An Improved Selective Mapping Method for PAPR Reduction in OFDM/OQAM System

doi:10.4236/cn.2013.53B2011

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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

Email: [email protected]

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

G. B. CHENG ET AL.

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]





Mjjmt



taeegt





 

 



 

, (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



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

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





and

mp,0



if . mp

It can be seen from equation (1) that the transmitted

signal



t is the summation over all the statistically

independent subcarriers, if the number of subcarr iers

is large enough, the amplitude of



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]:



0,..., 1

10 2

max{|| }

()10log ,

{|| }

PAPRdBEs



 (4)

where k

is the OFDM signal and is the mean of







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

may be longer than 0, it is reasonable to use equation

(4) for PAPR measurement in OFDM/OQAM system

[9].

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





, 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

cmM )





is a point of a

-QAM constellation, the randomly

generated codes are

such that is a point of the same





(, )0,...,11,...,dmu MU





-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].

Assume the pulse shape is of length





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 .



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:



mn mn

aanb



01,1

bmn

mMn b

Aa 

 (6)

3) Considering the





2,(21)

Ibb







A

interval,

then the corresponding matrices can be expressed

as:

 



212 ,2101

bbmb

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

A0



21b



21 b



4) Generalization on the k

, interval. Let 2kb

 



1,1

kkmk

AAa



 







(8)

and proceed as in step 3. Then for a given i,





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

b matrix

such that:



B





0,..., 1

,2 1,..., 1

mn nk bk





 

 (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.

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

1) Generating U codes of length M and the original

symbol ,mn is coded by the code and we get the

code denoted by .



2) Constructing the first two OFDM symbols with

randomly selection and associated coded symbols are

stored as:







01,1

mn mMn

Aa   

2

(10)

3) Considering the





2,4I0







A

interval, then the

corresponding matrices can be expressed as:

 



32,3

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



A.

4) Generalization on the k

, interval. Let 2k

 





1,1

kkmk

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.







Figure 2. CCDF performance comparison between OFDM,

OSLM and the proposed method with the number of sub-

carriers N = 64.







Figure 3. CCDF performance comparison between OFDM,

OSLM and the proposed method with the number of sub-

carriers N = 128.







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

, 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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