Introduction to Spread Spectrum

(1)

Introduction to

Spread Spectrum

(2)

Contents

• Introduction

• DS/SS

• Frequency hopping

(3)

K.B.Lee 확산대역 시스템 및 코드분할 다중접속 3

• Initial application: military

• Benefits

- Anti-jamming

- Robust to multipath fading

- Multiple User Access (CDMA) - High resolution ranging (DS)

Introduction

(4)

DS/SS

) (f S_d

) (f S_c

) (f S_r

)

'(f

S_d

1 / Ts

1 / Tc

DATA Source

c(t) cos_ct cos_ct c(t)

d(t) r(t) r'(t) d'(t)

0 T_s

z

d(t)

c(t)

r(t)

=r'(t)

d'(t)

T_s

(5)

Anti-Jamming effect

• Interfering Signal: tone

S

_J

( ) f

S

_J_

( ) f

f

1 / Ts ^{1 / Tc}

f

• Tone Jamming signal is spread out by despreading operation.

• Small part of a jamming signal goes through the rx filter.

• Jamming effect reduction factor : Ts Tc

(6)

Frequency hopping

• The carrier frequency is pseudo randomly hopped over various frequencies.

DATA Mod

d(t)

Filter BPF BPF Data

demod

....

Freq. Synthesizer

Code Generator

....

Freq. Synthesizer

Code Generator

Slow hopping : T symbol < T hopping Fast hopping : T symbol > T hopping

* Noncoherent scheme is common.

(7)

Performance of SS

(Jamming)

(8)

Contents

• Performance in partial band jamming in DS/CDMA systems

• Pulse noise jammer in DS/CDMA systems

• Partial band jammer in FH systems

• Reference : “ Introduction to spread spectrum

communications. ” by peterson …

(9)

Performance in partial band jamming

S f_s( )

W

f

W 0 S_s f

I( )

f

f S_n f

j( )

W

f S_n f

j I( )

W

N

_J

2

 1



N J

W

J

2  2

Total Jamming Power = J

PBJ PSD=

      t s t n t n   t s   t BW W PBJ BW W

r   

_j

;

의

 ,

의

 

 1 2^J

N ^J

N

(10)

n

_J

t

I

( ) w

J

( ) t p t ( )

W t n t p t

R R R

S f S f S f

T c T S f d

T c T d

N T c T d

J J

W N p

W n p

c c N

f W c

f W

c N

J

c c

f W

I

J JI

J J I

JI

J

( ) ( ) ( )

sin ( ) ( )

sin ( )

 

  

 

 















z z

z

  

 

  



 2

2

2 2

2

(11)

J

c c

W

c

c c

c J c

J W

c c

J W

c

c W

W c J W

W N J T

JT J S

T If W

JT W

J T

T N W

N T S

T T c

W

N T S

If W

d T c

T N S

J J

2 )

0 (

1 , 2

W

W )

0 (

1 ) (

1 sin

, small

9 . 0 ) 0 ( 1 ,

2

) (

sin )

0 (

1

2 1

2 2

2



















 







Case 1 : 

Case 2 :

(12)

Pulse noise jammer

• Jamming power J is fixed

J

t

t J



T

T

(13)

equation BER

:

) 1

/ (

0

0 0

 

 





 

 



 

 



 







N f E

N f E N

N f E

b

b J

b



 

• Prob. of Error =

• Assume f E

N

P f E

N f P

R J f P

J R

b

e

b J 0

F 0

HG I

KJ 

 F

HG I

KJ  F 

HG I

KJ

 F 

HG I

KJ

,

   

 

W

/ /

J b

N  J W E  P R

(14)

P Q E N

P Q E

N Q P

R J

e

b

e

b J

 F

HG I

KJ

 F

HG I

KJ  F 

HG I

KJ

2

2 2

0

    W

In pulse noise jamming

Case 1:  

 F

HG I

KJ

1

P Q 2 E

e

N

b J

Case 2: 

 2

2 E N P

b J

e

is small



P_e

E /N

P_e

10 log PW

 2

• For BPSK,

(15)

• example

0.00032

2 1 1 1562.5 10 log (1562.5) 32

2

PW PW

RJ RJ dB



 



     

P

_e

10 log 10 log ^s

J

E PW

RJ N

 

    

 

   



2  0 00016.

32dB

2 (0.00032) (0.1587)

e

P Q P W

   R J 

         

• Optimal

• Pulse noise jammer in DS-CDMA systems and systems without spreading



(16)

Partial band jammer in FH system

 W W S

_N

f

J

( )

f

P f E

N N f E

N f E

e

N

b J

b b

J





F H GG G

I K JJ

J   F

HG I

KJ  F

HG I

 KJ



  

0 0

1

( )

•