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The Eighth International Conference on Electronic Measurement and Instruments ICEMI’2007

Analysis of BER for MC-CDMA with Effect of Multi-path

Yang Qi Shi Haoshan Han Zhongxiang

Electronic Information Department, Northwestern Poly-technical University,

Xi’an, 710072, China

Abstract: This paper introduces a telecommunication

technology-- multi - carrier CDMA based on OFDM system,

presents its structure, and compares it to CDMA system.

MC-CDMA has better BER than CDMA due to frequency

diversity and the capabilities in dealing with multi-path time

delay. In conclusion, MC-CDMA than CDMA in spectral

frequency, and anti - interference ability.

Key words: OFDM; MC-CDMA; BER;MUI;

1. Introduction

It is well known that Direct-Sequence (DS) Code

Division Multiple Access (CDMA) has emerged as the

predominant air interface technology for the 3G

cellular standard, because of its increasing capacity of

system, effective suppression of interference,

low-power and superior performance of secrecy,

compared to conventional multiple access techniques

like frequency-division multiple access (FDMA) and

time-division multiple access (TDMA). In the

downlink, DS-CDMA relies on the orthogonality of

spreading codes to separate different users. However,

inter-chip interference (ICI) destroys the

orthogonality among users, which causes Multi-user

interference (MUI). Since MUI is essentially caused

by the multi-path channel, linear chip-level

equalization, followed by correlation with the desired

user’s spreading code, suppresses MUI. However,

chip equalizer receivers suppress MUI only

statistically, and require receiver’s diversity to cope

with the effects caused by deep channel fades, and for

increasing data rates, the underlying multi-path

channels become more disperse, causing inter-symbol

interference (ISI) and ICI. On the other hand,

orthogonal frequency-division multiplexing (OFDM),

also called multi-carrier (MC) modulation, with cyclic

prefixing (CP) constitutes an elegant solution to

combat the wireless channel impairments. It converts

a frequency-selective channel into a number of

parallel flat fading channels by multiplexing blocks of

information symbols on orthogonal sub-carriers using

implementation efficient fast Fourier transform (FFT)

operations. Hence, the complex equalizer commonly

encountered in single-carrier systems reduces to a set

of parallel and independent single-tap equalizers.

2. MC-CDMA System Structure

Figure 1 describes the MC-CDMA transmission

and reception scheme. We consider the MC-CDMA

system serving M active users within its coverage area,

and mth user ÿs data sequence bm(k), its value as f

1ˈwith a rate 1/Tb, replicator repeats bm(k) N times

and to multiply cm(k)ˈ [0, 1]i N , yield bm(k), its

value as f1 w̍ith a rate 1/Tb, replicator repeats bm(k)

N times and to multiply cm(k)ˈ , yield the

transmission sequence:

[0, 1]i N

)()/22cos(

)()(1

)('

0

1

0

bT b

k

N

i

mmm

kT t P T it t f

ick b N

t s

b

¦¦f

f

S S

˄1˅

Where--0 /i b f f i T is the frequency of ith

sub-carrier, and is unit pulse with width-- .bT P bT

VS 6 &3

0XOWL

FKDQQHO

K

&DQF

HO

&3

,QWHJUDWRU

(0)m

c

(1)m

c

#

)2cos( 0t f S

)1( N cm)2cos( 1t f N S

)2cos( 1t f S )(k sm

)(k r m

)(t n6

)(k d m

)(k bm

)0(mc

)1(mc

)1( N cm

)2cos( 0t f S

#

)2cos( 1t f S

)2cos( 1t f N S

Figure 1 the MC-CDMA transmission and reception scheme

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After modulation, the rear L symbols of OFDM

sequences are moved to front by CP, and constitute a

protecting space. So the receiver could suppress and

even counteract the ISI after getting rid of the

protecting space if the space time is greater than thetime of channel delay

' ( ) 0( )

' ( ) 0

m b

m

m b b

s t t s t

s t NT LT t

d - ®

d¯

NT

˄2˅

The channel is Rayleigh channel, described as:

0

( ) ( ) L

l

N j

l l

l

h t a t eT

G W

¦

(3)

Where L

N is the number of most propagation

multi-path,l l l a W T represent random amplitude,

propagation time delay, and phase of the ith path

respectively. The structure equals the channel model

of L

N taps, and its time delay isl W . Because of CP,

there is no ISI. The bandwidth of every sub-carrier is

very narrow, often less than the bandwidth of

correlation, so there are no distortions of amplitude

and phase. And the channel frequency characteristic of

mth user for corresponding sub-carriers:

,

0 ,( ) m i j

m m

b

ii H f e

T

T U

˄4˅

Where,mi U is independent random variable of

Rayleigh distribute, and represents the coefficient of

signal amplitude fading,,m iT is independent random

variable of equality distribute, and describes the

distortion of phase. After brushing off CP, the receive

signal:

)()(

)/22cos(

)()(1

)(

,0

1

0

,

t nkT t P

T it t f

ick b N

t r

bT

imb

k

N

i

mmimm

b

¦¦f

f

T S S

U

˄5˅

Where represents additive white Gaussian

noise, its power density of single band is . We

consider the system serving M active users, the

receive signal:

( )n t

0 N

)()(

)/22cos(

)()(1)(

,0

1

0

1

0

,

t nkT t P

T it t f

ick b N

t r

bT

imb

k

M

m

mm

N

i

im

b

¦ ¦¦f

f

T S S

U

˄6˅

MC-CDMA is an integrated technology of

OFDM and CDMA. Both technologies could cancel

ISI if only the protected space is greater than

maximum delay time-- . But they have

differences with the solution of using sub-carrier. In

OFDM technology, a sub-carrier correspond to an

information symbol, so to avoid the effect of deep

fading, there must be some redundant sub-carriers to

provide correction protection. But in MC-CDMA, the

same information symbol has different frequency

spreading chips with different sub-carriers. In other

words, a symbol has different sub-carriers, which

enables frequency diversity and does not need

correction coding. In addition, there are differences in

orthogonality. In OFDM symbols rely on orthogonal

sub-carriers, but in MC-CDMA the orthogonalities are

among different sub-carriers and users’ frequency

spreading code sequences, the earlier could increase

the spectral efficiency, and the latter allows sharing

system frequency resource as well as increasing the

spectral efficiency. Compared to OFDM, MC-CDMA

has superior spectral efficiency in theory.

maxT

We should understand the orthogonality of

sub-carriers in this way: system distributes an

orthogonal PN sequence with length of N for different

users, which chip corresponds to a frequency of

sub-carrier, --system divides the bandwidth into N

parallel sub-channels, the frequency of sub-carrier is

0 ( 0,1, 1i f f i f i N ) ' " , where0

f is practical

transmission carrier’s frequency,b

F f

T ' is distance

between sub-carriers, is a positive integer, T is F b

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distance between symbols of user’s data. We can

prove the orthogonality between N sub-carriers easily:

( 1)01

exp( 2 )1

b

b

m T

m

b mT

m n j f t dt

m nT S

z- ®

¯³ ˄7˅

Where0

10, 1,

b

f F f T

' . In theory, the

spectral efficiency is maximum if there is no

disturbance between sub-carriers and the distance is

minimum.

3. Analysis of BER

Consider receiver has super synchro ability for

phase and frequency, and with EGC diversity

technology, and equalizing coefficient is “1”, so the

decision output of the th information symbol from

th user sent is:

k

g ( 1) 1

0 ,

0

( 1) 1

0 ,

0

1 1 1

, ,

0 0 0

0

2( ) ( ) ( )cos(2 2 / )

2( ) ( )cos(2 2 / )

ˆ( ) ( ) ( ) ( ) cos

2( ) ( )cos(2

b

b

b

b

k T N

g g b

ib kT

k T N

g b

ib kT

N M N

g g i m m g m i m i

i m im g

g

b

d k r t c i f t it T dt T

n t c i f t it T dt T

b k b k c i c i

n t c i f T

S S T

S S T

U U

S

z

¦³

¦³

¦ ¦¦

( 1) 1

,

0

2 / )b

b

k T N

b g i

ikT

g g n

t it T d

d I I

S T

¦³

,

g i

g i

T

t

]b

˄8˅

Suppose the data was transmitted of “1” during

by the th user, and consider [ , ( 1)bkT k T g

1

,

1

N

g g i

i

U U

¦ , because, g i U is i.i.d, known from the

theory of center & limit, g

U and g d submit to

Gaussian distribution.

,

2 2

,

( ) ( ) ( )

1( )

2 2

2

g g g

g i

g

E d E NE

N E

N

U U

S U

S U

i

˄9˅

let 2

,

1(

2

2 2 2

, ,{ ( ) [ ( )] }

(2 )2

g g d g i

g

N E E U V V U U

S U

2

g i

m i

˄10˅

in equation 8th

ˈ

1 1

, ,

0 0

ˆ( ) ( ) ( ) cosM N

g m m g m i

m im g

I b k c i c i U T

z

¦¦ ˈ and

, ,ˆ

m i g i m i,T T T submit to equality distribution during

[0,2 ]S ˈ g I contains ( 1)M N u i.i.d Gaussian

variablesˈso g I also submit to Gaussian distribution.

1 1

0 0( ) [ ( )] ( ) ( )

M N

g m m

m im g

E I E b k c i c i

z

¦¦g

(11)

, ,ˆ( ) ( ) (cos ) 0 g m i m ic i E E U T

(12)

2 2

,

2

,

1 ˆ( 1) [ ( ) ( ) ( ) cos ]2

1( 1) [ ] ( 1)

2

g , I m m g m i m i

m i m

M NE b k c i c i

M NE M

V U

U U

T (13)

[ ] 0n E I ˈvariance˖ 2

0n I

b

N N

T V Ǆ

Hence results in submitting to Gaussian

distribution, and mean and variance are:

( ) g d k

2

0

[ ( )]2

(2 ) ( 1)2

g g

g m

b

E d k N

N M N

T

S P U

S V U U

(14)

Because of the data transmitted during

[ , ( 1)kT k T ]b b by th user is “1”, so at receiver the

BER of decoding output is:

g

2

2

[ ( ) ]0

2

( ) [ ( ) 0]

1

2

1( )

2 2

g

e e g

d k

p g P d k

e d

erfc

P

V

SV

P

V

f z

³

) g g i N E U U ˈso

(15˅

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Where

22( ) t

xerfc x e dt

S

f ³

˄16˅

4. Simulation Results

In order to verify the validity of this MC-CDMA

scheme, the software, MATLAB, is used to simulate

MC-CDMA system.

Generally, the MC-CDMA system described by

the equation 15th

has optimistic performance in BER.

The Monte_Carlo method is often adopted in practice

to numerically analyze system’s BER. By setting

different parameter on simulation platform,

MC-CDMA system’s corresponding BER curve is got

to verify its performance.

Every time 64000 bits data is sent. After err

calculating, as SNR is added 1db and another 64000

bits’ Monte-Carlo simulation is applied.

First, the difference between MC-CDMA and

traditional CDMA in BER performance is simulated

under the condition of 12 multi-path, BPSK,

non-prefix, the same coding condition. As Fig 2

showing, when the number of multi-path is 12, which

is more than protection space, the un-coded

MC-CDMA has better BER performance than CDMA,

which presents its excellent ability to suppress ISI and

multi-path interference. This capability is very

important for wireless broad band system. Fig 3 shows

un-coded MC-CDMA system’s BER Performance in

the different condition of multi-paths (10,20,40),

BPSK, and non-prefix. The result proves that system

BER be increased as the number of multi-path is

increased.

SNR

B E R

Figure 2 the BER Comparison between CDMA and

MC-CDMA under the condition of multi-paths

Figure 3 the influence of multi-paths to MC-CDMA BER

5.Conclusion

MC-CDMA combines the merits of both OFDM

and CDMA. Although CDMA has good performance,

MC-CDMA is comparatively better in frequency

efficiency and mitigation of multi-path interference.

However, MC-CDMA has some disadvantages, such

as the frequency spectra of sub-carriers are overlapped,

and its envelope is variable, which result in being

sensitive to the frequency shift and nonlinear

distortion. But these are not important, compared to its

merits. There have been a lot of research on this

subject recently, and to resolve these problems is

possible.

References:

[1] PENG Ling .The 3nd Generation Technology of Mobile

Communication. Publishing House of Electronics

Industry.2003,2.

[2] K. Fazel. Performance of CDMA /OFDM for Mobile

Communication System[ J ]. IEEE 2nd Int. Conf. on

Universal Personal Communicationˈ Canadaˈ 1993ˈ

(2) : 975 - 979.

[3] B. G. Kang. On the Performance of an OFDM /CDMA

System under Realistic Channel Conditions[C ]. IEEE

1997.

[4] YEE NˈLinnartz J PˈFettweis G. Multicarrier CDMA in

Indoor Wireless Radio Networks.IEICE tran.Comun ˈ

1994;E77-B(7):900̚ 904

[5] Han Fangming. The Performance Contrast Between

MC-CDMA and DS-CDMA. Communications technology.

No.2,2003.No.134,totally.

[6] GUO Ling, SHAO Shixiang. Multi-carrier CDMA

Technology Based on OFDM. Telecommunications for

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Electric Power System. Vol 26 No.150, Apr 10,2005.

[7] LIAO Ming, YU Ping. Broadband Data Transmission.

Electronic Communication Technology.No.4,2003

Author Biographies

YANG Qi, : born in 1969, pursuing PhD degree in Electronic

Information Department of Northwestern Polytechnical

University in China now. His interest research area is radio

communication.

Shi Hao-shan: born in 1946, professor and PhD tutor in

Electronic Information Department of Northwestern

Polytechnical University in China now. His research areas

include modern communication and network techniques.

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