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©1999 BG Mobasseri 1 04/20/23
SPREAD SPECTRUM
Hiding Information in noise
©1999 BG Mobasseri 2 04/20/23
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
©1999 BG Mobasseri 3 04/20/23
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”
©1999 BG Mobasseri 4 04/20/23
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
©1999 BG Mobasseri 5 04/20/23
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)
©1999 BG Mobasseri 6 04/20/23
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)
©1999 BG Mobasseri 7 04/20/23
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
©1999 BG Mobasseri 8 04/20/23
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
©1999 BG Mobasseri 9 04/20/23
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
©1999 BG Mobasseri 10 04/20/23
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
©1999 BG Mobasseri 11 04/20/23
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
©1999 BG Mobasseri 12 04/20/23
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
©1999 BG Mobasseri 13 04/20/23
Properties
# of 1’s are always one more than the number
of 0’s
Period: 2m-1
Very desirable (tight) correlation
©1999 BG Mobasseri 14 04/20/23
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
©1999 BG Mobasseri 15 04/20/23
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
©1999 BG Mobasseri 16 04/20/23
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]
©1999 BG Mobasseri 17 04/20/23
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
©1999 BG Mobasseri 18 04/20/23
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
©1999 BG Mobasseri 19 04/20/23
General Rule
Bandwidth spreads by a factor equal to the
processing gain
spread bandwidth Wss=(Tb/Tc)W=PGxW
©1999 BG Mobasseri 20 04/20/23
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
©1999 BG Mobasseri 21 04/20/23
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
©1999 BG Mobasseri 22 04/20/23
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.
©1999 BG Mobasseri 23 04/20/23
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
©1999 BG Mobasseri 24 04/20/23
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)
©1999 BG Mobasseri 25 04/20/23
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
©1999 BG Mobasseri 26 04/20/23
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
©1999 BG Mobasseri 27 04/20/23
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
©1999 BG Mobasseri 28 04/20/23
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
⎛
⎝ ⎜
⎞
⎠ ⎟
©1999 BG Mobasseri 29 04/20/23
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
⎛ ⎝
⎞ ⎠
©1999 BG Mobasseri 30 04/20/23
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
©1999 BG Mobasseri 31 04/20/23
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.
©1999 BG Mobasseri 32 04/20/23
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
©1999 BG Mobasseri 33 04/20/23
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
©1999 BG Mobasseri 34 04/20/23
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
©1999 BG Mobasseri 35 04/20/23
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( ) + ...
©1999 BG Mobasseri 36 04/20/23
How are users separated?
The familiar correlation receiver will do the
job
a1
a2
a3
b1
b3
b2
X
X
X
∫
∫
∫
©1999 BG Mobasseri 37 04/20/23
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
©1999 BG Mobasseri 38 04/20/23
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
©1999 BG Mobasseri 39 04/20/23
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.
©1999 BG Mobasseri 40 04/20/23
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
©1999 BG Mobasseri 41 04/20/23
Generating an FH/MFSK Signal
k-bit segments of the PN code drive the
synthesizer-->2^k frequencies
M-ary FSK
Freqsynthesizer
PN codegenerator
BPF FH/MFSKX
©1999 BG Mobasseri 42 04/20/23
Parameters of the 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
©1999 BG Mobasseri 43 04/20/23
Illustrating Slow FH
freq
uen
cyR
s
1/Rhtime
1/Rs
001 110 011 001PN
4 FSK tones, 8 hops, PN period 16,
©1999 BG Mobasseri 44 04/20/23
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
©1999 BG Mobasseri 45 04/20/23
Time-Frequency Plane of Fast FH
time
freq
uen
cy
symbol
4 MFSK tones, 2 hops per symbol(hop rate=bitrate), 8 possible hops