MULTIUSER BER ANALYSIS OF CS-QCSK MODULATION SCHEME IN A CELLULAR SYSTEM

International Journal of Wireless & Mobile Networks (IJWMN) Vol. 4, No. 6, December 2012
DOI : 10.5121/ijwmn.2012.4611 139
MULTIUSER BER ANALYSIS OF CS-QCSK
MODULATION SCHEME IN A CELLULAR
SYSTEM
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, chaotic communication is a hot research topic and it suits better for the emerging
wireless networks because of its excellent features. Different chaos based modulation schemes have
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 modulation scheme called code shifted Quadrature chaos shift keying
(CS-QCSK) is proposed and its suitability in a multiuser scenario is tested in this paper. The analytical
expressions for the bit-error rate for Multi-user CS-QCSK scheme (MU-CS-QCSK) under Rayleigh
multipath fading channel is derived. The simulation result shows that, in multiuser scenario 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);
Multiuser code shifted Quadrature chaos shift keying ( MU-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
varying bit-energy problem in DCSK, which is very well explored in [5], [6]. The limitation of
the work is that the analysis was purely simulation based with a constant gain channel model.
In [7], the role of synchronization in digital communications using chaos was discussed. At
receiver, the two pieces of chaotic signals are correlated, and then the binary symbol is decoded

140
based on the sign of the correlator output. The DCSK communication schemes, which exploit
the repetitive nature of the chaotic signal, extending from simple binary communications to
more sophisticated detectors, have been discussed [8]. In [9], a discrete-time approach for CSK
system with multiple users and the multiple-access DCSK (MA-DCSK) system was
investigated in depth and a mixed analysis-simulation (MAS) technique was developed to
calculate the bit error rates (BERs) using the derived BER analytical expressions. Multipath
performance of binary DCSK systems using a standard correlation detector was discussed in
[10]-[11]. 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 [12]. In [13]-[15], the performance of the DCSK system over a channel
with Rayleigh fading and 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 in [16]-[17]. In [18], the
generation of inherent wideband signal with constant energy per bit, which can be achieved by
using the combination of frequency modulation with QCSK was discussed. The high-level
constellation in FM-QACSK which can improve the speed of chaos shift keying is examined in
[19]. In [20], the performance analysis and optimization of multiuser differential chaos shift
keying, using dynamically improved gaussian approximation(DIGA) method was discussed.
The DCSK system incorporated with two-user cooperative diversity technique and multiple
accessing, using the features of Walsh code sequences was discussed in[21]. It was discussed
with the signal structure of chaotic pulse cluster resolving the technical problem and offering a
desired solution to multi-user’s communication systems using Walsh function division scheme
[22]. In[23]a high-efficiency differential chaos shift keying (HEDCSK) with new correlation-
based communication scheme, was introduced as an enhanced version of DCSK allowing an
increased data rate compared to DCSK with the same bandwidth occupation, but has poor BER
performance and bandwidth efficiency. CS-DCSK uses code domain approach, the reference
and the information bearing signals are transmitted at the same time slots, it offers bandwidth
efficiency but poor BER performance, as discussed in [24]. In [25], the authors discussed that,
using the generalized code-shifted DCSK (GCS-DCSK) modulation scheme, the CS-DCSK was
extended to transmit multiple bit streams by means of one reference wavelet but has poor BER
performance. In [26], a novel chaos based modulation scheme CS-QCSK was proposed and was
thoroughly analysed for single user scenario.
In this paper, the analysis of multiuser performance of a novel CS-QCSK modulation scheme is
proposed, which is the blend 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 [24], [12].
Analytical expressions for computing BER for the proposed approach has been derived. Further
simulation results prove its supremacy over the classical chaos modulation schemes.
The remaining part of the paper is organized as follows: In section 2, conventional schemes and
the proposed system model with problem formulation is described. Section 3, elaborates the
analytical BER derivation for Rayleigh fading channel. 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 MU-CS-QCSK system, a brief introduction to DCSK, QCSK, CS-DCSK
and CS-QCSK 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 [4]. The transmitted DCSK signal has two parts; the first part of the

141
signal is the reference signal, while the next part denotes the information-bearing signal. If the
bit ‘1’ is to be 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 DCSK transmitted symbol can be represented as,
( )
( )
DCSK
x t 0 t
2S t
x (t T / 2)
2
T
T
t T

≤ <
= 
+ − ≤ <

(1)
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 [12]. 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 let 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
2S 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 same duration of 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 requires two independent
channels for the transmission of reference and information bearing signals. Further, it requires a
delay component both in the modulator and demodulator circuits and halves the data rate. To

142
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 [25].
The transmitted CS-DCSK signal is given by,
( ) ( ) ( )
1 N 1
R ,k 1 c I,k 1 c
0 k 0
S t W C t kT a W C t kTCS DCSK
N
k
− −
+ +
= =
− = − + −∑ ∑ (6)
Where, Ts=NTc, 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. Code Shifted - Quadrature Chaos Shift Keying (CS-QCSK)
The aforementioned CS-DCSK has poor BER performance and minimum data rate. To
overcome this drawback, a novel chaos based modulation scheme Code shifted-Quadrature
Chaos Shift Keying (CS-QCSK) is proposed. In this scheme, both the reference and the
information bearing signals are transmitted in the same time slot, using walsh codes and the
difference is information bearing part holds two bits of information. CS-QCSK can also be said
as Hybrid of QCSK and CS-DCSK which will hold the advantage of both the schemes, so that it
provides a higher data rate, bandwidth efficiency and better BER performance.The CS-QCSK
transmitted signal is given by,
( ) ( ) ( ) ( )
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
S t W C t kT a W C t kT a W C t kT
N
k k k
CS QCSK
− − −
+ +− +
= = =
= − + − + −∑ ∑ ∑ (7)
Where, Ts=NTc ,WI1,k+1 and WI2,k+1 are the information signal ,Cx(t-kTc) is the chaotic signal and
the Cy(t-kTc) is the orthogonal chaotic signal, Ts is the symbol duration and Tc is the chip
duration. The limitation of this system is its increased complexity and the performance of the
system begins to deteriorate for large number of users. The next section briefly explains the
multiuser CS-QCSK system model and its performance analysis in the Rayleigh multipath
environment.
2.5. System Model of Multiuser 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 figures 1 and 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 MU-
CS-QCSK scheme in the continuous-time domain admits an equivalent discrete-time
representation. From the earlier stated discussions, it can be concluded that, by combining CS-
DCSK and QCSK schemes, a novel CS-QCSK modulation scheme can be realised and it is
thoroughly analysed in the presence of multiple users.
2.5.1. Transmitter
In MU-CS-QCSK system, the symbol ‘S’ is transmitted with the reference signal and
information signal in the same time slot but separated by Walsh code sequences. Let there be
‘Nu’ number of users.
The MU-CS-QCSK transmitted signal is given by,
( ) ( ) ( ) ( )
1 N 1 N 1
R,k 1 x c I1 ,k 1 x c I2 ,k 1 y c
0 1 0 0
1 2
S t W C t kT W C t kT W C t kT
uN
u u
k u k k
M u u
N
a a
− − −
+ + +
= = = =
= − + − + −
 
 
 
∑ ∑ ∑ ∑ (8)

143
Where, Ts=NTc, a1uЄ {-1, 1}, a2uЄ {-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 WI1u,k+1 , WI2u,k+1
represent the Walsh code for the two consecutive information bits, C(t) is the chaotic signal
with duration of Tc and u=1,....,Nu represents the number of users in the system. Both the
reference and the information signal are transmitted in the same time slot as given in equation
(8). The orthogonality of two signals are given by,
( )
( )x c c
x c
c t kT t ( 1)T
C t k T
0 o th erw ise
k ≤ < +
− = 
 (8.a)
( )
( )y c c
y c
c t k T t ( 1)T
C t k T
0 o th erw ise
k ≤ < +
− = 
 (8.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
u u u u
k k k
dt
= − − −
+ + +
= = =
∆ = − − −∑ ∑ ∑∫ (9)
2
0
( ) ( ).
sT
b yE c t c t dt= ∫ (9.a)
(.) .T
Transporse of vector=
( ) ( )x x cc t C t kT ; k= − ∀
(9.b)
( ) ( )cc t C t kT ;y y k= − ∀
(9.c)
Figure 1. Block diagram of Multiuser CS-QCSK Transmitter
Referring to the transmitter block diagram of figure 1, the CS-QCSK modulation scheme
consist of chaos signal generator, 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

144
chip duration. The three Walsh function generator, generate Walsh codes, WR,k+1 for reference
signal, and WI1u,k+1 , WI2u,k+1 for information signal for ‘u’ users, where, u=1,....Nu. 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 first information signal of the uth
user’s Walsh code ‘WI1u,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 second information signal of the uth
user’s walsh code
‘WI2u,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 for ‘u’ users and it is further summed with the switching unit S1 to
obtain the final output. The composite CS-QCSK signal is finally obtained.
2.5.2. Receiver
Figure 2. Block diagram of MU-CS-QCSK Receiver
Figure 2. shows the possible hardware realisation of MU-CS-QCSK receiver. The receiver unit
consists of band pass filter with the bandwidth of 2B which can pass the received signal ru(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 0
( ) W C t kT a W C t kT a W C t kT n(t)
uN
u u u u
k k k k
u
N
tr
− − −
+ + +
= = = =
 
= − + − + − + 
 
∑ ∑ ∑ ∑ (10)
( ) c c
x c
1 ,kT t ( 1)T
rect t kT
0 ,otherwise
k≤ < +
− = 

(10.a)
( ) c c
y c
1 ,kT t ( 1)T
rect t kT
0 ,otherwise
k≤ < +
− = 

(10.b)
Let,
( ),k 1 x cX=W rect t kTR + −
,
( )I1u,k 1 x cY=W rect t kT+ −
,
( )1 I2 ,k 1 cZ =W rect t kTu y+ −
and
Let,
( ) ( )
1
,k 1 x c
0
A t W rect t kT
N
RM
k
S
−
+
=
= −∑ (11)

145
( ) ( )
1
I1u,k 1 x c
0
B t W rect t kT
N
M
k
S
−
+
=
= −∑ (12)
( ) ( )
1
I2 ,k 1 y c
0
t W rect t kT
N
uM
k
C S
−
+
=
= −∑ (13)
The integrator output is thus,
0
.
s cT NT
Z ABC dt
=
= ∫ (14)
Substituting, equation (8) in (11),(12)and(13). The equations (15), (16) and (17) 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
u u u u
k k k
− − −
+ + + +
= = =
= − + − + −∑ ∑ ∑ (15)
( ) ( )
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
u u
− −
+ +
= =
= − + −∑ ∑ (16)
( ) ( )
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
u u
− −
+ +
= =
= − + −∑ ∑ (17)
Substituting equation (14), (15) and (16) in (13), the observation vector ‘Z’ is obtained as,
( ) ( ) ( )
( ) ( ) ( ) ( )
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
0 k 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
u u u u
N N
u u u u
Z
= − − −
+ + + +
= = =
− − − −
+ + + +
= = = =
= − + − + −
− + − − + −
 
 
 
   
  
   
∑ ∑ ∑∫
∑ ∑ ∑ ∑ dt
(18)
The above equation (18) can be simplified as,
1 2u u bZ a a E≅ (19)
3. BER ANALYSIS FOR MULTIPATH RAYLEIGH FADING
SCENARIO
The analytical expression for the BER of MU-CS-QCSK under the multipath Rayleigh fading
channel is derived in the following section to validate the simulated results.
3.1. MULTIPATH RAYLEIGH FADING CHANNELS
From the receiver unit, the obtained observation variable ’Z’ 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
u ur r
k
t t
+−
+ + +
=
   =
   ∑ ∫ (20)

146
( )
( ) ( )]
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 1 1kT
W W W W a W a W ..
uu
u u u u u u c
u u
c t kT n t dt
NN+−
+ + + + + +
= = =
= + + − +
 
 
 
 
 
∑ ∑ ∑∫ (21)
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 a1u=a2u=+1 sequence. The logistic
map is defined in the continuous time domain. In order to convert into the discrete time domain,
consider Cj to be the samples of chaotic signal and ηj be its corresponding channel noise. Then,
‘Z’ the equation for discrete time equivalent is defined 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 .u u u u u k m k m
Z c β β
η
−
+ + + + + + + +
= =
= + + + ∑ ∑ (22)
Where,
, ( 1)
0 ,
m
k m
c m k
c
otherwise
β
κβ κβ β
+
≤ + < +
= 

(23)
From the equation (22), the decision variable is decomposed into three terms,
A B CZ Z Z Z= + + (24)
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 u u u u u u k mZ c β
−
+ + + + + + +
= =
= + +
 
∑ ∑ (25)
( )
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 u u u u u u k m k mZ c β βη
−
+ + + + + + + +
= =
 = + + ∑ ∑ (26)
)(
βN 1
2
R,k 1 I1 ,k 1 I2 ,k 1
k 0 m 1
W W WC u u k mZ c β
−
+ + + +
= =
= ∑ ∑ (27)
By applying, expectation and variance to the above equations, the expectation and variance
values of these variables are obtained as follows:
{ } { } ( ) { }2 2 21
| 1 | 1 3 1
2
A A ju u
E Z b E Z a N N E CN Nβ β  = = = + = + +
 
(28)
{ } { }| 1 | 1 0B BE Z b E Z a= = = + = (29)
{ } { }| 1 | 1 0C CE Z b E Z a= = = + = (30)
{ } { } { }62 2 2 2 27
| 1 | 1 9
4
A A ju
Var Z b Var Z a N N Var CNβ β= = =+ = + (31)

147
{ } { } ( ) { }2 222 22
0| 1 | 1 4 1B B ju u
Var Z b Var Z a N N N Var CNβ= += = + = (32)
{ } { } 2
0| 1 | 1C CVar Z b Var Z a N Nβ= = = + = (33)
Where, E{.} represents the expectation operator and var{.} represents the variance operator
,then
{ } { } ( ) { }2 2 21
| 1 | 1 3 1
2
ju u
E Z b E Z a N N E CN Nβ β  = = = + = + +
 
(34)
{ } { } { } ( ) { }
22 262 2 2 2 2 2 2 2 2
0 0
7
| 1 | 1 9 4 1
4
j u ju uVar Z b Var Z a N N Var C N N N Var C N NN Nβ β β β= = = + = + + ++
(35)
For the transmission of ‘a1u=a2u= -1’ sequence, the expectation and variance of observation
variable is derived similarly.
{ } { }| 1 | 1E Z a E Z a= − = − = + (36)
{ } { }| 1 | 1Var Z a Var Z a= − = = + (37)
It is assumed, that the probability distribution of the observation variable can be approximated
and the transmitted bits are equiprobable. Therefore, the bit error rate of MU-CS-QCSK
modulation scheme is obtained as,
1 1
Pr( 0| 1) Pr( 0| 0)
2 2
mu muBER Z b Z b= < = + ≥ = (38)
1 1
Pr( 0 | 1) Pr( 0 | 1)
2 2
mu muZ a Z a= < = + + ≥ = −
{ }
{ }
| 11
2 2 | 1
mu
mu
E Z a
erfc
Var Z a
 = +
 =
 = + 
Where, m=2; represents the number of information bits transmitted per time slot and u=1, ...,Nu;
represents the number of users. For logistic maps, the expectation of chaos signal is
{ }2
1/ 2jE C = and variance of chaos signal is { }2
1/ 8jVar C = . By substituting, the
expectation values in the numerator and variance values in the denominator in the above
equation, it becomes
( ) { }
{ } ( ) { }
2 2 2
62 2 2 2 2 2 2 2 2
0 0
22 2
1
3 1
1 2
2 7
2
4
19 4
ju u
j ju u u
N N E C
erfc
N N Var C N N N Var C N N
N N
N N
β β
β β β β
 
  + +
  =
  
 + + +    
+
(39)
The conditional BER measured for the multipath channel is given by,
BER (α0, α1………… αL-1) = BER (γb) (40)
Where, γb = (Eb/No) (α0, α1………… αL-1) = ( γ0 + γ1 +………………+ γL-1 ).

148
Let, L be the number of propagation paths, ‘αl’ be the gain of the lth
path, τl be the delay of the
lth
path. The gains αl of the propagation paths is assumed to be independent identical distributed
Rayleigh random variables. The probability density function (PDF) of γi is an exponential
distribution given by,
( )
1
exp( )
k k
x
f x
γ γ
−
= (41)
The probability density function (pdf) of γb is obtained as,
( ) ( ) ( ) ( )b 0 1 1γ γ γ . γLf f f f −= ⊗ ………… ⊗
(42)
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
∞
= ∫ (43)
It is assumed to have two propagation paths, and then the bit error rate expressions for Multiuser
CS-QCSK (MU-CS-QCSK) can be simplified as,
( )
( )
2
6 22 2
1
3 .
1 2
2 7 1
9 2
4 4
1
2
b u
MU CS QCSK
bu u
K
BER erfc
K K K K
N
N N
γ
γ
− −
 
 +
 =
  
 + + +    
(44)
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. RESULTS AND DISCUSSION
The BER performance of MU-CS-QCSK modulation scheme is analyzed through Matlab
simulation. Simulation parameters taken for the analysis are:
Table 1. Simulation Parameters
Parameters Values / Types
Chip duration(Tc) 2 microsecond
Symbol duration(Ts) 2 millisecond
Transmission power(P) 43dBm
Noise power spectral density(No) 1 dBm
Chaotic Mapping Types Bernoulli map, Logistic map, Cubic map
Spread factor(K) 4,8,20
Total number of users 100
Fading Channel type Rayleigh

149
The BER performance of proposed MU-CS-QCSK scheme for various parameters under
multipath Rayleigh fading channel is discussed further with the obtained graphs.
4.1. BER Performance of Multipath Rayleigh Channel
0 5 10 15 20 25
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Eb/No(dB)
BER
Theoretical BER
Simulated Fit
Figure 3. BER performance of MU- CS-QCSK modulation scheme.
From the figure.3, it is inferred that BER performance of MU-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 16.5dB(approximately).
0 5 10 15 20 25
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Eb/No(dB)
BER
Logistic Map
Cubic Map
Bernoulli Map
Figure 4. BER performance of MU- CS-QCSK modulation scheme for various chaotic maps
BER performances of MU-CS-QCSK modulation schemes for various chaotic maps were
plotted. From the figure, it is inferred that, the logistic map and cubic map has similar and better
BER performance compared to the Bernoulli map. For simulation purpose logistic mapping
method is used because of its supermacy.

150
0 2 4 6 8 10 12 14 16 18 20
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Eb/No
BER
MU-CS-DCSK
MU-CS-QCSK
Figure 5. Comparison of BER performance of MU-CS-QCSK modulation scheme
From Figure 5, it can be inferred that, the proposed MU-CS-QCSK scheme offers better BER
performance compared to the other multiuser scheme.For the BER of 10-6, the proposed MU-
CS-QCSK requires16dB(approx) and theMU-CS-DCSK requires19.1dB(approx).
0 5 10 15 20 25
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Eb/No(dB)
BER
users=10%
users=20%
users=30%
Figure 6. Performance analysis for varying the percentage of users
The BER performance of MU-CS-QCSK modulation scheme for different number of users were
plotted. From the graph, it is infered that as the number of user increases the BER performance
is limited(i.e) for 10 % ,20% and 30% of the users it requires around 19.1 dB, 22dB and 24dB
respectively.This is because, as the number user increases the orthogonality in walsh codes
cannot be maintained.

151
Figure 7. BER analysis under varying Spreading factors
BER performance of CS-QCSK modulation scheme for various spreading factors (K=5,
K=10, K=15) are plotted. Figure 7. shows that, as the K value increases the noise
performance become worse. In general, smaller Spreading factor corresponds to minimum
noise level.
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 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 for a multiuser scenario. The proposed
MU- 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. However, the proposed logic suffers from a
marginal increased system complexity. The performance of the proposed modulation scheme is
analyzed in a multipath fading channel. Analytical expressions for the BER of MU- CS-QCSK
is derived and verified with matlab simulation. Simulation results, shows that the MU-CS-
QCSK has better BER performance than the other chaos based multiuser modulation schemes.
This proves the suitability of the proposed modulation technique for a mobile radio scenario,
which is the need of the hour.
6. REFERENCES
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0 5 10 15 20 25
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-6
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-5
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-4
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-3
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-2
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-1
10
0
Eb/No(dB)
BER
k=5
k=10
k=15

152
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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 in Department
of ECE from Pondicherry Engineering College, Puducherry. Her research
activities are focussed on Cooperative Communication in Cellular Networks,
mainly on Modulation and coding techniques. oto

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