(Y=0/X=0) = 1-p p(Y=1/X=0) = p

� p(Y=0/X=1) = p p(Y=1/X=1) = 1-p

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Rate & Capacity

� For a given channel and given X, we have a certain value of I(X,Y),

� information being transmitted through the channel.

� I(X,Y) per second, information bits transmitted per second is known as Rate R.

� Shannon defined Capacity of channel as the maximum information it can transfer

in unity time.

� For a given Channel, there exists some X for which I(X,Y) is maximum, i.e.

� I(X,Y)=C

� For other X, I(X,Y) will be less than C.

� I(X,Y)<C

� Therefore the maximum value R can take is C.

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Shannon Theorem

� The capacity of a channel is given by

where I(X,Y) is the mutual information between the channel input X and the

output Y. If the transmission rate R is less than C, then for any ε>0 there exists a

code with block length n large enough whose error probability is less than ε. If

R>C, the error probability of any code with any block length is bounded away from

zero.

),(1

maxlim)(

YXITxp

CT ∞>−

=

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Channel Behavior

CHANNELTransmitter Receiver

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Sea Surface

Sea bottom

Tx

Rx

Channel Behavior

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� Channel distorts the signal received at receiver.

� distort /corrupt the information

� At receiver we want to remove the distortion and noise

� Because we want to estimate X from Y.

� As we are only concerned with the information that we have transferred,

� Information represents the complete source output

� We are interested in extracting information about X from Y.

� Receiver will be designed so as to extract the information

� in best possible way,

� in efficient way.

� And should extract maximum information.

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Channel Coding

� Can we do something with the transmitted bits to minimize this corruption.

� The encoder bits (transmitted signals) are modified

� to protect the information from corruption.

� The protection depends upon channel,

� but still we have certain general protection

� You wear sweater, when it is cold etc.

� Adding this protection is called Channel coding.

� We add redundant bits in some particular manner.

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Channel Codes

� Parity bit

� Hamming code

� Convolution codes

� Erasure codes

� Golay code

� BCH codes

� Hadamard code

� Reed-Muller code etc.

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SinkSource

Decoding

Error

Control/

Channel

Decoding

Demod-

ulation

Receiver

/

Filter

Channel

SourceSource

Coding

Error

Control/

Channel

Coding

Modulation

Transmitter

/

Filter


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Summary

� By Source coding we have compressed the signal as much as possible.

� By adjusting the rate we know that error free communication is possible

� By channel coding we have added the protection to the signal.

� Now we want to transmit the signal,

� It will physically be transmitted

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Modulation

� Information signal is generally a low frequency Signal,

� It is difficult to transmit low frequency signals

� we required large height antenna.

� To transmit it over a long distance, we need a carrier.

� Carrier is high frequency signal, which carries the information signal from source to the

receiver.

� Carrier is generally a high frequency sinusoid.

� Carrier frequency depends upon the channel, transducer etc.

� Carrier carriers the information from the source to the transmitter,

� Information can be carried in amplitude of carrier : amplitude modulation

� Frequency of carrier : frequency modulation

� Phase of carrier : phase modulation

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Digital Communication

� When the information transmitted is in the form of bits we have digital

communication.

� Amplitude modulation � Amplitude shift keying

� Frequency Modulation�Frquency shift keying

� Phase modulation� Phase shift keying

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Analog vs. Digital Communication

� Analog communication uses continuous-time signals that

� Can (in principle) take any real value

� When received, produce an output that also varies continuously

� Digital communication uses continuous-time signals that:

� Represent bits or bit groups using a finite, standard alphabet

� Continuous-time inputs are sampled, giving discrete-time series that are digitized and

encoded before being transmitted

� Can be “cleaned up” from some distortion and noise, but generally do

� Digital is profoundly different from analog

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Why Digital Communication

� Digital encoding uses a finite alphabet to represent bits or bit groups.

� The transmitted alphabet has to be a member of this finite set.

� Therefore when receiver receives the corrupted signal, it can be corrected to the

nearest possible member of the set.

� Distortion and noise don’t matter, as long as each digital waveform can be

recognized and distinguished from a small set of other waveforms

� Digital communication changes the paradigm from waveform replication to

waveform recognition.

� Digital techniques greatly reduce the effects of noise and distortion, and make it

possible to approach theoretical information-capacity limits

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Phase Shift Keying

� Phase of the carrier is varied with the information bits.

� Information bits are mapped to a finite set of alphabets.

� Each alphabet gives a corresponding phase shift to carrier.

� E.g. Let us assume that the information bits are mapped to set of 4 alphabets

(M=4).

� Two bits together will form one alphabet.

� Let us assume that the elements of the sets are {A,B,C,D}

• 00�A�phase change of ‘0’ degree

• 01�B�phase change of ‘90’ degree

• 10�C�phase change of ‘180’ degree

• 11�D�phase change of ‘270’ degree

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Example

� Input bits are

� input bits {1 0 1 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 }

� Alphabates {C D B D A B C B D }

� Phase changes{180 270 90 270 0 90 270 90 270}

00�A�phase change of ‘0’ degree

01�B�phase change of ‘90’ degree

10�C�phase change of ‘180’ degree

11�D�phase change of ‘270’ degree

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2- 3

- 2

- 1

0

1

2

3

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PSK modulation

)_2

2cos()()( alphabetinputM

tftatx c

ππ +=

input bits {1 0 1 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 }

Alphabates {C D B D A B C B D }

Alphabates {2 3 1 3 0 1 2 1 3 }

Phase changes{180 270 90 270 0 90 270 90 270}

Phase change Alphabates *2 π/4

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PSK Constellation

A, 00

B, 01

C, 10

D, 11

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De-Modulation

� Demodulation is the processes of removing the carrier from the transmitted signal.

� Estimate the change in the corresponding quantity of the carrier.

� Estimate the change in corresponding amplitude, frequency or phase…

� In Digital Communication, as we had finite alphabet set, the corresponding

change can be corrected to possible value

• replication to recognition.!!

� PSK modulation, estimate the change in the phase,

� Approximate it to the allowed values of phase change

� De-map phase change � alphabet� information bits.

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Receiver Chain

� Detect the incoming signal

� Differentiate from noise.

� Adjust the amplitude of receiving Signal : Automatic Gain Controller

� Most Important in AM

� Remove the Channel multi-path effect : Equalizer

� Synchronize the Clock of Receiver to transmitter

� Carrier Synchronization

• Moving platform can add Doppler and change the carrier frequency

� Timing Synchronization

� Undo the What we have done knowingly at the transmitter

� Channel Decoder

� Source Decoder

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Channel Equalization

CHANNELEQUA-

LIZER

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Performance

� Bit error Rate vs. SNR

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SinkSource

Decoding

Error

Control/

Channel

Decoding

Demod-

ulation

Receiver

/

Filter

Channel

SourceSource

Coding

Error

Control/

Channel

Coding

Modulation

Transmitter

/

Filter


Modulation

Transmitter

/

Filter

Channel

Receiver

{AGC,

Detector

Equalizer

Synchronizer}

Demod-

ulation

Error

Control/

Channel

Decoding

Source

DecodingSink

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MIMO Communication

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MIMO Systems

Multiple transmitters and multiple receivers are used simultaneously

to increase rate, range etc. of communication system.

User data streamUser data stream

.

.

1

2

MT

.

.

.

1

2

MR

.

.

.

.

.

channel

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SISO

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MIMO

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Error Rate in Fading Channel

An Observation

For the Fading channel

QPSK and other

schemes (designed for

AWGN channel) results

into degradation in

probability of error.

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Bandwidth requirement and range of a 1 Gb/s link using MIMO technology

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Classical receive diversityClassical receive diversity

H11

H21

+=

*

22 HHIdetlogt

T

nσ

PC

Capacity increases logarithmically

with number of receive antennas...

=

21

11H

H

H

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Multiple Input Multiple Output systemsMultiple Input Multiple Output systems

H11

H22

H12

H21

=

2221

1211

HH

HHH

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Interpretation

λ1

λλλλ2222

m=min(MT, MR) parallel channels,

Power allocated to each ”pipe” depends upon the eigen

values of HH†

ReceiverTransmitter

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Other Communication Techniques :OFDM

� Orthogonal frequency-division multiplexing (OFDM) is a method of digital

modulation in which a signal is split into several narrowband channels at different

frequencies.

� OFDM is combination of modulation and multiplexing

� Parallel channel transmission so that the effective data rate of each channel is low – multi-carrier modulation

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Ch.1

Ch.2 Ch.3 Ch.4 Ch.5 Ch.6 Ch.7 Ch.8 Ch.9 Ch.10

Saving of bandwidth

Ch.3 Ch.5 Ch.7 Ch.9Ch.2 Ch.4 Ch.6 Ch.8 Ch.10

Ch.1

Conventional multicarrier techniques

50% bandwidth saving

frequency

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CDMA

� Code division multiple access (CDMA), is a spread spectrum multiple access

technique

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Conclusions

� We studied the basic of Communication systems

� Overview of the advances in communication Technology.

Thank You!Thank You!Thank You!Thank You!

Communication Systemspkalra/OLD-COURSES/siv864-2010/session-08-11.pdf · Tx Rx. IIT Delhi Nov 6,...

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Transcript of Communication Systemspkalra/OLD-COURSES/siv864-2010/session-08-11.pdf · Tx Rx. IIT Delhi Nov 6,...