Abstract

Al-Khwarizmi
Engineering

Journal
Al-Khwarizmi Engineering Journal, Vol. 4, No. 4, PP 82-90 (2008)

Peak to Average Power Ratio Reduction of OFDM Signals Using

Clipping and Iterative Processing Methods

Ahmed K. Hassan
Electromechanical Engineering Department/ University of Technology

(Received 5 March 2008; accepted 10 September 2008)

Abstract

One of the serious problems in any wireless communication system using multi carrier modulation technique like
Orthogonal Frequency Division Multiplexing (OFDM) is its Peak to Average Power Ratio (PAPR).It limits the

transmission power due to the limitation of dynamic range of Analog to Digital Converter and Digital to Analog

Converter (ADC/DAC) and power amplifiers at the transmitter, which in turn sets the limit over maximum achievable

rate.

This issue is especially important for mobile terminals to sustain longer battery life time. Therefore reducing PAPR

can be regarded as an important issue to realize efficient and affordable mobile communication services.

This paper presents an efficient PAPR reduction method for OFDM signal. This method is based on clipping and

iterative processing. Iterative processing is performed to limit PAPR in time domain but the subtraction process of the
peak that over PAPR threshold with the original signal is done in frequency domain, not in time like usual clipping

technique. The results of this method is capable of reducing the PAPR significantly with minimum bit error rate (BER)

degradation.

Keywords: OFDM, PAPR Reduction, Clipping Method, Iterative Processing Method.

1. Introduction:

Multi-carrier transmission, also known as

Orthogonal Frequency Division Multiplexing
(OFDM) or Discrete Multi-Tone (DMT), is a

technique with a long history that has recently

seen rising popularity in wireless and wire line
application. The recent interest in this technique is

mainly due to the recent advantage in digital

signal processing technology and semiconductor
technology. International standards making use of

OFDM for high speed wireless communications

are already established or being established by

IEEE802.11, IEEE802.16, IEEE802.20 and
European Telecommunications Standards Institute

(ETSI) Broadcast Radio Access Network (BRAN)

committees [1]. For wireless application, an
OFDM based system can be of interest because it

provides greater immunity to multi-path fading

and impulse noise eliminates the need of

equalizers, while efficient hardware
implementation can be realized using Fast Fourier

Transform (FFT) techniques.

Unfortunately, one particular major problem

with multi carrier signals that is often cited as the
major drawback of multi carrier transmission is its

large envelope fluctuation, which is quantified by

the parameter called Peak to Average Power Ratio
(PAPR). Since most practical transmission

systems are peak power limited, designing the

system to operate in perfectly linear region often
implies operating at power levels well below the

maximum power available [2]. In practice, to

avoid operating the amplifier with extremely large

back offs occasional saturation of the amplifiers
or clipping in Digital to Analog Converters

(DAC) must be allowed. This additional process is

a non linear process which creates inter-
modulation distortion that increases the bit error

rate(BER) in standard linear receiver, and also

causes spectral widening of the transmit signal

that increase adjacent channel interference to the
other users [3].

Ahmed K. Hassan Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 82-90 (2008)

In this paper an efficient PAPR reduction

method for OFDM signals is presented. This
method is based on clipping; clipping is

introduced to limit the peak power. However, this

clipping process does not introduce spectral
broadening, as exist in conventional clipping

process, because the subtraction to the original

signal is processed in frequency domain instead of

in time domain and only affects minimum bit

error rate (BER) performance degradation. The

clipping process is also done iteratively because
zero padding operation in frequency domain

causes peak growth after converting to the time

domain. The iterative processing method gives
good results for PAPR reduction and suitable

BER performance degradation.

2. OFDM System:

Orthogonal Frequency Division Multiplexing

(OFDM) system may be viewed as a conventional
Frequency Division Multiplexing (FDM) system,

as shown in Fig.(1-a). In this arrangement, the

spectra of different subchannels do not overlap. In
such a system, there is a sufficient guard space

between adjacent subchannels to isolate them at

the receiver using the conventional filters. This

arrangement does not achieve effective use of
bandwidth. A much more efficient use of

bandwidth can be obtained with a parallel system

if the spectra of the individual subchannels are
permitted to overlap, as shown in Fig.(1-b). With

the addition of coherent detection and the use of

subcarrier separated by the reciprocal of the signal
element duration, independent separation of the

multiplexed subcarriers is possible. If this

condition is satisfied then this OFDM system will

achieve orthogonality among its consistent
subcarriers [4].

Consider the system in Fig.(2). The

transmitted spectral shape is chosen so that

InterCarrier Interference (ICI) does not occur; that

is, the spectra of the individual subcarriers are

maximum at their frequency and zero at other
subcarrier frequencies. The N serial data elements

(spaced by T=1/R where R is the symbol rate)

modulate N subcarrier frequencies, which are then
frequency division multiplexed. The symbol

duration (Ts) has been increased to (NT), which

makes the system less susceptible to delay spread

impairments [5].

The subcarrier frequencies are separated by

the multiples of (1/NT) so that, with no signal

distortion in transmission, the coherent detection
of a signal element in any subcarrier of OFDM

system gives no output for a received element in

any other subcarriers. Hence, the N received
signal elements, corresponding to the N

subcarriers of OFDM system, are said to be

orthogonal. So, no further filtering is needed to

separate the different subcarriers. In other words,
the power density spectrum has a central positive

peak at an individual carrier frequency, and zeros

at all other subcarrier frequencies [5].

fc1 fc2

fc3 fc4

Subchannel Subchannel Subchannel
Subchannel

1 2 3
4

A
m

p
li

tu
d
e

(a) Non-overlapped System (b) Overlapped System

fc1 fc2 fc3

fc4

Subchannel Subchannel Subchannel
Subchannel

1 2 3 4

Frequency

A
m

p
li

tu
d
e

Fig.1. Transmitted Signal Spectrum of FDM System.

Frequency

A
m

p
li

tu
d
e

Ahmed K. Hassan Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 82-90 (2008)

3. Implementation of OFDM Using Fast

Fourier Transform (FFT):

The main objections to the use of parallel
systems are the complexity of the equipment

required to implement the parallel system and the

possibility of severe mutual interference among

subchannels when the transmission medium
distorts the signal. System design is greatly

reduced by eliminating any pulse shaping and

demodulated by using Discrete Fourier Transform

(DFT) to implement the modulation process [6].
The transmitted OFDM symbol waveform can

be represented as:










 




)2exp()(Re)(
1

tfjkdtS
k



where d(k) is the modulated data symbol, fk is the
subcarrier frequency of k

th
subcarrier which is

equal to (fc+k∆f).

M
o
d
u
la

to
r

Serial to Parallel

Conversion

M
u
ltip

le
x
e
r

tfj
e 0

2

tfj
e 1

2

tNfje 1
2 

d(0)

d(1)

d(N-1)

d(k)
S(t)

Serial binary

input

T=1/R

(a)

Parallel to Serial

Conversion

)(d̂ 1

)(d̂ 0

)N(d̂ 1

tfj
e 0

2

tfj
e 1

2

tNfje 1
2 

R(t)

D
e
m

o
d
u

la
to

(b)

Fig. 2. Basic OFDM System (a). Transmitter (b). Receiver


sT

Ahmed K. Hassan Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 82-90 (2008)

fc is the carrier frequency, ∆f is the subcarrier

spacing (bandwidth) equal to (1/NT)
T is the symbol time duration.

N is the subcarriers number.

This expression represents the passband
OFDM signal. The equivalent complex baseband

notation is given by:






)2exp()()(
1

tfkjkdtS
N



If the signal is sampled at a rate of (T), then

(t=nT), and for orthogonality ∆f=(1/NT), then
equation (2) can be rewritten as:

)3...( )2exp()()(
1






NnkjkdnS
N



Equation (3) is exactly the Inverse Discrete

Fourier Transform (IDFT) of data sequence d(k).

All operations that occur in the transmitter are
reversed in the receiver. Further reductions in

complexity are possible by using the Fast Fourier

Transform (FFT) algorithm to implement the
DFT. To eliminate the Intersymbol Interference

(ISI) almost completely, a guard time is

introduced for each OFDM symbol. The guard
time is chosen larger then the expected delay

spread such that multipath components from one

symbol can not interfere with the next symbol.

The guard time could consist of no signal at all.
However, the problem of Intercarrier Interference

(ICI) would arise. ICI is a crosstalk between

different subcarriers, which means that they are no
longer orthogonal. To eliminate ICI, the OFDM

symbol is cyclically extended in the guard time,

which is done by taking symbol period samples
from the end of OFDM symbol and appending

them to the start of OFDM symbol.

4. Mathematical Formulation of an OFDM

Signal and PAPR:

If N is the number of sub carriers in an

OFDM, then N distinct mapped QPSK symbols
are grouped as a set X={X1 , X2 ,….,XN}. Each

value in a set is a complex value. An IFFT of

vector X would result in N evenly spaced sample

values of an OFDM signal in time domain. If the

samples are shown as x={x1, x2, …., xN} then
each sample can be derived as [7]:

)4...(
1

2




kij

ik
eXx



Each OFDM symbol has time duration T, is

relatively very large compared to symbol duration

of a single carrier system. Orthogonal condition is
attained by maintaining the sub carrier frequency

spacing of 1/T. At the receiver end sampling, the

received signal and applying FFT followed by de_
mapping can demodulate the OFDM signal. The

discrete PAPR of an OFDM signal is defined

as [7]:

)5...(
}{

)max(
)(



x
xPAPR

where E{.} is the mean of the sequence. The

discrete PAPR is a good approximation of exact

PAPR if the sampling rate is high enough. This
can be assured by over-sampling the OFDM

signal before computing discrete PAPR. It has

been shown that over-sampling by 4 will make
discrete PAPR sufficiently reliable.

5. Clipping Processing Technique:

Clipping method is the simplest way to reduce
PAPR. This method is based on clipping the

signal, such that the peak amplitude becomes

limited to some desired maximum level. This

technique is performed by passing the OFDM
modems output base band signal through a digital

limiting device prior to transmitter stage, as

shown in Fig.(3).
The disadvantage of this method is the distortion

of the OFDM signal amplitude and this problem

can be solved by optimum choice of clipping level

for each designed system. This made depending
on the analysis of system performance at different

clipping level, such that the minimum PAPR with

good BER performance can be achieved [2].

Ahmed K. Hassan Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 82-90 (2008)

6. Iterative Processing Technique:

Fig. (4) shows the transmitter structure of

OFDM with iterative processing method.
Modulated data are converted from serial to

parallel, and then it is transformed to OFDM

symbol in time domain by IFFT. The peak power

components which exceed permission PAPR in
each OFDM are detected by peak detector to

obtain s(n). s(n) is defined by:

)6...(
|)(|.

|)(|

)(
)(

|)(|)(

)(

















nx
nx

nxnx

where x(n) is the n

th
sampling signal in each

OFDM symbol and λ is the desired PAPR

threshold. Signal s(n) is then FFT to obtain the

frequency domain peak cancellation signal S(k) as









1

)(
1

)(
N

knj

ens
N



)7...( 10  Nk

The peak cancellation signals S(k) is then

subtracted from the input modulated symbols, so

that the peak generation is avoided . The target
PAPR lower bound can not be attained in single

execution, therefore require iteration, as the name

implies.

Modulation

QPSK

S/P

IFFT

Tx Data

Fig.3. Block Diagram of OFDM Transmitter using Clipping Method.

P/S

Output signal

limiter

S/P

IFFT

P/S

Peak

Detector

FFT

-
-

S(k)

s(n)

Fig.4. Iterative Processing Structure at the OFDM Transmitter.

Ahmed K. Hassan Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 82-90 (2008)

7. Experimental Results:

Simulation of PAPR reductions using clipping

and iterative processing method are carried out
using technical (MATLAB) package. Fig.(5)

shows flowchart of PAPR using Iterative

Processing. PAPR reduction calculation
conducted by computer simulation are plotted in

Fig.(6), Fig.(7), Fig.(8) and Fig.(9). These graph
are generated from 10000 randomly distributed

symbols with QPSK modulation and OFDM sub

carriers are generated from FFT points of 1024.

Fig.(6) shows BER performance degradation
using clipping method assuming the channel is

AWGN. Fig.(7), Fig.(8) and Fig.(9) show BER

performance degradation using iterative

start

Modulate the input stream using QPSK

Convert the signal from serial to parallel (S/P)

Apply IFFT

Calculate PAPR

Calculate the peak detector depending on the threshold

value

Apply FFT to the output peak detector signal to obtain the

peak cancellation signal

Subtract the peak cancellation signal from the input

modulated signal

End of

iteration?

Compute PAPR and BER

end

Fig. 5. Flowchart of PAPR Using Iterative Processing.

yes

Ahmed K. Hassan Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 82-90 (2008)

processing method for iteration 1, iteration 2, and

iteration 3 respectively. BER degradation depends
on the iteration time; large iteration caused deep

BER degradation compared with clipping method

and iterative processing method gives high PAPR
reduction compared with clipping method.

Fig.(10) shows comparison of BER performance

between different iteration for λ=0.9 of maximum
value of OFDM coefficients. It is shown that at

BER of 10
-4

the total degradation is about 4dB

after three time iteration.

Fig.7. BER Performance for QPSK

OFDM with Iterative1.

PAPR=6 dB

PAPR=7 dB

Fig.6. BER Performance for QPSK

OFDM with Clipping Method and the

Channel is AWGN.

PAPR=9 dB

PAPR=8 dB

PAPR=7.5 dB

Fig.8. BER Performance for QPSK

OFDM with Iterative2.

PAPR=6.5 dB

PAPR=5.5 dB

Fig.9. BER Performance for QPSK OFDM

with Iterative3.

PAPR=5.46 dB

PAPR=4.5 dB

Ahmed K. Hassan Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 82-90 (2008)

8. Conclusions:

The following points are concluded from the

simulation results:
1- Iterative processing method gives higher

PAPR reduction compared with clipping

method (i.e., PAPR is about 7.5 dB for
clipping method and about 4.5 dB for iterative

method when  =0.8 max(OFDM), therefore
there is gain about 3 dB with suitable

degradation in BER).

2- Iterative processing method using one
iterative gives minimum BER degradation

compared with two and three iterative.

3- Iterative processing method using three
iterative gives higher PAPR reduction

compared with one and two iterative.

4- Threshold value (λ=0.9*max (OFDM)) gives
minimum BER degradation compared with
threshold value (λ=0.8*max (OFDM)).

5- Threshold value (λ=0.8*max (OFDM)) gives
higher PAPR reduction degradation compared
with threshold value (λ=0.9*max (OFDM)).

9. References:

[1] G. Redaelli et al., "Analysis of two digital

adaptive pre-correctors for non-linearity in

OFDM systems", Proceedings of 1999 IEEE
international conference on communications,

vol.1, 172-7, June 1999.

[2] R. Van. Nee and R. Prasad, "OFDM for
wireless multimedia communications", Artech
House, 2000.

[3] Seung Hee Han and Jae Hong Lee, "An
overview of peak to average power ratio
reduction techniques for multicarrier

transmission", IEEE wireless communication,

April 2005.
[4] Cimini, Leonard, "Analysis and Simulation of

Digital Mobile Channel using Orthogonal

Frequency Division Multiplexing ", IEEE

Trans. Comm.33, No.7, July 1985, pp665-
675.

[5] Louis Litwan and Michael Pugel, " The
Principles of OFDM", RF Signal Processing,
January 2001.

[6] Mohanad E. Al-Madi, "HF Data Transmission
Using Orthogonal Frequency Division

Multiplexing ", Msc Thesis, College of
Engineering, Al-Mustansirya University,2004.

[7] Azhar Qasim Taha," Performance analysis of
ICC technique for OFDM PAPR reduction
and its application over BTC", Master degree

project Stockholm, Sweden, 2006.

Fig.10. Comparison of BER Performance

Between Different Iteration for

λ=0.9*max(OFDM).

(2008 )90-82، صفحت 4، العذد 4 هجلت الخىارزهً الهنذسٍت الوجلذ احوذ كاهل حسٍن

تقلٍل نسبت القذرة العضوى الى القذرة الوعذلت الشارة هقسن التردد العاهىدي باستخذام

طرٌقتً التقٍٍن والوعالجت الوتكررة

احوذ كاهل حسن
انجايعت انخكُٕنٕجٛت/ قسى انُٓذست انكٓزٔيٛكاَٛكٛت

الخالصت

( OFDM)احذٖ انًشاكم انًًّٓ فٙ يُظٕيت االحصاالث انالسهكّٛ باسخخذاو انخضًٍٛ انًخعذد انخحًٛم يثم يقسى انخزدد انعًٕد٘ انًخعذد

ٔانخٙ حسبب حقهٛم انقذرة انًزسهت ٔكذنك حقهم انًذٖ انذُٚايٛكٙ نخحٕٚم (PAPR )ْٙ يشكهت َسبت انقذرة انعظًٗ انٗ انقذرة انًعذنت

(ADC ) ٔ(DAC) ْذِ انًشكهّ يًّٓ . ٔانخٙ حٕد٘ انٗ حقهٛم انقذرة انًكبزة فٙ االرسال ٔانخٙ حٕثز بذٔرْا عهٗ يعذل انًعهٕياث انًُجزة

ٚعخبز يٍ االيٕر انًًّٓ انخٙ حزٚذ كفائت خذيت احصاالث PAPRفٙ يحطاث انًٕباٚم انخٙ حغذ٘ بطارٚت ٔبعًز اطٕل ٔنذنك حقهٛم

ْذِ انطزٚقت حسخُذ عهٗ انخقهٛى ٔ انًعانجت انًخكزرةنخقهٛم . (OFDM) الشارة PAPRفٙ ْذا انبحث حى اسخخذاو طزٚقت فعانت نخقهٛم .انًٕباٚم

بعذ اجزاء انخقهٛى يٍ االشارة االصهٛت حخى فٙ يجال انخزدد ٔنٛس فٙ يجال انزيٍ كًا PAPR فٙ يجال انزيٍ ٔنكٍ عًهٛت طزح PAPRقًٛت

. BERيع ٔجٕد اضًحالل قهٛم فٙ قًٛتPAPR أٌ انُخائج نٓذِ انطزٚقت اعطج قذرة عهٗ حقهٛم .فٙ طزق انخقهٛى انشائعت