ECE 4371, Fall, 2015

Introduction to Telecommunication Engineering/Telecommunication Laboratory

Zhu Han

Department of Electrical and Computer Engineering

Class 6

Sep. 10th, 2015

                                                           

                                                           

OverviewOverview

Cochannel interference

Analysis of Noise– Math model (good thing, not required)

– Noise shape, preemphasis/deemphasis

– FM threshold effects

Security basics

Good news: This is the last class for exam 1

                                                           

Co-channel InterferenceCo-channel Interference Source: Acoswct, Interference: Icos(wc+w)t

r(t)= Acoswct+Icos(wc+w)t=E(t)cos(wct+)

=tan^-1(Isinwt/(A+Isinwt))~=(I/A)sinwt

PM: y=(I/A)sinwt, FM =(Iw/A)coswt

When A is large, suppress weak interference better than AM.

Capture effect– Winner takes all

– 35dB for AM

– 6 dB for FM/PM

White Gaussian noise– Noise increases linearly with frequency in FM.

                                                           

System Model and Noise ModelSystem Model and Noise ModelDiscriminator consists of a slope network and an envelope detector.

                                                           

Signal after bandpass filterSignal after bandpass filter The incoming FM signal s(t) is

defined by

At the bandpass filter output

                                                           

Discriminator OutputDiscriminator Output Note that the envelope of x(t) is of no interest to us (limiter)

(2.141) )()( sin)( 2

1)(

where

tttrdt

d

Atn

c

d

)138.2( )()(sin)(

)()(

)( Because

ttA

trtt

trA

c

c

(2.139) )()(sin)(

)(20

ttA

trdm k

c

t

f

noise additivemessage

(2.140) )()(

)(

2

1)(

2.40) (Fig isoutput tor discrimina The

tntmkdt

tdtv

df

                                                           

Noise After DiscriminatorNoise After Discriminator

(2.142) )(sin)(2

1)( ttr

dt

d

Atn

cd

(2.143) )(sin)()(

have we, )( and )( of definition From

ttrtn

ttr

Q

(2.144) )(

2

1)(

dt

tdn

Atn Q

cd

as )(simplify may We

signal. message oft independen is )(then

),2 (0,over ddistributeuniformly is )()( Assume

tn

tn

tt

d

d

The quadrature appears

                                                           

Noise After Discriminator cont.Noise After Discriminator cont. The average output signal power = kf

2P

Recall fjdt

d TF

2.

nQ(t) nd(t)

dt

d

Ac21

)( fSQN )( fS

dN

(2.145) )()(2

2

fSA

ffS

Qd Nc

N

                                                           

Noise After Discriminator cont.Noise After Discriminator cont. Assume that nQ(t) has ideal low-pass characteristic with

bandwidth BT(2.146)

2 , )(

2

20 T

cN

Bf

A

fNfS

d

(2.147) , )(

output receiver At the

2 If

2

20

0Wf

A

fNfS

WB

cN

T

                                                           

SNR of FMSNR of FM

effect quieting noise 1

(2.148) 3

2

)( ofpower Average

2

2

30

22

0

0

c

c

W

Wc

A

A

WN

dffA

Ntn

(2.149) 2

3)SNR(

30

22

FM, WN

PkA fcO

(2.150) 2

)SNR(

isbandwidth messagein power seaveragenoi the

,2

is )( ofpower average The

0

2

FM,

0

2

WN

A

WN

Ats

cC

c

(2.151) 3

)SNR(

)SNR(2

2

FMW

Pk f

C

O

71

                                                           

Single Tone FM SNRSingle Tone FM SNR

)2sin(2cos)( t f

f

ft fAts m

mcc

2.4) Example (from 3

1

)SNR(

)NR( , AM tocompare

C

O

AM

S

)2cos()( sideboth

)2sin()(2 , may write We0

t fk

ftm

dt

d

t ff

fdm k

mf

mm

t

f

2

2

2

)( is load) 1 (across )( ofpower average The

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A

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fA ccO

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30

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FM,4

3

4

)(3)SNR( (2.149), From

(2.152) 2

3)(

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)SNR(

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FM

W

f

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O

FM. widebandand FM narrowbandbetween n transitio theas 5.0 Define

471.03

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e.performancbetter has FM , 3

1

2

3When 2

                                                           

FM Preemphsis and DeemphasisFM Preemphsis and Deemphasis

                                                           

FM Preemphsis and DeemphasisFM Preemphsis and Deemphasis

                                                           

FM Threshold EffectFM Threshold Effect

2

)( toequal isoutput tor discrimina The

2 decreasesor increases (t)

,origin thearound sweepmay ly,Occasional

)(

)(tan)(

(2.153) )2sin()()2cos()()(

input tor discriminafrequency at the signal composite The

d.unmodulate iscarrier i.e., signal, no is When there

'

1

1

t

P

tnA

tnt

t ftnt ftnAtx

Ic

Q

cQcIc

nQ(t)r(t)

x(t)

Ac(t)

P1

0 P2

nI(t)

                                                           

ExampleExample Illustrating impulse ike components in (t) d(t)/dt

produced by changes of 2 in (t); (a) and (b) are graphs of (t) and (t), respectively.

                                                           

Threshold EffectThreshold Effect Dependence of output signal-

to-noise ratio on input carrier-to-noise ratio for FM receiver. In curve I, the average output noise power is calculated assuming an unmodulated carrier. In curve II, the average output noise power is calculated assuming a sinusoidally modulated carrier. Both curves I and II are calculated from theory.

                                                           

Comparison of modulation systemsComparison of modulation systems

                                                           

Comparison of the noise Comparison of the noise performance of various performance of various CW modulation systems. CW modulation systems. Curve I: Full AM, Curve I: Full AM, = 1. = 1. Curve II: DSB-SC, SSB. Curve II: DSB-SC, SSB. Curve III: FM, Curve III: FM, = 2. = 2. Curve IV: FM, Curve IV: FM, = 5. = 5. (Curves III and IV include (Curves III and IV include 13-dB pre-emphasis, de-13-dB pre-emphasis, de-emphasis improvement..)emphasis improvement..)

                                                           

EncryptionEncryption Encryption is a translation of data into a secret code. Encryption is the

most effective way to achieve data security. To read an encrypted file, you must have access to a secret key that enables you to decrypt it. Unencrypted data is called plain text; encrypted data is referred to as cipher (text).

Encryption can be used to ensure secrecy, but other techniques are still needed to make communications secure: authentication, authorization, and message integrity.– Message integrity - both parties will always wish to be confident that

a message has not been altered during transmission. The encryption makes it difficult for a third party to read a message, but that third party may still be able to alter it in a useful way.

– Authentication is a way to ensure users are who they say they are - that the user who attempts to perform functions in a system is in fact the user who is authorized to do so.

– Authorization protects computer resources (data, files, programs, devices) by allowing those resources to be used by resource consumers having been granted authority to use them.

– Digital rights management etc.

                                                           

Encryption – cipher taxonomyEncryption – cipher taxonomy

CIPHERS

MODERNCIPHERS

CLASSICALCIPHERS

PUBLIC KEY

PRIVATE KEY

SUPERPOSITION

TRANSPOSITION

ROTORMACHINES

QuantumCIPHERS

                                                           

Transposition MethodTransposition Method

Da Vinci’s code

Ex.

I am a student

I m s u e t

a a t d n

                                                           

Substitution MethodSubstitution Method

Shift Cipher (Caesar’s Cipher)

I CAME I SAW I CONQUERED

H BZLD H TZV H BNMPTDSDC

Julius Caesar to communicate with his army

Language, wind talker

                                                           

Rotor MachineRotor Machine The primary component is a set of rotors, also termed wheels or drums,

which are rotating disks with an array of electrical contacts on either side. The wiring between the contacts implements a fixed substitution of letters, scrambling them in some complex fashion. On its own, this would offer little security; however, after encrypting each letter, the rotors advance positions, changing the substitution. By this means, a rotor machine produces a complex polyalphabetic substitution cipher.

German Enigma machine used

during World War II for submarine.

Movie U571, Italian Job

                                                           

KeyKey

                                                           

Public Key System - RSAPublic Key System - RSA

Named after its inventors Ron Rivest, Adi Shamir and Len Adleman

Base on Number Theory

y=ex (mod N) => x=??

If the size of N is 100, it takes 100 billion years to decipher with 1GHz computer.

Applications– Digital Signatures

– Digital Cash: Movie, swordfish

– Timestamping Services: Movie, entrapment

– Election

Movie, mercury rising

                                                           

Encryption – cipher taxonomyEncryption – cipher taxonomy

Historical pen and paper ciphers used in the past are sometimes known as classical ciphers. They include substitution ciphers and transposition ciphers.

During the early 20th century, more sophisticated machines for encryption were used, rotor machines, which were more complex than previous schemes.

Encryption methods can be divided into symmetric key algorithms and asymmetric key algorithms. In a symmetric key algorithm (DES, AES), the sender and receiver must have a shared key set up in advance and kept secret from all other parties; the sender uses this key for encryption, and the receiver uses the same key for decryption.

In an asymmetric key algorithm (RSA), there are two separate keys: a public key is published and enables any sender to perform encryption, while a private key is kept secret by the receiver and enables him to perform decryption.

                                                           

Quantum CryptographyQuantum Cryptography

Use physics law, if the signal is measured (eavesdropped), the receiver can always detected.

                                                           

Mission is really impossibleMission is really impossible

When you see it, the information has been already changed