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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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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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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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• 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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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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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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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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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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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

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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

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• 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

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((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

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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%