Performance analysis of papr reduction techniques in multicarrier modulation system

IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163
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Volume: 02 Issue: 06 | Jun-2013, Available @ http://www.ijret.org 991
PERFORMANCE ANALYSIS OF PAPR REDUCTION TECHNIQUES IN
MULTICARRIER MODULATION SYSTEM
Nidhi chauhan1
, B.V.R.Reddy2
1, 2
Department of Electronics and Communication Engineering,University School of Information and
CommunicationTechnology, GGSIPU, New Delhi-110075, India, er.nidhi026@gmail.com, Profbvreddy@gmail.com
Abstract
Orthogonal FrequencyDivisionMultiplexing (OFDM) is one of the many multicarrier modulation techniques which provide high
spectral efficiency, less vulnerability to echoes,low implementation complexity and resilience to non – linear distortion. It is used in
communication systems due to its various advantages. However, while this system is implemented problem of high peak – to – average
power ratio(PAPR) is encountered. The reason behind this drawback is the existence of manyindependent subcarriers, due
towhichthesignal amplitudecanhavehighpeakvalues as compared to average of whole system. The high PAPR in multicarrier
transmission systems causes power degradation and spectrum spreading.Interleaving, Tone Reservation, Peak Reduction Carrier,Block
Coding, Active Constellation Extension, Envelope ScalingareamongmanyPAPRreductionschemesthathavebeenproposedas a remedy to
thisproblem. In this paper, performances of Amplitude Clipping and Filtering, Selected Level Mapping (SLM), and
PartialTransmitSequence (PTS) techniques of PAPR reduction in OFDM systems by parameter variations are analyzed, based on
Complementary Cumulative Distribution Function. An attempt has been made to simulate clipping and filtering technique with
iterations and the simulation shows that PAPR problem is reduced as number of iterations increases. The attempts have also been
made to simulate SLM technique and PTS technique by varying number of phase sequences, number of sub-blocks in SLM, PTS
respectively and simulation results shows that by increasing the number of phase sequences, sub-blocks, PAPR can be reduced
significantly.The mathematical equations are incorporated here to compute the maximum expected PAPR from an OFDM signal
which shows when there is phase alignment of all sub carriers and sub carriers are equally modulated, then signal peak value hits the
maximum. Besides these computer simulations, a comparative study of these three techniques is done.
Index Terms:Multi-Carrier Modulation(MCM), Orthogonal Frequency Division Multiplexing (OFDM),Peak-To-Average
Power Ratio(PAPR),ComplementaryCumulativeDistributionFunction(CCDF), Repeated Clipping and Filtering (RCF),
PartialTransmitSequence(PTS), Selected Level Mapping (SLM), Clipping Ratio (CR).
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1. INTRODUCTION
Multi-Carrier Modulation(MCM) is a technique that has
recently seen gaining popularity in wireless and wireline
applications. In the past few years wireless communications
have experienced arapid growth due to the high mobility that
they allow. However, wireless channels have some
disadvantages, like signal fading due to multipath, that make
them difficult to deal with. Orthogonal Frequency Division
Multiplexing (OFDM) is a modulation technique that
efficiently deals with selective fading channels. The advancing
capabilities of digital signal processors make this technique of
utmost interest.
Moreover for wireless applications, OFDM- based systems are
of great interest since they provide a greater immunity to
impulse noise and fast fading and eliminate the need for
equalizers. The signal processing techniques like Fast Fourier
transform (FFT) enables efficient hardware implementations
for small numbers of carriers and make their realization
simpler.OFDM (orthogonal frequency division multiplexing)
has been proposed for many different types of systems from
television broadcasting to wireless LANs (local area
networks).
OFDM is based on the principle of splittinga high-rate data
stream intoa number of lower rate streams which are
transmitted simultaneously on number of subcarriers. These
subcarriersare overlapped with each other. Asduration of
symbolincreases forlower rate parallel subcarriers, the relative
amount of dispersion caused by multipath delay spreadis
decreased. The introduction of a guardtimeineveryOFDM
symbol eliminates Inter- symbol interference
(ISI)almostcompletely.
OFDM faces severalchallenges. The major challenge is the
large peakto average ratio duetononlinearbehaviour of
amplifier.Large peak-to-average power ratio (PAPR) distorts
the signal ifthe transmitter containsnonlinearcomponents
suchas power amplifiers (PAs). Thisnonlinear

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distortioncauses bothin-band radiation and out-of-band
interference to signals. Therefore for distortion less
transmission, the power amplifiers require a back off which
isapproximately equaltothe PAPR. This decreasestheefficiency
foramplifiers. This is the reason whicharises the need for
reducing the high PAPR.
PAPR can be analyzed by its complementary cumulative
distribution function (CCDF). In this probabilistic approach
certain methods have been proposed by researchers
includingconstellationmapping, phase optimization,
ToneReservation(TR) and Tone Injection(TI) [9,10], coding
schemes [8], nonlinear commanding transforms, Partial
Transmission Sequence (PTS) and Selective Mapping (SLM)
[4].
There are certain parameters like data rate loss,
implementation complexity, capacity of PAPR reduction,
transmission power, Bit-Error-Rate (BER) etc. and an
effective PAPR reduction technique should be given the best
trade-off between these parameters. However, simple PAPR
reductioncan be achieved by the proposed repeated clipping
and filtering method in this paper. Further, this workpresents
PAPR reduction technique based on selective mapping (SLM)
under different phase sequences V and PTS under different
sub-blocks M.
The remainder ofthis paperis organized as follows.Section
II,presents some basicsabout PAPR problem in
OFDM.Section III describesPAPR reductiontechniques. In
Section IV the overallanalysis ofthe threetechniques amplitude
clipping, SLM and PTS is given. Simulation results are shown
in Section V. SectionVI concludes the article.
2. PEAK-TO-AVERAGE POWER RATIO (PAPR)
The presenceoflargenumberofindependently modulatedsub-
carriersinanOFDMsystem, results in the
highpeakvalueofOFDM signal
ascomparedtotheaveragevalue.Thisratioofthispeaktoaveragepo
wervalueistermed asPeak-to-Average PowerRatio. Besides,
the coherent additionofNsignalswith samephasegeneratesa
peakwhichisN times the average signal.
2.1 PAPR of A Multicarrier Signal
Letthe block of data of length N be represented by a vector
X = [X0, X1, … , XN−1]T
The symbol duration ofanysymbol XK.
inthe set X is T and itrepresentsoneofthe set ofsub–carriers
.Asthe N sub–carriers whichare chosentotransmitthe signalare
orthogonaltoeachother,soit gives fn = n∆f where n∆f = 1/NT
and NT is the durationoftheOFDM datablock X.
Thecomplexblock of data fortheOFDMsignaltobe
transmittedis –
x k =
1
N
Xnej2πn∆fkN−1
n=0 ,0≤ k ≤ NT (1)
ThePAPR of the signal to be transmittedis defined as
PAPR =
max 0≤k≤NT x(k) 2
1
NT
x(k) 2dk
NT
0
(2)
The main aim of PAPR reduction techniques is to reduce
the max x(k) .
2.2 Effects of high PAPR
The number of sub carriers is very large in typical OFDM
systems as a result of which the amplitude of the transmitted
signal has a large dynamic range. It leads to in-band noise and
out-of-band radiation when the signal is allowed to pass
through the nonlinear region of PAs.
Although the problem mentioned above can be avoided by
operating the amplifier in its linear region, but this results in a
reduced power efficiency.
Besides, it also increases the complexity of analog to digital
and digital to analog converter.
2.3 Complementary Cumulative Distribution
Function(CCDF)
TheCumulativeDistribution Function (CDF)is one ofthe most
commonlyused parameters to
measuretheefficiencyofanyPAPRtechnique.Normally,
theComplementaryCDF(CCDF)isusedinsteadofCDF and it
helpsto measurethe probabilitythat the PAPR ofa certain data
blockexceeds thegiven threshold.
The CDF of the amplitude of a signal sample is given by-
F(z) = 1 - exp(-x)
TheCCDFofthePAPRofblock of datais desiredto analyze the
performances of various peak reduction techniques.
P(PAPR > x) = 1- P(PAPR ≤ x)
= 1 − F(x)N
=1 − (1 − exp⁡(−x))N
(3)
2.4 Maximum expected PAPR from an OFDM signal
In an OFDM System, the high data rate information is grouped
into smaller data which are placed orthogonal to each-other. It
is basically the sum of multiple sinosoids of having frequency
separation 1/T where each sinusoid gets modulated by
independent information bn.Mathematically,
Transmitted signal is-

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x t = bne
j2πnt
T
N−1
0
Assuming, bn=1,
Therefore, peak value of signal is-
max[x t x∗
(t)]
= max bne
j2πnt
T
N−1
0
bn
∗
e
−j2πnt
T
N−1
0
= max bnbn
∗
e
j2πnt
T e
−j2πnt
T
N−1
0
N−1
0
= N2
And
Mean Square Value-
E x t x∗
(t) = E bne
j2πnt
T
N−1
0
bn
∗
e
−j2πnt
T
N−1
0
= E bnbn
∗
e
j2πnt
T e
−j2πnt
T
N−1
0
N−1
0
= N
PAPR =
N2
N
Therefore, PAPR= N (4)
It is clear from (4), that for given N subcarriers and all sub –
carriers are given same Modulation maximum expected PAPR
from a OFDM signal is N.
3. PAPR REDUCTION TECHNIQUES
Several PAPR reduction techniques have been proposed in the
literature[6].The PAPR reduction techniques vary in
accordance with the needs of system and are dependent on
various factors such as BER increase, data rate
loss,computation complexity,transmit power increase e.t.c.
These techniques are divided into two groups - signal
distortion techniques and data scrambling techniques which
are as follows-
3.1) Signal Distortion Techniques
3.1.1 Clipping and Filtering
3.1.2 Peak Reduction Carrier
3.2) Data Scrambling Techniques
In scrambling techniques, each OFDM signal is mixed with
different scrambling sequences and the signal which has
smallest PAPR value is transmitted.
3.2.1 Selected Mapping (SLM)
3.2.2 Partial Transmit Sequence (PTS)
3.2.3 Block Coding Techniques
3.2.4 Tone Reservation (TR)
3.1.1 Clipping and Filtering
Amplitude clipping is one of the simplest techniques for
PAPR reduction in OFDM system. In this technique, initially a
threshold value of amplitude is set and any subcarrier having
more amplitude compared to the threshold is clipped or that
sub-carrier is filtered to lower PAPR value[4].Basically,
Clipping works on the idea of reducing large peaks by non-
linearly distorting the signal. It does not scramble the signal
and too large peaks occurs less often so the signal is seldom
distorted .The maximum peak power allowed is decided by the
system specifications, generally by the linear region of the
power amplifier.
Mathematically,
C x =
x , x ≤ k
kejφ x
, x > 𝑘
(5)
Where, C(x) is the amplitude value after clipping, k is the
threshold set by user and x is the initial value of signal.
The Clipping Ratio (CR) can be determined by-
CR = 20 log
k
rx
db(6)
Where rxis the rms value of x.
Clipping is a non linear process which introduces in-band
noise, also called clipping noise, out of band noise and inter-
carrier interference, as a result of which the system
performance is degraded and spectrum efficiency is affected.
However, filtering after clipping can reduce out of band
noisebut it cannot reduce in-band distortion.Clipping may
cause some peak re-growth and the signal after amplitude
clipping and filtering will exceed the clipping level at few
points.The proposed repeated filtering and clipping method
can be implemented to solve this problem. However,
thedesired amplitude level is only achieved after several
iteration of this technique.
3.2.1 Selected Level Mapping (SLM)
In this a set of some different blocks of data representing the
information similarto the original data blocks are selected. The

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data blocks with low PAPR are then selected for
transmission.[6]
Selective Mapping (SLM) is used for lowering the peak to
average transmit power of multicarrier system with selected
mapping. A complete set of member signals is generated
representing the same information in selected mapping, and
then the most favorable signal is selected with low PAPR and
transmitted.
Fig -1: Block diagram of SLM technique
Each block of data is multiplied by V different phase
sequences, having length N,Bv =
[bv,0, bv,1, … . . , bv,N−1]T
(v=0,1,..,V-1) resulting in V modified
blocks. Thus, the Vth phase sequence after multiplication is –
Xv
= [X0bv,0, X1bv,1, … . . , XN−1bv,N−1]T
v = 0,1, … , V − 1 .
Among the data blocks Xv
v = 0,1, … , V − 1 , only the lowest
PAPR data block is selected for transmission and the
corresponding selected phase factors Bv,n should also be sent
as side information to the receiver [6][7]. Amount of PAPR
reduction for SLM depends on the number of phase sequences
and the design of phase sequences. This technique applies
scrambling rotation independently to all sub-carriers.
The positive side of selected mapping method is that it doesn’t
eliminate the peaks, and can handle large number of
subcarriers.
The limitation of this method is the overhead of side
information that requires to be sent to the receiver in order to
reproduce information.
3.2.2Partial Transmit Sequence(PTS):
In the PTS technique, input data block X is partitioned in M
disjoint sub – blocks.
Xm = [Xm,0, Xm,1, … . . , Xm,N−1]T
m = 0,1, … , M − 1 such that Xm
M
m−1 = X and the sub-
blocks are combined to minimize the PAPR in the time
domain. TheS times over-sampled time domain signal of
Xm m = 0,1, … , M − 1 is obltained by taking the IDFT of
length NS on Xm concatenated with (S-1)N zeros.Complex
phase factorsbm = ejφm , m = 0,1, … , M − 1 are introduced to
combine the PTS. The set of phase factors is denoted as
vectorb = [b0, b1, … , bM−1]T
.
The time domain signal after combining is given by
x′
b = bm xm
M−1
m=0 (7)
Where,x′
b = [x0
′
(b), x1
′
(b), … , xNL−1
′
(b)]T
PTS scrambles only part of sub-carriers. The basic principle
behind this method is to divide original OFDM signal into
many subsequences and they are further multiplied by
different weights until an optimum value is selected.[4]
Fig -2: Block diagram of PTS technique
This method is flexible and efficient for OFDM system. The
PTS method is a modified method of SLM. The merit of this
methodis that there is no need to transmit any side information
to the receiver s, when differential modulation is applied in all
sub blocks.[4]
4. STUDY OF DIFFERENT PAPR REDUCTION
TECHNIQUES
The PAPR reductiontechnique should beselected with
awarenessaccordingto various system requirements.

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Table 1: Comparative Study of PAPR reduction Techniques
Technique Advantage Disadvantage
Clipping and
Filtering
No data rate loss,
No transmit power
increase
Signal Distortion
Selected
Mapping(SLM)
Independent of
number of carriers,
Distortionless
Side information
needed, data rate
loss
Partial
Transmit
Sequence (PTS)
Less complex,
Distortionless
Side information
needed, data rate
loss
Thereare manyissuestobeconsideredbeforeusingthe PAPR
reduction techniquesina digitalcommunication system.
Theseissues include PAPRreduction capacity, lossindata
rate,transmit power increase,BER increase
atthereceiver,computational complexity increase and soon.
Table 1show that all PAPR reduction techniques havesome
advantages anddisadvantages and arebasedon
particularaspectof
system.ThesePAPRreductiontechniquesshouldbechosen
carefully forgettingthedesirable minimumPAPR. For instance,
if BER is considered to be crucial requirement of the system,
SLM or PTS can be chosen. However if transmit power, data
rate is to be considered then Clipping and filtering is the best
solution.
5. SIMULATION RESULTS
5.1. Simulation 1
Fig -3:PAPR’s CCDF using different number of sub-bands
(N)
5.2. Simulation 2
Fig -4:PAPR’s CCDF using Repeated Clipping and Filtering
(RCF) with different Clipping levels.
5.3. Simulation 3
Fig -5:SLM method with different Phase sequences
5.4. Simulation 4
Fig -6:PTS method with different sub-blocks(M)

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5.5. Simulation 5
Fig -7:Comparison of RCF, SLM and PTS
In this section, CCDF performances of the Original OFDM
Signal, Amplitude Clipping and Filtering, SLM and PTS are
analyzed through computer simulations by varying parameters
like phase, sub-blocks, sub-bands .The simulations for the
OFDM system are achieved on 105
randomly generated
OFDM symbols employing a QPSK modulation with 64 sub-
bands.
Fig.03 shows that a decrease in number of sub-bands causes
PAPR reduction by approximately 1dB.In this the OFDM
system is analyzed by taking sub-band values 32, 64, 128 and
256.This simulation employs no reduction technique.
However, equation [4] supports the simulation which states
PAPR increases with increase in number of sub-carriers.
Fig.04 shows CCDF performances of RCF with different
clipping levels. At CCDF = 10−3
, simulation shows, 5.66 dB
reduction in PAPR with CR=1.3 as compared to 2.69 dB
reduction with CR=4.It is therefore obvious that Clipping
scheme can improve its performance of PAPR reduction by
reducing its CR.
Fig.5analyzes the performance of SLM technique of PAPR
reduction. It simulates SLM for different values of phase
sequences V while the number of sub-carriers is fixed to
N=64. The algorithm executes 100000 times , over- sampling
factor is taken 4 for V= 1,2,4,8,16. V=1 is when no SLM
technique is applied. The simulation shows 5.7 dB reduction
in PAPR at CCDF = 10−3
compared to when no SLM
technique is applied. The parameter V<16is chosen practically
to compromise with the computational complexity for
performance improvement.
Fig.06 shows CCDF performances of PTS with different
number of sub-blocks(M). Number of sub-bands is kept fixed
at 64 and sub-blocks are varied M [4,7] with phase factors
taking values {±1,±i}. At CCDF = 10−3
, simulation shows,
5.7 dB reduction in PAPR with M=4 as compared to the
original OFDM Signal.It is therefore evident that performance
of PTS is improved with increase in number of sub-blocks.
Fig.07 compares the three PAPR reduction techniques.It
shows CCDF performances of Repeated Clipping and
Filtering ,SLM and PTS .The RCF is simulated with iterations
I= [1,2,3,4] which shows 6.5 dB PAPR reduction with number
of iterations equivalent to four as compared to 3.2 dB
reduction when only one iteration is applied. Obviously,
performance of PAPR reduction of clipping technique is
improving when iterations are increased. However, at CCDF =
10−3
, simulation shows 6.5 dB, 3dB, 1.6 dB PAPR
reductionfor RCF, PTS, SLM respectivelycompared to the
original OFDM signal. Therefore, from fig.07, it can be
observed that Repeated Clipping and Filtering method gives a
better PAPR reduction performance than SLM and PTS.
CONCLUSIONS
OFDM is a very efficient technique for multicarrier
transmission andfor high – speed data transmission;it has
become one of the standard choices. It has many advantages,
but also has one major drawback - it has a very high PAPR.
Thesimulation results shows that clipping scheme can improve
its performance of PAPR reduction by reducing its Clipping
levels, SLM performs better when number of phase sequences
are increased and performance of PTS is improved with
increase in number of sub-blocks.
In contrast to conventional Amplitude Clipping method,
Repeated Clipping and Filtering is proposed which gives
better PAPR reduction performance than SLM and PTS.
ACKNOWLEDGEMENTS
The authors would like to thank University School of
Information and Communication Technology for supporting
the work.
REFERENCES
[1] R.Prasad, “OFDM for Wireless Communications
System”,1st
ed. Artech house, August 2004.
[2] A.R.S. Bahai and B.R. Saltzberg, “Multi-carrier Digital
Communications Theory and Applications of
OFDM”,2nd
ed. Springer October 2004.
[3] M.Parker“Digital Signal Processing,Elsevier”,Inc2010.
[4] SuvernaSengarand ParthaPratim Bhattacharya, “
Performance improvement in OFDM system by PAPR
reduction”, Signal & Image Processing : An
International Journal (SIPIJ) Vol.3, No.2, pp.157-
169,April 2012 .
[5] Md. Ibrahim Abdullah, Md. Zulfiker Mahmud, Md.
ShamimHossain, and Md. NurulIslam,“Comparative

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study of PAPR reduction techniques in OFDM”,
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pp.263-269, November 2011.
[6] AmitAhlawat,“Comparison of Peak To Average Power
Reduction Techniques”,Journal of Energy
Technologies and Policy ,Vol.1, No.2, pp.10-17, 2011.
[7] Md. MahmudulHasan, “An Overview of PAPR
Reduction Techniques in OFDM
Systems”,International Journal of Computer
Applications, Volume 60– No.15, pp.33-37, December
2012.
[8] T. Jiang and Y. Wu, “An overview: peak-to-average
power ratio reduction techniques for OFDM signals,”
IEEE Trans. Broadcast., vol. 54, no. 2, pp. 257-268,
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[9] X. Li and L. J. Cimini, “Effects of clipping and filtering
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[10] S. S. Yoo, S. Yoon, S. Y. Kim, and I. Song, “A novel
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BIOGRAPHIES:
Nidhi Chauhan was born in India on
March 2, 1988. She received B.Tech (2010)
in Electronics & Communication
Engineering from Gautam Buddha
Technical University (G.B.T.U), Lucknow
(U.P.),India. She served as a lecturer in
B.I.T., Meerut, U.P., India. She is a final
year student of M.Tech in Digital and
Wireless Communication, at University School of Information
and Communication Technology, GGSIPU, Delhi, India.
B.V. R. Reddy is Professor in USIT. He
obtained his ME and Ph. D (ECE) degrees
during 1991 and 1998 respectively. He has
about 20 years of experience in teaching
and research. Before joining GGSIPU, he
served as Asst. Professor at NIT Hamirpur.
He has about 20 publications in
International Conferences and journals to
his credit. He is a member of professional bodies such as
IEEE, ISTE, SEMCEI and a fellow of IETE . He has guided
few scholars leading to M. Tech and Ph.D's. His broad
research interest includes Wireless communications which
include computer communication networks, mobile,
Adhocand sensor based networks, microwave , optical
communications, Semiconductor and VLSI circuits.

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