PERFORMANCEJunji

COMPARISON
OF COMMUNICATIONUSING CHAOS SYNCHRONIZATION

Kawatal,

Yoshi@mi

1 Tokushima Bunri University,

Nishio2,

2 Tokushima

University,

the performanceof some communication

systems

is evaluated and compared.

The eval-

1. INTRODUCTION
chaos and its possible

application

to communications

have received a great deal of attention. At the beginning vigorous
efforts for communication
schemes utilizing chaos synchronization [ 1]–[5] have been paid, while in the most recently studies onmultiple access digital communications
employing the property ofwide-band and uncorrelated chaotic signals [6]–[9] have attractedattention. For realization of chaos-based communication
systems,in either case, it is of significance to find or develop communication systems with a practically usable performance.
In this sense
performance evaluation of chaos-based communication
systems
and those comparison are very important.
However performancecomparison of chaos-based communication
systems have been reported only in [6],[9]. Further it has been pointed out that chaos
synchronization
can not be used for communications
because of
the effect of a noisy and band-limited
channel [6],[7].
Howeverthis has not been confirmed for all communication
systems using
chaos synchronization.
Therefore in this study we evaluate the performance of somecommunication
systems using chaos synchronizationand comparethem in order to confirm whether the assertion is true or not andwhich system has best performance.
As examples of communication systems using chaos synchronization,
the chaotic masking[1], chaotic coding [2] and chaotic modulation [3],[4] systems aretaken in this article, which are shown in Figs. 1–3. In order toconsider

the attenuation,communication

impedancemismatchand noise of realchannels, we use a channel model shown in Fig.

4. In this model, a transmission line is matched with its matching impedance, where an additive white Gaussian noise is added
to the transmission

signal similarly

to [7],[9].

An amplifier

is tocompensate the effect of attenuation as in [10].
For the performance evaluation the bit error rate (BER) is simulated for not lossy and noisy communication
channel but ideal
one, because the BER of chaos-based communication
systems is
not always zero even for noise-free case. The BER evaluation of
three systems is done and it seems that the performance of chaotic
coding and modulation
analog communication

and Akio

Ushida2

770 Japan,

CH- 1015, Lausanne, Switzerland

2. CHAOTIC

uation of bit error rate is done for not ideal communication
channelbut lossy and noisy one. It is confirmed that a chaos-based communication system has a good performance which may be almost
the same compared with conventional analog modulation schemes.

Recently

Tokushima,of Technology,

ABSTRACT
using chaos synchronization

Dedieu31314-1 Shido, Okawa, 769-21 Japan, kawata@is.bunri-u.ac.jp,

3 Swiss Federal InstituteIn this article,

Hervk

SYSTEMSsystems are as good as that of conventional
schemes.

COMMUNICATIONThe circuit configurations
tems investigated

SYSTEMSof the chaos-based communication

sys-in this article are shown in Figs. 1–3.

In the chaotic masking system [1] shown in Fig. 1, an information signal s(t) is masked by chaotic signal Vcl generated by
the transmitter and then transmitted. Subtracting the signal I&l reproduced by the receiver from the received signal, the informations’(t) can be recovered if the transmitter and receiver synchronize.
In the chaotic communication
system [2], an information signal s(t) is coded by the chaotic signal Vcl. The system using acoding function c = VCI + s(t) is shown in Fig. 2. The modulated signal VR (t) is transmitted to the receiver. The information
signal can be recovered as the potential s’(t) when the transmitter and receiver synchronize.
We call the system chaotic coding
system to discriminate from chaotic modulation system [3],[4].
In the chaotic modulation
system [4] shown in Fig. 3, a current signal i.(t) which depends on an information
signal s(t) isinjected into the transmitter and modulates the chaotic signal Wcl.
The modulated signal Vcl is then transmitted to the receiver andthe recovery of information
can be achieved by detecting the current Zd(t) flowing into the receiver.
The transmitter and receiver in all systems are constructed by
Chua’s circuit and connected with a communication
channel. In
the systems we can expect that if the channel is lossless, perfectlymatched and noiseless then the transmitters and receivers will synchronize. But real communication
channels are lossy, noisy, andoften imperfectlymatched, the performance of the systems mustbe evaluated under such conditions. For the purpose proper channel models are required. In [7],[9] AWGN (additive white Gaussian noise) channel models have been used. We will use a model
as shown in Fig. 4. This model contains a transmission line andits matching impedance. The transmission line is further modeledby convenient models [ 11],[ 12] shown in Fig. 5 which are widelyused for the transient simulation of transmission lines. An additive
white Gaussian noise is added to the transmission signal similarly
to [7],[9]. An amplifier is to compensate the effect of attenuation
as in [10].
In order to evaluate the performance fairly we fix the parameters of Chua’s circuitin all systems as follows:

R = l/G = 1700[Q],C, = 10[nF], C5 = 100[nF],
L = 18[mH],rrzo = –0.75[mS],rn, = –0.41[mS],
B,=
1 [v]
and the line parameters:
Rd = 20[~/km],
Ld = 0.25[mH/km],
cd = 100[nF/km],
Gd = OIS/km]

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(1)

The value of matching

impedance

is calculatedby the following

equation.

Zm=Izo(jcd)l=G3. PERFORMANCEIn this section we investigate
formance evaluationthat the SNR requiredtion is about 60[dB].

COMPARISON

the bit error rate (BER) for the per-of the systems. The performanceis evaluatedfor not only lossy and noisy communication
channel but also ideal
one, because the BER of chaos-based communication
systems is
not always zero even for noise-free case. In all of evaluations
we simulate the systems using fourth
where a bit sequence withsignal.

order Runge-Kutta

104 bits is transmitted

First the ideal BER performance=50[f2], T =0.5[msec]and K

sys-1, where K is the gainof the amplifier.
The ideal performance is shown in Fig. 6 The
chaotic masking system can cause undesirable transients at bit
switching of information digital signal, which often result in desynchronization (bit error). So a low-pass filter (LPF) is introduced inorder to reduce the transients and its output is used for the BER
evaluation.
Note that it is not shown in Fig. 1. In the chaotic
coding system the BER for smaller amplitude is only shown because the system became unstable for larger one. In contrast tothe chaotic coding
chaotic modulation

to detect the current

id in thesimulation. We can evaluate it only by applying difference approximation, but this caused “spike-like”
error in the recovered signal
when \clv~l /dtl becomes larger. Smaller amplitude is affected
fairly by this error, thus relatively larger amplitude is used.
In the chaotic masking system the BER becomes better if bit
rate is lower. On the other hand, in the chaotic coding and modulation systems, the BERs are less than 10–4 and remain unchanged
for the change of amplitude and bit rate. They have a good perfor-

as analog com-munication

schemes, but this must be confirmedwith increasingtransmission

bits at least by 106. In the point of implementation

the chaotic modulation system has advantages, because the chaotic
coding system has the current-controlleddependent source and it
is difficult

for the carrier-to-noise

to realize ideal one.
4. CONCLUSIONSIn this article we have evaluated the performance of some communication systems using chaos synchronization and compared them.
The chaotic

codingand modulation

system have a good perfor-

mance even if their parameters have a small mismatch. The chaoticmodulation system has advantages in the sense of good quality andfacility for realization.
We intend to evaluate the performance of other chaos-based
communication
systems, e.g., chaotic inverse system.
5. REFERENCES[1]

L. Kocarev et aL, “Experimental demonstration of secure communication via chaotic synchronization;’ Int. J. Bijurc. Chaos, vol. 2, pp.
7’09-713,

1992.

[2] C. W. Wu and L. 0, Chua, “A simple way to synchronize
systems with applications to communications,”
VO1. 3, pp. 1619–1627,
1993.

through modulation of chaos;’ [nt. J. Bijia-c. Chaos, vol. 2, pp. 469–477, 1992.

[4] M. Itoh, H. Murakami

and L. O. Chua, “Communicationsystems via
chaotic modulations,” IEICE Trans. Fundamentals., vol. E-77-A, no.
6, pp. 1000-1005, Jun. 1994.

[5] H. Dedieu,

M. P. Kennedy and M. Hasler, “Chaos shift keying
Modulationand demodulationof a chaotic character using selfsynchronizing
Chua’s circuits,” IEEE Trans. Circuits Syst. II, vol.
40, no. 10, pp. 634-642, Oct. 1993.

ratio (CNR) is

evaluated regarding the chaotic signal generated in the transmitterswith no input signal as the carrier signal. In general the signal-tonoise ratio (SNR) is used for performance evaluation, but the av-[6] G. Kolumban et al., “Performanceerage power of information[7] M. P. Kennedy, “Chaos communications:signal in the three systems is different

because of the above mentioned reason. Consequently the performance comparison using SNR is not fair, thus we prefer to use
CNR than SNR. For the parameters of transmitter (1) the average
power of the carrier in all systems is about 3.586. Also it can be
expected that the recovered signals are affected by noise and so on,thus a LPF is introduced

in order to reduce such effects. The LPF

with the time constant 0.2[msec]
estimation,

is used for the following

BER

of noise performance,chaos communication
1996.

evaluation and comparison ofsystems,” Proc. of NDES ’96, pp. 105–1 10,tation,” Proc. of ECCTD’97, pp. 272–277,

From theory to implemen1997.

[8] G. Kolumb&r,

M. P. Kemedy and G. Kis, “Performance improvement of chaotic communication
systems,” Proc. of ECCTD ’97, pp.

284-289, 1997.
[9] J. Schweizer, “’Performance comparison of periodic and nonProc. of ECCTD
periodic wave forms in digital communication”’97, pp. 330-335, 1997.
[10] J. Kawata, Y. Nishio,

which is not shown in Figs. 1–3.

In the estimation

chaotic
Int. J. Bi@-c. Chaos,[3] K. S. Halle et al., “Spread spectrum communication

mance for ideal conditions.
Next noise performance

10–6 in analog communica-

the chaotic coding and modulation

systems may have almost the same performancesystem, only larger amplitude is used for thesystem. In the system the quantity Cl cJo&/dt

in the receiver must be estimatedthemethodof the communication=to get BER

Therefore

as information

tems is evaluated for ideal channel (i.e. the channel is lossless, perfectly matched and noiseless). The channel parameters are 20 =Z~

lation systems become better as noise decreases. In particular

BERs of the chaotic coding and modulation systems are less than
10–4 for CNR 40[dB] and over, similarly to ideal case. Moreover
this is also applied to the case that there is a small parameter mismatch between the transmitter and receiver. It is generally said

digital1[km] Iossy transmis-sion line is used, where the number of cells JV is 25 and the gain K
is 1.06. Fig. 7 shows the BER obtained. Further the performancefor small parameter mismatch on linear resistor R is also investigated and illustrated, because it is difficult to match perfectly thecomponent values of the transmitter and receiver in real circuits.
For larger noise level the chaotic masking system has a best performance, while the performance of the chaotic coding and modu-H. Dedieu and A. Ushida, “Transmission
ofsignal and evaluation of bit error rate in a chaotic masking

communicationsystem.” Proc. of ECCTD’97, pp. late21- l–late21-4, 1997.
[11]

F. H. Branin, Jr., “Transient analysis of lossless transmission
Proc. IEEE, vol. 55, pp. 2012–2013, Nov. 1967.

[12]

H. W. Dommel, “Digital computer solution of electromagnetic transients in a single or multiphase networks,” IEEE Trans. Power App.
Sy.st., vol. PAS-88, pp. 388-399, Apr. 1969.

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

line;’s(t)channel:6R}

~Li?

LL
—

—

Trarrsmitter

ReceiverFigure1: Chaotic masking

system.

+ s’(t)++)3

channels(t)RRtL&+L&~;

471

v&2

c,—c,—

Transmitter
Figure2:—

Receiver

Chaotic cdingsystem.

~edimond

shaped cuentsource

isacument-controlled‘E’)‘mLcIT””l~ (%Transmitter

ReceiverFigure 3: Chaotic

modulation

system.

white Gaussian
noise
AmplifierINdependent source,Transmission

lineK
1P
z.

matching
impedance-——

Figure4

Channel model using transmission

line.

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.----------------.----.
;+lt 2N#1il

i2#2+ZllztJ‘uel——ez—Gdl
2Ncell(b)(a)

Figure 5: (a) Characteristic~o-lmodel of lossless transmission

.

~o-l

$m

P4
Q

10-2 10-3.

amplit~de=O.001 ~amphtude=O.OI *amplitude=O.I ~
1o-.

~03

102

system.

104-line and (b) modelinggm

10-2 -:L
102

103

(a)

(b)
in the chaotic communication

For only chaotic masking

systems.

-line.

anrplitude=O.I eamplitude= 1 u--

10-2:L~oz

104

bit rate [bps]of lossy transmission

1o-1

amplitnde=O.001 u-amphtude=O.O1 -o--bit rate [bps]Figure 6: Ideal performance
modulation{t--.---------.---------.

3E3W~~TLu

10SS1’C?SS
line

~———

: Gdl
:%

V2
—

t

losslessline+++#N~~

2N

losslessline

~03

104

bit rate [bps](c)(a) chaotic masking

system, (b) chaotic coding system, (c) chaotic

system a LPF with the time constant 0.2[msec]

is used. The dark shaded mark denotes a

BER less than 10-4.

1001’~o-l

1

no mismatch e0.2?70mismatch U-

no mismatch -o0.2% mismatch -&!-Qm 10-2
10-3

10–4

1020

30

4050

60

1020

CNR [dB](a)
Figure 7: Noise performance

4050

*60

10

CNR [dB](b)in the chaotic communication(b) chaotic coding system (amplitude=O.Ol

30systems.

[V], bit rate=2000[bps]),

For all systems a LPF with the time constant 0.2[msec](a) chaotic masking(c) chaotic modulation

20304050●:60

CNR [dB](c)system (amplitude=O.1[V], bit rate=200[bps]),system (amplitude=0.5[V],is used. The dark shaded mark denotes a BER less than 10-4.

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bit rate=2000[bps]).