Communications and Network, 2013, 5, 394-397
http://dx.doi.org/10.4236/cn.2013.53B2072 Published Online September 2013 (http://www.scirp.org/journal/cn)
Reduction of the Clipping Noise for OFDM/OQAM System
Guobing Cheng, Qifu Lv, Shaoqian Li, Lisha Gong, Binhong Dong, Su Hu
National Key Laboratory of Science and Technology on Communications,
University of Electronic Science and Technology of China, Chengdu, China
Received August, 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. This paper
focuses on the reduction of the clipping noise and out-of band radiation caused by the clipping process. The basic prin-
ciple is to estimate the clipping noise and then eliminate it from the received signal. Analysis and simulation results
show that, with one time iteration, the proposed method can effectively improve the bit error ratio (BER) performance.
Keywords: OFDM/OQAM; PAPR Reduction; Clipping Noise
1. Introduction
As well as the other kinds of MCM systems, since the
resulting OFDM/OQAM signal is the summation over all
the statistically independent subcarriers, it also has the
intrinsic characteristic of high peak-to-ratio (PAPR). And
for a given power amplifier, it always has a certain linear
amplification range that distortion will be created when
working at the nonlinear range. Furthermore, the power
amplification of signals having a large dynamic range
may introduce inter-modulation between subcarriers and
cause interferences [1]. These distortion and interference
lead to performance degradation, which is in close rela-
tion with the PAPR of the signal.
There have been some literatures attributed to the re-
duction of the PAPR in OFDM/OQAM system. In [2],
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
[3], 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 joint optimization has been presented to reduced
the PAPR. Corresponding to the selective mapping (SLM)
method in OFDM system [4], th e authors in [5] propo sed
an overlapped selective mapping (OSLM) method for
OFDM/OQAM system. However, a pulse shape that may
cover several OFDM symbols is introduced in OFDM/
OQAM system, resulting in the typical SLM and PTS
PAPR reduction methods of traditional OFDM system
cannot be directly applied to the OFDM/OQAM system.
And this disadvantage can be only partly overcome at the
price of higher complexity and/or poorer system per-
formance [4-7].
On the other hand, clipping is a simple and efficient
method for reduction of PAPR that there have been many
literatures for that of the traditional OFDM system.
However, there has few public literature that been attrib-
uted the clipping method to OFDM/OQAM system. In
this paper, we consider the application of clipping
method to OFDM/OQAM system and focus on the re-
duction of the clipping noise. Firstly, we deduce the ex-
pression of the clipped OFDM/OQAM signal. Then a
novel clipping noise reduction algorithm of traditional
OFDM system proposed in [8] is introduced and we
analyze the applying of this algorithm to the OFDM/
OQAM system. The analysis and simulation results show
that the iterative clipping noise reduction method of the
OFDM system can be directly applied to the OFDM/
OQAM system and it can efficiently improve the system
performance. Furthermore, the out-of-band radiation
caused by clipping process with and without filter is dis-
cussed in this paper.
2. OFDM/OQAM System Model and PAPR
Definition
2.1. System Model
The baseband version of a continuous-time OFDM/
OQAM transmitted signal can b e written as [9]
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opyright © 2013 SciRes. CN

G. B. CHENG ET AL. 395
 
,0
12
,
0
,
mn
Mjjmt
mn
nm
staeegt n


0

 
 

  (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 is
obtained owing to the following real orthogonal condi-
tion

 

*
,,, ,,
|
mnpqmnpqmp nq
gggtgt ,

  
 (3)
where is the taking real part operator.

,1
mp


if and mp,0
mp

 if mp

.
It is shown in equation (1) that the transmitted signal

s
t is the summation over all the statistically inde-
pendent subcarriers. If the number of subcarriers M is
large enough, the amplitude of


s
t also varies in a
large range, leading to high PAPR.
2.2. PAPR Definition of OFDM/OQAM System
The PAPR is an important parameter to measure the sen-
sitivity to non-linear amplification of a transmission
scheme having a non-constant envelope [5]. And the
PAPR of the OFDM signals with M carriers in discrete-
time version is defined as [4]

2
0,..., 1
10 2
max{|| }
()10log ,
{|| }
k
kM
k
s
PAPR dBEs

 (4)
where k
s
is the OFDM signal and is the mean
of

*E


*.
Since OFDM and OFDM/OQAM systems transmit the
equivalent of one complex symbol at rate 0 1T, it is rea-
sonable to use equation (4) for PAPR measurement in
OFDM/OQAM system [5].
The PAPR of the OFDM/OQAM system is also a
random variable and its behavior is to compute the prob-
ability to exceed a given threshold


dB  and the
CCDF gives this probability for every

, which is given
by


CCDF=P PAPR>.

(5)
Even though a pulse shape is introduced in OFDM/
OQAM system, it has been proven that the whole class of
orthogonal prototypes such as the square root of raised
cosine (SRRC) and isotropic orthogonal transform algo-
rithm(IOTA), that are only nearly-orthogonal, also pro-
vide optimal CCDFs [2] .
3. Reduction of Clipping Noise in
OFDM/OQAM System
3.1. Reduction of Clipping Noise in OFDM
System
A novel iterative estimation and cancellation of clipping
noise algorithm for OFDM system has been proposed in
[8]. It concluded that for an 802.11a system, the PAPR
can be reduced to 4dB while the system performance can
be restored to less than 1dB of the non-clipped case with
only moderate complexity increase and with no band-
width expansion. The detail principle of iterative clipping
noise reduction is given in section II of [8].
3.2. Reduction of the Clipping Noise in
OFDM/OQAM System
Now we apply the clipping noise reduction algorithm to
the OFDM/OQAM system. Assume that the OFDM/
OQAM transmitted signal ()
s
t is oversampled at time
intervals 0/tTJM

, where J is the oversampling
factor. Then the resulting discrete version o() f
s
t can
be expressed as
(),
n
ssntn

 (6)
Let n
s
pass through a clipper with a given threshold
A
, and then we get the clipped signal, denoted by n
s
that
.
nn
nn
s
sA
s
A
sA




 (7)
Because n
s
is the summation over a large number
independent subcarriers, according to the law of large
numbers, it can be characterized as a discrete complex
stationary Gaussian process. Suppose that n
s
is routed
to a device with memoryless nonlinearity. Applying the
Bussgang’s theorem [11], the output can be written as
[10]
,
nnn
s
sd


 (8)
where the distortion term is uncorrelated with nn
d
s
and the attenuation factor

is a function of the clip-
ping ratio

, defined as in
A
P

 , with the av-
erage power before clipping, that in
P

2
1.
2
eerfc




  (9)
The block diagram of baseband equivalent transmitter
and receiver with iterative clipping noise cancellation are
given in Figure 1.

G. B. CHENG ET AL.
396
Using (8), the term C in Figure 1 can be expressed
as
kk
CCD  
k
k=0,…, JM-1, (10)
where k and are the DFT of Ck
Dn
s
and re-
spectively. n
d
Assuming perfect synchronization and following DFT,
the signal at the receiver can be expressed as

kkkk
kkK k
kk kkk
YHCZ
H
CD Z
H
CZHD





(11)
where k 0,..., 1,kJM
H
is the complex channel
gain of the k-th sub-carrier that assumed to be perfectly
known and k
Z
is the additive white Gaussian noise. It
is shown in Equation 11 that the term kk
H
D is the
component caused by clipping process. Since the clip-
ping course is known by the receiver side, estimation of
k, denoted by , can be gotten by passing
through the same clipping and filtering process as in the
transmitter, and then subtracted by that
Dˆk Dˆk C
ˆk
C 

ˆˆˆ ˆˆ ˆ
kk kkkkk
DG CCDCD     (12)
Then is passed through the channel
ˆk
Dk
H
and
we get that

ˆˆ
ˆ
kk kk
kkkk kk
YYHD

H
CZHDD 


(13)
If k , the clipping noise component in Equation
13 can be removed absolutely. On the other hand, from
Equation 12, since the estimation of k has little to do
with the accuracy of , incremental gains diminish
after the first iteration.
ˆk
DD
D
ˆk
C
Furthermore, in order to remove the out-of-band radia-
tion caused by clipping process, a pair of time-frequency
domain transform has to be included both in transmitter
and in each iteration process of receiver, as shown in
Figure 1. This results in the increasing of calculation
complexity and bit error ratio (BER). While in OFDM/
OQAM system, the out-of-band radiation of the clipped
signal is still in the acceptable range. Therefore we can
omit the out-of-band removal stage in both transmitter
and receiver, as shown in the simulation results.
4. Simulation Results
In this section, it aims to evaluate the efficiency of the
clipping noise cancellation algorithm in OFDM/OQAM
system.
Figure 2 presents the BER to the signal-to-noise ratio
(SNR) in AWGN channel for clipping noise removal
with threshold=6dB. It shows that, through clipping noise
removal process, the system performance can be largely
recovered. Secondly the results of 1 and 2 times iteration
are almost overlapped, implying that 1 time iteration is
enough, which is consistent with the analysis results.
In Figure 3, it compares the power spectrum density
(PSD) for different threshold and with or without filter. It
is shown that the out-of-band radiation is regrown by
clipping. The traditional out-of-band removal method,
i.e., padding zeros with the middle

1
J
M points,
ˆ
C
ˆ
C



G


Y
ˆ
Y
C
ˆ
D
Figure 1. The baseband equivalent transmitter and rec eiver
with iterative clipping noise cancellation.
Figure 2. The BER to the SNR in AWGN channel for clip-
ping noise removal with threshold=6dB.
PSD (dB)
Figure 3. The PSD for OFDM/OQAM clipped signal with
and without filter.

G. B. CHENG ET AL.
397
has little effect on the out-of-band removal and it even
becomes worse when threshold is high, e.g., threshold =
8dB in Figure 3. On the other hand, since the clipping
noise removal process includes the same process in
transmitter, the including out-of-band removal will
largely increase the computation complexity.
5. Conclusions
The reduction of clipping noise in OFDM/OQAM system
is discussed in this paper. It is shown that the system
performance can be largely recovered through iterative
clipping noise cancellation. Furthermore, since the out-
of-band radiation of the clipped signal is at a consider-
able low level, there is no necessary to include the out-
of-band filtering process in OFDM/OQAM system.
6. Acknowledgements
This work is supported in part by the National Science
Foundation of China under Grant number 61101101,
National Grand Special Science and Technology Project
of China under Grant No. 2010ZX03006-002-02, , Pro-
gram for New Century Excellent Talents in University of
China ((NCET110058), the Foundation Project of Na-
tional Key Laboratory of Science and Technology on
Communications under Grant 9140C020404120C0201,
and Key Laboratory of Universal Wireless Communica-
tions, Beijing university of Posts and Telecommunica-
tions, Ministry of Education, China (No. KFKT-
2012102).
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