International Journal of Scientific & Engineering Research, Volume 4, Issue 1, January-2013 1

ISSN 2229-5518

Performance of Chaos-Based MC-MC-CDMA in

Frequency Selective Fading Channel

Maha George Zia

Abstract— This paper presents the effect of chaos sequences on the performance of multi-code multi-carrier code division multiple access (MC-MC-CDMA) communication system. Since a chaotic system dependence on its initial conditions, the multi-carrier scheme is established by using one chaotic sequence generator with different initial conditions for the code sequence set of M-ary modulation, and the multi-carrier scheme is established by using another chaotic generator with another different initial conditions. The simulation results demonstrated that the chaos – based MC-MC-CDMA system achieves significant performance improvement compared to Walsh- Hadamard codes in the conventional MC-MC-CDMA system.

Index Terms— chaos based spread spectrum, chaos generator, MC-MC-CDMA system, Walsh-Hadamard codes, fading channel, multicarrier system, spreading codes

1 INTRODUCTION

—————————— ——————————
n order to spread the bandwidth of the transmitting sig- nals, pseudo-noise (PN) sequences have been used exten- sively in spread-spectrum (SS) communication systems. The maximal-length linear code sequences (m-sequences) have very desirable autocorrelation functions. However, large spikes can be found in their cross-correlation functions, espe- cially when partially correlated, as in the case of multi-path environments. It is proposed to use chaotic sequences as spreading sequences in SS systems. One major difference be- tween chaotic sequences and the PN sequences is that chaotic sequences are not binary and the auto-correlation of these se- quences is a delta-function while their cross-correlation is
identically zero [1].
Based on Chaos theory, [2] provided a new method for de- tection of Direct Sequence Spread Spectrum (DSSS) signal. According to the analysis of intermittent chaos, chaotic oscilla- tors array was used in the method. In addition, the system of
Duffing Chaotic Oscillators Array was constructed for blind detection in very low signal-to-noise ratio (SNR). This detect- ed method was effective when compared with wavelet de- composition at lower detection threshold which enhanced the performance system at very low signal-to-noise ratio (SNR).
A support vector machine receiver (SVM) for a multi-code Chaos-based CDMA (MC-CB-CDMA) system was proposed in [3], where the main aim for the assigning multiple spread- ing codes for each user was to provide unequal error protec- tion on the transmitted data without using further error cor- rection coding (ECC). The proposed SVM receiver was simpli- fied by the recursive feature elimination algorithm so that it has a less complexity than the conventional correlator receiver
and huge performance gain was achieved due to the multi-

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Maha George Zia is currently an assistant professor in Software engineer- ing department in College of Engineering - Salahaddin University, Iraq,. E- mail: mahageorge11@gmail.com

user detection capability from the SVM receiver [3].
A scheme of chaotic spreading sequence for multi- carrier code division multiple access system (MC-CDMA) was pro- posed in [4] to estimate the transmission channel. The pro- posed system used a chaotic sequence generated by a logistic
map as a training signal and estimated channel parameters according to dynamics of the chaotic sequence. Encoding data by chaotic sequences was first built and then the orthogonal codes were used to spread the encrypted data for multiusers scheme. At the reception, first the channel parameters were identified using a training chaotic sequence in order to equal- ize the received data, and then the encrypted information was decoded for the desired user. The proposed system (chaos plus orthogonal codes) significantly outperforms the Walsh- Hadamard code spreading in MC-CDMA system. Moreover, chaotic code spreading approach for channel identification achieved significant improvement in the channel identifica- tion, comparing to using others training sequence or the least square method [4].
A chaos modulation scheme called initial condition modu- lation (ICM) which is based on chaotic signal separation was proposed in [5]. The proposed scheme transmitted two M-ary symbols in one period, its data rate is 2 log2(M) times higher than other binary chaotic schemes under the assumption of the same bandwidth usage. In this system, the success of sig- nal separation makes it possible to transmit multiple infor- mation streams through single channel. It also significantly improves data transmission rate and implies good information security [5].
This paper demonstrate the performance of MC-MC- CDMA system employing chaotic sequences and the simula- tion results show that this system can be better than the con- ventional MC-MC-CDMA system that uses Walsh-Hadamard codes in terms of symbol error rate (SER) probabilities.
The paper is organized as follows; section 2 describes the system model of MC-MC-CDMA based chaos sequences. The system analysis is presented in section 3. In section 4, the sim- ulation results of SER performance of MC-MC-CDMA using chaos and Walsh-Hadamard codes are presented. Finally, con- clusions are presented in section 5.

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2 SYSTEM MODEL

Consider MC-MC-CDMA system [6]. The proposed system

3 SYSTEM ANALYIS

Consider each user has the same code sequence set
uses 4-ary modulation called M-code sequence, where M= 4.

vm (n)

1  m M , 0  n N  1 as shown in Fig.(1).

As shown in Fig. 1, 4-ary symbol selects one of the 4 pre- mapped code sequences using one chaotic generator for transmission. The chaotic generator [7] and transmitted signal can be expressed as:
User k's ith M-ary data symbol (bk,i) is mapped to one of the code sequences in the code sequence set [6].

vk ,i (n)  vk ,i , i  1,2,..., M ,1  n N is the ith chaotic

transmit sequence of length N of user k and is generated from
equation (1). Each symbol of the length N chaotic sequence

vn 1

4 v3

 3 vn


, v  1

(1)

vk ,i

is copied onto L subcarries branches and multiplied with

v1 if

v2 if

v3 if

symbol"0" is transmitted

symbol"1" is transmitted

symbol"2" is transmitted

(2a) (2b)
(2c)
the user specific scrambling code from (2) and can be written as:

C  [c , c ,...., c ]T

S k , i vk ,i . C k ,i

Ck ,i

which is generated
(5) (6)
After that

S k ,i

will go through IFFT of size L and the

v4 if

symbol"3" is transmitted

(2d)
transmitted signal of user k can be written as:
Assuming that the chaotic sequences are generated inde- pendently of one another and the mean value of each of the chaotic sequences is zero in order to avoid transmitting any dc component which is a waste of power. In other words,

L

sk (n)  (1 / L) S k ,i (l ) e

l 1

j 2 n l / L

(7)

Ev

i , k

(n) 0

, i  1,2,..., M

and k  1,2,..., K

(3)

Each chaotic sequence v(n) has a time domain spreading ra- tio of N. For kth user, each symbol of the length N chaotic se- quence is copied onto L subcarries branches and multiplied with the user specific scrambling code ck,1, ck,2, …. ck,L as shown in Fig.1 [6]. The user specific scrambling code is generated from another chaotic generator by changing its initial condi- tion and is considered as spreading in frequency. The user specific scrambling code is generated using the chaotic genera- tor [8]:

cn 1

 4 cn (1  cn )

(4)

In [6], subcarrier multiplications and summation are used in the transmitter and receiver. In this work, Inverse Fast Fou- rier Transform (IFFT) and Fast Fourier Transform (FFT) each of size L replaces the subcarrier multiplications and summa- tion at the transmitter and receiver respectively. Also, because intersymbol interference (ISI) is minor in multicarrier CDMA, cyclic prefix is not employed.
At the receiver of Fig.1, a size L-FFT is applied to the input and the output of the FFT is then despread to generate each of the received chaotic sequence of length N. The received N chaotic sequence is correlated with each of the possible four chaotic sequences (v1(n), v2(n),.., v4(n)) and the sequence that gives maximum correlation is then mapped back into an 4-ary symbol.

Fig.1 Transmitter and receiver of MC-MC-CDMA sys- tem

sk (n) passes through frequency selective Rayleigh fading channel which is modeled using Jake's model [9]. In the re-

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International Journal of Scientific & Engineering Research Volume 4, Issue 1, January-2013 3

ISSN 2229-5518


ceiver of Fig.1, a size L FFT is applied to the input and the output is then despread to generate the received sequence code which can be written as:

r (n)  [ R , R ..., R ]T

k 1 2 L

M K L

  

k ,l

k ,i

k ,l

1 2 L

[

i 1

h v

k 1 l 1

c ]  [w , w ,..., w ]T

where hk ,l

(8)

is a Rayleigh distributed amplitude attenuation,
and wl
is the additive white Gaussian noise with zero mean
and unit variance. The N despread bits from a degenerated
code sequence are correlated with each of M possible code
sequences. The sequence that gives maximum correlation is
then mapped back into an M-ary symbol.

4 PERFORMANCE COMPARISONS OF MC-MC-CDMA BASED CHAOS AND WALSH- HADAMARD CODES

The simulation results of SER performance of MC-MC- CDMA system based chaos and Walsh-Hadamard codes are presented using MATLAB. QPSK is used in the system, the channel is considered as frequency selective Rayleigh fading channel modeled as Jake's model [9].

Fig. 2 shows the SER performance of the MC-MC-CDMA system with different values of N and L=16. Both M-code se- quence and the spreading code use the chaos generator repre- sented by( 1) and (4) respectively. It can be noticed that as N increases, the SER performance gets better.
In Fig. 3, the system uses different number of subcarriers for N=16 and SER performance gets improved as L is in- creased.
Walsh-Hadamerd codes and chaos codes are used in an al- ternative forms in Fig.4 for N=L=16. Four curves of SER per- formances are described. The first curve shows SER perfor- mance using chaos code for both M-code sequence and the spreading code. The second curve shows SER performances using chaos code for M-code sequence and Walsh-Hadamerd code for the spreading code. The third curve shows SER per- formances using Walsh-Hadamerd code for M-code sequence and chaos code for the spreading code. The fourth curve shows SER performance using Walsh-Hadamerd code for both M-code sequence and the spreading code. It can be notice that curve A outperforms curve D by 2.3 dB at SER = 10-4.
Fig. 5, 1 and 4 users are applied to MC-MC-CDMA system
based chaos for N = L = 16. It can be noticed that as the num-
ber of users is increased the SER becomes worse.

Fig.2 SER performance of the MC-MC-CDMA

system with different values of N and L=16

Fig.3 SER performance of the MC-MC-CDMA

system with different values of L and N=16

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Fig.4 SER performance of the MC-MC-CDMA

system with different codes and N = L=16

Fig.5 SER performance of the MC-MC-CDMA

system with different users and N = L=16

5 CONCLSIONS

In this paper, MC-MC-CDMA system based chaos was presented and the SER performance was measured using MATLAB program for different values of M- sequence code length and spreading code length. Simu- lation results showed that MC-MC-CDMA system based chaos performs better than MC-MC-CDMA system based Walsh-Hadamard code in terms of SER perfor- mance.

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