SPREAD SPECTRUM

©2000 Bijan Mobasseri 1

SPREAD SPECTRUM

Hiding Information in noise


Origins of Spread Spectrum

Military communication has always been

concerned with the following two issues– Security

– Jam resistance

In civilian communications, above issues take

on different interpretations– privacy

– unintentional interference


Spread Spectrum:Data Hiding

Spread spectrum is in effect a way to “hide”

information

Useful information is buried in noise. To an

eavesdropper, the intercepted message looks

juts like noise

The intended receive however is able to

recover the information from noise using a

special “key”


Types of Spread Spectrum

There are two main types of spread spectrum– Direct Sequence(DS)

– Frequency Hopping(FH)

in DS/SS, digital data is multiplied by another

bitstream running several hundred times

faster

In FH/SS, carrier frequency, normally fixed,

jumps around in a “random” manner known

only to the intended receive


Direct Sequence

Take the baseband digital data b(t) and

modulate it by a “random” bit pattern c(t). The

resulting bitstream is m(t)=c(t)b(t)

Tb

Tc

b(t)

c(t)


Notations

There are a number of important parameters

in SS– b(t): data sequence

– c(t): spreading sequence

– Tb: bit length

– Tc: chip length

– N=Tb/Tc: number of chips per bit

– N=3 in this figure

Tb

Tc

b(t)

c(t)


Communications model: Jamming

The classic jamming model is shown below.

we will demonstrate that an SS signal

provides superior protection against

intentional jamming

b(t)

c(t)

m(t)X

i(t)

r(t)

interference


Spreading Code: PN Sequences

Clearly, randomness is at the heart of spread

spectrum

However, if truly random codes are used to

spread the signal, receiver would never be

able to recover the information

Therefore, we need a “pseudo” random noise

known as PN sequences. Pseudo because if

you wait long enough, they will repeat


Main Features of PN Sequences

To a casual observer, a PN sequence looks

like a random alternations of +/-1.

In truth, however, a PN sequence repeats.

Can you spot the period here?

The key to “cracking” the code is to find

where the period ends


Where is the “spread”?

It is said that spread spectrum signal looks

like random noise to all others but why?

Consider this

m t( ) =c t( )b t( )M ω( ) =C ω( )* Bω( )Bm=Bc + Bb =100Bb + Bb

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-0.5

0

0.5

1PN and DATA SPECTRUM

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1


PN sequence Generation

PN sequences can be generated by a set of

flip-flops with appropriate taps

1 0 0

+

outputSo S1 S2

Initial state: 100

1 0 0 1 1 0 1 1 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 0

output: 0 0 1 1 1 0 1 0


m-sequences

The preceding sequence repeats itself with a

period of 23-1=7

In general, for an m-stage shift register, the

period is at most

If the period is equal to the above, we have

maximal length or m-sequences

2m −1


Properties

# of 1’s are always one more than the number

of 0’s

Period: 2m-1

Very desirable (tight) correlation

More on this next


Autocorrelation of m-sequences

Let c(t) be an m-sequence. Its autocorrelation

function is given by

Rc τ( )=1Tb

c(t)c(t−τ)dt,−Tb20

Tb

∫ ≤τ≤Tb2

Tb

Shifted by <Tc


Behavior of autocorrelation

The significant property of correlation here is

that it can discriminate against the slightest

shifts. In fact, shift of just a single chip drops

the function by a factor of NRc()1

-1/N


How to pick an m-sequence?

Once you pick a length N, the question is how

do we generate an m-sequence?

N, fixes the number of shift register stages

but you can connect them in many ways

Only a few connections give you valid m-

sequences(see Table 9.1 and Figure 9.4)

1 2 3 4 5

+++

N=25-1=31, taps at [5,4,2,1]


Example

A PN sequence is generated using a feedback

shift register of length 4. The chip rate is 107

pulses per second. Find– a):PN sequence length

– b): Chip duration

– c):PN sequence period

Answers– a): if an m-sequence, period is 24-1=15. Less if not

– b): 1/107=10-7 sec

– c):T=NTc=15x10-7 sec


Processing Gain

Probably the single most important

component of an SS system is a quantity

called processing gain(PG)

PG is defined by

PG=N=Tb/Tc

In other words PGis given by the number of

chips within a bit


General Rule

Bandwidth spreads by a factor equal to the

processing gain

spread bandwidth Wss=(Tb/Tc)W=PGxW


Bandwidth of an SS signal: example

Want to know the bandwidth of a digital

signal running at 28.8 Kb/secafter spreading

Consider a m=19 stage shift register– PN sequence period N=219-1~219

– There are 219 chips inside a bit, i.e. Tb=NTc

– Therefore, Rc=1/Tc=N/Tb=219x 28.8 Kb/sec

Since bandwidth is proportional to bitrate, the

new bandwidth is now 219 or 57 dB higher

than the unspread signal


Communications model: Jamming

The classic jamming model is shown below.

we will demonstrate that an SS signal

provides superior protection against

intentional jamming

b(t)

c(t)

m(t)X

i(t)

r(t)

interference


Jamming Scenario

A jammer or interference i(t) tries to interfere

with a spread spectrum signal

The corrupted spread spectrum signal at the

receiver is put through a conventional

correlation detector

r t( ) =mt( ) + i t( ) =b t( )c t( ) + i t( )

0

Tb∫

r(t)

c(t)

z(t)

Data pn seq.


Signal+Jammer at the Output

Let’s walk the spread spectrum signal

through the receiver

z t( ) =c t( )r t( ) =c t( ) b t( )c t( )+ i t( )[ ] =

c2 (t)b t( ) + c t( )i t( ) =b t( ) +c t( )i t( )

desired data

interference


Stopping the Jammer

The jammer appears as c(t)*i(t). In other

words we have created a spread spectrum

signal out of the jammer!

The bandwidth of a SS signal is very large

making it look like white noise. Therefore, a

lowpass filter integrator) will let the message

b(t) through but will stop most of the jammer

appearing as c(t)*i(t)


DS/BPSK

So far we have looked at DS/SS in baseband.

For the actual transmission we need to

modulate the signal

Spreading can be done either before or after

carrier modulation. See Fig. 9.7, 9.8 and 9.9

while listening to this slide


How does SS provide Protection against Jamming?

It can be shown that the SNR at the input and

output of correlation detector is given by

SNR( )o =2EbJTc

J : jammer power

Tc : chip length

SNR( )i =EbJTb


Processing Gain

The improvement in SNR is caused by the

processing gain, Tb/Tc. This ratio can be

several hundreds or thousands

SNR gain can be as high as 1000(30dB)

SNR( )o =2TbTc

SNR( )i


BER in the Presence of Jamming

A DS/BPSK in Gaussian noise had a BER of

In the presence of jammer(but no noise)

BER=12erfc

Eb

No

⎛

⎝ ⎜

⎞

⎠ ⎟

BER=12erfc

EbJTc

⎛

⎝ ⎜

⎞

⎠ ⎟


Jammer acts as white noise

Comparison of the two BER expressions

Equivalently, Eb=PTb where P is the average

signal power. Then

No2

=JTc2

EbNo

=TbTc

⎛ ⎝ ⎜

⎞ ⎠ ⎟ PJ

⎛ ⎝

⎞ ⎠


Jamming Margin

We just saw that processing gain helps

counter jamming power

The ratio of jammer power to signal power is

called Jamming margin

J/P=PG/(Eb/No)

In dB

jm=PG-Eb/No


Example

Digital data is running with bit-lengthTb=4.095

ms.This data is spread using a chip length of

Tc=1 microsecond using DS/BPSK. What is

the jamming margin if the required BER=

10-5.?

In the presence of random noise alone we

need Eb/No=10 to achieve BER= 10-5.


Interpretation

The processing gain is Tb/Tc=4095. Plugging

these numbers in the JM expression, we get

JM |db=10log4095-10log(10)=26.1 dB

We can maintain BER at the desired level

even in the presence of a jammer 26dB(400

times) higher than the desired signal


CDMA:spread spectrum at work

Code Division Multiple Access is one of the

two competing digital cellular standards (IS-

54). The other is TDMA-based IS-136

In this area, Comcast has adopted IS-136. Bell

Atlantic and Sprint PCS have gone the way of

CDMA.

These digital services coincide with the AMPS

infrastructure


Differences among the three

AMPS is an example of FDMA. Users are on

all the time but on different frequency bands

TDMA uses the same 30KHz band of AMPS

but services 3 users. Users are on only during

their time slot.

In CDMA, there is neither frequency nor time

sharing. Everyone is on simultaneously thus

taking up the whole spectrum


CDMA Signal Model

In CDMA, kth user’s signal is spread by a PN

code ak unique to the subscriber

M users can be on at the same time

sk t( ) = aki=1

N

∑ bi(k) t( )cosωct( )

s t( ) = a1i=1

N

∑ bi(1) t( )cosωct( ) + a2

i=1

N

∑ bi(2) t( )cosωct( ) + ...


How are users separated?

The familiar correlation receiver will do the

job

a1

a2

a3

b1

b3

b2

X

X

X

∫

∫

∫


Frequency Hopping SS

Transmitter and receiver always operate on a

known frequency band. Once found, anyone

can listen in

Imagine a scenario where carrier frequency

“hops” around in a random pattern

This pattern is known only to the intended

receiver thus nobody else can follow the hop


FH/MFSK

One obvious way to implement FH is to use

MFSK.

In the conventional MFSK, carrier frequency

jumps are controlled by the message

In FH/MFSK, additional jumps are introduced

by a PN sequence


FH Modalities

Slow frequency hopping– Symbol rate Rs of the MFSK signal is an integer

multiple of Rh, the hop rate; several symbols are transmitted on each frequency hop

0 0.5 1 1.5 2 2.5 3-4

-3

-2

-1

0

1

2

3

4

three symbols,same carrier freq.


FH Modalities

Fast frequency hopping– The hop rate Rh is an integer multiple of the MFSK

symbol rate Rs; the carrier frequency will change several times even before the symbol ends.

one symbol

0 0.5 1 1.5 2 2.5 3-4

-3

-2

-1

0

1

2

3

4


Generating an FH/MFSK Signal

k-bit segments of the PN code drive the

synthesizer-->2k frequencies

M-ary FSK

Freqsynthesizer

PN codegenerator

BPF FH/MFSKX


Parameters of slow FH

Chip: an individual

FH/MFSK tone of

shortest duration

In general, Rc=max(Rh,Rs)

For slow FH

Rc =Rs=RbK

≥Rh

0 0.5 1 1.5 2 2.5 3-4

-3

-2

-1

0

1

2

3

4

Rc=1 per secRs=1 per secRh=1/3 per sec

1 FH chip


Illustrating Slow FH

freq

uen

cyR

s

1/Rh

time

1/Rs

001 110 011 001PN

4 FSK tones, 8 hops, PN period 16,


Fast FH

Carrier frequency hops several times within

one symbol

one symbol

0 0.5 1 1.5 2 2.5 3-4

-3

-2

-1

0

1

2

3

4


Time-Frequency Plane of Fast FH

time

freq

uen

cy

symbol

4 MFSK tones, 2 hops per symbol(hop rate=bitrate), 8 possible hops

SPREAD SPECTRUM

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