Reduction of the Clipping Noise for OFDM/OQAM System

doi:10.4236/cn.2013.53B2072

Paper Menu >>

Journal Menu >>

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

Email: [email protected]

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]

G. B. CHENG ET AL. 395





Mjjmt

staeegt 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



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 is

obtained owing to the following real orthogonal condi-

tion



 



,,, ,,

mnpqmnpqmp nq

gggtgt ,



 

 (3)

where is the taking real part operator.



,1





if and

mp,0



 if mp



It is shown in equation (1) that the transmitted signal



t is the summation over all the statistically inde-

pendent subcarriers. If the number of subcarriers M is

large enough, the amplitude of





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]



0,..., 1

10 2

max{|| }

()10log ,

{|| }

PAPR dBEs



 (4)

where k

is the OFDM signal and is the mean







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







and the

CCDF gives this probability for every



, which is given





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 ()

t is oversampled at time

intervals 0/tTJM



, where J is the oversampling

factor. Then the resulting discrete version o()

t can

be expressed as

(),

ssntn



 (6)

Let n

pass through a clipper with a given threshold

, and then we get the clipped signal, denoted by n

that









 (7)

Because n

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

is routed

to a device with memoryless nonlinearity. Applying the

Bussgang’s theorem [11], the output can be written as

[10]

nnn





 (8)

where the distortion term is uncorrelated with nn

and the attenuation factor



is a function of the clip-

ping ratio



, defined as in



 , with the av-

erage power before clipping, that in



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

CCD





k=0,…, JM-1, (10)

where k and are the DFT of Ck

and re-

spectively. n

Assuming perfect synchronization and following DFT,

the signal at the receiver can be expressed as



kkkk

kkK k

kk kkk

YHCZ

CD Z

CZHD







(11)

where k

0,..., 1,kJM

is the complex channel

gain of the k-th sub-carrier that assumed to be perfectly

known and k

is the additive white Gaussian noise. It

is shown in Equation 11 that the term kk

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

ˆk





ˆˆˆ

ˆˆ

kk kkkkk

DG CCDCD

 

  (12)

Then is passed through the channel

ˆk

and

we get that



ˆˆ

kk kk

kkkk kk

YYHD



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

ˆk

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



M points,











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).

REFERENCES

[1] L. Hanzo, M. Miinster, B. J. Choi and T. Keller, “OFDM

and MC-CDMA for Broadband Multi-Users Communica-

tions,” WLANs and Broadcasting, IEEE press. Wiley Se-

ries, 2003.

[2] A. Skrzypczak, P. Siohan and J. P. Javaudin, “Analysis of

the Peak-to-average Power Ratio for OFDM/ OQAM,”

IEEE 7th Workshop on Signal Processing Advances in

Wireless Communications, July 2006.

[3] D. M. Qu, S. X. Lu and T. Jiang, “Multi-Block Joint Op-

timization for the Peak-to-average Power Ratio Reduction

of FBMC-OQAM Signals,” IEEE Transactions on Signal

Processing, Vol. 61, No. 7, 2013, pp. 1605-1613.

doi:10.1109/TSP.2013.2239991

[4] R. W. Bauml, R. F. H. Fischer and J. B. Huber, “Reduc-

ing the Peak-to-Average Power Ratio of Multicarrier

Modulation by Selected Mapping,” Electronics Letters,

Vol. 32, No. 22, 1996, pp. 2056-2057.

doi:10.1049/el:19961384

[5] A. Skrzypczak, P. Siohan and J. P. Javaudin, “Reduction

of the peak-to-average Power Ratio for OFDM-OQAM

Modulation,” in Proc.63rd IEEE VTC, May 2006, pp.

2018-2022. doi:10.1109/LSP.2007.898351

[6] Y. Xiao, X. Lei, Q. Wen and S. Li, “A Class of Low

Complexity PTS Techniques for PAPR Reduction in

OFDM Systems,” IEEE, Signal Processing Letters, 2007.

doi:10.1109/LSP.2007.898351

[7] Y. Xiao, S. Li, X. Lei and Y. Tang, “Clipping Noise Miti-

gation for Channel Estimation in OFDM Systems,” IEEE

Communications Letters, 2006.

[8] H. Chen, A. M.Haimovich, “Iterative Estimation and

Cancellation of Clipping Noise for OFDM Signals,”

IEEE Communication Letter, Vol. 7, No.7, 2003, pp.

305-307. doi:10.1109/LCOMM.2003.814720

[9] B. Le Floch, M. Alard and C. Berrou, “Coded Orthogonal

Frequency Division Multiplex,” Proceedings of the IEEE,

Vol. 83, 1995, pp. 982-996. doi:10.1109/5.387096

[10] H. Ochiai and H. Imai, “Performance Analysis of Delib-

erately Clipped OFDM Signals,” IEEE Transactions

Communications, Vol. 50, 2002, pp. 89-101.

doi:10.1109/26.975762

[11] H. E. Rowe, “Memoryless Nonlinearities with Gaussian

input: Elementary Results,” Bell System Technical Jour-

nal, Vol. 61, 1982, pp. 1519-1525.

doi:10.1002/j.1538-7305.1982.tb04356.x