AN OVERVIEW OF PEAK-TO-AVERAGE POWER RATIO REDUCTION TECHNIQUES FOR OFDM SIGNALS

International Journal of Mobile Network Communications & Telematics (IJMNCT) Vol. 6, No.3, June 2016
DOI : 10.5121/ijmnct.2016.6301 1
AN OVERVIEW OF PEAK-TO-AVERAGE POWER
RATIO REDUCTION TECHNIQUES FOR OFDM
SIGNALS
Zhuo Wang 1
, Enchang Sun 2
, Yanhua Zhang 3
1,2,3
College of Electronics Information and Control Engineering, Beijing University of
Technology, Beijing, China
ABSTRACT
OFDM (Orthogonal Frequency Division Multiplexing) has been widely adopted for high data rate wireless
communication systems due to its advantages such as extraordinary spectral efficiency, robustness to
channel fading and better QoS (Quality of Service) performance for multiple users. However, some
challenging issues are still unresolved in OFDM systems. One of the issues is the high PAPR (peak-to-
average power ratio), which results in nonlinearity in power amplifiers, and causes out of band radiation
and in band distortion. This paper reviews some conventional PAPR reduction techniques and their
modifications to achieve better PAPR performance. Advantages and disadvantages of each technique are
discussed in detail. And comparisons between different techniques are also presented. Finally, this paper
makes a prospect forecast about the direction for further researches in the area of PAPR reduction for
OFDM signals.
KEYWORDS
OFDM, PAPR, Clipping, Companding
1. INTRODUCTION
OFDM (Orthogonal Frequency Division Multiplexing) [1]-[3] is a multicarrier orthogonal digital
communication scheme where the whole available bandwidth is divided into many streams of low
data rates and then modulated simultaneously by multiple carriers. It has been widely used for
wireless applications such as Digital Audio Broadcasting (DAB), Terrestrial Digital Video
Broadcasting (DVB-T), and IEEE 802.11a standard for Wireless Local Area Networks (WLAN)
and IEEE 802.16a standard for Wireless Metropolitan Area Networks (WMAN). It provides
greater immunity to multipath fading and impulse noise, and eliminates the need for equalizers,
while efficient hardware implementation can be realized using Fast Fourier Transform (FFT)
techniques.
When the several individual signals, which are modulated over a group of orthogonal subcarriers,
are added up coherently, the problem of PAPR arises. PAPR is the ratio of the maximum power to
the average power of a given signal. Whenever high PAPR occurs, the Digital-to-Analog
Converter (DAC) and High Power Amplifier (HPA) require large dynamic ranges to avoid
amplitude clipping, which increases both power consumption and component cost of the
transceiver. Therefore, it is important and necessary to reduce the PAPR for making the system
efficient.

2
Various approaches have been proposed to reduce the PAPR such as clipping and filtering [4]-[8],
peak windowing [9]-[11], companding [12]-[18], coding techniques [19]-[27], selected mapping
[28]-[30], partial transmit sequence [31]-[35], interleaving [36][37], tone injection [38][39], tone
reservation [38]-[40], active constellation extension [41] and so on. Although some techniques of
PAPR reduction have been summarized in [42], it is still needed to give a comprehensive review
including some motivations and innovations of PAPR reductions in recent years, such as reduced
complexity and power saving. This paper also analyzes advantages and disadvantages of every
techniques, and makes comparisons among them. In practical applications, different techniques
should be chosen according to different systems. An effective technique should be given the better
PAPR reduction performance and tradeoff among computational complexity, power consumption
and Bit Error Rate (BER) performance, etc.
The rest of this paper is organized as follows: Section 2 gives a brief review of the definition of
OFDM and PAPR. In Section 3, different PAPR reduction techniques are introduced and many
modified methods based on these techniques, which have been proposed in recent years, are also
presented. The criteria of PAPR reduction in OFDM systems is discussed in detail in Section 4,
and then a summary of the lessons learned and suggestions on choosing proper PAPR reduction
techniques in practical systems are provided in Section 5. Finally, we conclude this survey in
Section 6.
2. OFDM SYSTEM MODEL AND PAPR
In a typical OFDM system, frequency bandwidth B is divided into N non-overlapping orthogonal
subcarriers of bandwidth, where , 1/ .B N f f NT    Then, each subcarrier of a given OFDM
symbol is modulated by a known constellation. Let T
0 1 1[ , , , ]NX X X X  denote input symbol
vector in the frequency domain, where nX represents the complex data of the th
n subcarrier. Then
after performing an N length Inverse Fast Fourier Transform (IFFT) on X , we obtain time
domain OFDM sequences
T
0 1 1[ , , , ]Nx x x x  , where
1
2
0
1
(t) ,0 .
N
j n ft
n
n
x X e t NT
N




   (1)
Due to the statistical independence of all subcarriers, the instantaneous amplitudes of the different
signals may have high peaks aligned at the same time, leading to high PAPR which can be defined
as:
2
0,1, , 1
2
max ( )
PAPR
[ ( ) ]
n N
x t
E x t
 
 (2)
where [ ]E  denotes the expected operator. To better approximate the PAPR of OFDM signals, the
OFDM signal samples are usually performed by L times oversampling. So these L times
oversampled time domain samples are LN point IFFT of the data block with ( 1)L N zero
padding. Therefore, the PAPR that are computed from the L times oversampled time domain
signal samples is given by [42]
 
2
0 1
2
max
PAPR
k
k NL
k
x
E x
  
 (3)
where kx are samples of the OFDM signal.

3
Figure 1. Classification of PAPR reduction techniques
3. PAPR REDUCTION TECHNIQUES
Numerous techniques have been proposed and optimized in the literature to reduce the PAPR of
OFDM signals. These techniques are usually classified into three main categories: signal distortion
techniques, probabilistic techniques and coding techniques as shown in Figure 1.
In this section, we will briefly review the principles of these PAPR reduction techniques. At the
same time, we mainly focus on the important optimization among these techniques and point out
the advantages and disadvantages of them.
3.1. Signal Distortion Techniques
Signal distortion techniques, including clipping and filtering, peak windowing and companding,
distort the OFDM signals before power amplifier to reduce PAPR. These techniques are able to
reduce PAPR in great level, but result in signal distortion, which leads to worse BER performance.
3.1.1. Clipping and Filtering
Amplitude clipping is a very basic and simple method to reduce PAPR. It employs a clipper that is
used to limit the amplitude peaks of the input signal to a predetermined value if the signal exceeds
it. Otherwise, the clipper passes the signal without any change. It could be described by a function
as:
( )
x,
( )
,j x
x A
B x
Ae x A
 
 

(4)
where x is the original OFDM signal, x（）is the phase of x , A is the predetermined clipping
level, and ( )B x is the signal after clipping. Clipping method introduces in-band distortion and out-
of-band radiation, both due to its nonlinear processing, which can degrade the system performance
such as BER and spectral efficiency. Filtering the clipped OFDM signal is a good method to
reduce or remove out-of-band radiation, but it may cause some peak regrowth, because the signal

4
after clipping and filtering may exceed the clipping level at some points. To solve this problem,
Repeated Clipping and Filtering (RCF) [6] operation is generally used by clipping the oversampled
time domain signals followed by filtering the clipped signals at the cost of additional
computational complexity. Then a novel Iterative Clipping and Filtering (ICF) technique was
proposed in [7], which could obtain a more desirable PAPR reduction level and cancel the
distortion caused by clipping noise. But the major limitation of this method is requiring many
iterations, resulting to high complexity.
Therefore, various methods proposed in some papers were developed to optimize ICF technique
majoring in reducing computational complexity. Reference [43] presented a modified ICF scheme
which limits the distortion on each subcarrier of the OFDM signals to achieve both low PAPR and
low BER with fast convergence. In [44], the authors proposed an optimized ICF method which
determines an optimal frequency response filter for each iteration using convex optimization to
minimize signal distortion, so that the PAPR is reduced under a specified threshold. The authors
claimed that this method achieves a desired PAPR reduction after only 1 or 2 iterations, whereas
the conventional clipping and filtering method requires about 8 to 16 iterations to achieve the
similar PAPR reduction. A novel Custom Conic Optimized Iterative Adaptive Clipping and
Filtering (COIACF), which is also known as convex optimization, was proposed in [45] to reduce
the PAPR of OFDM signals with lower complexity and bit error rate. The authors modified the
filter response to produce a better reduction in PAPR and a better performance in in-band
distortion and out-of-band radiation in less number of iterations due to the functionality of FFT.
3.1.2. Peak Windowing
This method reduces the peak value through multiplying a window function by the original OFDM
signals [9]-[11], which can be used to suppress out-of-band radiation after clipping. The main idea
of this method is that the valleys of window function are multiplied by the signal peaks while the
high peaks of window function are multiplied by the signal valleys. Many window functions can
be used in this process as long as they have good spectral properties. Hamming, Hanning and
Kaiser windows are the most widely used window functions. This scheme attenuates signal peaks
in a much smoother way, but the peak reduction worsens as the number of peak signals increases.
3.1.3. Companding Transform
Companding transform is one of the most attractive techniques of PAPR reduction with lower
computational complexity that is not affected by the number of subcarriers. And side information
is not necessary to be transmitted, leading to no loss in bit rates.
Companding transforms are firstly and typically applied to speech signals to optimize the required
number of bits per sample. Since OFDM and speech signals have some similarities in the aspect
that high peaks occur infrequently, same companding transforms can also be used to reduce the
OFDM signal’s PAPR [34].
In fact, the companding transforms can be viewed as an optimized clipping scheme. The biggest
difference between them is that companding transforms enlarge the small signals while
compressing the large signals in order to eliminate interference from noise, whereas clipping
method does not change the small signals. This is the exact reason why clipping method suffers
from in-band distortion and out-of-band radiation. Additionally, clipping method deliberately clips
large signals when the amplitudes of the original OFDM signals are larger than the given threshold,
resulting in clipped signals unrecoverable at the receiver. However companding transforms
compand original OFDM signals using the strict monotone increasing function. So the companded

5
signals at the transmitter can be recovered correctly and easily through the corresponding inversion
of the transform function at the receiver.
Companding transform is an extra operation after the modulation of OFDM signals which
definitely generates companding distortion. Hence, how to reduce the negative impact of
companding distortion on the BER performance is the key part in designing companding transform.
The first applicable nonlinear companding transform is the  -law companding that mainly
focuses on preserving the high peaks and enhancing the low amplitudes of the signals. Therefore it
keeps the peak power unchanged but increases the average power, leading to reduce of the PAPR
[12]. The resulting companded signal  cx n using the  -law companding can be expressed as [13]:
 
  sgn log 1 [ ]/
log(1 )
c
A x n x n A
x n


   

(5)
where A is a normalization constant such that 0 [ ]/ 1x n A  ,  is the companding parameter and
sgn( [ ])x n denotes the sign of [ ]x n . Figure 2 shows that the uncompanded envelope of an OFDM
signal [ ]x n and the  -law companded envelope corresponding to it with 3  .
Figure 2. Uncompanded and companded using  -law OFDM envelopes
However, the  -law companding scheme reduces PAPR at the expense of the increase in the
average signal power. Later, error companding transforms and exponential companding transforms
were developed in [14] and [16], respectively. Both of them have less impacts on the original
power spectrum comparing to the  -law companding scheme. It is the major reason that the error
companding schemes and the exponential companding schemes not only enlarge the small
amplitude signals but also compress the large amplitude signals. Both maintain the average power
invariable by properly choosing parameters, which prevents small amplitude signals from noise.
Reference [17] proposed a new companding scheme that transforms the Gaussian distributed
signal into a distribution form with a linear piecewise function. Although, this companding scheme
can reduce PAPR effectively, the computational complexity is increased at the same time. Then, a
low-complexity linear companding transform (LCT) was investigated in [46] to reduce peak power
by linearly transforming the small and large signal amplitudes with different scales. But this
method can not keep signal power at the same level for the input and output. Also, additional side
information was needed at the decompanding operation, because LCT method does not have one-
to-one mapping. In order to maintain the average signal power unchangeable and obtain a one-to-
one mapping, a new scheme was investigated in [47], called two-piecewise companding (TPWC)
scheme, which transforms small amplitudes with a scale and large amplitudes with both a scale

6
and a shift. A new piecewise linear companding transform was designed in [48], in which the
signals with amplitudes over a given companded peak amplitude are clipped for peak power
reduction, and the signals with amplitudes close to the given companded peak amplitude are
linearly scaled for power compensation. The authors proved that this proposed piecewise linear
companding scheme can reduce companding distortion and PAPR effectively. Besides, uniform
companding[15], logarithmic companding and hyperbolic tangent companding transforms [18],
with proper companding coefficients, were used in the literature to reduce PAPR.
3.2. Probabilistic Techniques
Due to the high PAPR appears randomly, these techniques focus on lower probability of high
peaks of OFDM signals. The principle of these techniques is that different scrambling sequences
are weighted to original OFDM signals to optimize phase sequences. Then, one combination
between OFDM signal and phase sequence that has minimum PAPR is selected to be transmitted.
The probability of high peaks occurrence will be reduced through this way and then PAPR is
reduced.
3.2.1. Selective Mapping
Selective Mapping (SLM) is a relatively simple approach to reduce PAPR. A block diagram of the
SLM technique is shown in Figure 3 [51]. The transmitter generates a set of sufficiently different
candidate data blocks, all representing the same information as the original data blocks. Then each
data block is multiplied by U different phase sequences
,0 ,1 ,n 1( ) [ , , , ] , 1,2, , .T
u u uB u b b b u U  After combining phase factors with data blocks, the
modified data blocks 0 ,0 1, ,1 1 , 1( ) [ , , ] , 1,2, ,T
u u N u NX u X b X b X b u U   are obtained. Then IFFT is
performed on the sub-blocks and the time domain signals become
1
( ) 2
,
0
1
( ) ,0 , 1,2, .
N
u j n ft
n u n
n
x t X b e t NT u U
N




    (6)
Among the modified data blocks ( ),X u only one with the lowest PAPR is selected for transmission
and the corresponding selected phase factor ,u nb is also transmitted to receiver as side information
to allow the recovery of original symbol sequences, which results in the data transmission rate loss.
2Log u bits are needed as side information (SI) and U times inverse discrete Fourier transform
(IDFT) operations are also implemented in this process. So the extent of PAPR reduction achieved
and the computational complexity for SLM depend on the number and design of the phase
sequences.
Figure 3. Block diagram of the SLM technique [51]
In the conventional SLM scheme, although, SI allows the recovery of original symbol sequences at
the receiver, it will reduce the data transmission rate. On the other hand, an erroneous detection of
the SI at the receiver may lead to a significant performance deterioration on the BER. Therefore,

7
several blind SLM schemes [53]-[56] were produced to transmit signals without side information.
In [55], the maximum likelihood decoder is firstly produced, which shows the same BER
performance as the conventional SLM scheme assuming perfect side information recovery, but it
causes large decoding complexity at the receiver. A new blind SLM scheme with low decoding
complexity was then proposed in [56], in which the side information is embedded into each phase
sequence by giving the phase offset to the elements of the phase sequences, which are determined
by the bi-orthogonal vectors for the partitioned sub-blocks. At the same time, a maximum
likelihood decoder with lower decoding complexity was derived for this scheme, which reduces
the decoding complexity by ( 2) /M M compared with the conventional blind SLM scheme in [55],
where M denotes the times of IDFT operations. In [57], the authors proposed a suboptimal blind
method based on Dummy Sequences Insertion (DSI) technique to reduce the PAPR level. Only a
few sequences of zeros need to be inserted into the original signal. Besides, the signal recovery at
the receiver is guaranteed by this embedded signaling, which is based on calculating the energy of
the received signal. Any explicit SI is not needed to be transmitted in this proposed method, and
simulations showed that this method does not only serve to reduce the PAPR level but also
achieves a better BER performance.
Additionally, many attempts in the literature have been made to solve the problem of increased
computational complexity, since the size of OFDM blocks may be large and the number of phase
sequences M and IFFT operations may be huge [58]-[61], when a substantial PAPR reduction is
required. In order to address the problem of multiple IFFT operations, some new architectures
have been proposed [60] [61], in which the frequency domain phase rotation operations are
converted into time domain equivalent operations. However, the selections of sequences are
limited and the adopted sequences are not randomly generated, resulting that the performance of
PAPR reduction is affected. In view of the above literature, reference [62] proposed a new low
complexity architecture, in which frequency domain cyclic shifting, complex conjugate and
subcarrier reversal operations are all applied to increase the diversity of the candidate signals
instead of only frequency domain phase rotation used in traditional SLM scheme. These four
frequency domain operations are all converted into time domain equivalents similar to [60] [61] to
avoid the problem of multiple IFFT operations. Then, the authors adopted various ways of
partitioning and reassembling the subcarriers according to different phase rotations to reduce the
computational complexity. The theoretical analysis and simulation results showed that this
proposed scheme almost has the same PAPR reduction performance as the traditional SLM
method but with a significantly reduced computational complexity.
3.2.2. Partial Transmit Sequences
In the PTS technique, an input data block containing N symbols is partitioned into many disjoint
sub-blocks, on which IFFT is performed separately and then weighted by a phase factor. The phase
factors are selected in such a way as to minimize the PAPR of the combined signals of all the sub-
blocks. Figure 4 [51] shows the block diagram of the PTS technique. Let an input data block
1 2[ , , , ]NX X X X be partitioned into M disjoint sub-blocks
,1 ,2 ,[ , , , ],1 ,m m m m NX X X X m M   any two of these sub-blocks are orthogonal and X is denoted
as the combination of all sub-blocks
1
.
M
m
m
X X

  Then the IDFT operation is performed on each
sub-block mX , and weighted by a complex phase factor ,mj
mb e 
 where [0,2 ),m 1,2, , .m M  
The set of phase factors is denoted as a vector 1 2[ , , , ] .T
Mb b b b The time domain signals after
combining can be described as
1
,
M
m m
m
x b x

  where mx is the time domain signal of mX . Then the

8
objective is to find the set of phase factors that minimizes the PAPR of x , which is chosen for
transmission.
Figure 4. Block diagram of the PTS technique [51]
In general, the number of phase factors is limited to a set in order to reduce search complexity in
the process of selecting the optimum one. The set of allowed phase factors can be described as
2j k
e
W
P e

 , where W is the number of allowed phase factors. The phase factor 1b is usually set to 1
without any loss of performance, therefore, 1M  phase factors are alternative to be found and
1M
W 
sets of phase factors are searched to find the optimum one. The performance of PAPR
reduction and the search complexity depend on M and W , since PTS needs M IDFT operations
for each data block, and the number of required side information bits is 1
2log M
W 
   , where
y   denotes the smallest integer that does not exceed y [42]. Another factor that may affect the
PAPR reduction performance in PTS is the method of division of sub-block partitioning. There are
three kinds of sub-block partitioning schemes: adjacent, interleaved, and pseudo-random
partitioning. Among them, pseudo-random partitioning has been proved to be the best choice,
which can be seen from Figure 5, where the original data block is partitioned into four sub-blocks
and QPSK is used in this simulation.
Figure 5. CCDF for sub-block partitioning schemes
How to reduce the high computational complexity for searching the optimal phase factors while
maintaining a substantial reduction in PAPR has always been a huge problem. Various methods
have been proposed in the literature to reduce the computational complexity in PTS, including
iterative flipping algorithm [63], gradient descent search [64], sign-selection algorithms [65],

9
genetic algorithm [66], sphere decoding algorithm [67], adaptive PTS approach [68] and many
other optimized methods. Reference [69] proposed a modified flipping algorithm based on
iterative flipping algorithm. This new technique partitions the formed sub-blocks into even and
odd number of groups and then ‘flipping’ operation will be applied into group by group. That
means two groups of four sub-blocks are formed after performing IDFT operations. Then the best
combination between phase sequences and groups, which gives minimum PAPR value, is selected
to be transmitted. Simulation result showed that this proposed flipping scheme offers better PAPR
reduction and performance/complexity tradeoff than iterative flipping algorithm and conventional
PTS. A novel PTS scheme using genetic algorithm with lower computational complexity was
proposed in [70], in which candidate signals were generated using a set of matrices called seed
matrices for a given weight set and block size. Through this way, one candidate sequence can be
generated by combination of other sequences, since high degree of correlation is exhibited among
them. Therefore, computational complexity is reduced without decreasing the number of sub-
blocks and candidate signals.
3.2.3. Interleaving
The interleaving technique is extremely similar to SLM technique. In this method, a set of
interleavers, devices that permute or reorder symbols in a specific way, instead of phase sequences
is used to reduce the PAPR. So original data block 0 1 1[ , , , ]T
NX X X X  becomes many different
permuted blocks by the use of these interleavers. Then the IDFT operation is performed on each
one of these different permutations separately to generate multiple OFDM signals. The one with
the smallest PAPR is chosen for transmission. To recover the original data block correctly, the
receiver only need to know which interleaver is used at the transmitter, thus, the number of
required side information bits is 2log k , where k represents the number of interleavers. So the
amount of PAPR reduction and the degree of complexity in this method depend on k and the
design of the interleavers.
3.2.4. Tone Reservation
The basic idea of Tone Reservation (TR) is that a small number of subcarriers that are also called
tones are not used for data transmission instead for PAPR reduction. A structured time domain
vector c is added to the original OFDM signal x to change its statistical distribution to reduce
PAPR. If we add a frequency domain vector 0 1 1[ , , , ]T
NC C C C  to X , X and C are restricted to
lie in disjoint frequency subspaces, the new time domain signal can be represented as
' { }.x x c IDFT X C    Then the objective is to find the proper time domain signal c to be added
to make the new time domain signal 'x with low PAPR. Assume that there are L unused tones in
the OFDM signal, correspondingly a set of L nonzero subcarriers in C , that is
 1 20, , , ,n LX n i i i  and  1 20, , , , .n LC n i i i  The L nonzero positions in C are called peak
reduction carriers (PRCs). Since subcarriers of OFDM signals are orthogonal, these PRCs have no
distortion effect on the data bearing subcarriers. To find the correct value of nC ,  1 2, , , ,nn i i i
it could draw support from a convex optimization problem, which can be cast as a linear
programming (LP) problem of complexity 2
( )o LN [38][78]. The receiver only needs to know the
positions of these tones, which are served as overhead information.
Many different kinds of methods based on TR technique have been proposed in the literature.
Clipping Control TR (CC-TR) [72], as the simplest TR scheme, in which the original signal is
clipped firstly, then the signal above the predetermined threshold is mapped to the reserved carrier
in frequency domain to reduce the PAPR. But some disadvantages lie in this method such that

10
excessive iterations and slow convergence rate. The Adaptive Amplitude Clipping TR (AAC-TR)
method and least squares approximation based TR (LSA-TR) method were introduced in [73] and
[74] respectively. Both of them overcame shortcomings in CC-TR method, and had a better
performance in PAPR reduction and computational complexity. In [75], authors proposed a new
method based on the optimal prototype signal and least squares approximation algorithm, which
were used to approximate the clipping noise just in the time domain by circularly shift and scale to
reduce the PAPR of OFDM signals. In [76], an improved TR method based on the maximum
likelihood estimate (MLE), called the MLE-TR algorithm, was proposed. This algorithm generates
peak-canceling signals by use of the clipping noise that is created in clipping operation, and then
uses the MLE algorithm to get an optimized factor to make the amplitude of peak canceling signals
close to the clipping noise. Thus a better performance of PAPR reduction can be achieved in the
case of a fast convergence. A novel curve fitting based tone reservation (CF-TR) method was
investigated in [77], the key idea behind this method is to fit the peak-canceling signal waveform
to the clipping noise waveform to get the peak canceling signal iterative. Besides, authors obtained
the optimal clipping threshold that should be ln ,
N
A
M
 where  is the mean power of the
OFDM signals, M denotes peak reduction tones and N is the number of data symbols. Simulation
results showed that the proposed CF-TR method had better performance in PAPR reduction with
computational complexity decreased.
3.2.5. Tone Injection
In this technique, the constellation size is increased in order to make each of the points in the
original basic constellation mapped onto several other points in the expanded constellation. So the
same information can be carried by any of these points, correspondingly some symbols of original
OFDM signal are replaced by appropriate alternatives in an extended constellation, which is in
favor of PAPR reduction. One point in the original basic constellation may be substituted for one
in the expanded constellation, which is equivalent to injecting a tone of proper frequency and
phase to the original OFDM signal. This is the origin of the name of this method. Assume that
QAM is used as a modulation scheme and its original constellation size is M , the minimum
distance between points in this square QAM constellation is d . The th
k QAM symbol on a single
subcarrier with all its original and expanded constellation points can be described as
' ,k k k kX X p D jq D   where kX is the th
k original QAM symbol, kp and kq are integer numbers
that are used to change the real and imaginary parts of kX respectively. D , a positive real number
known at the receiver, represents the spacing between each original point in the original
constellation and its equivalent points in the expanded constellation. The value of D should be
,D d M where 1  , in order not to increase BER at the receiver [78]. The procedure of tone
injection technique with 16-QAM constellation is shown in Figure 6 [79], where the original
constellation point A maps to one of , 1,2, ,8iA i  , according to changes in the value of kp and
kq . Then one of these expanded constellation points is chosen for transmission to reduce PAPR.
There is no loss of bit rates in tone injection technique because it does not need side information at
all and only two simple modulo- D operations are required at the receiver, which can be neglected
in computational complexity. But tone injection technique can increase average signal power at the
transmitter due to the use of enlarged signal constellation and the search complexity is also
increased.
A new hexagonal constellation was proposed in [80]. More spaced signaling points can be packed
using this hexagonal constellation than QAM constellation of the same area. So PAPR is reduced
due to the extra degree of freedom and power increase is less compared to the QAM constellation.

11
A new TI scheme that uses the clipping noise to find the optimal equivalent constellations is
introduced in [81]. By projecting the clipping noise that is taken from the signals lager than a
predetermined threshold to the nearest equivalent constellation points, the peak cancellation signal
is easily determined, which reduces the complexity dramatically while maintaining a good PAPR
performance. In [82] and [83], authors proposed a linear programming algorithm and parametric
minimum method respectively as lower complexity solutions to the tone injection technique.
Figure 6 Tone injection technique for 16-QAM constellation [79]
3.2.6. The Active Constellation Extension Technique
The key idea behind the ACE method is to extend outer boundaries of the signal constellations in
frequency domain. That is to say, some constellation points are extended toward the outside of the
original constellation such that the PAPR of the OFDM data blocks in time domain may be
reduced. The principles can be explained in Figure 7 [79] and Figure 8 [79], where QPSK and 16-
QAM modulation assumed to be used. The shaded regions in Figure 7 and Figure 8 and the
straight lines starting at the non-corner constellation points to infinity in Figure 8 represent the
region of increased margin for the data symbols. A reasonable combination of these additional
signals can be partly used to cancel the peaks of time domain signals and then reduce the PAPR of
the transmit signals. Waveforms of original signals and after ACE and the constellations are shown
in Figure 9 and Figure 10 respectively with QPSK modulation and 256 subcarriers.
Figure 7 Active constellation extension technique with QPSK modulation [79]
Comparing Figure 9 and Figure 10, it is shown that the ACE method is more applicable to small
constellations, because all the points in the QPSK constellation can be extended, nevertheless, only
small parts of the points in the 16-QAM constellation have room for increased margin. In addition,
there is no loss in data rates and no side information is required at the receiver. Furthermore, the
increase in average transmit power resulted from constellation extention can be neglected, which

12
leads to almost no significant degradation in BER performance. For practical implementation, fast
convergence rate of ACE algorithm is an important issue. Smart gradient-project (SGP) algorithm
[41], adaptive scaling (AS) algorithm [84] and adaptive clipping control ACE algorithm [85] were
introduced respectively for fast convergence rate. A modified method of adaptive clipping control
ACE algorithm was proposed in [86]. By increasing the step size both for peak canceling signal
and clipping level control, the convergence rate was improved with lower PAPR.
Figure 8 Active constellation extension technique with 16-QAM modulation [79]
Figure 9 Waveforms before ACE and after ACE
Figure 10 Constellations after ACE with QPSK modulation

13
3.3. Coding Techniques
The basic idea of coding techniques is to choose a set of code words with lower PAPR. Then the
input data blocks are mapped into these selected code words by various coding method. Therefore
some peak amplitudes that lie in small part of original OFDM signals may be disappeared such
that PAPR is reduced.
A simple linear block coding (LBC) scheme was proposed in [19], where 3 bits are mapped into 4
bits code word by adding a parity bit. Then Cyclic Coding (CC) that is applicable for any number
of subcarriers was introduced in [20], which can reduce PAPR by more than 3 dB. In [88], Sub-
block Coding (SBC) scheme was proposed, where long data blocks are divided into many sub-
blocks, each of them adds an odd parity bit. The position of the added parity bit has an influence
on the degree of reduction of PAPR. All the above schemes require side information to be
transmitted to the receiver, which need to know the locations of the parity bits. In [89], authors
proposed a new scheme, in which standard arrays of linear block codes are used for PAPR
reduction. The coset leaders of a linear code are used for scrambling, which leads to no side
information required to be transmitted, and the received signals can be decoded by syndrome
decoding at the receiver. A low complexity Complement Block Coding (CBC) scheme was
proposed in [90], few complement bits are added to the original information bits to form a new
code word to reduce the probability of the peak signals occurrence. CBC scheme has no restriction
on frame size and has lower implementation complexity, therefore it is used more widely.
In [23], authors proposed to apply fountain codes to control the PAPR of OFDM signals at a
desired level. The principle of this scheme is that original source packets are fountain encoded to a
semi-infinite packet stream. Then the fountain coded packets are fed to a N point IDFT operation
and PAPR control block. The PAPR control block is used to check whether the PAPR of the
output signal after IDFT operation is at the desirable level or not. If the PAPR level exceeds the
predetermined threshold, this OFDM symbol will be discarded. Otherwise, this symbol will pass
without any change. Once the receiver gets enough packets for recovering the original source
packets successfully, the fountain encoder will stops the ongoing packet transmission. This scheme
works well in practice since the codes are rateless, though the complexity may be little higher.
Golay complementary sequences with different constellations can be used as code words to
achieve the PAPR reduction [91]-[93], more than 3 dB PAPR reduction can be obtained in this
method. Reed Muller codes [94] is another efficient coding scheme. It separates the code words
with high PAPR by dividing non-binary Reed-Muller codes into many cosets, thus PAPR is
reduced.
Coding technique is a nonlinear processing procedure, which do not appear clipping noise like the
clipping method. But it increases the complexity both at the transmitter and the receiver, due to
the additional information added to the original data blocks, which also results in some data rate
loss and bandwidth expansion.
Table1 Comparison between PAPR reduction techniques
PAPR Reduction
Method
BER Increase Bit Rate Loss Complexity Power Increase Bandwidth
Expansion
Distortion-less
Clipping yes no low no no no
Companding yes no low no no yes
SLM no yes high no yes yes
PTS no yes high no yes yes
Interleaving no yes high no yes yes
TI no no high yes yes yes
TR no yes high yes yes yes
ACE no no high yes yes yes
Coding yes yes high no yes no

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4. CRITERIA FOR SELECTION OF PAPR REDUCTION TECHNIQUES
As mentioned above, every technique has their own advantages and disadvantages. So it is
supposed to choose techniques or hybrid techniques (in which two or more techniques are
combined) according to practical demand and some following factors should be considered before
choosing the proper techniques.
High capability of PAPR reduction: Obviously, this is the primary and most important factor to be
considered in selecting the PAPR reduction techniques. The level of PAPR reduction should be as
large as possible when other factors are not greatly affected.
Low average power: The increase in average power can reduce PAPR, but it requires a larger
linear operation region in HPA, which results in higher distortions and BER performance
degradation.
Low computational complexity: Generally, the more complex the technique is, the more PAPR
reduction capability it will get. However, complex techniques require additional time, hardware
and power that should be as minimal as possible in overall systems.
Less bandwidth expansion: The bandwidth expansion occurs when side information is needed to
be transmitted in some PAPR reduction techniques such as PTS and interleaving. Considering the
bandwidth is a rare resource in communication systems, it is desirable to reduce PAPR at the
expense of no bandwidth expansion.
Less BER performance degradation: BER performance degradation is also an important factor in
communication system that should be considered. The goal in PAPR reduction is to get better
system performance including BER.
Other Factors: Some nonlinear devices such as digital-to-analog converter, HPA and mixer also
should be taken into consideration as they can protect PAPR reduction without nonlinear distortion.
Additionally, the cost of these devices is also an important factor that should be considered in
practical systems.
Table 1 summarizes some PAPR reduction techniques and performance impacting factors
mentioned above. It can be clearly seen that no specific PAPR reduction technique achieves the
best performance in all situations. Therefore, proper techniques should be selected based on
practical systems, i.e. available resources and performance constraints.
5. LESSONS LEARNED AND SUGGESTIONS
The topic of PAPR reduction in OFDM systems is still an active area for further researches, since
no PAPR reduction technique has been proved to be the best one. In practical application, global
consideration should be taken into to help us to select proper techniques that can reduce PAPR
largely and keep good performance in terms of the performance factors mentioned above at the
same time.
In modern OFDM based wireless communication standards, high data rates and mobility are basic
requirements, which need a large number of subcarriers to support them. For example, WiMAX,
LTE and DVB-T support up to 512, 2048 and 8192 subcarriers respectively. A high number of
subcarriers will lead to high PAPR but causes a huge problem in PAPR reduction: computational
complexity. Probabilistic techniques are suffered from higher complexity due to the increase of the
number of subcarriers. Take SLM and PTS methods for example, the number of subcarriers is
denoted as N , M represents the number of IFFT blocks as well as the number of phase sequences.
For SLM technique, 23 (1 log ) ( 1) 1MN N M N    additions and 22 (1 log )MN N M 
multiplications are needed, while 23 log [2 ( 1) 1]MN N M N M   additions and 22 log 2 1MN N N 

15
multiplications are needed in PTS method [79]. Clearly, it is shown that computational complexity
grows rapidly as the number of subcarriers increases. Additionally, most of coding schemes are
also limited to use in practical application due to their high implementation complexity and many
of them are not applied to large number of subcarriers. Therefore, repeated clipping and filtering
method with lower complexity is widely used in practical systems, under the condition of a
tolerable BER. Many modifications in the literature have been proposed recently to solve the
problem of high complexity such as blind SLM, genetic algorithm and iterative flipping algorithm
in PTS, which are mentioned above. These attempts may lead to viability in practical systems,
which seems to become a promising direction for further researches in the area of PAPR reduction
for OFDM based systems.
Another issue that needs to be mainly focused on should be the transmitted power constraint,
which means that the average power of transmitted signals is likely to be unchanged. Because the
power amplifier’s gain must be dynamically adjusted according to the power of the signal, which
increases the hardware cost. Absolutely, it is desirable to maintain the average power constant with
minimum extra complexity. Some PAPR reduction techniques including tone reservation, tone
injection and ACE reduce PAPR at the cost of increasing the average power, while clipping and
filtering method is an example that reduces average power. In addition, the concept of energy
efficiency and green networks has been proposed and attracted increasing attention recently. Due
to the fact that energy consumption of networks is growing fast and the trend of achieving green
power in wireless communication systems is becoming popular, therefore, reducing power
consumption and improving energy efficiency in power amplifier as much as possible at the
process of reducing PAPR is a rich subject for conducting further research.
In future development of PAPR reduction techniques, practical potential should be firstly
concerned rather than just seeking possible theoretical solutions. Therefore, an efficient PAPR
reduction method in practical system should be the lower value of PAPR while keeping the
minimum computational complexity and power consumption. This makes sense since other
undesirable effects resulting from PAPR reduction techniques could be mitigated by other modules
or the disadvantages could be acceptable in wireless systems as well as some performance metrics
such as throughput, QoS and reliability are above a desirable level.
6. CONCLUSIONS
OFDM is an efficient modulation technique for high data rate transmission in wireless
communication systems. However, high PAPR is one of the serious drawbacks of OFDM signals
which may result in nonlinear distortions and spectral spreading in power amplifier. In this paper,
we provides an overview of some conventional PAPR reduction schemes. All of them have the
potential to provide substantial reduction in PAPR at the cost of data rate loss, increase in
computational complexity, BER and transmit power and so on. Therefore, many modifications
based on these conventional PAPR reduction schemes in the literature that are committed to
performing better PAPR reduction level, reducing complexity, BER and transmit signal power are
also summarized in this paper. Then comparisons among these techniques are presented and
discussed. It is clear that any specific PAPR reduction technique has not been proved to be the best
one so far, as each of them has its own advantages and disadvantages. Therefore, performance
impacting factors that are mentioned above should be carefully chosen according to specific
system requirements. Since high data rates need a large number of subcarriers and energy
efficiency is the future trends in OFDM systems, we demonstrate that reducing computational
complexity, due to the high number of subcarriers, and power consumption in power amplifier at
the process of PAPR reduction is a promising direction for conducting further research in most
OFDM based systems.

16
ACKNOWLEDGMENTS
This work was financially supported by the National Natural Science Foundation of China under
Grant 61372089 and 61571021, the Science and Technology Development Project of Beijing
Municipal Education Commission under Grant KM201610005007.
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AUTHORS
Zhuo Wang ， born in 1991. He is currently working toward the Master degree in
Information and Communication Engineering in Beijing University of Technology, Beijing,
China. His current research interests include communication and information theory, multi-
carrier communications and cooperative communications.
Enchang Sun, is a senior member of Chinese Institute of Electronics (CIE), and a
chartered member of the Institution of Engineering and Technology (IET) and IEEE senior
member. He received the M.Sc. (M.S.E.) degree in Electrical Engineering (EE) from China
Academy of Telecommunication Technology (CATT), Beijing, P.R. China, in 2004, and the
Ph.D. degree in Information and Telecommunications Engineering from Xidian University,
Xi’an, P.R. China, in 2008. Now he is an Associate Professor with the School of Electronic Information and
Control Engineering, Beijing University of Technology, Beijing, P.R. China. His current research interests
include communication and information theory with special emphasis on wireless digital communications,
green communications and networks, and multicarrier communications.

AN OVERVIEW OF PEAK-TO-AVERAGE POWER RATIO REDUCTION TECHNIQUES FOR OFDM SIGNALS

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