Communications and Network, 2013, 5, 53-56
http://dx.doi.org/10.4236/cn.2013.53B2011 Published Online September 2013 (http://www.scirp.org/journal/cn)
An Improved Selective Mapping Method for PAPR
Reduction in OFDM/OQAM System
Guobing Cheng, Huilei Li, Binhong Dong, Shaoqian Li
National Key Laboratory of Science and Technology on Communications,
University of Electronic Science and Technology of China, Chengdu, China
Received May, 2013
ABSTRACT
Orthogonal frequency division multiplex/offset QAM (OFDM/OQAM) has been proven to be a promising multi-carrier
modulation (MCM) technique for the transmission of signals over multipath fading channels. However, OFDM/OQAM
has also the intrinsic disadvantage of high peak-to-average-power ratio (PAPR) that should be alleviated. In this paper,
a novel selective mapping (SLM) method is proposed for OFDM/OQAM system. Since the pulse shape may cover a
few OFDM symbols, the basic principle of the proposed method is to apply the SLM method in the range of the most
relevant OFDM symbols. Analysis and simulation results show that, compared to the existing SLM algorithms for
OFDM/OQAM system, the proposed method has better PAPR performance and lower computation complexity.
Keywords: OFDM/OQAM; PAPR Reduction; Selective Mapping
1. Introduction
Orthogonal frequency division multiplexing (OFDM) is
an efficient and popular multi-carrier modulation (MCM)
scheme that it has been some practical applications such
as the 3rd generation mobile communication system,
digital subscriber lines (xDSL) and digital video broad-
casting (DVB). However, OFDM has some intrinsic
drawbacks. Firstly, the rectangular pulse shape leads to
high sensitivity to the inter-carrier interference (ICI).
Secondly, its robustness to multi-path pro pagatio n effects
comes from the insertion of a cyclic prefix (CP), i.e.,
obtained at the price of a reduced spectral efficiency.
Furthermore, it has high out-of-band radiations, leading
to severe adjacent channel interference. In order to alle-
viate these drawbacks, OFDM/offset QAM (OFDM/
OQAM) is another MCM scheme which may be the ap-
propriate alternative [1-3]. Compared to traditional
CP-OFDM, OFDM/OQAM may provide a higher useful
bit rate since it operates without CP. The introduced
pulse shapes with good time-frequency localization (TFL)
characteristic lead to more immunity to inter-symbol
interference (ISI), ICI and out-of-band radiation [4].
Therefore, it is an efficient transmission technique and
has attracted increasing attention.
However, as well as the other kinds of MCM systems,
since the resulting OFDM/OQAM signal is the summa-
tion over all the statistically independent subcarriers, it
has the intrinsic characteristic of high peak-to-ratio
(PAPR). For a given power amplifier, it always has a
certain linear amplification range and distortion will be
created when working at the nonlinear range. Further-
more, the power amplification of signals having a large
dynamic range may introduce inter-modulation between
subcarriers and cause interferences [5]. These distortion
and interference lead to performance degradations, which
are in close relation with the PAPR of the signal.
There have been some literatures attributed to the re-
duction of PAPR in OFDM/OQAM system. In [6], the
authors derived an approximate expression of the well-
known complementary cumulative density function
(CCDF) for OFDM/OQAM system. It concluded that the
expression of CCDF of OFDM/OQAM is similar to that
of the OFDM system and the common orthogonal pulse
shapes also can provide optimal CCDF performance. In
[7], the authors analyzed the application of the partial
transmit sequence (PTS) method to OFDM/OQAM sys-
tem and a novel algorithm based on dynamic program-
ming (DP) joint optimization has been presented to re-
duced the PA PR. Co rr espo nd in g to the selective mapping
(SLM) method in OFDM system [8], the authors in [9]
proposed an overlapped selective mapping (OSLM) me-
thod. It shows that the performance increases with the
number of SLM codes, but is also dependent on the
length of the pulse shape th at the longer the length of the
pulse shape is, the worse the CCDF performance will be.
In this paper, we also focus on the application of SLM
method to OFDM/OQAM system. In contrast to the
OSLM method that the selective mapping method is used
C
opyright © 2013 SciRes. CN

G. B. CHENG ET AL.
54
for the real-valued data and all the overlapped OFDM
symbols are considered, the proposed method applies the
SLM method for the combined complex-valued data and
considers the overlap only in the most relevant symbols.
The simulation results and analysis show that the pro-
posed method outperforms the OSLM method and it can
achieve almost the performance of the SLM algorithm in
OFDM system. Furthermore, the calculation complexity
is largely reduced. The rest of this paper is organized as
follows. In section II, we recall the basics of OFDM/
OQAM system and the OSLM algorithm is presented in
section III. We present our improved SLM method for
OFDM/OQAM and compare it with OSLM algorithm in
section IV. The simulation results and ana lysis a re sho wn
in section V. Brief conclusion is given in section VI.
2. OFDM/OQAM System Mode
The baseband version of a continuous-time OFDM/
OQAM transmitting signal can be written as [1]
 
,0
12
,0
0
mn
Mjjmt
mn
nm

s
taeegt

n

 
 

 
, (1)
with M an even number of sub-carriers, ,mn the real-
valued symbol conveyed by the sub-carrier of index m
during the symbol time of index n, g the pulse shape, 0
a

the subcarrier spacing and 0

the time offset between
the adjacent real part and imaginary part of an OFDM/
OQAM symbol. 00 0
112T

  , with 0 T, the dura-
tion of the complex-valued symbols. ,mn

is an addi-
tional phase term given by

,0()mod
2
mn mn


,

    (2)
where 0

can be arbitrarily chosen.
For a distortion-free channel, perfect reconstruction of
real symbols is obtained owing to the following real or-
thogonal condition

 

*
,,, ,,
|
mnpqmnpqmp nq
gggtgt,

  
 (3)
where is the real part operator.

,1
mp


if
and mp,0
mp

if . mp
It can be seen from equation (1) that the transmitted
signal

s
t is the summation over all the statistically
independent subcarriers, if the number of subcarr iers
M
is large enough, the amplitude of

s
t also varies in a
large range.
3. The OSLM METHOD for OFDM/OQAM
3.1. Basic Definition of PAPR in OFDM/OQAM
System
The PAPR is an important parameter to measure the sen-
sitivity to non-linear amplification of transmission
schemes having a non-constant envelope [9]. And the
PAPR of the OFDM signals with M carriers in discrete-
time version is defined as follows [8]:

2
0,..., 1
10 2
max{|| }
()10log ,
{|| }
k kM
k
s
PAPRdBEs

 (4)
where k
s
is the OFDM signal and is the mean of

*E


*.
Since both OFDM and OFDM/OQAM systems trans-
mit the equivalent of one complex symbol at rate 0 1T,
even the length of the OFDM/OQAM pulse shape
g
may be longer than 0, it is reasonable to use equation
(4) for PAPR measurement in OFDM/OQAM system
[9].
T
The PAPR is a random variable of OFDM/OQAM
system and its behavior is to compute the probability to
exceed a given threshold and the CCDF gives
this probability for every

dB 

, which is given by

CCDF=P PAPR>


(5)
3.2. The SLM Method for OFDM System
The SLM technique is a simple and undistorted process-
ing way to reduce the PAPR of OFDM signals [8]. The
basic principle of SLM is to generate different versions
of the same OFDM symbol and transmit the one with the
lowest value of PAPR, see Figure 1. To create these dif-
ferent versions of the same OFDM symbol, we consider
U codes of length M and these codes are such that the
initial constellation remains unchanged. If
(0,..., 1
m
cmM )


2
2
is a point of a
K
-QAM constellation, the randomly
generated codes are
such that is a point of the same

u
m
m
c

(, )0,...,11,...,dmu MU
2
2


u
m
d
K
-QAM
constellation. In order to retrieve the original data, the
receiver requires a perfect knowledge of the used code.
Therefore 2 bits are needed to be transmitted as
side information to recover them perfectly, leading to
reduction of the useful data rate.
log U
Figure 1. The SLM scheme for PAPR reduction in OFDM
system.

G. B. CHENG ET AL. 55
3.3. The OSLM Method for OFDM/OQAM
System
The SLM for OFDM/OQAM system has a similar struc-
ture of SLM for OFDM system. The transmitted data is
selected by the lowest PAPR of U dependent coded
symbols. But for the reason that the pulse shape is intro-
duced in OFDM/OQAM system and the length of pulse
shape may be longer than the symbol period 0, the tra-
ditional SLM scheme can not directly be applied to
OFDM/OQAM system any more. In order to apply the
SLM technique and keep and perfect recovery, the
OSLM method is proposed in [9].
T
Assume the pulse shape is of length


0
bT bN

21b, then the overlapping is caused by the

pulse
shapes, and all the associated overlaps have to be taken
into account. The brief description of OSLM is given as
follows [9]:
1) Generating U codes of length M and the original
symbol ,mn is coded by the code and we get the
code denoted by .
a

i
m
d

,
i
mn
a
2) Constructing the b first OFDM symbols. For a pulse
shape of length 0, overlaps only occur for duration
equal to . Therefore, the first 2b symbols can be ran-
domly chosen. Let , then the selected
codes and the associated coded symbols are stored as:
bT

1
,,
,2
mn mn
aanb
2


1
2,
01,1
bmn
mMn b
Aa   (6)
3) Considering the


20
2,(21)
b
Ibb
0

 

21
i
b
A
interval,
then the corresponding matrices can be expressed
as:
 

212 ,2101
ii
bbmb
mM
AAa

 






(7)
The associated OFDM/OQAM signals are generated
for all i. Then, to take into account all the modifications
brought by the addition of a new pulse shape, the index
code 21b selected is the one that provides the lowest
PAPR value on the last interval of length and then
set .
i
b
A0
bT

21b
i
A

21
21 b 
4) Generalization on the k
I
, interval. Let 2kb
 
 1,1
01
,
ii
kkmk
mM
AAa

 



(8)
and proceed as in step 3. Then for a given i,

1
i
k
A

is a
matrix. But knowing that any new added
pulse shape only corrupts the signal on a 0 length
interval, the matrices associated to the different signals
can be restricted in time leading to a
(1Mk)bT
2
M
b matrix
such that:

1
i
k
B






11 0,..., 1
,2 1,..., 1
,
ii
kk mM
mn nk bk
BA
 
 
 (9)
We can see that, for the OSLM method, the selective
mapping procedure is carried out in each real symbol
period 0

. Therefore, compared to the SLM in each
complex symbol period 0, it costs twice the calculation
quantity while achieves higher PAPR results. On the
other hand, the OSLM does not consider the fact that, for
the common pulse shapes introduced in OFDM/OQAM
system such as the isotropic orthogonal transform algo-
rithm (IOTA) and square-root raised cosine (SRRC),
most of the energy is lo cated in the main lobe.
T
4. The Proposed SLM for OFDM/OQAM
In this paper, an improved OSLM algorithm is proposed
to reduce the PAPR in OFDM/OQAM system that the
data matrix is limited to two OFDM symbols and the
SLM algorithm is carried out in each complex-valued
OFDM symbol . The proposed method is depicted as
follows. 0
T
1) Generating U codes of length M and the original
symbol ,mn is coded by the code and we get the
code denoted by .
a

i
m
d

,
i
mn
a
2) Constructing the first two OFDM symbols with
randomly selection and associated coded symbols are
stored as:



1
2,
01,1
mn mMn
Aa    2
(10)
3) Considering the


30
2,4I0

 

21
i
b
A
interval, then the
corresponding matrices can be expressed as:
 

32,3
01
ii
mmM
AAa
 






 (11)
The associated OFDM/OQAM signals are generated
for all i. Then the index code 3 selected is the one that
provides the lowest PAPR value and then set
i

3
33
i
A
A.
4) Generalization on the k
I
, interval. Let 2k
 

 1,1
01
,
ii
kkmk
mM
AAa

 






 (12)
and proceed as in step 3. Then the index that provides the
lowest PAPR value can be selected step by step.
5. Simulation Results
In this section, it aims to compare the performance of
proposed SLM with OSLM for OFDM/OQAM system
and the traditional SLM for OFDM system is also given.
The pulse shape introduced in the simulation is the IOTA
filter.
Figure 2 and Figure 3 show the results of CCDF to
the threshold

and the number of subcarriers are N =
64 and N = 128 respectively. It can be seen that in both
scenarios, the proposed method outperforms the OSLM
and has almost the same performance to the SLM in
OFDM system.
In Figure 4, it shows the CCDF performance of the
proposed method in condition of different length of pulse

G. B. CHENG ET AL.
56


dB 
Figure 2. CCDF performance comparison between OFDM,
OSLM and the proposed method with the number of sub-
carriers N = 64.


dB 
Figure 3. CCDF performance comparison between OFDM,
OSLM and the proposed method with the number of sub-
carriers N = 128.


dB 
Figure 4. CCDF performance of the proposed method in
condition of different length of pulse shape is considered.
shape is considered. We set the calculated length of the
relevant symbol to 0 and 0. The simula-
tion results show that they can achieve the similar per-
formance. This indicates that we can limit the calculation
atrix to
2WT5WT
2
M
, leading to that the amount of calcula-
tion is greatly reduced.
6. Conclusions
In this paper, an improved OSLM method is proposed for
OFDM/OQAM system and it achieves a better perform-
ance than the OSLM method while with lower calcula-
tion complexity. It can be concluded that, as to the SLM
method, the OFDM/OQAM system has the similar CCDF
performance to that of the OFDM system and has little to
do with the length of the pulse shapes.
7. Acknowledgements
This work is supported in part by National Sci. & Tech.
Major Project of China under Grant2010ZX03006-002-
02 and Program for New Century Excellent Talents in
University of China ((NCET110058).
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