BERPERFORMANCEOF

INCLUDING
Masahiro

WADA,Dept.

of Electricalt Dept.

of InformationTel:+81-886-56-7470,

A

CHAOS

MODULATION- DEMODULATION

Junji

Yoshifumi

KAWATAt,& ElectronicEng.,

Science

Tokushimaand Systems

thisarticle,

performance+81-886-56-7471,

error

rate

includingmodulation

gated.

We observe

lationcircuitsof bitchaos

communicationinfluences

systemvarious- demodu-

by computer

simulation.

of modulation- demodu-

severalcircuits

also

influence

communication(e.g.

and SPICE

is calculated

chaossynchroniza-quality.

Since

variousnonlinear

beenchaoticfor

MODEL

Our

communication

systemforgenerating

chaotic

by many

researchers.

Especiallychaos

a resistor

attract

researchers’

synchronization

to transmit

influences

radio

frequency.
andon the quality
systems

discussed
In thisulationtransistor

The

rectifier,an RC filter

signaltomodu-influence

influence

ofcircuits.

by voltage

buffers

to reproducenal

as shownin Fig.

The

circuitparametersbeen

attractor

influenceof chaoscom-modulation

and

Two

chaotic- demodulation= 5.56[nF],

areconnected●We

use a sim-

chaotic

maskingcommunication

systemusingChua’s

Almost[4].

sumsignalfrom

Chua’scase.

circuitandamplitude

digitalmodulation

chaotic

information

signal(AM)

circuit.

is modulatedTheradio-band

by

which

con-We model

thefor a computersim-

is const ruttedby acircuits.

circuitFurther,two

are interconnected

the originalof Chua’s
circuitcircuitfor

C’z = 50[nF],

chaotic

sig-

are givenassingle-spiral

L = 7.14[mH],rnO = 0.241 [mS],

Settingsystems
circuits.

circuitsof(b),
3(a)

ml

chaotic
G =l/RBp= 0.807[mS]

andfor- scroll= 1.OIV].

ple chaos

Theand3(b).

of Chua’s= 0.7 [mS],double-in Fig.

systemelements.

severalon Chua’s

has not2(a)showncircuitandbased● Settingdemod-demodulation

at-in Fig.

modelsubsystems

Cl
includingas the Ebers-MollWe

andmodulation
some1(b).

of chaotic

spiralcircuitandis character-types

as shown

amplitudeof a transistor

in communica-

synchronization

attractor

A modulation

ulation,real

However,as single-hand,a badcircuits

we investigatesystems

by modulationthathavesistsare called

a wellelements,

as Fig.

has two

repro-

showsiV~ whichpiecewise-linear

circuitfrequency,

otherchaoticknown

circuits

chaos

the

chaotic

respectively.
is a typical

ef-now.

study,

munication

the1(a)memoryChua’sus-circuits

and

Fig.

resistor

circuitfor reproducing

three

which

scrollthechannelby radio

basebanddemodulation

using

until

research

Onof communication.
andof

on communication

signals

It is generally

beenaccuracy

toterminal.
chaotic

demodulation

modulation

tractors,of communication

to modulatelationhave

circuit,circuitincludingnonlinearbyseveraloscillation.

segment

obtained

circuitcircuitandthatcircuit,on a Chua’sized by t hreeknowsynchronization

the

it is importantor nonlinearity

it is necessarychaos[3] anddirectlytransmissionin ordertionsystems,role

Therefore,systems

at-andof a Chua’schaotic

Chua’s

A varietyapplications.

communication

importantincludingmany

one of engineeringof noiseoriginal

systems[1] [2]. In thesefecttheknown

reportedquality.

in

based

forratebitareside.

BER

a modulation

to a demodulation

circuithaveon chaosandiscovered

consists

signal,a demodulationtransmittingapplicationsof studies
plays

werefrequency,

CIRCUIT

some chaos

considered

communication
tentions

phenomena

systems,

carrier

receiving

qpality,2.

ducingseveralat theare tuned)for

INTRODUCTION-u.ac.jp

voltageing a transistor,
1.

JAPANUniversity,communication

conditions

simulation

nonlinearity

770, JAPANis demodulated

to estimateof modulationthat

andsignalorder

USHIDAwada(lee.tokushima

signal

BER

and

Bunri

simulation.

simulation.

tion

Tokushima

computercomputer

Akio

Tokushima

information

circuits

We confirm
lationandis investi-- demodulation

by bothInCIRCUITS

University,e-mail:(BER)

SYSTEMNISHIO

modulated

estimation

in a generalEng.,

Fax:

ABSTRACTInCOMMUNICATION

Cl
Twoof

Chua’scircuitdoubleattractor
parameters
The

different= 5. O[nF]
typeandof chaotic

0-7803-4455-3/98/$10.00 (c) 1998 IEEEarethesameparameters

as thesingle- spiralare

G = 0.75[mS].
attractors

for theseparametersareshownin Fig.

culatethefrom

the

2 (a)

and

naturalvalue

At

Influence
first,

fromsignal

is modulated

theChua’ssimulateddouble- scroll

obtained(a-2)
signalFigs.

Chua’scircuitattractor

waveform,(d)(e) is reproduced

chaotic

the receiverat the receiverside,(b) is(c) is modulated
chaotic

attractor.

BecauseChua’scircuitcanchaos

pletely

without

carried

out

SPICE

verified

that

both

Next,

noise,well.

forscrollchaotic

attractors

both(a) is thenal w(C’1)+ VS, (d)chaotic

and(g)

low-pass

namelyBitthebitwe canalmost

obtained

from

the

severalfirmedchaotic
signalv,,

anddigital

waveformwidth

isisreproduce
theIn Fig.

informationof
sig-VX, (e) is

VZ – v(C1’).

Webestgenerating
103
In[bps],Fig.

error

circuits

as llO[kHz]double-scroll

We calculatequalityv:

toperformancebitis changing.

theamplitudeat O. 10[V]andBER

9 shows

E is changing,f. andbit

areshownwhilecanquency
especiallythetiuencedmeanconcludejc cannot
byBER

performanceof E cannot

Itmeans

E. Fig.

spiralrate

was atproducebit

10 shows

error

wasBER

while

case BER

tends

decreases,

case BER

that

that

high

producetends

theotherto be slightly

double- scroll

case is strongly
circuits.

theytransmitted

been

voltagechaotic

by highinTheya suitable

to thefre-

and thatchaotic
to applysignalE or lower

performance- demodulation

it is importanthave

voltagea goodor information

4.

bit

rate

signalandfrequency

carrier.

CONCLUSIONS

article,estimation

communication

systemulation

have

that

systems
nonlinearity

influenced
tion

chaos

quality.

nicationof BER
includingbeen

performancein chaosmodulation- demod-investigated.

We confirmedof modulation-

demodulationsynchronization

andIt

is importanttosystems

considering

influence

also

designcircuits
communica-

chaos

commu-of modulation-demodulation.

5.
[1]

Special1076,[2]

on Applications

Sessionon SpreadAug.

8, 9 andj,v~

information

signalbitof digital

information

furcation

1037–andfrom

G. Kolumb6n,
Theoryvol.

K. S. Halle,viaCommunica-

1, pp.

pp.

“ChaosCom-Implementation,”272–277,

K. Eckert

Demonstration
ChaotictoAug.

1997.

and L. O. Chua,of Secure

Synchronization,”

Chaos, vol. 2, pp. 709-713,1992.

0-7803-4455-3/98/$10.00 (c) 1998 IEEE

1,

1997.

P. Kennedy“ExperimentalSpectrum

Proc. ECCTD ’97, vol.

Chaos,[4] L. Kocarev,

frequency

in Com-2, pp.

1997.

andnicationof ChaosISCAS ’97, vol.

Proc.

Jun.

SpecialM.

REFERENCES

Sessionmunications,influence

E of therate

as E
attrac-voltages

single-modulation

272-341,

circuits.

in Figs.

carrierare
BERcase was decreasing

as bit- scroll

respectively.

case of single-spiral

best

Thereducedob-ratereduced.

was con-of communication- demodulation[bps],of BER.

Proc. ECCTD’97,

modulationof BER- spiralof Fig.

by voltage

doubletions

BER

showsof single

thetheBERtheaffected[3]

for the estimation

results
8 firstly

is changing,is fixed

BER

includingSimulated
10. Fig.

ofcasetoOthera better

6,quality.

Simulationtransi-in the

E= O.1O[V].

munications:
3.2.

a little

has

attractor

However,

we can confirm

way,

Meanwhile

only

it

and 2.65x103

directly

signals

inputting

bit

fixed

while

perfor-– v(C1’),

forby

and modulation-demodulationon communicationv(C1),
sumis theinformation7, some7, re-waveform

10–4 [see].

circuits

simdouble-

6 andas 2.65x

original

receivercircuits.

ofchosen
3.78x

and

waveform

signalresults

In thisof chaoticv.

tainedspiralthe BER

as ~C increases.

Secondlyandcomputer(f)attractor.

ratecase of singlethat

case,

contradistinction

chaotic

aroundtheis(c)v(C1’),

parametersrate

betterchaoticforIn

We alsosystemin Figs.

is demodulated

circuitperformance.

spiraloriginal

filteredsuitableThesingle-are shown

waveform

reproduced

error

same

signal.

of theinformation

chaotic

chooseagree

informationthat
com-circuits.

the case of transmission

resultscase ofknown

synchronization

results

including

is digital

wassynchronizationof thesignal

original

thethe orig-

for theitsimulationulated(b)side.

reproduce

demodulation

we consider

spectively.

at the receiverespecially- scroll

anyis going- scroll

Weandcannot

completely,

mancedoublechaotic

waveform,[bps].

we can confirm

to be violently

is re-

doubledue to the modulation-

original(a-3)

waveformachieveissignal,

is demodulated

We can see that

and(a-1)

betweenchaotic

waveform,

attractor,

tor,

at the transmit-

synchronization

chaotic

as 2.65x103

chaotic

increases.

5 are com-respectively.

chaotic

is fixedof theamplitude

4 andcase of single-spiraland reproduced

signalsignalChaotic

in thethe original

chaotic

chaotictransistor

3(a).

constructed

inal

only

attractors,

from

shows

Demodulation

is modulated.

a typical

resultster

cal-circuit.

andcase thatin Fig.

chaotic

attractor

cantioncircuitbycircuitputer

chaotic

as 8.4[kHz]circuit

SIMULATION

we consider

side,Weof theof Modulation

obtained
modulation

respectively.

L in Chua’sof Cz and3.
3.1.

(b),

frequency

Commu-Int. J. Bi-(a)FigureaMM(b)1: Chua’scircuit.

(c)

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