eee 461 1 chapter 5 digital modulation systems huseyin bilgekul eee 461 communication systems ii...
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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
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
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)
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
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
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
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
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
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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Waveforms at the Waveforms at the transmitter transmitter
Tb Bit interval Tc Chip interval
PG= Tb/Tc
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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
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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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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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
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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• 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
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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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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• 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
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
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.
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
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
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
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
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
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.
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
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
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
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)
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)
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
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
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
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
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
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
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)
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%
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