Dr. Moshe Ran- Spread Spectrum 1 טכניקות בתקשורת מרחיבת סרט (Spread Spectrum) Chapter 2b ד"ר משה רן מצגת זו תכלול כנראה דיון של

Dr. Moshe Ran- Spread Spectrum1

טכניקות בתקשורת מרחיבת סרט

(Spread Spectrum) Chapter 2b

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Dr. Moshe Ran / Spread Spectrum2

נושאי לימוד

הרחבת ספקטרום – Spread Spectrumמבוא הסטורי לטכניקות לשם מה? חזרה- מושגי יסוד ועקרונות של מערכות תקשורת ספרתיות; רעשים והפרעות במערכות תקשורת, דרישות מערכתיות על התקשורת,

השוואת שיטות אפנון ספרתיות, יעילות ספקטרלית.

1פרק

: קונספט ( -Spread Spectrum)מבוא למערכות מרחיבות סרט מרחיבות סרט; שיטות הרחבת סרט המבוססות על ומודלים למערכות

(FH)( דילוגים בתדר ( THדילוגים בזמן ((DSהרחבה ישירה

2פרק

3פרק LFSR, Gold Sequence, Walsh - סדרות קוד למערכות מרחיבות סרט

; ביצועים של מערכות עם (DS) ביצועים של מערכות עם הרחבת סרט ישירה Spread ; שיטות גילוי, עקיבה וסנכרון של אותות (FH)דילוגי תדר

Spectrum

4פרק

עם קודים Spread Spectrum קודים לתיקון שגיאות, ביצועים של מערכות Viterbi לתיקון שגיאות, אלגוריתם

5פרק

6פרק בתקשורת תאית CDMAעקרונות

7פרק Spread Spectrumשימושים ואפליקציות של מערכות

שו"ת 8

שו"ת8

שו"ת8

שו"ת8

שו"ת8

שו"ת8

שו"ת4


Chapter 2b – Frequency- Hop Spread Spectrum


1. Basics of Frequency Hopping

Method to change the carrier frequency periodically

0 1 2 2, kf f f f

Typically, modulation code is k-bits that select 1-out-2k

frequencies )or frequency bands( which are spaced approximately

1/ hf T

Rx removes the FH by mixing )down-converting( with LO signal which is hopping synchronously with the received signal.

Usually coherent FH is not implemented – since carrier phase estimation is required per each hop.


1.1 Classification of Frequency Hopping Systems

Academic Classification

Slow Frequency Hopping

In every hop there are more than one symbol

Fast Frequency Hopping

In every hop there is one symbol or less

Industrial Classification

Slow Frequency Hopping: Less then 50hps

Medium Frequency Hopping: 50hps to 500hps

Fast Frequency Hopping: More then 500hps

h ST T

h ST T

1/h hR T


2.1 Coherent slow FH Spread Spectrum

Tx implementation for Coherent slow FH Spread Spectrum

( )d t

Code

GENERATOR

Data

Modulator

( )ds t

Frequency

synthesizer

nf

Bandpass

filter( )Th t

1 2 3 k

FH code clock

( )ts t

02 cos(2 )P f t

NRZ data

Data modulated carrier


Coherent slow FH Spread Spectrum Receiver

nd

Code

GENERATOR

Image reject

filter

( )ds t

Frequency

synthesizer

nf

Bandpass

filter( )Rh t

1 2 3 k

FH code clock

Data demod

( )y t


Analysis of Coherent slow FH Spread Spectrum

Output of freq. synthesizer at Tx is the “hop carrier” hT(t): bandpass signal with random sequence of tones fn, of duration Th

( ) 2 ( )cos(2 )T h n nn

h t p t nT f t

1 0,

0 otherwiseh

hT

t Tp t

, 1, 2, , 2kn m m

Coherent assumption: the same phase is used each time m

( )Th t returns to the same frequency mf

)1(


PSD of transmitted slow FH

Analysis of Coherent slow FH Spread Spectrum – cont.

( ) ( ) ( )t d hS f S f S f

is the convolution of the two signals

The transmitted signal is the data-modulated carrier up-converted to a new frequency f0+fn for each FH hop

( ) ( ) ( )t d Ts t s t h t

22

21

2 2 22

' '1 1 ' 1

''

1( ) ( )

1 2(1 ) ( ) ( ) ( )

k

k k k

h m mn m h hh

m m m m m m mm m mh h

m mm m

n nS f p G f

T TT

p p G f p p e G f G fT T

)2(

)3(

)4(


Notations:


2 ( )cos( ) 00 elsewhere

= Pr

( ) exp [ ( ) ] [( ) ]

exp [ ( ) ] [( ) ]

( )

m m

m h m h m m h

h m h m m h

m m hp t t t Tm

p f f

G f T j f f T Sinc f f T

T j f f T Sinc f f T

g t

PSD Sh(f) can be simplified by assuming

m'

'

( ) and G ( ) are nonoverlapping for m m'

( ) ( ) 0

m

m m

G f f

G f G f

This assumption is valid whenever 1/Th is small compared to the minimum frequency spacing i.e. Slow FH

)5(

)6(

)7(


Simplified PSD – further assume


22

21

22

1

1( )

( 2 )

1 1 11 ( )

2 2

k

k

h mkn mh h h

mk kmh

n nS f G f

T T T

G fT

1,

2m kp m

Note: PSD has discrete components, due to the “coherent FH assumption”. The same phase is used each time hT(t) returns to frequency fm . If

2 1khT

Then - the discrete components are negligible.

)8(


Example:

Calculate the PSD of a transmitted coherent slow FH signal with the following parameters.Modulation: BPSK, Rb=1Mbps, Rh=100Khops/sec, 4 frequencies are employed, minimum spacing equals data rate.

Solution:

Since minimum spacing >> hop rate

we can use simplified PSD formula.510 , 2 4, ( ) given by (7)kh mT G f

22 2

21

22 2

1

1( ) { [( )] [( )]} ( )

2

11 [( ) ] [( ) ]}

2 2

k

k

h m h m hkn m h

hm h m hk k

m

nS f Sinc n f T Sinc n f T f

T

TSinc f f T Sinc f f T


Receiver for slow FH

The received signal

0 0

( )

2 ( ) cos[( ) ( ) ( ) ]

t d

d h n n d d n dn

s t T

P p t T nT t t T T

This signal is down converted using hR)t(

ˆ ˆ( ) 2 ( )cos(2 )R d h n n n dn

h t p t T nT f t T

)9(

)10(

Assuming d̂ dT T No tracking errors

( ) ( ) ( )t d R bpfy t s t T h t


Receiver for slow FH

0

0 0

( ) ( ) ( )

2 ( )cos[ ( ) ( )]

2 cos[ ( )]

t d R bpf

d h d d dn

d d d

y t s t T h t

P p t T nT t T t T

P t T t T

d̂ dT TUsually- there are tracking errors and

Thus – the recovered carrier is phase modulated by terms with the form:

ˆ( )d d nnT T

)11(

Recovered data-modulated carrier

)12(


Dealing with tracking errors in slow FH:

Need means for coherent carrier tracking, independent of the FH tracking loop.

Possible way: estimating Rx phase every hop – “feed forward carrier phase estimation” using

known sync. Word– Need to protect sync. word to avoid hostile jammer

)I.e., by changing periodically the sync word(


Non coherent slow FH

Coherent FH are complex to implement– Non-coherent – Differentially coherent

When freq. synthesizer phase is random for each successive time interval, PSD of hT(t)

2

2 2

1

( ) [( ) ] [( )2

k

hh m h m hk

m

TS f Sinc f f T Sinc f f T

)13(


Typical Example of Slow non coherent FH:

Data modulation: 2L-ary FSK Each Ts=LTb sec. the modulator outputs 1-out-2L

tones

Spacing between the tones 1/LTb

Bd, Bandwidth of modulated signal: Bd = 2L/LTb

Each Th the data modulated signal is translated to a new frequency by a FH modulator, 2k

frequency bands of wide Bd

Total BW of system: Bss=2kBd

Th > LTb slow FH condition

Plot this for k=3 and L=2 .

That is 4-FSK and 8 bands for the FH signals


Non Coherent fast FH

Here , sh s b

h

TT T LT K T

o Hop-bands can change many times per symbol

o Data modulator can operate in different modes with different complexities. Can use the K hops per symbol based on majority vote or Maximum Likelihood sequence estimation.

Benefits: frequency diversity gain on each transmitted symbol

o Partial-band jammer

o improving performance in “fast fading” multipath channel


Typical Example of Fast non coherent FH:

Data modulation: 2L-ary FSK Each Th=(1/K) * Ts sec. the modulator outputs 1-out-2L

tones. That is – the tones are subdivided into K “chips”

Spacing between the tones 1/Th = K / LTb =K / Ts

Bd, Bandwidth of modulated signal: Bd = 2L / Th= K2L / LTb

Each Th the data modulated signal is translated to a new frequency by a FH modulator, 2k

frequency bands of wide Bd

Total BW of system: Bss=2kBd

Th < LTb fast FH condition

Plot this for L=K=k = 2 .

That is 4-FSK and 4 bands for the FH signals


Combined DS-FH spread spectrum transmitter + DPSK data modulator

Code

GENERATOR

( )dss t

Frequency

synthesizer

nf

Bandpass

filter( )Th t

1 2 3 k

FH code clock

( )ts t

( )d tDifferential

encoder

02 cos(2 )P f t

NRZ data

Data modulated carrier

( )c t

'( )d t


Combined DS-FH spread spectrum receiver + DPSK data demodulator

Code

GENERATOR

BP

filter

( )ds t

Frequency

synthesizer

nf

Bandpass

filter( )Rh t

1 2 3 k

FH code clock

nd

DPSK demod

( )y t

Bandpass

filter

ˆ( )dc t T

02cos[( ) ]IF t

Documents

Dr. Moshe Ran- Spread Spectrum 1 טכניקות בתקשורת מרחיבת סרט (Spread Spectrum) Chapter 2b ד"ר משה רן מצגת זו תכלול כנראה דיון של