ISSN: 2278 1323

International Journal of Advanced Research in Computer Engineering & Technology

Volume 1, Issue 4, June 2012

456
All Rights Reserved 2012 IJARCET

PAPR Reduction of an MC-CDMA system
using SLM technique
Gagandeep Kaur, Rajbir Kaur


Abstract- Multicarrier Code Division Multiple Access is the
most promising technique for high speed data transmission.
However, the MC-CDMA signals are characterized by large
peak to average power ratios (PAPR), which can reduce the
system efficiency. In this paper PAPR reduction of an MC-
CDMA system using SLM technique is investigated for
different modulation schemes. The binary phase sequences
considered in this paper are generated from hadamard
matrix.

Index terms- MC-CDMA, PAPR and Complementary
Cumulative Distribution Function.
I. INTRODUCTION
Multicarrier code division multiple access (MC-CDMA)
is a promising candidate for 4G wireless communication
system. It is a technique that combines advantages for both
OFDM and CDMA schemes that provide many advantages
such as high data rate transmission, high bandwidth
efficiency, frequency diversity and interference reduction.
MC-CDMA has attracted much attention as fourth
generation mobile communication system because it can
realize high data rate and high capacity transmission by
multiplexing information symbols of many users with
orthogonal codes [1-4].
However, inspite of all such advantages, it is not yet
problem free. MC-CDMA suffers from high PAPR when
using large number of sub-carriers. Large peak-to-average
power ratio (PAPR) distorts the signal if the transmitter
contains non-linear components such as power amplifier.
The non-linear effects on the transmitted MC-CDMA
symbol are spectral spreading, inter-modulation and
changing the signal constellation. Therefore PAs require a
back off which is approximately equal to the PAPR for
distortionless transmission. This decreases the efficiency
for amplifier. Hence it is desirable that transmitted signal
possess reduced peaks and in order to achieve this there are
several PAPR reduction techniques.

Manuscript received May 2012
Gagandeep Kaur, pursuing M.Tech(ECE), University College of
Engineering, Punjabi University Patiala, Patiala, India, 0171-2551636,
(email: gaganksodhi@gmail.com)
Rajbir Kaur, Assistant Professor (ECE), University College of
Engineering, Punjabi University Patiala, Patiala, India, +919779160093,
(email:rajbir277@yahoo.co.in)

These techniques are divided into three groups: signal
distortion techniques, signal scrambling techniques and
coding techniques. Signal distortion schemes reduce the
amplitude by linearly distorting the MC-CDMA signal at or
around the peaks. This includes techniques like clipping,
peak windowing, and peak cancellation [1], [5]. It is the
simplest technique but it causes in-band and out-band
distortion. Scrambling scheme is based on scrambling each
MC-CDMA signal with large PAPR. It includes techniques
such as Selected Mapping (SLM), and Partial Transmit
Sequence (PTS). In case of PTS technique [7-8], MC-
CDMA sequences are partitioned into sub-blocks and each
sub-block is multiplied by phase weighting factor to
produce alternative sequences with low PAPR. However
large number of phase weighting factors increase the
hardware complexity and makes the whole system
vulnerable to the effect of phase noise. The SLM technique
[9-16] pseudorandomly modifies the phases of the original
information symbols in each MC-CDMA block several
times and selects the phase modulated MC-CDMA with
best PAPR performance for transmission.
In this paper PAPR reduction of an MC-CDMA system
using SLM technique is investigated for different
modulation schemes. The binary phase sequences
considered in this paper are generated from hadamard
matrix.
II. SYSTEM DESCRIPTION

A. MC-CDMA system
The transmitter structure of an MC-CDMA system is
shown in fig.1. It is assumed that there are K active users
and each user transmits M parallel modulated symbols.
( ) ( ) ( ) ( )
1 2
[ , ,..., ]
k k k k T
M
d d d d = Denotes the M modulated data
symbols of kth user, k=1, 2, K. Modulated data symbols of
kth user
( ) k
m
d are converted from serial to M parallel data
streams. After this serial to parallel conversion each
complex symbol is spread by the user specific code
( ) ( ) ( ) ( )
1 2
[ , ,..., ]
k k k k
L
c c c c = where L denotes the spreading factor
(SF). As the spreading sequences orthogonal sets of
sequences are preferred for reducing low multiuser
interference. Walsh-Hadamard (WH) sequences are used as
spreading sequences in this procedure. Then the input of K
users is summed up, and is interleaved in frequency domain
as to achieve frequency diversity as
ISSN: 2278 1323
International Journal of Advanced Research in Computer Engineering & Technology
Volume 1, Issue 4, June 2012

457
All Rights Reserved 2012 IJARCET

( )
0 1 1
1
, ,..., ] [
K
k T
N
k
X X X X X

=
= =

to achieve frequency
diversity. After interleaving the symbol element are then
input to the IFFT block of size N M L = .
The resultant baseband signal for one MC-CDMA
0 s t T s s symbol is represented as
( ) ( ) 2 ( ( 1) ( 1)) /
1 1 1
1
( )
K M L
k k j M l m t NT
m l
k m l
d c e
N
s t
t +
= = =
=

(1)


Fig. 1. MC-CDMA transmitter
B. PAPR
The PAPR of the MC-CDMA symbol is defined as ratio
of the peak power and the average power:
10
2
max ( )
10log
2
( )
peak
average
s t
p
PAPR
p
E s t
= =
(
(

(
(
(2)

Where peak p represents output peak power, average p means
output average power.
| | denotes the expected value.
The cumulative distribution function (CDF) is one of the
most regularly used parameters, which is used to measure
the efficiency on any PAPR technique. Normally, the
Complementary CDF (CCDF) is used instead of CDF,
which helps us to measure the probability that the PAPR of
a certain data block exceeds the given threshold [4].
The CDF of the amplitude of a sample signal is given by
( ) 1 exp( ) F z z =
(3)

The CCDF of the PAPR of the data block is desired is
our case to compare various reduction techniques. This is
given by [3]:
( ) 1 ( ) P PAPR z P PAPR z > = s
1 ( )
N
F z =
1 (1 exp( ))
N
z =
(4)
When calculating the PAPR, we have to consider the
actual time domain signal that is in analog form. The IFFT
outputs, which are symbol spaced sampling values, will
miss some of the signal peaks. Therefore, if we calculate
PAPR by using these sample values, then the calculated
PAPR is less than the actual PAPR [6]. This is an optimistic
result and will not illustrate the real situation. However,
they are enough for signal reconstruction. To account for
this issue, oversampling is performed by low pass filtering
the IFFT signal and then sampled at higher rate. Now, the
increased samples are close to the real analog signal and
calculation of PAPR based on these samples will give a
better estimated PAPR.
III. SELECTED MAPPING (SLM) METHOD
A block diagram of SLM is shown in fig.2. In SLM, U-1
statistically independent phase sequences are generated.
Symbol sequences are multiplied by the U-1 different phase
sequences {b
u
, u = 1, 2, , U-1}, whose length is equal to
number of carriers before IFFT process. The PAPR is
calculated for U-1 phase rotated symbol sequences and one
original phase sequence. Then the symbol sequence with
the lowest PAPR is selected and transmitted as side
information. The receiver performs the reverse operation to
recover the data symbol. Since SLM is a linear operation, it
does not cause non-linear operation. However, SLM needs
the IFFT process for each phase sequence, that is, U IFFT
processes. Thus, a large amount of calculation is needed in
SLM.

Fig. 2. A block diagram of selected mapping
The block diagram of MC-CDMA system with SLM
technique is shown in fig.3. The input data sequences of
each user
( ) ( ) ( ) ( )
1 2
[ , ,..., ]
k k k k
M
d d d d = with length M are first
converted into M parallel data sequences
( ) ( ) ( ) ( )
1 2
[ , ,..., ]
k k k k
L
c c c c = and then each S/P converted output
is multiplied with the spreading code with length L.
Multiplexed symbol sequences
( )
0 1 1
1
, ,..., ] [
K
k T
N
k
X X X X X

=
= =

are multiplied by U-1

different phase sequences
0 1 1
[ , ,..., ]
u u u u
N
b b b b

= whose
length is equal to the number of carriers before IFFT
process resulting in U-1 modified data blocks
ISSN: 2278 1323
International Journal of Advanced Research in Computer Engineering & Technology
Volume 1, Issue 4, June 2012

458
All Rights Reserved 2012 IJARCET

1
( ) ( ) ( )
0 0 1 1 1 1
0
[ , ,..., ]
U
u u u u T
n n N N
u
S X b X b X b X b

=
= =

. After the IFFT

process, the PAPR is calculated for U-1 phase rotated
symbols sequences
1
( ) ( ) ( )
0 0 1 1 1 1
0
( ) [ , ,..., ]
U
u u u u T
n n N N
u
s t x b x b x b x b

=
= =

and one original

sequence and then the symbol sequence with lowest PAPR
is selected for transmission and the corresponding selected
phase sequence
{ }
{ }
1
(0) (2) ( 1) ( ) ( )
0 1
(1), (2),..., ( 1) 0
, ,..., argmin max
U
U u v
n
n N
b b b U u
b b b b x

s s
=
| |
=
|
\ .

is
also transmitted to the receiver side for transmission [10-
16].

Fig. 3. MC-CDMA system using SLM

IV. SIMULATIONS
In this section the performance MC-CDMA system is
evaluated using SLM. Table I below shows the simulation
parameters. If we oversample a transmitted signal by a
factor of four, the discrete PAPR is almost the same as
continuous PAPR [16]. Thus we oversample the transmitted
signal by a factor of four in IFFT process.

TABLE I
SIMULATION PARAMETERS
Spreading codes Walsh Hadamard
Modulation process BPSK, QPSK, MSK
Processing Gain (L) 8
Number of data symbols per an
MC-CDMA symbol (M)
16
Number of sub-carriers (N) 128
Number of active users (K) 8
Number of phase sequences
(U)
4,8 and16
Oversampling factor 4

The performance metric utilized in evaluating PAPR
reduction scheme is CCDF of the PAPR of transmitted
continuous time signal. The resulting CCDF curves are
presented for 1,000 input symbol sequences for different
number of phase sequences (U=4, 8 and 16) when
considered number of active users to be equal to 8. The
phase sequences used are binary phase sequences {1,-1}.
The rows of hadamard matrix are used in phase factor
generation, in this case, with processing gain equal to 8.
The system consists of 128 subcarriers with modulation
schemes used to be BPSK, QPSK, and MSK. The results
are compared with the original MC-CDMA signal.

Fig. 4. CCDF of PAPR of MC-CDMA using SLM for various
U where QPSK is used as a modulation technique.
In fig. 4, at CCDF=10
-3
, MC-CDMA with SLM method
applying QPSK as modulation technique, the PAPR is
reduced by 0.7dB, 1.1dB, 1.5dB for values of U=4, 8 and
16 respectively when compared with the original MC-
CDMA signal.

Fig. 5. CCDF of PAPR of MC-CDMA using SLM for various U
where BPSK is used as a modulation technique.
ISSN: 2278 1323
International Journal of Advanced Research in Computer Engineering & Technology
Volume 1, Issue 4, June 2012

459
All Rights Reserved 2012 IJARCET

In fig. 5, at CCDF=10
-3
, MC-CDMA with SLM method
applying BPSK as modulation technique, the PAPR is
reduced by 0.9dB, 1.7dB, 2.45dB for values of U=4, 8 and
16 respectively when compared with the original MC-
CDMA signal.

Fig. 6. CCDF of PAPR of MC-CDMA using SLM for various U
where MSK is used as a modulation technique.
In fig. 6, at CCDF=10
-3
, MC-CDMA with SLM method
applying MSK as modulation technique, the PAPR is
reduced by 0.95dB, 1.9dB, 2.2dB for values of U=4, 8 and
16 respectively when compared with the original MC-
CDMA signal.

Fig. 7. Comparison of PAPR reduction performance for SLM at
U=4 by different modulation techniques
In comparison of performance on PAPR reduction of
MC-CDMA system using SLM at U=4 for described
modulation schemes (BPSK, QPSK, MSK) as shown in fig.
7 BPSK has better performance of PAPR reduction than
QPSK and MSK. For the same CCDF probability 10
-3
, the
PAPR value equals to 9.4dB when BPSK is employed,
while the PAPR raise upto10.05dB for MSK and the value
further rises to 12.75dB when QPSK is employed under the
same circumstances.

V. CONCLUSION
In this paper we examined the effect of SLM to reduce
PAPR of MC-CDMA for different modulation schemes.
The binary phase sequences considered in this paper are
generated from hadamard matrix. From the MATLAB
simulation, the results shows that PAPR reduction
performance depends upon various number of phase
sequence factors (U) and it significantly improves with
increase in number of U. PAPR performance is also
compared for different modulation schemes (QPSK, BPSK
and MSK) and the result showed that SLM is more
effective when BPSK is used as modulation scheme.
ACKNOWLEDGMENT
We are grateful to the University College of Engineering,
Punjabi University, Patiala for providing necessary support
and infrastructure.
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ISSN: 2278 1323
International Journal of Advanced Research in Computer Engineering & Technology
Volume 1, Issue 4, June 2012

460
All Rights Reserved 2012 IJARCET

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Gagandeep Kaur: Designation: Student,
Academic Qualifications: Currently pursuing M.Tech (ECE) from UCOE,
Punjabi University, Patiala. Done B.Tech (ECE) from RIMT-IET, Mandi
Gobindgarh. Areas of interest: Wireless Communication and MATLAB.
Published Work: International Conferences: 1



Rajbir Kaur: Designation: Assistant
Professor, Electronics and Communication Engineering. Academic
Qualifications: M.Tech., pursuing PhD. Area of Specialization: Analog
and Digital communication systems. Published Work: National
Conferences: 6, International Conferences: 1, International Journal: 1,
National Conference/Seminar Presentation: 1. M.Tech/M.Phil Students
Guided / Underguidance : 04