SPREAD SPECTRUM

1
SPREAD SPECTRUM

• Hiding Information in noise

2
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

3
Spread SpectrumData 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

4
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

5
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)

b(t)
Tb
Tc
c(t)
6
Notations

• There are a number of important parameters in SS
• b(t) data sequence
• c(t) spreading sequence
• Tb bit length
• Tc chip length
• NTb/Tc number of chips per bit
• N3 in this figure

b(t)
Tb
c(t)
Tc
7
Communications model Jamming

• The classic jamming model is shown below. we will
  demonstrate that an SS signal provides superior
  protection against intentional jamming

m(t)
b(t)
r(t)
X
c(t)
i(t)
interference
8
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

9
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

10
Where is the spread?

• It is said that spread spectrum signal looks like
  random noise to all others but why?
• Consider this

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PN sequence Generation

• PN sequences can be generated by a set of
  flip-flops with appropriate taps

1
0
0
output
So
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
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m-sequences

• The preceding sequence repeats itself with a
  period of 23-17
• 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

13
Properties

• of 1s are always one more than the number of
  0s
• Period 2m-1
• Very desirable (tight) correlation
• More on this next

14
Autocorrelation of m-sequences

• Let c(t) be an m-sequence. Its autocorrelation
  function is given by

Tb
Shifted by ? ltTc
15
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 N

Rc(?)
1
?
-1/N
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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
N25-131, taps at 5,4,2,1
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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 24-115. Less if
  not
• b) 1/10710-7 sec
• c)TNTc15x10-7 sec

18
Processing Gain

• Probably the single most important component of
  an SS system is a quantity called processing
  gain(PG)
• PG is defined by
• PGNTb/Tc
• In other words PGis given by the number of chips
  within a bit

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General Rule

• Bandwidth spreads by a factor equal to the
  processing gain
• spread bandwidth Wss(Tb/Tc)WPGxW

20
Bandwidth of an SS signal example

• Want to know the bandwidth of a digital signal
  running at 28.8 Kb/secafter spreading
• Consider a m19 stage shift register
• PN sequence period N219-1219
• There are 219 chips inside a bit, i.e. TbNTc
• Therefore, Rc1/TcN/Tb219x 28.8 Kb/sec
• Since bandwidth is proportional to bitrate, the
  new bandwidth is now 219 or 57 dB higher than the
  unspread signal

21
Communications model Jamming

• The classic jamming model is shown below. we will
  demonstrate that an SS signal provides superior
  protection against intentional jamming

m(t)
b(t)
r(t)
X
c(t)
i(t)
interference
22
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)
z(t)
c(t)
Data pn seq.
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SignalJammer at the Output

• Lets walk the spread spectrum signal through the
  receiver

interference
desired data
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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)

25
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

26
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

27
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)

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BER in the Presence of Jamming

• A DS/BPSK in Gaussian noise had a BER of
• In the presence of jammer(but no noise)

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Jammer acts as white noise

• Comparison of the two BER expressions
• Equivalently, EbPTb where P is the average
  signal power. Then

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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/PPG/(Eb/No)
• In dB
• jmPG-Eb/No

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Example

• Digital data is running with bit-lengthTb4.095
  ms.This data is spread using a chip length of
  Tc1 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/No10 to achieve BER 10-5.

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Interpretation

• The processing gain is Tb/Tc4095. Plugging these
  numbers in the JM expression, we get
• JM db10log4095-10log(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

33
CDMAspread 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

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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

35
CDMA Signal Model

• In CDMA, kth users signal is spread by a PN code
  ak unique to the subscriber
• M users can be on at the same time

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How are users separated?

• The familiar correlation receiver will do the job

b1
X
a1
b2
X
a2
b3
X
a3
37
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

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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, jumps are controlled by a PN sequence

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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

three symbols,same carrier freq.
40
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
41
Generating an FH/MFSK Signal

• k-bit segments of the PN code drive the
  synthesizer--gt2k frequencies

FH/MFSK
M-ary FSK
BPF
X
Freq synthesizer
PN code generator
42
Parameters of the Slow FH

• Chip an individual FH/MFSK tone of shortest
  duration
• In general, Rcmax(Rh,Rs)
• For slow FH

1 FH chip
Rc1 per sec Rs1 per sec Rh1/3 per sec
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Illustrating Slow FH
frequency
1/Rs
Rs
time
1/Rh
001
110
011
001
PN
4 FSK tones, 8 hops, PN period 16,
44
Fast FH

• Carrier frequency hops several times within one
  symbol

one symbol
45
Time-Frequency Plane of Fast FH
frequency
time
symbol
4 MFSK tones, 2 hops per symbol(hop
ratebitrate), 8 possible hops