EE 372 – Communication Theory and Systems I

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ةبيط ةعماج

EE 372 – Communication Theory and Systems I

(Lecture 2 )

Omar Siddiqui

Department of Electrical Engineering College of Engineering

Taibah University

Madinah

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 Fundamental Limits of a Communication System

 Noise Limitation

 Bandwidth Limitation

 Shannon’s Theorem and exchange between the SNR and Bandwidth

 Modulation

 Analog and Digital Communication Systems

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 They can be solved in theory but cannot be solved practically with the available resources

 Examples are hardware availability, government regulations etc

Fundamental Limitations of a Communication System

Two Types of Limitations are faced by a Communication Engineers Technological Limitations

 They cannot be solved theoretically

 Their sources are natural

 The two fundamental limits on a communication system are Bandwidth and Noise

Fundamental Limitations

Bandwidth Limitation Noise Limitation

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 Bandwidth corresponds to the highest signal content

When a signal changes rapidly with time, its frequency content or spectrum extends over a wide range and we say that the bandwidth of the signal is large

What is bandwidth of a signal?

Higher Frequency signal Lower Frequency signal

m(t)

M(f)

t m(t)

M(f) B

B FT

FT

Fundamental Limitations of a Communication System: Bandwidth

BW

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Fundamental Limitations of a Communication System: Bandwidth

Why Systems have a finite Bandwidth?

Electric systems contain energy-storage elements (such as inductors and capacitors) that cannot be changed

instantaneously (transit time). Hence each communication system has a finite bandwidth (B)

Slow charging Smaller Bandwidth

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• Because of the Finite bandwidth, different frequency components in a signal are attenuated differently

• They also suffer a different phase shift while passing through the communication system

• Both of these cause the signal to distort

Effect of Finite Bandwidth

channel

TX RX

Amplitude reduced

Rounded corners

Fundamental Limitations of a Communication System: Bandwidth

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• Kinetic Theory: at temperatures above absolute zero, the thermal energy

causes the microscopic particles to exhibit random motion

• The random motion of charged

particles generates electric current or voltages called thermal noise

• It can be reduced by reducing the temperature of the system

Fundamental Limitations of a Communication System: Noise Cause of Noise: Random motion of small particles

N = kTB

K = Boltzman's Constant = 1.38 *10-23 T = Absolute Temperature (K)

B=Noise Bandwidth

Thermal Noise N

Source of Thermal Noise

channel

TX RX

Distortion + Noise

Screen shot of an oscilloscope

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• Measuring signal power and

dividing it by the noise power gives the signal to noise ratio

• SNR is a measure of quality of transmission (better fidelity in analog systems and less errors in digital systems)

• Increasing signal power increases the SNR and reduces the effect of noise

• Increasing SNR allows

transmission over long distances

How to measure noise in a system?

Signal to Noise Ratio

Signal To Noise Ratio

• Can amplifiers be used to improve SNR at the output?

A. The answer is no because both signal and noise gets amplified and moreover, amplifier noise is added to the signal

How to Improve SNR

A

S

_i

/N

_i

AS

_i

/AN

_i

For the solution to improve the signal quality, we have to study the

Shannon’s Theorem!!

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The rate of information (C) that can be transmitted over a channel is related to channel bandwidth (B) and the signal to noise ratio (SNR) by the following relation:

C=B log₂(1+S/N) (bps)

It is an upper bound on the channel capacity given the channel bandwidth and SNR

Shannon’s Theorem

C = Maximum bit rate that can be transmitted over a channel S = Signal Power

N = Noise power

S/N = Required SNR to transmit the bit rate C B = Signal bandwidth

C S

B

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Shannon’s Theorem: Exchange Between B and SNR

Assuming SNR>>1:

S

₁

B

Example: Consider the Signal to noise ratio required to transmit a signal with

bandwidth B over a channel with capacity C is (SNR)

₁

. Find the required signal to noise ratio if the bandwidth is doubled (B

₂

= 2B

₁

). Assume SNR>>1

The rate of information (C) that can be transmitted over a channel is related to channel bandwidth (B) and the signal to noise ratio (SNR) by the following relation:

C=B log₂(1+S/N) (bps)

C C  B

₁

log

₂

( 1  SNR

₁

) ) 1

(

log

₂ ₂

2

SNR

B

C  

) (

log

₂ ₁

1

SNR

B

C  C  B

₂

log

₂

( SNR

₂

)

Dividing log ( )

1  B

¹ ²

SNR

¹

log ( ) log ( )

^B²¹

B

SNR SNR 



C

1 1

1

SNR

N S 

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Shannon’s Theorem: Exchange Between B and SNR

S

B

Example: Consider the Signal to noise ratio required to transmit a signal with

bandwidth B over a channel with capacity C is (SNR)

₁

. Find the required signal to noise ratio if the bandwidth is doubled (B

₂

= 2B

₁

). Assume SNR>>1

The rate of information (C) that can be transmitted over a channel is related to channel bandwidth (B) and the signal to noise ratio (SNR) by the following relation:

C=B log₂(1+S/N) (bps)

C 2B

2 1 2 1

1

2 ¹

1

SNR

^B

B



1



2

2B

B 

1

2

SNR

SNR 



1 2

2

SNR

N S 

SNR

1

S

₂

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 By using modulation schemes that produce wide bandwidth modulated signals such as frequency and phase modulation schemes

 By using digital signals

Some Ways to increase Bandwidth

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Modulation is a process of modifying the baseband signal (the message signal) so that it becomes suitable for the channel

 Modulating Signal: The message or the baseband signal

 Carrier: The high frequency signal which carries the modulating signal

 Modulated Signal: The baseband signal changes one of the parameters of the carrier and the resulting high frequency signal is called a modulated signal

Modulation

Example of a Carrier Baseband Signal

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Demodulation

 Reverse of Modulation

 The modulated signal has to pass through the demodulation process so reconstruct the baseband signal

Example of a Carrier Baseband Signal

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The amplitude of the carrier wave is modified by the baseband signal.

The information is in the amplitude of the carrier

Types of Modulation

Amplitude Modulation (AM)

Carrier

Modulating or baseband

AM

FM Frequency of the carrier wave is

modified by the baseband signal. The information is in the frequency of the carrier

Frequency Modulation (FM)

Phase of the carrier wave is modified by the baseband signal. FM and PM effectively produce the same results.

Collectively they are referred to as

Phase Modulation (PM)

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Advantages of Digital Signals

1. Noise Immunity

Digital Systems perform better in noisy environment.

 Recovering exact pulse shape is not important

 The receiver can detect the

amplitude of the signal and make a decision based on thresholds

Transmitted digital signal

Received signal without noise

Received signal with noise

Regenerated signal

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Advantages of Digital Signals

2. Regeneration at repeaters

The digital signal can be amplified and regenerated from the distorted signal

 If analog signals are amplified, more noise is added and therefore cannot be regenerated

 Long haul communications are possible

channel

TX RX

Distortion + Noise

A Decision

Repeater

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Advantages of Digital Signals

3. Hardware Implementation is flexible because availability of digital microprocessors, switching, and integrated circuits

4. Digital coding provides lower error rates 5. Multiplexing is possible

6. Exchange between SNR and bandwidth 7. Cheap storage devices

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