SCYR 2010 - 10th Scientific Conference of Young Researchers – FEI TU of Košice

Chaotic sequences in MC-CDMA Systems

Henrieta Palubová

Dept. of Electronics and Multimedia Communications, FEI TU of Košice, Slovak Republic

henrieta.palubova@gmail.com

Abstract—The chaotic sequences in MC-CDMA Systems are

presented in this paper. Performance evaluation and comparison of multi-carrier code division multiple access system model for different spreading sequences with chaotic sequences at the presence of Saleh and Rapp model of high power amplifier (HPA) is investigated. The simulation results in Matlab are presented here.

Keywords—MC-CDMA, Saleh model, Rapp model, Chaotic sequences

I. INTRODUCTION

Sequences derived from chaotic phenomena are actively being considered for spread-spectrum communications [10]. In recent years there has been an increasing amount of interest in chaotic sequences in CDMA systems. MC/DS CDMA is described in [11]. Comparison of chaotic sequences and another type of pseudorandom sequences in CDMA systems is described in [13], [14], [15]. This paper is deal with chaotic sequences in MC CDMA systems. Chaos is a deterministic, random-like process found in non-linear dynamical system, which is non-periodical, non-converging and bounded. Moreover, it has a very sensitive dependence upon its initial condition and parameters. The generation of orthogonal sequences is utmost importance in MC-CDMA systems, in order to increase the spectrum efficiency in multirate communications systems. In CDMA, sets of non-correlated sequences with good autocorrelation and crosscorelation properties are required in order to provide low interference between users [12].

Section II. described MC-CDMA system model, section III. deal with nonlinear models, section IV. described chaotic sequences versus another type of pseudorandom sequences in MC-CDMA systems.

II. MC-CDMA SYSTEM MODEL

In MC-CDMA, instead of applying spreading sequences, in the time domain, we can apply them in the frequency domain, mapping a different chip of a spreading sequence to an individual Orthogonal Frequency Division Multiple Access (OFDM) subcarrier. Hence each of OFDM subcarrier has a data rate identical to the original input data rate and the multicarrier system absorbs the increased rate due to spreading in wider frequency band.

In MC-CDMA transmitter, the information bits to be transmitted by a particular user, are firstly base-band

modulated (QAM, PSK) into some modulation symbols and then are spreaded by using a specific spreaded sequence cm. In the case of MC-CDMA, as the spreading codes Walsh codes, Gold codes, Zadoff-Chu codes, Golay codes and Chaotic sequence codes can be used. The spreaded symbols are modulated by multi-carrier modulation implemented by IFFT (Inverse Fast Fourier Transform) operation. The IFFT after parallel-to-serial conversion represents the input signal of a HPA (High Power Amplifier), (see Fig. 1). The receiver consists of serial-to parallel converter, FFT (Fast Fourier Transform), BMF (receiver-Bank of Matched Filters), block of linear or non-linear transformation (labelled as T) and a decision device. Here, the operation of a single-user receiver known as BMF consists of a set of simple matched filters (correlators). In order to extend BMF into a multi-user receiver, the T-transformation block is included in the receiver structure [3]. In this paper, the linear MMSE-MUD [4] as well as nonlinear MSF-MUD for MC-CDMA [5], [6] are considered. The T-transformation block in MMSE-MUD is represented by multi-channel linear Wiener filter. In the case of MSF-MUD, the T-transformation block is represented by a complex valued-multichannel nonlinear microstatistic filter (C-M-CMF). C-M-CMF is the minimum mean-square error estimator based on the estimation of desired signals by using a linear combination of vector elements obtained by threshold decomposition of filter input signals [5], [2].

The main benefit of combining OFDM with DS-spreading is that it is possible to prevent the obliteration of certain subcarriers by deep frequency domain fades [1].

A block diagram of the simplified baseband model of MC-CDMA transmitter is given in Fig. 1 [2].

The basic structure of receivers considered in this paper is sketched in Fig. 2.

Fig. 1 MC CDMA transmitter

III. NONLINEAR MODELS

There are two major types of power amplifiers used in communications systems:

SCYR 2010 - 10th Scientific Conference of Young Researchers – FEI TU of Košice

Fig. 2 MC CDMA receiver

• Traveling wave tube amplifiers (TWTA) • Solid state power amplifiers (SSPA)

A common characteristic of both devices is that the signal at their output is a nonlinear function of the input signal at both the present and previous instants [7]. The output y(t) of the nonlinear amplifier is given by

( ) ( )( ) ( )( ) ( )( )( )txjorgtxjtxFty +Φ= exp (1)

where ( )tx is the amplitude (nonnegative voltage envelope)

of ( )tx , arg ( )( )tx is the phase of ( )tx , ( )•F is the

amplitude-to-amplitude (AM/AM) conversion and ( )•Φ is

the amplitude-to-phase (AM/PM) conversion [9]. For Saleh Model is AM/AM given as

( )2.1

.

xG

xGx uX

uuG

+=

κ (2)

and AM/PM as

( )2

2

.1

.

x

xx uX

uu

Φ

Φ

+=Φ

κ (3)

The Saleh model is commonly used for TWTA modelling. For Rapp Model is AM/AM given as:

( )ss

sat

x

xGx

O

u

uuG

2

12

1

.

+

=κ (4)

and AM/PM as

( ) 0=Φ xu (5)

The Rapp model is commonly used for SSPA modelling. The AM/AM and AM/PM are nonlinear characteristics

where nonlinearity depends on position of operating point. The operating point of the amplifier is defined by input

back-off (IBO) parameter, which is determined by the ratio between the saturation power of the amplifier and the average power of the signal. The HPA operation in the region of its nonlinear characteristic causes a nonlinear distortion of transmitted signal, that subsequently results in higher BER and outof-band energy radiation. IBO is given as

[ ]dBPx

inPIBO

= max,log10 10

(6)

The measure of effects due to nonlinear HPA could be decreased by the selection of relatively high value of IBO.

IV. CHAOTIC SEQUENCES VERSUS ANOTHER TYPE OF

PSEUDORANDOM SEQUENCES IN MC-CDMA SYSTEM

MC-CDMA performance analysis presented in this section is based on computer simulations. The basic scenario of the simulations is represented by the uplink MC-CDMA transmission system performing through AWGN transmission channel, at 16-QAM or 8-PSK baseband modulation, for K active users (K = 3 and K= 9).

As the spreading sequences, Walsh codes, Gold codes with period of 32 chips as well as complementary Golay codes, Zadoff-Chu codes and Chaotic sequences with period of 31 chips have been applied. The total number of sub-carriers has been set to N = 128. In order to avoid aliasing and the out-of-band radiation into the data bearing tones, the oversampling rate of 4 has been applied [2]. Then, Nu = 32 (Walsh codes, Gold codes) and Nu = 31 (complementary Golay codes, Zadoff-Chu codes and Chaotic sequences) carriers per transmitted block have been used for the spread 16-QAM and 8-PSK symbol transmission. The three types of systems are described here. The first one is the Linear MC-CDMA System, the second one is the nonlinear MC-CDMA System with Saleh Model and the third one is the nonlinear MC-CDMA System with Rapp Model.

A. Linear MC-CDMA System

The number of 100 000 input bits, the number of 3 users and the modulation type of 16-QAM and 8-PSK was used for simulations.

In the Fig. 3 the signal constellations at the outputs of 16-QAM mapper and BMF for Eb/No = 12 dB are given. For first user chaotic sequence is generated by chaotic map with different slopes with q = 0.5, r = 0.1 and initial condition x0 = 0.1. For second user chaotic sequence is generated by logistic map with initial condition x0 = 0.01. For third user chaotic sequence is generated by tent function with initial condition x0 = 0.012, and parameter a = 0.05. The type of chaotic sequences is detailed described in [8].

In the Fig. 4, the BER vs. Eb/No for MC-CDMA transmission system for different spreading sequences and 16-QAM is given. The AWGN channel model and 9 users was used in this simulation. It can be seen from Fig. 4, that all the types of sequences and receivers have the similar performance, except chaotic sequences in combination with BMF. Chaotic sequences in combination with BMF have the worse performance.

SCYR 2010 - 10th Scientific Conference of Young Researchers – FEI TU of Košice

-1.5 -1 -0.5 0 0.5 1 1.5-1.5

-1

-0.5

0

0.5

1

1.5

1 st user

2 nd user3 rd user

Fig. 3 Original symbol constellation at the output of the 16-QAM

B. Nonlinear MC-CDMA System – Saleh Model

For the specification of the Saleh model of HPA, the parameters kG = 2, χG = χФ = 1 and kФ = π/3 have been chosen.

The Saleh nonlinearity type has very destructive effect on QAM modulation (Fig. 5) [9]. The number of 100 000 input bits, the number of 3 users and the modulation type of 16-QAM or 8-PSK was used for simulation. In the Fig. 5, the signal constellations at the outputs of 16-QAM mapper and BMF for Eb/No = 12 dB are given.

0 2 4 6 8 10 1210

-4

10-3

10-2

10-1

100

Eb/No

BE

R

chs-bmfchs-mmse

chs-msfgy-bmf

gy-mmsegy-msf

gd-bmf

gd-mmsegd-msf

Fig. 4 BER vs. Eb/No for MC-CDMA transmission system for different spreading sequences and 16-QAM modulation

In the Fig. 6, the BER vs. Eb/No for MC-CDMA transmission system for different spreading sequences and 8-PSK is given. The AWGN channel model, 9 users and IBO = 2 dB was used in these simulations. It can be seen from Fig. 6, that all the types of sequences and receivers have the similar performance, except sequences in combination with BMF. All the types of sequences in combination with BMF are not available.

-1.5 -1 -0.5 0 0.5 1 1.5-1.5

-1

-0.5

0

0.5

1

1 st user

2 nd user3 rd user

Fig. 5 Original symbol constellation at the output of the 16-QAM – Saleh model

C. Nonlinear MC-CDMA System – Rapp Model

For the specification of the Rapp model of HPA, its parameters have been set to kG = Osat = 1 and s = 3.

The number of 100 000 input bits, the number of 3 users and the modulation type of 16-QAM and 8-PSK was used in simulation. In the Fig. 7 the signal constellation at the outputs of 16-QAM mapper and BMF for Eb/No = 12 dB are given.

In the Fig. 8, the BER vs. Eb/No for MC-CDMA transmission system for different spreading sequences and 8-PSK is given. The AWGN channel model, 9 users and IBO = 2 dB was used in this simulation. It can be seen from Fig. 8, that the best performance can be provided when we used Golay sequences in combination with MSF-MUD, MMSE-MUD or BMF. When we used the chaotic sequences, MSF-MUD and MMSE-MUD have the same performance, receiver BMF is not available. The worse performance has the Zadof-Chu sequences.

V. CONCLUSION

In this paper, the performance of MC-CDMA transmission system for two different models of HPA (Saleh and Rapp model), the different spreading sequences and receiver types is investigated. It has been found that Saleh model of HPA introduces much higher nonlinear distortion and causes more significant degradation of MC-CDMA transmission system performance than that of Rapp model. The best performance we can obtained when we used the Golay sequences in combination with MSF-MUD or MMSE-MUD. Chaotic sequences have similar performance like Golay sequences. MMSE-MUD and MSF-MUD have equivalent performance in linear and nonlinear MC-CDMA system. The worse performance we can obtain with using Gold or Zadof-Chu sequences. When we compare the modulation type, the best performance has 8-PSK. 16-QAM and 16-PSK have the similar performance.

ACKNOWLEDGMENT

This work was supported by the project VEGA 1/0045/10 – Nové metódy spracovania signálov pre rekonfigurovateľné bezdrôtové senzorové siete.

SCYR 2010 - 10th Scientific Conference of Young Researchers – FEI TU of Košice

0 2 4 6 8 10 1210

-4

10-3

10-2

10-1

100

Eb/No

BE

R

chs-bmf

chs-mmsechs-msf

gy-bmf

gy-mmse

gy-msf

gd-bmfgd-mmse

gd-msf

Fig. 6 BER vs. Eb/No for MC-CDMA transmission system for different spreading sequences (8-PSK modulation, Saleh

model, IBO = 2 dB)

-1.5 -1 -0.5 0 0.5 1 1.5-1.5

-1

-0.5

0

0.5

1

1.5

1 st user

2 nd user3 rd user

Fig. 7 Original symbol constellation at the output of the 16-QAM – Rapp model

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0 2 4 6 8 10 1210

-4

10-3

10-2

10-1

100

Eb/No

BE

R

chs-bmf

chs-mmsechs-msf

gy-bmf

gy-mmse

gy-msfzchu-bmfzchu-mmse

zchu-msf

Fig. 8 BER vs. Eb/No for MC-CDMA transmission system for different spreading sequences (8-PSK modulation, Rapp

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