A NOVEL CHAOS BASED MODULATION SCHEME (CS-QCSK) WITH IMPROVED BER PERFORMANCE

Sundarapandian et al. (Eds): CoNeCo,WiMo, NLP, CRYPSIS, ICAIT, ICDIP, ITCSE, CS & IT 07,
pp. 45–59, 2012. © CS & IT-CSCP 2012 DOI : 10.5121/csit.2012.2406
A NOVEL CHAOS BASED MODULATION
SCHEME (CS-QCSK) WITH IMPROVED BER
PERFORMANCE
K.Thilagam1
and K.Jayanthi 2
1
Research Scholar, Department of ECE,
Pondicherry Engg. College, Puducherry, India
thilagam.k@pec.edu
2
Associate Professor, Department of ECE,
Pondicherry Engg. College, Puducherry, India
jayanthi@pec.edu
ABSTRACT
In recent years, various chaos based modulation schemes were evolved, of which the CS-DCSK
modulation technique provides better BER performance and bandwidth efficiency, due to its
code domain approach. The QCSK modulation technique provides double benefit: higher data
rate with similar BER performance and same bandwidth occupation as DCSK. By combining
the advantage of code shifted differential chaos shift keying (CS-DCSK) and Quadrature chaos
shift keying (QCSK) scheme, a novel CS-QCSK modulation scheme called code shifted
Quadrature chaos shift keying is proposed. The noise performance of CS-QCSK is better to
most conventional modulation schemes and also provides an increased data transmission rates
with greatly improved robustness. Analytical expressions for the bit-error rates are derived for
both AWGN channel and Rayleigh multipath fading channel. The simulation result shows that
the proposed method outperforms classical chaotic modulation schemes in terms of bit error
rate (BER).
KEYWORDS
Differential chaos shift keying (DCSK) ; Quadrature chaos shift keying (QCSK); Code shifted
differential chaos shift keying (CS-DCSK); code shifted Quadrature chaos shift keying ( CS-
QCSK); Bit Error Rate(BER).
1. INTRODUCTION
In the last few years, a great research effort has been devoted, concerning chaotic carrier
modulation. In contrary to the conventional modulation schemes, a wideband, non-periodic
chaotic signal is used as carrier, which results in good correlation characteristics and robustness
against multipath fading effects. The basic concept of chaos based modulation techniques for
coherent and non-coherent systems have been analyzed and studied in [1] &[2]. For a coherent
system, the receiver needs an exact replica of the chaotic signal, such robust synchronization
techniques are still not realizable in a practical environment [3].It is worth mentioning the
evolution of various types chaos based modulation schemes and their significance and this section
is devoted for summarizing the literature survey/ research findings of such schemes. The DCSK
scheme, discussed in [4] represents a more robust non-coherent scheme, in which the exact
knowledge of the chaotic basis functions is not needed at the receiver. To further enhance the
DCSK scheme, frequency-modulated DCSK (FM-DCSK) was introduced to overcome the

46 Computer Science & Information Technology ( CS & IT )
varying bit-energy problem in DCSK, which is very well explored in [5], [6]. The study of
multipath performance of the frequency-modulated DCSK (FM-DCSK) system is analyzed in
[8],[12]. The analysis was simulation based and the path that suffers from random fading, to be
incorporated in the channel model was assumed an ideal constant gain value.
In [7], the role of synchronization in digital communications using chaos was discussed. At
receiver, the two pieces of chaotic signals are correlated, then the binary symbol is decoded based
on the sign of the correlator output. The DCSK communication scheme, which exploit the
repetitive nature of the chaotic signal, extending from simple binary communications to more
sophisticated detectors, have been discussed [8]. Multipath performance of binary DCSK systems
using a standard correlation detector was discussed in [9]-[10]. Quadrature CSK (QCSK) is a
multilevel version of DCSK, based on the generation of an orthogonal of chaotic functions. It
allows an increase in data rate occupying same bandwidth with respect to DCSK [11]. In
[13],[18] the performance of the DCSK system over a channel with Rayleigh fading or Ricean
fading was discussed with the necessity to model the effects of multipath delay spread as well as
fading. A multiple-access technique with differential chaos shift keying using a one dimensional
iterative map to generate the chaotic signals for all users and similar average data rates for the
users have been discussed [14]-[15],[19]. In [16] FM-QCSK discusses the generation of inherent
wideband signal with constant energy per bit, which can be achieved by using the combination of
frequency modulation with QCSK. The high-level constellation in FM-QACSK which can
improve the speed of chaos shift keying is examined in [17] .The ultra wide band systems based
on DCSK and FM-DCSK schemes and the implementation in both analogy and digital technology
is discussed in [20].The DCSK system incorporated with two-user cooperative diversity
technique and multiple accessing is adopted and discussed in[21] as a result excellent cross-
correlation characteristics of Walsh code sequences is obtained. CS-DCSK uses code domain
approach, the reference and the information bearing signals are transmitted at the same time slots,
it offers better BER performance and bandwidth efficiency, as discussed in [22]. In this paper, a
novel CS-QCSK modulation scheme is proposed, which is the combination of CS-DCSK and
QCSK modulation schemes. In addition to high data rates, it offers the advantage of both the CS-
DCSK and QCSK schemes [22], [11].
The remaining part of the paper is organized as follows: In section 2, the proposed system model
and problem formulation is described. Section 3, elaborates the analytical BER derivation for
different channel conditions. Simulation results are discussed in Section 4. Section 5, deals with
the conclusion of the paper.
2. OVERVIEW ON CHAOS BASED MODULATION SCHEMES
In order to explain the CS-QCSK system, a brief introduction to DCSK, QCSK and CS-DCSK
methods is essential and details are given in this section.
2.1. Differential Chaos Shift Keying (DCSK)
In DCSK system, for each symbol period two chaotic sample functions are used to represent, one
bit of information. The transmitted DCSK signal has two parts, the first part of the signal is
reference signals, while the second denotes the information-bearing signals. If the bit ‘1’ is to
transmitted, then the information bearing signal is the replica of the reference part. If the bit ‘0’ is
to be transmitted, then the information bearing signal is the inverted copy of the reference part.
The i-th symbol can be represented as,
( )
( ) i
DCSK
x t t t ( )
2S t
x (t T / 2) ( ) ( )
2
i
i i
T
t
T
t t t T

≤ < +
= 
+ − + ≤ < +

(1)

Computer Science & Information Technology ( CS & IT ) 47
where, ‘T’ is the symbol duration. In the receiver, the original information is extracted by
computing the correlation between two received sample functions. The output of the correlator is
sampled over each symbol period and the output is finally given to the decision device to
determine the binary values 1’s or 0’s.
2.2. Quadrature Chaos Shift Keying (QCSK)
Similar to DCSK method, each symbol period of QCSK also has two parts, but the modification
is, information-bearing signals holds two bits of information by means of quadrature chaos shift
keying technique. Since two bits of information are transmitted, it is possible for QCSK scheme
to obtain higher data rate. Quadrature chaotic signals are produced by an orthonormal basis
chaotic sample functions x(t) and y(t). Let, x(t) be the chaotic reference signal , assuming that
the signal x has zero mean value and is defined as
( )
1
s in ( )
k
k kx t f k tω ϕ
∞
=
= +∑ (2)
and y(t) be the quadrature chaotic reference signal, obtained by changing the phase of each
fourier frequency component by π/2, and is defined as,
( )
1
sin( / 2)k k
k
y t f k tω ϕ π
∞
=
= + −∑ (3)
The signals x(t) and y(t) are orthogonal in the interval It = [0,t] and is defined as,
( ) ( )
0
0x y x t y t d t
τ
⊥ ⇔ =∫ (4)
The transmitted QCSK signal is given by,
( )
( )
( )
x
QCSK
1 x 2 y
c t 0 t
2
S t
(a c t T / 2 a c (t T / 2))
2
b
b
T
T
t T
E
E

< <
= 
 − + − ≤ <

(5)
where Eb is the bit energy over T / 2 period, satisfying the orthogonal relations.
Cx(t-T/2) is chaotic signal with duration T/2 and Cy(t-T/2) is chaotic signal orthogonal to
Cx(t-T/2) with duration T/2.
2.3. Code Shifted - Differential Chaos Shift Keying (CS-DCSK)
In DCSK, the reference and the information bearing signals are transmitted in two consecutive
time slots because of its TDMA approach. This time domain approach provides two independent
channels for the transmission of reference and information bearing signals. With this, it
requires a delay component both in the modulator and demodulator circuits and halves
the data rate. To overcome this drawback, an alternative approach used is CS-DCSK,
where both the reference and the information bearing signals are transmitted in the same
time slot because of its code domain approach (i.e) the two signals are separated by walsh
codes instead of time delay. The transmitted CS-DCSK signal is given by,
( ) ( ) ( )
1 N 1
b R ,k 1 c I,k 1 c S C
0 k 0
S t W C t kT a W C t kT T NT
N
k
− −
+ +
= =
= − + − =∑ ∑ (6)

Where, WR,k+1 is the reference signal,WI,k+1 is the information signal ,C(t-kTc) is the chaotic signal,
Ts is the symbol duration and Tc is the chip duration. The limitation of this system is, with the
increased complexity the Bit Error Rate obtained by this system is more or less similar when
compared with the existing system.
2.4. System Model of CS-QCSK Modulation
The aim of this section is to illustrate the practical importance of CS-QCSK modulation scheme,
whose simplified transmitter and receiver block diagram are shown in figure.1and figure.2
respectively. A baseband system is considered for simplicity. But it is understood, that if the
scheme is to be employed for wireless communications a modulator is in need to generate the
corresponding RF passband signal. Furthermore, it is assumed that the description of the CS-
QCSK scheme in the continuous-time domain admits an equivalent discrete-time representation.
It discussed in the above, briefly about the advantage of CS-DCSK and QCSK schemes, by
combining these two techniques a novel CS-QCSK modulation scheme can be arrived at.
2.4.1. Transmitter
In CS-QCSK, the symbol S is transmitted with the reference signal and information
signal in the same time slot but separated by Walsh code sequences. The CS-QCSK
transmitted signal is given by,
( ) ( ) ( ) ( )
1 N 1 N 1
b R,k 1 x c 1 I1,k 1 x c 2 I2,k 1 y c S C
0 0 0
S t W C t kT a W C t kT a W C t kT T NT
N
k k k
− − −
+ + +
= = =
= − + − + − =∑ ∑ ∑ (7)
Where a1Є {-1, 1}, a2Є {-1, 1} is mapped from b Є {0,1} which is the information bit to
be transmitted. This scheme uses different Walsh code for the reference and information
signal ,where WR,k+1 represent the Walsh code for reference signal and WI1,k+1 , WI2,k+1
represent the Walsh code for information signal, C(t) is the chaotic signal with duration
of Tc. Both the reference and the information signal are transmitted in the same time slot
as given in equation (7). The orthogonality of two signals are given by,
( )
( )x c c
x c
c t kT t ( 1)T
C t kT
0 otherwise
k ≤ < +
− = 
 (7.a)
( )
( )y c c
y c
c t kT t ( 1)T
C t kT
0 otherwise
k ≤ < +
− = 
 (7.b)
Let,
( ) ( ) ( )
1 N 1 N 1
R,k 1 x c 1 I1,k 1 x c 2 I2,k 1 y c
0 0 00
W C t kT a W C t kT a W C t kT .
s NTc
T
N
k k k
dt
= − − −
+ + +
= = =
∆ = − − −∑ ∑ ∑∫ (8)
2
0
( ) ( ).
sT
b yE c t c t dt= ∫ (8.a)
(.) .T
Transporse of vector=

( ) ( )x x cc t C t kT ; k= − ∀
(8.b)
( ) ( )cc t C t kT ;y y k= − ∀
(8.c)
The orthogonality of the signal is assured by walsh code sequences, therefore the
reference and the information signal are independent of the chaotic carrier.
Figure.1 Block diagram of CS-QCSK Transmitter
Referring to the above transmitter block diagram, the CS-QCSK modulation scheme consist of
chaos signalgenerator,which generates chaos signal Cx (t) and its orthogonal signal Cy (t).The
orthogonal signal is obtained by taking the Hilbert transform of the chaos signal Cx (t). The
transmitter block consists of three Walsh function generator, which generates three different
Walsh code sequences that are orthogonal in nature. It has (N-1) delay elements of Tc chip
duration. The three Walsh function generator, generate Walsh codes, WR,k+1 for reference signal,
and WI1,k+1 , WI2,k+1 for information signal. The reference signal of Walsh code WR,k+1 is
multiplied with the chaos signal and the corresponding output is obtained by the switching unit
S1.It has a bit splitter, which splits the input bit stream into odd and even sequences. The
information signal of Walsh code WI1,k+1 is multiplied with the odd sequence of bits and the
chaos signal ,the corresponding output is obtained by the switching unit S2. The information
signal of Walsh code WI2,k+1 is multiplied with the even sequence of bits and the orthogonal
chaos signal, the corresponding output is obtained by the switching unit S3.The output obtained at
the switching unit S2 and S3 are summed and it is further summed with the switching unit S1 to
obtain the final output. The CS-QCSK signal is finally obtained.

2.4.2. Receiver
Figure.2 Block diagram of CS-QCSK Receiver
The above Figure.2 shows the block diagram of CS-QCSK receiver. The receiver unit
consists of band pass filter with the bandwidth of 2B which can pass the received signal
r(t) without any distortion. The receiver filter output with Additive White Gaussian Noise
(AWGN) n(t) is obtained as,
( ) ( ) ( )
1 N 1 N 1
~
R,k 1 x c 1 I1,k 1 x c 2 I2,k 1 y c
0 0 0
( ) W C t kT a W C t kT a W C t kT n(t)
N
r
k k k
t
− − −
+ + +
= = =
= − + − + − +∑ ∑ ∑ (9)
( ) c c
x c
1 ,kT t ( 1)T
rect t kT
0 ,otherwise
k≤ < +
− = 

(9.a)
( ) c c
y c
1 ,kT t ( 1)T
rect t kT
0 ,otherwise
k≤ < +
− = 

(9.b)
The receiver filter output is further given to the three mixer unit M1,M2 and M3.In the
mixer unit the filter output signal is multiplied by a rectangular function weighted by the
three Walsh code sequences. The transmitted signal is of Walsh codes incorporated with
three terms. In order to obtain those terms A, B and C the receiver filter output is
multiplied by a rectangular function. The output of M1, M2 and M3 is multiplied to
obtain the signal ABC. The multiplier output is then given to the integrator unit to obtain
the observation signal. The integrator output is given to the hard decision device, where
the bits are estimated by the decision rule. Using walsh code, the transmitted signal is
incorporated with three terms A, B and C. The three terms A, B and C can be obtained
by multiplying equation (7) that corresponds to reference signal and information signals
respectively. The terms X, Y and Z in the receiver block are
( ),k 1 x cX=W rect t kTR + −
,
( )I1,k 1 x cY=W rect t kT+ −
,
( )I2,k 1 cZ=W rect t kTy+ −
.
Where,
( ) ( )
1
,k 1 x c
0
A S t W rect t kT
N
R
k
−
+
=
= −∑ (10)

( ) ( )
1
I1,k 1 x c
0
B S t W rect t kT
N
k
−
+
=
= −∑ (11)
( ) ( )
1
I2,k 1 y c
0
S t W rect t kT
N
k
C
−
+
=
= −∑ (12)
0
.
s cT NT
Z ABC dt
=
= ∫ (13)
Substituting, equation (7) in (10),(11)and(12). The equations (14), (15) and (16) are
obtained.
( ) ( ) ( )
1 N 1 N 1
x c 1 R,k 1 I1,k 1 x c 2 R,k 1 I2,k 1 y c
0 0 0
A C t kT a W W C t kT a W W C t kT
N
k k k
− − −
+ + + +
= = =
= − + − + −∑ ∑ ∑ (14)
( ) ( )
N 1 1
R,k 1 I1,k 1 x c 1 x c
k 0 k 0
B W W C t kT a C t kT
N− −
+ +
= =
= − + −∑ ∑ (15)
( ) ( )
N 1 1
R,k 1 I2,k 1 x c 2 y c
k 0 k 0
C W W C t kT a C t kT
N− −
+ +
= =
= − + −∑ ∑ (16)
Substituting equation (14), (15) and (16) in (13)
( ) ( ) ( )
( ) ( ) ( ) ( )
1 N 1 N 1
x c 1 R,k 1 I1,k 1 x c 2 R,k 1 I2,k 1 y c
k 0 k 0 k 0
N 1 1 N 1 1
R,k 1 I1,k 1 x c 1 x c R,k 1 I2,k 1 x c 2 y c
k 0 k 0 k 0
0
k 0
C t kT a W W C t kT a W W C t kT .
W W C t kT a C t kT W W C t kT a C t kT
s cT NT N
N N
Z
dt
= − − −
+ + + +
= = =
− − − −
+ + + +
= = = =
= − + − + −
− + − − + −
 
 
 
   
   
   
∑ ∑ ∑∫
∑ ∑ ∑ ∑
(17)
The above equation (17) can be simplified as,
1 2 bZ a a E≅ (18)
3. ANALYTICAL DERIVATION OF BER UNDER VARYING CHANNELS
The analytical expression for the BER of CS-QCSK over AWGN and the multipath Rayleigh
fading channels are derived in the following section.
3.1. Additive White Gaussian Noise (AWGN) Channel
From the receiver unit, the observation variable obtained is given by
( )
( ) ( )
c
c
k 1 T1
~ ~
R,k 1 I1,k 1 I2,k 1
0 kT
Z W . W W . dt
N
r r
k
t t
+−
+ + +
=
   =
   ∑ ∫ (19)
( )
( ) ( ) ( )]
c
c
k 1 TN 1
2
R,k 1 I1,k 1 I2,k 1 R,k 1 1 I1,k 1 2 I2,k 1
k 0 kT
W W W W a W a W .c
c t kT n t dt
+−
+ + + + + +
=
= + + + − +
∑ ∫ (20)

There are different types of chaotic maps to generate the chaotic signals, they are classified as
(i)logistic map (ii) cubic map (iii) Bernoulli-shift map. In the proposed method, logistic map is
considered and is defined as, x (n+1) = 1-2x2
(n).Where, β =Tcfs is the number of samples in a
chip time and K=Tsfs=N β is the symbol duration. In the remaining part of the paper, ‘K’ is
referred as the spreading factor. Consider, the transmission of a1=a2=+1 sequence. The logistic
map is defined in the continuous time domain. In order to convert into the discrete time domain,
consider Cj be the samples of chaotic signal and ηj be the channel noise. Then, the equation for
discrete time equivalent is given as,
( )
βN 1
2
R,k 1 I1,k 1 I2,k 1 R,k 1 1 I1,k 1 2 I2,k 1
k 0 m 1
W W W W a W a W . k m k m
Z c β βη
−
+ + + + + + + +
= =
= + + + ∑ ∑ (21)
Where,
, ( 1)
0 ,
m
k m
c m k
c
otherwise
β
κβ κβ β
+
≤ + < +
= 

(22)
From the equation (21) ,the decision variable is decomposed into three terms,
A B CZ Z Z Z= + + (23)
where,
)( )(
βN 1
22
R,k 1 I1,k 1 I2,k 1 R,k 1 1 I1,k 1 2 I2,k 1
.k 0 m 1
W W W W a W a WA k mZ c β
−
+ + + + + + +
= =
= + +
 
∑ ∑ (24)
( )
βN 1
R,k 1 I1,k 1 I2,k 1 R,k 1 1 I1,k 1 2 I2,k 1
k 0 m 1
W W W W a W a W ( )( )B k m k mZ c β βη
−
+ + + + + + + +
= =
 = + + ∑ ∑ (25)
)(
βN 1
2
R,k 1 I1,k 1 I2,k 1
k 0 m 1
W W WC k mZ c β
−
+ + + +
= =
= ∑ ∑ (26)
By applying, Expectation and Variance to the above equations, (24), (25) and (26) the expectation
and variance values of these variables are obtained as,
{ } { } { }2
| 1 | 1 3A A jE Z b E Z a N E Cβ= = = + = (27)
{ } { }| 1 | 1 0B BE Z b E Z a= = = + = (28)
{ } { }| 1 | 1 0C CE Z b E Z a= = = + = (29)
{ } { } { }2
| 1 | 1 3A A jVar Z b Var Z a N Var Cβ= = =+ = (30)
{ } { } { }2
0| 1 | 1 2B B jVar Z b Var Z a N NVar Cβ= = =+ = (31)
{ } { } 2
0| 1 | 1C CVar Z b Var Z a N Nβ= = = + = (32)
Where, E{.} represents the expectation operator and var{.} represents the variance operator ,then
{ } { } { }2
| 1 | 1 3 jE Z b E Z a N E Cβ= = = + = (33)

{ } { } { } { }2 2 2
0 0| 1 | 1 3 2j jVar Z b Var Z a N Var C N NVar C N Nβ β β= = =+ = + + (34)
For the transmission of ‘a1=a2= -1’ sequence, the expectation and variance of observation variable
is derived similarly.
{ } { }| 1 | 1E Z a E Z a= − = − = + (35)
{ } { }| 1 | 1Var Z a Var Z a= − = = + (36)
It is assumed, that the probability distribution of the observation variable can be approximated by
gaussian approximation and the transmitted bits are equiprobable. Therefore, the bit error rate of
CS-QCSK modulation scheme is obtained as,
1 1
Pr( 0| 1) Pr( 0| 0)
2 2
m mBER Z b Z b= < = + ≥ = (37)
1 1
Pr( 0 | 1) Pr( 0 | 1)
2 2
m mZ a Z a= < = + + ≥ = −
{ }
{ }
| 11
2 2 | 1
m
m
E Z a
erfc
Var Z a
 = +
 =
 = + 
Where, m=2; represents the number of information bits transmitted per time slot.For logistic
maps, the expectation of chaos signal is { }2
1/ 2jE C = and variance of chaos signal is
{ }2
1/ 8jVar C = and therefore equation (37) becomes,
{ }
{ } { }( )
2
2 2 2
0 0
31
2 2 3 2
j
j j
N E C
erfc
N Var C N N Var C N N
β
β β β
 
 
=  
 + + 
 
( )
( )
0
0
3 /1
2 3 1
2 /
4 2
b
CS QCSK
b
E N
BER erfc
K K E N
−
 
 
 =
 
+ + 
 
(38)
3.2. Rayleigh Multipath Fading Channel
Considering the rayleigh multipath fading channels, the received signal is denoted as
( ) ( ) ( ) ( )r t h t x t n t= ⊗ + (39)
and the channel impulse response is given as
( )
1
0
( )
L
l
l
h t lα δ η
−
=
= −∑ (40)
Where, L is the number of propagation paths, αl gain of the lth path, τl is the delay of the lth
path
and δ(t) denotes the dirac delta function. The gains αl of the propagation paths are assumed to be
independent identical distributed Rayleigh random variables. The BER measured in Rayleigh
multipath channel is an approximation developed from the noise performance of AWGN channel.
The conditional BER measured for the multipath is given by,

BER (α0, α1………… αL-1) = BER (γb) (41)
Where, γb = (Eb/No) (α0, α1………… αL-1) = ( γ0 + γ1 +………………+ γL-1 )
The probability density function (PDF)of γi is an exponential distribution given by,
( )
1
exp( )
k k
x
f x
γ γ
−
= (42)
The probability density function (pdf) of γb is obtained as,
( ) ( ) ( ) ( )b 0 1 1γ γ γ . γLf f f f −= ⊗ ………… ⊗
(43)
Where, f(γk ) is the pdf of instantaneous (SNR) measured in the ith path. By averaging the
conditional bit error rates in the multipath channels, the total BER measured is obtained as,
( ) ( )b b b
0
γ γ γBER BER f d
∞
= ∫ (44)
In this paper, it is assumed to have two multipath channels with three propagation paths, then the
error rate expressions are
( )
( )
31
2 3 1
2
4 2
b
CS QCSK
b
BER erfc
K K
γ
γ
−
 
 
 =
 
+ + 
 
(45)
In order to validate the analytical approach of the proposed scheme, an attempt is made through
simulations. The next section presents the simulation analysis of the proposed scheme and it is
finally compared with the analytical results.
4. SIMULATION ANALYSIS
The BER performances of CS-QCSK modulation schemes for different channel conditions are
also analyzed through Matlab simulation. Simulation parameters taken for the analysis are chip
duration(Tc)=2millisecond,Symbol duration(Ts)=2 micro second, transmission
power(P)=43dBm, noise power spectral density(No)=1,spread factor(K)=40 , the channel types
are AWGN and Rayleigh . Firstly, the BER performance of AWGN channel is discussed,
followed by multipath Rayleigh fading channel.
4.1. BER Performance over AWGN Channel
0 5 10 15
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Eb/No (dB)
BER
Theoretical BER
Simulated BER
Figure. 3 BER performance of CS-QCSK modulation scheme for AWGN channel.

From the figure.3, it is inferred that BER performance of CS-QCSK scheme is plotted with the
theoretical and simulated values.The BER values calculated from the analytical expression and
the simulation are very similar and both the graph merge with each other.For the BER value of
10-6
, the required (Eb/No) value is 10dB(approximately).
0 5 10 15 20 25
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Eb/No
BER
kA
=40
kA
=60
kA
=120
Figure.4 BER performance of the CS-QCSK modulation scheme over AWGN
channel for various spread factor.
BER performance of CS-QCSK modulation scheme for various spreading factors (K=40,
K=80,K=120) were plotted. It is inferred from the above graph that, as the K value increases the
noise performance become worse. In general, smaller Spreading factor corresponds to minimum
noise level. Therefore, for smaller values of ‘K’ the BER performance is better.
0 5 10 15 20 25
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Eb/No(dB)
BER
DCSK
QCSK
CS-DCSK
CS-QCSK
Figure. 5 BER performance comparison for different modulation schemes with CS-
QCSK modulation scheme Over AWGN channel.
In the above graph, the BER performance of different modulation schemes were compared. For
the BER value of 10-1, the required Eb/No value for CS-DCSK, DCSK, QCSK and CS-QCSK is
18.4 dB, 17.8dB,17.2dB and 10.2dB respectively. On inferring these Eb/No values, the BER
performance of proposed CS-QCSK modulation scheme is better compared to the DCSK, CS-
DCSK and QCSK modulation schemes.

4.2. BER Performance over Rayleigh Multipath Channel
0 5 10 15
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Eb/No (dB)
BER
Theoretical BER
Simulated BER
Figure. 6 BER performance of CS-QCSK modulation scheme
for Rayleigh multipath channel.
From the above figure, it is inferred that BER performance of CS-QCSK scheme is plotted with
the theoretical and simulated values.The BER values calculated from the analytical expression
and the simulation are very similar and both the graph merge with each other.For the BER value
of 10-6
, the required (Eb/No) value is13.1dB(approximately).
Figure.7 BER performance of the CS-QCSK modulation scheme over
Rayleigh channel for various spread factor.
BER performance of CS-QCSK modulation scheme for various spreading factors (K=40,
K=80,K=120) were plotted. It is inferred from the above graph that, as the K value increases
the noise performance become worse. In general, smaller Spreading factor corresponds to
minimum noise level. Therefore, for smaller values of ‘K’the BER performance is better.
0 5 10 15 20 25
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Eb/No
BER
kR
=40
kR
=60
kR
=120

0 5 10 15 20 25
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Eb/No(dB)
BER
DCSK
QCSK
CS-DCSK
CS-QCSK
Figure. 8 BER performance comparison for different modulation schemes with CS-
QCSK modulation scheme Over AWGN channel.
In the above graph, the BER performance of different modulation schemes were compared. For
the BER value of 10-1, the required Eb/No value for CS-DCSK,DCSK,QCSK and CS-QCSK is
18.8 dB,18dB,17.4dB and 13.1dB respectively. On inferring these Eb/No values, the BER
performance of proposed CS-QCSK modulation scheme is better compared to the DCSK, CS-
DCSK and QCSK modulation schemes.
0 50 100 150 200
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
10
1
Spread factor
BER
Figure. 9 Effect of spreading factor on BER performance of the CS-QCSK modulation
scheme. Eb/No has been fixed at 10 dB.
BER is plotted against the spreading factor by fixing Eb / No at 10 dB.It is inferred that, larger the
spreading factor, worse the performance.
5. CONCLUSION
In the field of chaos-based communication, M-ary DCSK scheme seems to be the best known
modulation scheme. But, the drawback is, it requires (N-1) number of of delay lines both in the
transmitter and the receiver units. In this paper, an improved chaos-based communication method

using CS-QCSK technique is recommended. The proposed CS-QCSK scheme, avoids the use of
delay lines in the receiver units. It transmits the reference and information signals in the same
time slot and offers an increase in data rate, better BER performance and bandwidth efficiency.
The performance of the proposed modulation scheme is analyzed in context of AWGN and
multipath channels. Analytical expressions for BER of CS-QCSK are derived and verified with
matlab simulation. Simulation results, shows that the CS-QCSK has better BER performance in
AWGN and Rayleigh fading channels, when compared with the conventional modulation
schemes. This proves the suitability of the proposed modulation technique for a mobile radio
scenario, which is the need of the hour.
REFERENCES
[1] Abel and W. Schwarz, “Chaos communications—Principles, schemes, and system analysis,” Proc.
IEEE,vol. 90,pp. 691–710, May 2002
[2] G. Kolumbán, M. P. Kennedy, Z. Jako, and G. Kis, “Chaotic communications with correlator
receivers: Theory andperformance limits,” Proc.IEEE, vol. 90, pp. 711–732, May 2002.
[3] H. Dedieu, M. P. Kennedy, and M. Hasler,“Chaos shift keying: Modulation and demodulation of a
chaotic carrier using self-synchronizing Chua’s circuits,” IEEE Trans. Circuits Syst. II, vol. 40, pp.
634–642, Oct.1993.
[4] G. Kolumbán, B. Vizvári,W. Schwarz, and A. Abel, “Differential chaos shift keying: A robust coding
for chaos communication,” Proc. Int.Workshop Nonlinear Dynamics of Electronic Systems, pp. 87–
92, June 1996.
[5] G. Kolumbán, G. Kis, M. P. Kennedy, and Z. Jáko, “FM-DCSK: A new and robust solution to chaos
communications,” in Proc., Int. Symp. Nonlinear Theory Appl., HI, 1997, pp. 117– 120.
[6] M. P. Kennedy and G. Kolumbán, “Digital communication using chaos,”in Controlling Chaos and
Bifurcation in Engineering Systems, G. Chen, Ed. Boca Raton, FL: CRC, 2000, pp. 477– 500.
[7] G. Kolumbán and M. P. Kennedy, “The role of synchronization in digital communications using
chaos—Part III:Performance bounds for correlation receivers,” IEEE Trans. CircuitsSyst. I,
Fundamental. Theory Appl.,vol. 47, no. 12, pp. 1673–1683, Dec. 2000.
[8] G.Kolumban, Z. Jákó, and M. P.Kennedy, “Enhanced versions of DCSK and FM-DCSK data
transmissions systems,” in Proc. IEEE ISCAS’99,vol. IV, Orlando, FL, May/Jun. 1999, pp. 475–478.
[9] M. P. Kennedy, G. Kolumbán, G. Kis, and Z. Jákó, “Performance evaluation of FM-DCSK
modulation in multipath environments,” IEEE Trans.Circuits Syst. I, Fundam. Theory Appl., vol. 47,
no. 12, pp. 1702–1711, Dec.2000.
[10] G. Kolumbán, “Theoretical noise performance of correlator-based chaotic communications schemes,”
IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 47, no. 12, pp. 1692– 1701, Dec. 2000.
[11] Z. Galias and G. M. Maggio, “Quadrature chaos-shift keying: Theory and performance analysis,”
IEEE Trans.Circuits Syst. I, Fundam.Theory Appl., vol. 48, no. 12, pp. 1510–1519, Dec. 2001.
[12] G. Kolumbán and G. Kis, “Multipath performance of FM-DCSK chaotic communications system,” in
Proc. IEEE Int. Symp. Circuits and Systems, Geneva, Switzerland, May 2000, pp. 433–436.
[13] S. Mandal and S. Banerjee, “Performance of differential chaos shift keying over multipath fading
channels,” in Proc. Indian Nat. Conf. Nonlinear Systems and Dynamics, Kharagpur, India, Dec. 2003.
[14] G. Kolumbán, P. Kennedy, and G. Kis, “Multilevel differential chaos shift keying,” in Proc. Int.
Workshop, Nonlinear Dynamics of Electronics Systems, NDES’97, Moscow, Russia, 1997, pp. 191–
196.
[15] F. C. M. Lau, M. M. Yip, C. K. Tse, and S. F. Hau, “A Multiple-Access Technique for Differential
Chaos-Shift Keying” IEEE Trans.Circuits Syst. I, Fundam.Theory Appl., vol. 49, no. 1, January 2002.
[16] YiWei Zhang, Xubang Shen and Yi Ding, “Design and performance analysis of an FM- QCSK
chaotic communication system,” International Conference on Wireless Communications, Networking
and Mobile Computing, China, pp: 1-4, Sept. 2006.
[17] Jiamin Pan, He Zhang, “Design of FM-QACSK Chaotic Communication System” IEEE trans.
Wireless Communications & Signal Processing, 2009.
[18] Xia, Y.,Tse,C.K.& Lau, F.C.M, “Performance of differential chaos shift keying digital
communication systems over a multipath fading channel with delay spread,”IEEE Trans. Circuits
Syst.-II 51,680-684 ,2004.
[19] Yao,J.& Lawrance, A.J, “ Performance analysis and optimization of multi-user differential chaos-
shift keying communication systems,” IEEE Trans.circ. Syst.-I 53, pp.2075-2091, 2006.

[20] Wang,L.,Zhang,C.& Chen, G. “Performance of an SIMO FM-DCSK communication system,” IEEE
Trans.Circuits Syst.-II, 55, 457-461,2008.
[21] Min,X.,Xu,W.,Wang, L. & Chen, G., “Promising performance of an FM-DCSK UWB system under
indoor environments,” J. IET Commun. 4, pp.125-134, 2010.
[22] G.Koluban,W.K.Xu and L.Wang, “A Novel differential chaos shift keying modulation scheme,”
International journal of Bifurcation and chaos,2011,Vol.21,No.3,pp799-814
Authors
K.Jayanthi received B.E degree from University of Madras in 1997 and M.Tech
degree in Electronics and Communication Engineering and Ph.D from Pondicherry
University in 1999 and 2007 respectively. She has 13years of experience in teaching /
research. She is currently serving as Associate Professor in Department of Electronics
and Communication Engineering, Pondicherry Engineering College, Puducherry. To
her credit, she has around 12 journal papers and presented 18 papers in International
conferences. Her other areas of interest includes satellite communication, Wireless
multimedia networks, Spread spectrum communication, Image processing, etc. She
has authored a book on Qos Provisioning in Cellular Mobile Networks.
K.Thilagam received her B.Tech and M.Tech degrees in Electronics and
Communication Engineering from Pondicherry Engineering College in 2004 and 2007
respectively. She has 5 years of experience in teaching /research. She is currently
pursuing Ph.D in the area of Wireless Communication. Her research activities are
focussed on Cooperative Communication in Cellular Networks, mainly on Modulation
and coding techniques,etc

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