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EEE 461 1
Chapter 5Chapter 5Digital Modulation Digital Modulation
SystemsSystems
Huseyin BilgekulEEE 461 Communication Systems II
Department of Electrical and Electronic Engineering Eastern Mediterranean University
Spread Spectrum Systems
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EEE 461 2
Introduction to Spread Introduction to Spread SpectrumSpectrum
• Problems such as capacity limits, propagation effects, synchronization occur with wireless systems
• Spread spectrum modulation spreads out the modulated signal bandwidth so it is much greater than the message bandwidth
• Independent code spreads signal at transmitter and despread the signal at receiver
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EEE 461 3
Spread Spectrum SystemsSpread Spectrum Systems
• Multiple access capability
• Anti-jam capability
• Interference rejection
• Secret operation
• Low probability of intercept
• Simultaneous use of wideband frequency
• Code division multiple access (CDMA)
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EEE 461 4
• Multiplexing in 4 dimensions– space (si)– time (t)– frequency (f)– code (c)
• Goal: Multiple use of a shared medium
• Important: guard spaces needed!
s2
s3
s1
MultiplexingMultiplexing
f
t
c
k2 k3 k4 k5 k6k1
f
t
c
f
t
c
Channels ki
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EEE 461 5
Frequency Division Frequency Division MultiplexMultiplex
• Separation of spectrum into smaller frequency bands• Channel gets band of the spectrum for the whole time• Advantages:
– no dynamic coordination needed
– works also for analog signals
• Disadvantages:– waste of bandwidth
if traffic distributed unevenly
– inflexible
– guard spaces
k3 k4 k5 k6
f
t
c
Channels ki
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EEE 461 6
f
t
ck2 k3 k4 k5 k6k1
Time Division MultiplexTime Division Multiplex
• Channel gets the whole spectrum for a certain amount of time
• Advantages:– only one carrier in the
medium at any time– throughput high even
for many users
• Disadvantages:– precise
synchronization necessary
Channels ki
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EEE 461 7
f
Time and Frequency Division Time and Frequency Division MultiplexMultiplex
• A channel gets a certain frequency band for a certain amount of time (e.g. GSM)
• Advantages:– better protection against tapping– protection against frequency
selective interference– higher data rates compared to
code multiplex
• Precise coordinationrequired
t
c
k2 k3 k4 k5 k6k1
Channels ki
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EEE 461 8
Code Division MultiplexCode Division Multiplex
• Each channel has unique code• All channels use same spectrum at same time• Advantages:
– bandwidth efficient– no coordination and synchronization– good protection against interference
• Disadvantages:– lower user data rates– more complex signal regeneration
• Implemented using spread spectrum technology
k2 k3 k4 k5 k6k1
f
t
c
Channels ki
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EEE 461 9
DS/SS PSK SignalsDS/SS PSK SignalsDirect-sequence spread coherent phase-shift keying. Direct-sequence spread coherent phase-shift keying. ((aa) Transmitter. () Transmitter. (bb) Receiver.) Receiver.
( ) Re{ ( ) }
( ) ( ) ( )
For Direct Sequence SS
( ) ( ) ( )
( ) is the spreading code
j t
m c
c
s t g t e
g t g t g t
g t A m t c t
c t
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EEE 461 10
Waveforms at the Waveforms at the transmitter transmitter
Tb Bit interval Tc Chip interval
PG= Tb/Tc
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EEE 461 11
Spread Spectrum Spread Spectrum TechnologyTechnology
• Problem of radio transmission: frequency dependent fading can wipe out narrow band signals for duration of the interference
• Solution: spread the narrow band signal into a broad band signal using a special code
detection atreceiver
interference spread signal
signalspreadinterference
f f
power power
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EEE 461 12
Spread Spectrum Spread Spectrum TechnologyTechnology
• Side effects:– coexistence of several signals without
dynamic coordination– tap-proof
• Alternatives: Direct Sequence (DS/SS), Frequency Hopping (FH/SS)
• Spread spectrum increases BW of message signal by a factor N, Processing Gain
10Processing Gain 10logss ssB BN
B B
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EEE 461 13
Effects of spreading and Effects of spreading and interferenceinterference
P
fi)
P
fii)
User signalBroadband interferenceNarrowband interference
Sender
P
fiii)
P
fiv)
Receiver
f
v)
P
• The narrowband interference at the receiver is spread out so that the detected narrowband signal power is much lower.
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EEE 461 14
Spreading and frequency selective Spreading and frequency selective fadingfading
Narrowband signal
22
22
2
frequency
channelquality
1
spreadspectrum
frequency
channelquality
1 23
4
5 6
guard space
narrowband channels
spread spectrum channels
• Wideband signals are less affected by frequency selective multipath channels
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EEE 461 15
• Direct Sequence (DS) CDMA
• m(t) is polar from a digital source ±1.
• For BPSK modulation, gm(t) = Acm(t). The spreading waveform complex envelope gc(t) = c(t) c(t) is a polar spreading signal).
• The resulting complex envelope of the SS signal becomes g(t) = Acm(t)c(t).
• The spreading waveform is generated by using PN code generator. The pulse width of Tc is called the chip interval.
• When a PN sequence has the maximum period of N chips, where N = 2r -1, it is called a maximum length sequence (m-sequence). There are certain very important properties of m-sequences:
Direct Sequence Spread Spectrum Direct Sequence Spread Spectrum (DSSS) I(DSSS) I
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EEE 461 16
• Balance Property: In each period of maximum-length sequence, the number of 1s is always one more than the number of 0s.
• Run Property: Here, the 'run' represents a subsequence of identical symbols(1's or 0's) within one period of the sequence. One-half the run of each kind are of length one, one-fourth are length two, one-eighth are of length three, etc.
• Correlation Property: The autocorrelation function of a maximum-length sequence is periodic, binary valued and has a period T=NTc where Tc is chip
duration.
• The autocorrelation function is
Properties of Maximum Length Properties of Maximum Length SequencesSequences
1
0
1, ( ) = 1
- ,
1( ) = and 1
N
c
N
c n n k nn
k lNR k
k lNN
R k c c c
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EEE 461 17
((aa) Waveform of ) Waveform of maximal-length sequence maximal-length sequence for length for length mm 3 or period 3 or period NN 7. 7.
((bb) Autocorrelation ) Autocorrelation function. function.
((cc) Power spectral ) Power spectral density. density.
Maximum Length SequencesMaximum Length Sequences
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EEE 461 18
Feedback shift Feedback shift register.register.
Two different configurations of Two different configurations of feedback shift register of length feedback shift register of length mm 5. 5. ( (aa) Feedback connections [5, 2].) Feedback connections [5, 2]. ( (bb) Feedback) Feedback connections [5, 4, 2, 1].connections [5, 4, 2, 1].
Maximum Length SequencesMaximum Length Sequences
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EEE 461 19
• Codes are periodic and generated by a shift register and XOR
• Maximum-length (ML) shift register sequences, m-stage shift register, length: n = 2m – 1 bits
R()
-1/n Tc
-nTcnTc
+Output
Maximum Length SequencesMaximum Length Sequences
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EEE 461 20
Generating PN SequencesGenerating PN Sequences
• Take m=2 =>L=3• cn=[1,1,0,1,1,0, . . .],
usually written as bipolar cn=[1,1,-1,1,1,-1, . . .]
m Stages connected to modulo-2 adder
2 1,2
3 1,3
4 1,4
5 1,4
6 1,6
8 1,5,6,7
+Output
11/1
01
1
1
LmL
m
ccL
mRL
nmnnc
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EEE 461 21
Problems with Problems with mm-sequences-sequences
• Cross-correlations with other m-sequences generated by different input sequences can be quite high.
• Easy to guess connection setup in 2m samples so not too secure.
• In practice, Gold codes or Kasami sequences which combine the output of m-sequences are used.
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EEE 461 22
DSSS DSSS
• XOR the signal with pseudonoise (PN) sequence (chipping sequence)
• Advantages– reduces frequency selective
fading
– in cellular networks • base stations can use the
same frequency range
• several base stations can detect and recover the signal
• But, needs precise power control
user data
chipping sequence
ResultingSignal
0 1
0 1 10 1 0101 0 0 1 11
XOR
0 1 10 0 1011 0 1 0 01
=
Tb
Tc
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EEE 461 23
DSSS Transmitter and ReceiverDSSS Transmitter and Receiver
Xuser datam(t)
chippingsequence, c(t)
modulator
radiocarrier
Spread spectrumSignal y(t)=m(t)c(t) Transmit
signal
TRANSMITTER
demodulator
Receivedsignal
radiocarrier
X
Chipping sequence, c(t)
RECIVER
integrator decision
datasampledsums
Correlator
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EEE 461 24
DS/SS Comments DS/SS Comments • Pseudonoise (PN) sequence chosen so that its
autocorrelation is very narrow => PSD is very wide– Concentrated around < Tc
– Cross-correlation between two user’s codes is very small
• Secure and Jamming Resistant– Both receiver and transmitter must know c(t)
– Since PSD is low, hard to tell if signal present
– Since wide response, tough to jam everything
• Multiple access– If ci(t) is orthogonal to cj(t), then users do not interfere
• Near/Far problem: Users must be received with the same power
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EEE 461 25
Frequency Hopping Spread Spectrum Frequency Hopping Spread Spectrum (FH/SS)(FH/SS)
• A frequency-hopped SS (FH/SS) signal uses a gc(t) that is of FM type. There are M=2k hop frequencies controlled by the spreading code.
• Discrete changes of carrier frequency– sequence of frequency changes determined via PN sequence
• Two versions– Fast Hopping: several frequencies per user bit (FFH)– Slow Hopping: several user bits per frequency (SFH)
• Advantages– frequency selective fading and interference limited to short period– uses only small portion of spectrum at any time
• Disadvantages– not as robust as DS/SS– simpler to detect
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EEE 461 26
Illustrating slow-Illustrating slow-frequency hopping. frequency hopping.
((aa) Frequency ) Frequency variation for one variation for one complete period of the complete period of the PN sequence.PN sequence.
((bb) Variation of the ) Variation of the dehopped frequency dehopped frequency with time.with time.
Slow Frequency HoppingSlow Frequency Hopping
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EEE 461 27
Fast Frequency HoppingFast Frequency Hopping
Illustrating fast-Illustrating fast-frequency hopping.frequency hopping. ((aa) Variation of the ) Variation of the transmitter frequency transmitter frequency with time. with time.
((bb) Variation of the ) Variation of the dehopped frequency dehopped frequency with time.with time.
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EEE 461 28
FHSS (Frequency Hopping FHSS (Frequency Hopping Spread Spectrum) IISpread Spectrum) II
user data
slowhopping(3 bits/hop)
fasthopping(3 hops/bit)
0 1
Tb
0 1 1 t
f
f1
f2
f3
t
Td
f
f1
f2
f3
t
Td
Tb: bit period Td: dwell time
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EEE 461 29
FHSS Transmitter and ReceiverFHSS Transmitter and Receiver
modulatoruser data
hoppingsequence
modulator
narrowbandsignal
Spread transmitsignal
Transmitter
frequencysynthesizer
receivedsignal
Receiver
demodulatordata
hoppingsequence
demodulator
frequencysynthesizer
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EEE 461 30
Applications of Spread Applications of Spread
SpectrumSpectrum • In 1985 FCC opened 902-928 Mhz, 2400-2483Mhz
and 5725-5850 Mhz bands for commercial SS use with unlicensed transmitters.
• Cell phones– IS-95 (DS/SS)– GSM
• Global Positioning System (GPS)
• Wireless LANs– 802.11b
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EEE 461 31
Performance of DS/SS Performance of DS/SS SystemsSystems
• Pseudonoise (PN) codes – Spread signal at the transmitter– Despread signal at the receiver
• Ideal PN sequences should be– Orthogonal (no interference)– Random (security)– Autocorrelation similar to white noise (high at =0
and low for not equal 0)
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EEE 461 32
Detecting DS/SS PSK SignalsDetecting DS/SS PSK Signals
XBipolar, NRZm(t)
PNsequence, c(t)
X
sqrt(2)cos(ct + )
Spread spectrumSignal y(t)=m(t)c(t) transmit
signal
transmitter
X
receivedsignal
X
c(t)
receiver
integrator
z(t)
decisiondata
sqrt(2)cos(ct + )
LPF
w(t)
x(t)
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EEE 461 33
Optimum Detection of DS/SS Optimum Detection of DS/SS PSKPSK
• Recall, bipolar signaling (PSK) and white noise give the optimum error probability
• Not effected by spreading– Wideband noise not affected by spreading– Narrowband noise reduced by spreading
2 bb
EP Q
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EEE 461 34
Signal SpectraSignal Spectra
• Effective noise power is channel noise power plus jamming (NB) signal power divided by N
10Processing Gain 10logss ss b
c
B B TN
B B T
Tb
Tc
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EEE 461 35
Multiple Access Multiple Access PerformancePerformance
• Assume K users in the same frequency band,
• Interested in user 1, other users interfere
4
13
5
2
6
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EEE 461 36
Signal ModelSignal Model• Interested in signal 1, but we also get signals
from other K-1 users:
• At receiver,
2 cos
2 cos
k k k k k c k k
k k k k c k k k c k
x t m t c t t
m t c t t
12
K
kk
x t x t x t
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EEE 461 37
Interfering SignalInterfering Signal
• After mixing and despreading (assume 1=0)
• After LPF
• After the integrator-sampler
1 12 cos cosk k k k k c k cz t m t c t c t t t
1 1cosk k k k k kw t m t c t c t
1 10cos bT
k k k k k kI m t c t c t dt
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EEE 461 38
At ReceiverAt Receiver• m(t) =+/-1 (PSK), bit duration Tb
• Interfering signal may change amplitude at k
• At User 1:• Ideally, spreading codes are Orthogonal:
1 1 1 0 10cos k b
k
Tk k k k k kI b c t c t dt b c t c t dt
1 1 1 10bT
I m t c t c t dt
1 1 10 00b bT T
k kc t c t dt A c t c t dt
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EEE 461 39
Example of Performance DegradationExample of Performance Degradation
N=8 N=32
Multiple Access Interference Multiple Access Interference (MAI)(MAI)
• If the users are assumed to be equal power interferers, can be analyzed using the central limit theorem (sum of IID RV’s)
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EEE 461 40
Near/Far ProblemNear/Far Problem • Performance estimates derived using assumption that all users
have same power level
• Reverse link (mobile to base) makes this unrealistic since mobiles are moving
• Adjust power levels constantly to keep equal
1k
• K interferers, one strong interfering signal dominates performance
• Can result in capacity losses of 10-30%