a chaos based secure direct sequencespread spectrum

8/10/2019 A Chaos Based Secure Direct SequenceSpread Spectrum

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Hindawi Publishing CorporationAbstract and Applied AnalysisVolume , Article ID , pageshttp://dx.doi.org/ . / /

Research Article A Chaos-Based Secure Direct-Sequence/Spread-SpectrumCommunication System

Nguyen Xuan Quyen, Vu Van Yem, and Thang Manh Hoang

School of Electronics and elecommunications, Hanoi University of Science and echnology, Dai Co Viet, Hanoi, Vietnam

Correspondence should be addressed to Tang Manh Hoang; [email protected]

Received October ; Revised November ; Accepted November Academic Editor: Ivanka Stamova

Copyright Nguyen Xuan Quyen et al. Tis is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Tis paper proposes a chaos-based secure direct-sequence/spread-spectrum (DS/SS) communication system which is based on anovel combination o the conventional DS/SS and chaos techniques. In the proposed system, bit duration is varied according to achaotic behavior but is always equal to a multiple o the xed chip duration in the communication process. Data bits with variableduration are spectrum-spread by multiplying directly with a pseudonoise (PN) sequence and then modulated onto a sinusoidalcarrier by means o binary phase-shif keying (BPSK). o recover exactly the data bits, the receiver needs an identical regenerationo notonly thePN sequence but also thechaoticbehavior, andhencedatasecurity is improvedsigni cantly. Structureand operationo the proposed system are analyzed in detail. Teoretical evaluation o bit-error rate (BER) per ormance in presence o additive

white Gaussian noise (AWGN) is provided. Parameter choice or different cases o simulation is also considered. Simulation andtheoretical results are shown to veri y the reliability and easibility o the proposed system. Security o the proposed system is alsodiscussed.

1. Introduction

Studying the possibilities o using chaotic behavior [ , ]to improve eatures o communication systems has receivedsigni cant attention in the last several years [ ]. Many chaos-based communication systems were proposed [ , ]and most o them exploited chaotic behavior to convey in ormation. Communication systems basedon combinationo direct-sequence/spread-spectrum(DS/SS) and chaos tech-niques were presented in [ ]. It is well known that DS/SSis considered as a main technique o spread-spectrum digitalcommunications [ , ]. Te main difference between theconventional and chaos-based DS/SS systems is the use o spreading sequence. Instead o using the pseudonoise (PN)sequence [ , ] as in the conventional system, the spread-and despread-spectrum processes in the chaos-based systemare carried out by multiplying directly the binary data witha chaotic sequence generated by a chaotic map [ , , , ].

ime domain signals shown in Figures (a)and (b)illustratethe difference in the conventional and chaos-based DS/SS

systems, where and are xed bit and chip durations,respectively.In this paper, we propose a chaos-based secure DS/SS

communication system which is the combination o theDS/SS and chaos techniques. Bit duration is varied accordingto the behavior o chaotic map but always equal to amultiple o the xed chip duration. Variation in bit durationmakes the difference between our proposed system and theconventional ones. Te data bits with variable duration arespread in the requency domain by multiplying directly withthe PN sequence and then modulated onto a sinusoidalcarrier by means o the binary phase-shif keying (BPSK)[ , ]. Te spread-spectrum process o our proposed chaos-based DS/SS system is illustrated by time domain signalsas in Figure (c), where is the variable duration o theth bit. Since the proposed system operates based on theDS/SS using PN sequence, it inherits all advantages such asinter erence rejection, antijamming, ading reduction, multi-access potential, and low probability o interception rom theconventional DS/SS system [ , ]. In addition, data security


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Abstract and Applied Analysis

Binarydata

PNsequence

Spreadingsignal

T c

T b1

1

1

1

1

1

t

t

t

(a) Te conventional DS/SS system [ ]

Chaoticsequence

Binarydata

Spreadingsignal

T c

T b1

1

1

1

1

1

t

t

t

(b) Te conventional chaos-based DS/SS system [ ]

PNsequence

Spreadingsignal

T c

1

1

1

11

1

t

t

t

Binary data withvariable bit duration

T bnT b(n1) T b(n+1)

(c) Te proposed chaos-based DS/SS system

F : ime domain signals o the spread-spectrum process in the conventional and proposed DS/SS systems.

is improved signi cantly since the despread-spectrum anddata recovery process needs an identical regeneration o boththe PN sequence and chaotic behavior.

In the remainder o thepaper, thestructureand operationo the proposed communication system is presented inSection . Teoretical evaluation o BER per ormance inpresence o additive white Gaussian noise (AWGN) is provided in Section . Section presents analysis o parameterschoice or the system, based on that speci c parameters

or different cases o simulation system are chosen withproper values. Simulation results are then shown to veri y the theoretical ones. Discussions on security eatures arepresented in Section . Finally, theconclusion with some nalremarks is given in Section .

2. Structure and Operation of Chaos-BasedSecure DS/SS Communication System

In this section, we present a detailed analysis o the structureand operation o the chaos-based DS/SS communicationsystem proposed. Basically, the proposed system is builtaround a variable-position pulse and PN sequence (VPP-PNS) generator. Block diagrams o the proposed system andthat o the VPP-PNS generator are illustrated in Figures (a)and (b), respectively.

. . VPP-PNS Generator. In the VPP-PNS generator, clock pulses with a xed requency, = 1/, at the output o theclock generator are ed to the counter and the PN generator.

At the initial instance 0 , the clock generator starts workingand the sample-and-hold block (S/H as in Figure ) is loadedinitial value

0 . Te counter operates in ree running mode

to produce a discretely increasing signal, ( ) = 0

) =, at itsoutput,where is count-step (i.e., the increasing value in a clock cycle ) and is the count-number (i.e.,the number o input clock pulses rom the initial instance).When the signal ( ) reaches the value, 1 = (0), atthe output o the nonlinear converter (i.e., the block ()using the one-dimension chaotic map, = (1)), thecomparator generates a pulse with a xed width at theinstance, 1 = 0 + 0 . Te position o pulse at the output is determined by the interval, 1 0 = 1/ , with being the oor unction. Tis pulse simultaneously triggersthe PN sequence generator to start working and to allow S/Hstoring the value 1 . Afer that it triggers the counter to reset

thecount-number to zero.New iteration startsandpulses willbe generated as in theabove description. Ingeneral, the pulsetrain at the output is expressed as ollows:

() = =1 , ( )where the th pulse is generated at the instance

= 1 + 1 = 1 + , ( )


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1 12 2

Integrator Decisiondevice

Channel

Sampler

Transmitter Receiver

Reset

VPP-PNSgenerator VPP-PNSgenerator

Datasource

p(t) p( t)c( t) c(t)

b(t) d(t) e( t) r ( t) bn

n(t)

i( t)g (t) s(t) i(tn+1)

Acos(2f 0t) Acos(2f 0t)

(a) Te block diagram or the proposed chaos-based DS/SS communication system

+

Reset

Start

PN sequencegenerator

Counter Comparator

Clockgeneratorf c = 1/T c Xn1

S/H (X0)

T c

X( t)

XnF ( .)

c(t)

C(t)

p(t)1

2

m

(b) Te block diagram or the VPP-PNS generator

F : Structure o the proposed chaos-based DS/SS communication systems.

and its position is determined by the interval

0 =

=1 =

=1( ) 0 . ( )

( ) is the rectangular pulse shaping unction given by () = 1, 0 ,0, otherwise. ( )

It can be seen that the position o output pulses ( ) variesaccording to the chaotic signal ( ). With a speci c initialinstance 0 , ( ) points out that variation o position dependson the chaotic map (), initial value 0 , and count-step .Te PN sequence generated at the output with the xedchip duration o is expressed by a nonreturn-zero (NRZ)pulse train as ollows:

() = =1=1 ( 1) , ( )where and are the binary values (i.e., {1}) o the thchip and the number o chips in the duration o [, +1],respectively; the unction ( ) is as in ( ).

. . ransmitter. In the transmitter, each pulse o the train

( )triggers the data source to shif the data bit to the output.

It means that the nth bit is shifed at the instance and itsduration is equal to the interval o [,

+1

]. Based on ( ), the

duration o the nth bit is determined by

= +1 = = +1 = ( +1)

0 .( )

Equation ( ) shows that the bit duration varies accordingto the chaotic signal ( ) and depends on (), 0 , and .With a certain chaotic map (), in the iteration process, itsoutput values vary chaotically in the dimensionless range o [ min , max ]. Tis leads to the variation in the bit durationwithin the time range o [ min , max ]in the communicationprocess. Since the chip duration is xed, the number o chips per bit, = / , called the spreading actor, also varies in the range o [min , max ] what is determined in ( )as

min = min = min ,max = max = max .

( )

In the design process, the values o the parameters , min ,and max are predetermined to guarantee desired speci ca-tions o the system such as the bandwidth, average bit rate,


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and BER. Te chaotic map (), the range o [min , max ],and the count-step are then chosen so as to satis y ( ). Teanalysis o this choice will be presented in Section . .

Te binary data with variable bit duration at the output o the data source is ormatted in NRZ pulses and expressed by

() =

=1 , ( )where is the binary value (i.e., {1}) o the nth bit, and( ) is the rectangular pulse shaping unction de ned by () = 1, 0 ,0, otherwise. ( )

Te spectrum spreading process is carriedout by multiplyingthe data ( ) with the PN sequence ( ). Te spreading signal( ) is then modulated onto a sinusoidal carrier by means o BPSK, producing the DS/SS-BPSK signal given by

() = ()()cos

20

, ( )

with and 0 being the amplitude and requency o thecarrier, respectively. Te resulting signal ( ) is transmittedat the output o the transmitter.. .Receiver. Te VPP-PNSgenerators in the transmitter and

receiver are designed to work as digital modules which can beimplemented on the programmable devices such as the eldprogrammable gate array (FPGA), digital signal processing(DSP), and microprocessor (MP). In practice, this designcan be guaranteed such that there is nearly no parametersmismatchbetween the VPP-PNSgenerators. Itmeansthat the variable-position pulse train and PN sequence regenerated inthe receiver are identical to those in the transmitter. Tere-

ore, we can apply the available synchronization methods o the conventional DS/SS system [ , , ] or the proposedsystem. Here, or simplicity, the operation o the receiverassumes that the synchronization in the sinusoidal carrier, variable-position pulse train, and PN sequence is establishedand maintained.

Te received signal ( ) at the input is the sum o thetransmitted signal ( ) and channel noise ( ). Firstly, thereceived signal is multiplied with the PN sequence as ollows:() = ()() = (() + ())()= ()

2

()cos

20

+ ()()= ()cos 20 + ()(),( )

andthen the resultingsignal ( )is mixed with thesinusoidalcarrier by () = ()cos 20= ()cos2 20 + ()()cos 20= 22 () +

2

2 ()cos 40+ ()()cos 20 .( )

Te signal ( ) is ed to the integrator whose output isreset to zero by the trigger o each pulse o the train (.It means that the integration period o each bit is equalto the corresponding interpulse interval which is also thecorresponding bit duration. Be ore each reset instance, theoutput signal o the integrator, ( ), is sampled. Te output value o the sampler at the instance

+1 is determined by

+1 = +1 ()= 0

2

2 () + 02

2 ()cos 40+ 0 ()()cos 20

= 2

2 + 0 + 0 ()()cos 20

( )

where (2/2) is the energy o the desired signal;0 (2/2 )( )cos(40 ) equal to zero because the period is a multiple o the carrier cycle (i.e., 0 = 1/0);0 ( ) ( )cos(20 ) is the energy produced by the

channel noise. It is noted that the correlation between (and ( )cos(20 )isvery low and hence the noise energy ismuch less than the signal energy. Finally, the resulting sampleis ed to the decision device to recover the binary value o thenth bit as ollows:

= 1, +1 0,0, +1 < 0. ( )3. Theoretical Evaluation of BER Performance

In this section, BER per ormance o the proposed com-munication system with the channel noise being AWGNis evaluated theoretically. In the receiver, at each samplinginstance, an error decision leading to an error bit occurswhen the noise energy exceeds the signal energy in theopposite direction. Tere ore, signal-to-noise ratio (SNR) o each output sample is a key parameter or estimating theBER o the system. Let us consider the value o the ( + 1thsample with two energy component as given in ( ). Te rstcomponent is the signal energy whose absolute magnitude isdetermined by

= 22 = 2

2 . ( )Tesecondone is the noise energy which isa randomvariabledepending on the zero-mean Gaussian noise

( ) and thus


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its mean is also zero, while its variance can be calculated asollows:

2 = 0 ()()cos 202

= 2

0

2 02

()cos2

20 = 2

0

4 ,( )

where [] is the statistical expectation and 0 is the noisepower spectral density. Te SNR o the ( +1)th sample, SNR ,is determined as the absolute magnitude o the signal energy,, divided by the root-mean-square noise 2 [ ], so we

have

SNR = 2 = 2

0 = 2

0 = 2 0 ,( )

where = 2 /2is xed, and calledthe energy per chip; theratio / 0 is known asthe SNR per chip. It can be seen rom( ) that the SNR o each output sample depends on the ratio/ 0 and the correspondingspreading actor . Tere ore,the SNR or general case o the spreading actor being equalto is given by

SNR , / 0 = 2 0 . ( )In our proposed system, since the spreading actor varies

rom min to max in the communication process, the BER is estimated approximately by BER [ min , max ], / 0 =

max= min BER , / 0, ( )where is the probability to the spreading actor beingequal to , and BER , / 0 is the BER o the system orcase o the spreading actor being equal to . Assume thatthe chaotic values distribute uni ormly in [min , max ]. Itmeans that the probability is the same or all values o

[min

,max

], so we have

= 1max min + 1. ( )Based on the evaluation result o the error probability or theconventional DS/SS-BPSK system as mentioned in [ , ],the BER , / 0 is determined according to the SNR , / 0 by

BER , / 0 = SNR , / 0with [] = 1

2 2 /2 . ( )

From the obtained results in ( ), ( ), ( ), and ( ), thetheoretical evaluation o the BER per ormance or the pro-posed communication system is given by the ollowing:

BER [ min , max ], / 0

= 1max min + 1max= min 2 0 .

( )

Te evaluation BER per ormances according to ( ) ordifferent cases o [ min , max ]with the same average spread-ing actor as well as their comparison with the per ormanceo the equivalent conventional system are shown in Figure .With the above assumption o the uni ormly distributedchaotic values, the average spreading actor and averagebit rate are determined by

av

= (min

+ max

)/2 and

BR av = 2/((min + max )), respectively. In Figure (a), theper ormances o the proposedsystem or the cases o [ min =26,max = 36] and [min = 21,max = 41], are comparedto each other and to that o the conventional system [ ]which has a xed spreading actor, = av = 31. It canbe seen that the proposed system with the case o [min =26,max = 36]per orms slightly worse than the conventionalsystem with = 31 and better than the [min = 21,max =41] case. Similarly, we can observe rom Figure (b) that theper ormanceo [ min = 53,max = 73]case is between thoseo the conventional system with = 63 and the case o [ min = 48,max = 78]. It is clear that the per ormanceo the proposed system with

[min

,max

] is poorer than

that o conventional system with = av . In addition, thedifference between the per ormance o the proposed systemand that o conventional one tends to diminish as the average value (min + max )/2 gets closer to = av .4. Parameter Choice and Simulation Results

Tis section presents the analysis o parameter choice orthe proposed system. Based on the analysis, the speci cparameters or different cases o the simulation system arechosen with proper values. Te simulation results are thenshown inorder toveri yall thetheoreticalanalysesandresultsobtained.

. . Parameter Choice. In order to guarantee the desiredspeci cations o thesystemsuch as thebandwidth(i.e.,BW =1/), average bit rate (i.e., BR av = 2/((min + max ) ), andBER (i.e., BER [ min , max ], / 0 according to ( )), the valueso parameters , min , and max are predetermined. Techaotic behavior o the chaotic map () is based on that o a conventional chaotic map, = (1), denoted by (),whose output values vary in a known range o [min , max ].Te parameters , min , and max and the map () areconsidered as the predetermined parameters o the system.


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B E

R

107

106

105

104

103

102

101

13 12 11 10 9 8 7 6 5 4 3Ec /N 0 (SNR per chip )

Conventional system, N = 31Proposed system evaluation, (N min = 26, N max = 36)Proposed system evaluation, (N min = 21, N max = 41)Proposed system simulation, (N min = 26, N max = 36)Proposed system simulation, (N min = 21, N max = 41)

(a) Te conventional system with = 31 , the proposedsystem or min = 26 , max = 36 and min = 21 , max = 41

B E

R

107

106

105

104

103

102

101

13 12 11 10 9 8 7 6 5 4 3Ec/N 0 (SNR per chip )

Conventional system, N = 63Proposed system evaluation, (N min = 53, N max = 73)Proposed system evaluation, (N min = 48, N max = 78)Proposed system simulation, (N min = 53, N max = 73)Proposed system simulation, (N min = 48, N max = 78)

(b) Te conventional system with = 63 , the proposedsystem or min = 53 , max = 73 and min = 48 , max = 78

F : BER per ormances obtained rom the theoretical evaluation and numerical simulation or different cases o the proposed systemin comparison to those o the equivalent conventional system.

Using these predetermined parameters, the count-step andthe chaotic map () are chosen as ollows:

= max minmax min , = + = 1 + = 1 + = 1 .( )

It is easy to nd that the output value o the chaotic map () varies chaotically in the range o [min = min + ,max =max + ] and thus the initial value 0 will be chosen in thisrange. Here, is a shif value chosen to satis y ( ) as ollows:

min min < min + 1 min . ( )Te count-step and the parameters ,0 o the map ()are called the chosen parameters o the system.

. . Simulation Results. Numerical simulations or differentcases o the proposed system with the speci c parametersare carried out in Simulink. Te values o the predeterminedparameters o thesimulation systemare given as ollows: =1 ; our cases o [min , max ] = [26,36], [21,41], [53,73],and [48,78]; three conventional chaotic maps simulated inturn are ent map, Logistic map, and Bernoulli map [ , ,

, ], whose output values vary chaotically in [min =0,max = 1]. Based on the choice analysis above, the valueso the speci cationsandchosen parameters o the simulationsystem corresponding to the different cases o [min , max ]are determined and shown as in able .

ime domain signals obtained rom the simulation sys-tem using ent map or the case o

[min

= 21,max

= 41]

within duration rom the starting time 0 to 1000 arepresented in Figure . When the synchronization state o system is established and maintained, the signals o the VPP-PNS generators in the transmitter and receiver are identicaland shown as in Figures (a) (d). Te baseband signals in

the transmitter and receiver are given in Figures (e)- ( )and Figures (g) (i), respectively. Te chaotic behavior thenonlinear converter () is seen by the attractor diagram inFigure (a). It isclear thatthisis the attractoro ent map aferbeing shifed with a positive value, = 1.075. Te variationin bit duration according to the chaotic behavior is given inthe diagram as in Figure (b), where each point expresses therelation between the duration o previous bit and that o thepresent one. It can be seen that the bit duration varies in therange o [ min = 21 ,max = 41 ].

BER per ormance o the simulation system using entmap or the cases o [min = 26,max = 36], [min = 21,

max

= 41],

[min

= 53,max

= 73],

[min

= 48,max

= 78is presented in Figure to compare with the correspondingtheoretical per ormance. In order to investigate the per or-mance o the proposed system with different chaotic maps,the simulation systems using ent, Logistic, and Bernoullimaps or the cases o [min = 21,max = 41] and [min =26,max = 36] are carried out and the result is as shownin Figure . Here, the simulation BERs are calculated as thenumber o error bits divided by the total number o 108bits transmitted and the channel noise is AWGN. It canbe seen rom Figure , or each case, that the simulationand corresponding evaluation curves are nearly the same.Also, Figure shows that there is a slight difference in thesimulation curves o the different chaotic maps. Tese prove


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T : S p e c i c p a r a m e t e r s o f t h e s i m u l a t i o n s y s t e m f o r c a s e s o f [

m i n , m a x

] = [ 2 6 , 3 6 ] , [ 2 1 , 4 1 ] , [ 5 3 , 7 3 ] , [ 4 8 , 7 8 ] .

P r e d e t e r m i n e d p a r a m e t e r s

S p e c i c a t i o n s o f s y s t e m

C h o s e n p a r a m e t e r s

C h a o t i c m a p

[ m

i n , m a x

]

( ) :

=

(

1 )

[ m

i n = 0 ,

m a x

= 1 ]

B W

B R a v

B E R

( ) :

= (

1 )

[ m

i n =

, m a x

= + 1 ]

0

[ 2 6 , 3 6 ]

T e n t m a p :

= 2 0

. 5

0 . 5

1

.

K b p s

B l u e l i n e s i n F i g u r e ( a )

. / s

= 2 | 0

. 5

| 0 . 5

(

1

) | + |

.

.

s

[ 2 1 , 4 1 ]

L o g i s t i c m a p :

= 4

1 1

1

M H z

. / s

= 4 (

1

) ( 1

(

1

) ) +

.

.

[ 5 3 , 7 3 ]

[ 4 8 , 7 8 ]

B e r n o u l l i m a p :

=

2

1

m o d

.

K b p s

B l u e l i n e s i n F i g u r e ( b )

. / s

. / s

= ( ( 2 (

1

) ) m o d 1 ) +

.

.

.

.


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012

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1(ms)

C ( t )

(a) Te discretely increasing signal at output o thecounter

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1(ms)

11.41.8

X ( t )

(b) Techaotic signalat output o the nonlinear converter

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1(ms)

0

1 p

( t )

(c) Te variable-position pulse train at the output

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1(ms)

101

c ( t )

(d) Te PN sequence at the output

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1(ms)

101

b ( t )

(e) Te binary data with variation o bit duration

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1(ms)

101

d ( t )

( ) Te signal afer spreading

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1(ms)

500

50

i ( t )

(g) Te output signal o the integrator

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1(ms)

0 i ( t n

+ 1

) 50

50

(h) Te output signal o the sampler

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1(ms)

bn10

1

(i) Terecovered data bits at output o the decisiondevice

F : ime domain signals o the simulation system using ent map or case o [min = 21,max = 41].

1.1 1.3 1.5 1.7 1.9 2.1

1.3

1.5

1.7

1.9

1.1

2.1

Xn

Xn1

(a) Te attractor diagram o the chaotic map F ()

22 26 30 34 38 42

22

26

30

34

38

42

T bn

T b(n1)(s)

(b) Te variation diagram o bit duration

F : Te variation o bit duration according to the chaotic behavior.


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B E R

103

104

105

106

107

8 7 6 5 4 3Ec /N 0 (SNR per chip )

Simulation Tent map, (N min = 21, N max = 41)Simulation Logistic map, (N min = 21, N max = 41)Simulation Bernoulli map, (N min = 21, N max = 41)

(a) For the case o min = 21 and max = 41

B E R

103

104

105

106

107

8 7 6 5 4 3Ec/N 0 (SNR per chip )

Simulation Tent map, (N min = 26, N max = 36)Simulation Logistic map, (N min = 26, N max = 36)Simulation Bernoulli map, (N min = 26, N max = 36)

(b) For the case o min = 26 and max = 36

F : Simulation BER per ormances with different chaotic maps.

that the theoretical analysis and the result are reasonable andthe proposed communication system is totally easible.

5. Discussion on Security

It is clear that the conventional DS/SS-BPSK system, anintruder can break the security and recover success ully theoriginal data i he detects correctly the PN sequence and theintegration period which is equal to bit rate. Since the bitduration is the same and xed in the observation process, it isnot difficult or the intruder to detect exactly bit rate. Severaldetection methods o bit rate have been presented in [ , ].It means that the security o the conventional system mainly depends on the complication o PN sequence.

Since our proposed system is combined by the DS/SStechnique using PN sequence and chaotic modulation,the data transmitted by using the proposed system mustbe more secure rom eavesdroppers than that in case o using individual methods. In other words, the security hasbeen compromised by burying chaotic modulation in theconventional DS/SS technique. With the presence o theconventional DS/SS technique in the proposed system, thetransmitted signal has properties like random noise andoccupies a wide bandwidth with a very low power spectraldensity on the transmission channel. It means that theproposed system inherits the security advantages rom theconventional method such as the anti jamming capability and low probability o detection and interception [ , ].In addition, with the variation o bit duration according tothe chaotic behavior, the capability to protect data againstunauthorized accesses is improved signi cantly.

Morespeci cally, thedata security o theproposed systemis dependent onnot only on the complication o PN sequencebut also on the variation o the integration period (i.e., the

bit duration) according to the chaotic behavior. It is seenthat the generation o the chaotic behavior is quite simple

or the transmitter and the authorized receiver which has ullin ormation on the structure, the value o parameters and

unctions. In act, the exact regeneration o chaotic behaviorin the proposed system is very difficult or intruders tryingto detect them in the context that the chaotic system iscovered by the PN sequence generator. Due to the sensitivedependence o thechaotic behavioron the initialvalue, a very slight error in its detection leads to exponentially increasingerrors in the regeneration. In such case, the detection o the variation o bit duration is completely incorrect and thereceiver operates in the desynchronization state. As a result,BER will be very high and thus the unauthorized access is

ailed. Tese are proved by simulation results in Figures and, where the time domain signals and BER per ormances o

the receiver in the case o initial value mismatch (with a very small difference, 0 = 0.0001) are shown and comparedwith those in the case o no mismatch. We can observethat afer about 0.2ms rom the starting time, the mismatchsignals become totally different rom the corresponding no-mismatch signals. Te BER per ormance with the mismatchis much worse than that o the cases with no-mismatch.Particularly, although the ratio / 0 increases gradually, themismatches in BER are nearly unvaried and approximately equal to 1.6 101 . It is noticed that the set o values o ,0 ,and () is considered as a secret key. It is hard or theintruder to recover correctly the data without having ullin ormation on the structure o the system, the PN sequence,andthis secretkey. Furthermore, thegeneration o thechaotic values can easily be made as complicated as is desired. Forexample, instead o the one-dimension maps, we can usemultidimension chaotic ones. Also, several chaotic maps may be combined to increase the number o parameters involved.


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012

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1(ms)

(a) Te discretely increasing signal at output o thecounter

11.41.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1(ms)

(b) Te chaotic signal at output o the nonlinearconverter

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1(ms)

No mismatchInitial value mismatch

1

0

(c) Te variable-position pulse train at the output

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1(ms)

No mismatchInitial value mismatch

10

1

(d) Te recovered data bits at output o the decisiondevice

F : ime domain signals in the receiver o the simulation system using ent map or case o [ min = 21,max = 41]with no mismatchand with initial value mismatch ( 0 = 0.0001).100

101

102

103

104

105

106

10713 12 11 10 9 8 7 6 5 4 3

Ec/N 0 (SNR per chip )

(N min = 26, N max = 36) case, no mismatch(N min = 21, N max = 41)

N max = 41)

case, no mismatch(N min = 26, N max = 36) case, initial value mismatch, X0 = 0.0001(N min = 21, case, initial value mismatch, X0 = 0.0001

B E R

F : BER per ormances o the simulation system using ent map or cases o [min = 26,max = 36] and [min = 21,max = 41] withno mismatch and with initial value mismatch ( 0 = 0.0001).Te initial value can be changed or different communicationsessions. All these will improve signi cantly the security o the proposed method.

Mosto theattack methods areproposed in orderto break the chaotic communication systems [ ] operated basedon exploiting properties such as wave orm, spectrum, andattractor o the chaotic signal which masks the in ormationand is transmitted directly on the channel. In the proposedsystem, the signal transmitted on the channel is totally thesame as that o theconventional systemandwithout any traceo the chaotic behavior; thus, the existing attack methodsare inapplicable to the proposed system. It means that no

chance or the intruder to be able to detect the variationo bit duration rom the physical signal on the channel. Itis also clear that the conventional detection methods o bitrate mentioned above cannot detect in detail this variation.Tey may detect the variation range and average value o bitduration, but this is not sufficient or a success ul access.

6. Conclusion

Tis study has presented a chaos-based secure DS/SS com-munication system which is based on a novel combination o the conventional DS/SS and chaos techniques. Te structure,


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operation, and BER per ormance o the proposed systemare described and investigated by means o the theoreticalanalysis and numerical simulation. Te simulation resultagrees with the theoretical analysis. Te discussion showsthe potential o security improvement. It can be seen romthe obtained results, that is, (1) the proposed system inheritsall the advantages rom the conventional system such asthe inter erence rejection, antijamming, ading reduction,multiaccesscapability, andlowprobability o interceptiondueto its operation also based on the DS/SS using PN sequenceand BPSK technique; (2) with the variation o bit durationaccording to the chaotic behavior in the communicationprocess, the proposed system not only still maintains anapproximately good per ormance but also achieves signi -cant improvement on the data security in comparison withthe equivalent conventional system. All these eatures makethe proposed system easible and robust or the security required and DS/SS-based digital communication system.

AcknowledgmentTiswork is supported by the Vietnams NationalFoundation

or Science and echnology Development (NAFOS ED)under Grant no. . - . .

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