William Stallings

Data and Computer

Communications

Chapter 9

Spread Spectrum

1
Spread Spectrum
 important encoding method for wireless communications

 it was initially developed for military to make jamming

and interception harder

 analog & digital data  analog signal

 spreads data over wide bandwidth

 two approaches, both in use:

Frequency Hopping Spread Spectrum (FHSS)
Direct Sequence Spread Spectrum (DSSS)

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 2

BFSK - Review
 The BFSK: sd (t )  A cos(2 ( f0  0.5(bi  1)f )t )
where, A = amplitude of signal
f0 = base frequency
bi = value of the ith bit of data (+1 for binary 1 and -1 for binary 0)
f = frequency separation
T = bit duration
1/T = data rate
 During the ith bit interval, the frequency of data signal is f0 if the data bit is -1 and
f0+f if the data bit is +1

1 f0 + f
0 f0

0 1

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 3

BFSK FHSS

1 f8 + f0 + f
111 f8 + f0
0
1 f7 + f0 + f
110 0 f7 + f0
1 f6 + f0 + f
101 0 f6 + f0
1 f5 + f0 + f
100 0 f5 + f0
1 f4 + f0 + f
011 0 f4 + f0
1 f3 + f0 + f
010 0 f3 + f0
1 f2 + f0 + f
001 0 f2 + f0
1 f1 + f0 + f
000 0 f1 + f0

…
Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 4
MFSK - Review

11 f4
10 f3
01 f2
00 f1

00 01 10 11

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 5

MFSK FHSS

11
10
11 01
00
11
10
10 01
00
11
01 10
01
00
11
10
00 01
00

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 6

General Model of Spread
Spectrum System

Input fed to The signal is further At the receiving The signal is fed
channel encoder modulated using end, the same into a channel
that produces an spreading sequence spreading decoder to
analog signal with (spreading code) sequence is used recover the data
a relatively narrow to demodulate the
spreading code is
bandwidth around spread spectrum
generated using
some center signal
pseudorandom
frequency
number generator

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 7

Concept of Spread Spectrum
 Input fed to channel encoder that produces an analog signal with
a relatively narrow bandwidth around some center frequency

 The signal is further modulated using spreading sequence or

spreading code

 spreading code is generated using pseudorandom number

generator

 The effect of this modulation is to increase significantly the

bandwidth (spread the spectrum) of the signal to be transmitted

 At the receiving end, the same spreading sequence is used to

demodulate the spread spectrum signal.

 Finally, the signal is fed into a channel decoder to recover the

data

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 8

Spread Spectrum Advantages
 Several advantages can be gained from this apparent
waste of spectrum:
immunity from various kinds of noise and multipath
distortion
Hiding and encryption signals. Only a reception who
knows the spreading code can recover the encoded
information
several users can share same higher bandwidth
with little interference
CDM/CDMA Mobile telephones

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 9

Frequency Hopping Spread
Spectrum (FHSS)

Order

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 10

Frequency Hopping Spread
Spectrum (FHSS)

signal is broadcast over seemingly random

series of frequencies
receiver hops from frequency to another
over fixed intervals in synchronization
with transmitter
eavesdroppers hear unintelligible blips
jamming on one frequency affects only a few
bits

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 11

FHSS Basic Approach
 Number of channels allocated for a frequency hopping (FH) signal
 2k carrier frequencies forming 2k channels
 spacing between carrier frequencies (i.e., the width of each channel)
corresponds to the bandwidth of the input signal
 transmitter operates in one channel at a time for a fixed
interval
 during that interval, some number of bits is transmitted using some
encoding scheme

 spreading code dictates the sequence of channels used.

 Both transmitter and receiver use the same code to tune into
a sequence of channels in synchronization.
Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 12
FHSS (Transmitter)
 binary data are fed into a modulator using some digital-to-analog encoding
scheme, such as FSK or BPSK resulting signal sd(t) which is centered on some
base frequency
 pseudonoise (PN) source serves as an index into a table of frequencies
 each k bits of the PN source (i.e., spreading code) specifies one of the 2k
carrier frequencies
 at each successive interval, a new spreading code (k bits) is generated
 a new carrier frequency is selected
 frequency synthesizer generates a constant-frequency tone whose frequency
hops among a set of 2k frequencies, with the hopping pattern determined by
k bits from the PN sequence. It is known spreading or chipping signal c(t)
 c(t) is then modulated by the signal produced from the initial modulator to
produce a new signal with the same shape but now centered on the selected
carrier frequency
 bandpass filter is used to block the difference frequency and pass the sum
frequency, yielding the final FHSS signal s(t)
Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 13
 FHSS (Transmitter)

Binary data are fed

into a modulator
(FSK or BSK) Bandpass filter is used to
resulting signal sd(t) block the difference
which is centered on frequency and pass the
some base frequency sum frequency, yielding
the final FHSS signal s(t)
Spreading Code
(k-bit)

Table of 2k Carrier
Frequencies
Pseudonoise (PN) source
generates k-bit spreading Frequency synthesizer c(t) is then modulated by
code which specifies one generates a constant- the signal produced from
of the 2k carrier frequency tone which is the initial modulator to
frequencies from the called spreading or produce a new signal
channel table chipping signal c(t)

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 14

FHSS (Transmitter)
pT (t )  sd (t )c(t )  A cos(2 ( f0  0.5(bi  1)f )t ) cos(2fit )
pT (t )  0.5 A[cos(2 ( f 0  0.5(bi  1)f  fi )t )  cos(2 ( f0  0.5(bi  1)f  fi )t )]
s(t )  0.5 A cos(2 ( f 0  0.5(bi  1)f  fi )t )
sd (t )  A cos(2 ( f0  0.5(bi  1)f )t )

PT (t )

1 0 1 0 ...
c(t )  cos(2fit )

Spreading Code
(k-bit)

Table of 2k Carrier
Frequencies

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 15

FHSS (Receiver)

 signal s(t) is multiplied by a replica of the spreading signal

c(t) to yield a product signal sd(t)

 bandpass filter is used to block the sum frequency and

pass the difference frequency

 Output signal of bandpass filter is then demodulated to

recover the binary data.

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 16

FHSS (Receiver)

PR (t )

Bandpass filter is Output is then

used to block the demodulated to
sum frequency recover the
and pass the binary data
difference
frequency

Frequency synthesizer c(t) is then modulated by

generates a replica of the spread spectrum
spreading signal c(t) signal to produce sd(t)

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 17

FHSS (Receiver)
pR (t )  s(t )c(t )  0.5 A cos(2 ( f 0  0.5(bi 1)f  fi )t ) cos(2fit )
pR (t )  s(t )c(t )  0.25 A[cos(2 ( f0  0.5(bi 1)f  fi  fi )t )  cos(2 ( f0  0.5(bi 1)f )t )]

s(t )  0.5 A cos(2 ( f 0  0.5(bi  1)f  fi )t )

PR (t )

1 0 1 0 ...
c(t )  cos(2fit )
sd (t )  0.25 A cos(2 ( f 0  0.5(bi  1)f )t )

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 18

FHSS (Transmitter)
The BFSK input to FHSS system is:
sd (t )  A cos(2 ( f0  0.5(bi  1)f )t ) for iT < t < (i+1)T

where,
A = amplitude of signal
f0 = base frequency
bi = value of the ith bit of data (+1 for binary 1 and -1 for binary 0)
f = frequency separation
T = bit duration
1/T = data rate

 During the ith bit interval, the frequency of data signal is f0 if the data bit is -1 and
f0+f if the data bit is +1

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 19

FHSS (Transmitter)
The transmitter product signal ( pT (t) ) during ith hop is:
pT (t )  sd (t )c(t )  A cos(2 ( f0  0.5(bi  1)f )t ) cos(2fit )
where fi is the frequency generated by the frequency synthesizer during the ith hop.

Using the trigonometric identity:

1
cos( x) cos( y)  (cos( x  y)  cos( x  y))
2

 We have:
pT (t )  0.5 A[cos(2 ( f 0  0.5(bi  1)f  fi )t )  cos(2 ( f0  0.5(bi  1)f  fi )t )]

 The bandpass filter is used to block the differences frequency and pass the sum
frequency, yielding an FHSS signal:
s(t )  0.5 A cos(2 ( f 0  0.5(bi  1)f  fi )t )
 Thus, during the ith bit interval, the frequency of data signal is f0 + fi if the data bit is -1 and
f0+fi+f if the data bit is +1
Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 20
FHSS (Receiver)
The receiver product signal ( pR (t) ) during ith hop is:
pR (t )  s(t )c(t )  0.5 A cos(2 ( f 0  0.5(bi 1)f  fi )t ) cos(2fit )
where fi is the frequency generated by the frequency synthesizer during the ith hop.

Using the trigonometric identity:

1
cos( x) cos( y)  (cos( x  y)  cos( x  y))
2

 We have:
pR (t )  s(t )c(t )  0.25 A[cos(2 ( f0  0.5(bi 1)f  fi  fi )t )  cos(2 ( f0  0.5(bi 1)f )t )]

 The bandpass filter is used to block the sum frequency and pass the difference frequency,
yielding a signal of the form sd(t):
sd (t )  0.25 A cos(2 ( f 0  0.5(bi  1)f )t )

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 21

Pseudorandom Numbers (PN)
generated by algorithm using initial seed by
a algorithm
Deterministic, not actually random
Same seed produces same number
However, if algorithm good, results pass reasonable
tests of randomness
starting from an initial seed
need to know algorithm and seed to
predict sequence
hence only receiver can decode signal
Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 22
FHSS Using MFSK
 commonly use multiple FSK (MFSK)
 have frequency shifted every Tc seconds
 for data rate R
 bit duration Tb = 1/R sec
 signal element duration Ts = mTb

 if Tc is greater than or equal to Ts , the spreading modulation is

referred to as slow-frequency-hop spread spectrum; otherwise
it is known as fast-frequency-hop spread spectrum
Slow-frequency-hop spread spectrum Tc  Ts
Fast-frequency-hop spread spectrum Tc < Ts

 FHSS quite resistant to noise or jamming

 with fast FHSS giving better performance

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 23

FHSS Using MFSK
MFSK commonly used with FHSS
For one signal element MFSK
s t   A cos  2 f i t  , 1 i  M
fi  f c  (2i 1  M ) f d
fc = carrier frequency
fd = difference frequency
M = number of different signal elements = 2m
m = number of bits per signal element

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 24

FHSS Using MFSK - Example
 M = 4 frequencies encode 2 bits at a time
 MFSK bandwidth Wd = 2M fd
 Using FHSS with k = 2, 2k = 4 channels
 Each channel with bandwidth Wd
 Total bandwidth for FHSS: Ws = 2kWd
 Slow FHSS: Tc = 2Ts = 4Tb
Each 2 bits of the PN sequence is used to select one of the
four channels
channel held for duration of two signal elements, or four bits
 Fast FHSS: Ts = 2Tc = 2Tb
signal element represented in two channels

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 25

Slow MFSK FHSS

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 26

Slow MFSK FHSS

11

10

01

00

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 27

Fast MFSK FHSS

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Fast MFSK FHSS

11

10

01

00

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 29

Direct Sequence Spread Spectrum
(DSSS)
 each bit is represented by multiple bits using a
spreading code
 this spreads signal across a wider frequency band
 frequency band of signal is proportional to number of bits
10-bit spreading code  spreads the signal across
the frequency band 10 times greater than a 1-bit
spreading code
 Input is combined with spread code using XOR
input 0: spreading code unchanged
input 1: spreading code inverted

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 30

Direct Sequence Spread Spectrum
Example

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 31

Direct Sequence Spread Spectrum
(DSSS)
The BPSK signal is represented as:
sd (t )  Ad (t ) cos(2fct )

where,
A = amplitude of signal
fc = carrier frequency
d(t) = discrete function that takes on the value of +1 for one bit time
if the corresponding bit in the bit stream is 1 and the value -1
for one bit if the corresponding bit in the bit stream is 0

 To produce the DSSS signal, we multiply d(t) by c(t), which is the PN sequence
taking on values of +1 and -1:
s(t )  sd (t )c(t )  Ad (t )c(t ) cos(2f ct )

 At the receive, the incoming signal is multiplied again by c(t), but c(t)×c(t)=1 and
therefore, the original signal is recovered:
s(t )c(t )  Ad (t )c(t )c(t ) cos(2fct )  sd (t )

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 32

Direct Sequence Spread Spectrum
System

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 33

DSSS Example Using BPSK

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 34

Code Division Multiple Access
(CDMA)
a multiplexing technique used with spread
spectrum
given a data signal rate D
break each bit into k chips according to a
fixed chipping code specific to each user
Pattern unique for each user (user code)
resulting new channel has chip data rate kD
chips per second

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 35

CDMA – Example

User A code cA = <1, -1, -1, 1, -1, 1>

User B code cB = <1, 1, -1, -1, 1, 1>
User C code cC = <1, 1, -1, 1, 1, -1>

If A wants to send bit 1:

transmit chip code <1, -1, -1, 1, -1, 1>
If A wants to send bit 0:
transmit chip code <-1, 1, 1, -1, 1, -1>
i.e. 1’s complement (1, -1 inverted)

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 36

CDMA - Example

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 37

CDMA – Example
 If a receiver R receives a chip pattern d=<d1,d2,d3,d4,d5,d6> and
the receiver is seeking to communicate with a user u so that it
has at hand u’s code <c1,c2,c3,c4,c5,c6>, the receiver performs
the following decoding function:
Su(d) = d1×c1+d2×c2+d3×c3+d4×c4+d5×c5+d6×c6
 If u is actually user A, then
 If A sends 1:
d = <1, -1, -1, 1, -1, 1>
SA = 1×1+(-1×-1)+(-1×-1)+1×1+(-1×-1)+1×1= 6

 If A sends 0:
d = <-1, 1, 1, -1, 1, -1>
SA = -1×1+1×-1+-1×1+1×-1+1×-1+-1×1= -6

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 38

CDMA – Example

 If user B send 1, receiver using SA

d=<1, 1, -1, -1, 1, 1>
cA = <1, -1, -1, 1, -1, 1>
SA(d) = SA (1, 1, -1, -1, 1, 1)
= 1×1+1×-1+-1×-1+-1×1+1×-1+1×1= 0
 Same result if B sends 0

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 39

Orthogonal Codes

If A, B transmit same time, SA is used

only A signal is received, B is ignored
If A, B transmit same time, SB is used
only B signal is received, A is ignored
SA(cB) = SB(cA) = 0
Codes of A, B are called orthogonal

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 40

Orthogonal Codes
 Orthogonal codes are not always available
 More commonly, SX(cY) is small if X ≠ Y
 Thus, can distinguish when X = Y, X ≠ Y
 In the previous example
SA(cC) = SC(CA) = 0
SB(cC) = SC(cB) = 2
signal makes small contribution instead of 0

 Receiver can identify signal of user even if other users

transmitting at same time

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 41

CDMA – Example

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 42

CDMA – Example

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 43

CDMA Limitations

Receiver can filter unwanted users

either 0 or low-level noise

However, system will break down if

many users compete for channel
signal power from some users is too high because
some users are very near to receiver

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 44

CDMA for DSSS
 There are n users, each transmitting using different PN sequence
 For each user, data stream di(t) is BPSK modulated to produce signal with
bandwidth Wd and then multiplied by spreading code for that user ci(t)
 All of the signals, plus noise, are received at the receiver's antenna
 Suppose that the receiver is attempting to recover the data of user 1. The
incoming signal is multiplied by the spreading code of user 1 (c1(t)) and
then demodulated.
  Narrow the bandwidth of that portion of the incoming signal
corresponding to user 1 to the original bandwidth of the unspread signal
 Incoming signals from other users are not despread by the spreading code
from user 1 and hence retain their bandwidth of Ws
 Unwanted signal energy remains spread over a large bandwidth and the
wanted signal is concentrated in a narrow bandwidth
 Bandpass filter at the demodulator can therefore recover the desired signal

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 45

CDMA for DSSS

Dr. Mohammed Arafah William Stallings “Data and Computer Communications” 46

Summary
looked at use of spread spectrum techniques:
FHSS
DSSS
CDMA

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