A NOVEL PTS SCHEME FOR PAPR REDUCTION IN OFDM
SYSTEMS
Mihail P. Iliev, Viktor V. Hadzhivasilev
University of Ruse “Angel Kanchev”, Ruse, Bulgaria
Keywords: Orthogonal Frequency Division Multiplexing /OFDM/, Peak-to-Average Power Ratio /PAPR/, Partial
Transmit Sequence /PTS/, Selected Mapping /SLM/.
Abstract: One of the main drawbacks of orthogonal frequency division multiplexing /OFDM/ is the high peak-to-
average power ratio /PAPR/ of the transmitted OFDM signal. Partial transmit sequence /PTS/ technique can
improve the PAPR statistics of an OFDM signal. As ordinary PTS technique requires an exhaustive search
over all combinations of allowed phase factors, the search complexity increases exponentially with the
number of sub-blocks. This paper proposed a novel scheme which has an adjustable parameter enables us to
be able to obtain the best performance. Simulation results show that this scheme can significantly improve
the ordinal PTS scheme and greatly reduce the computation complexity.
1 INTRODUCTION
Orthogonal frequency division multiplexing
/OFDM/ is an attractive technique for wide-band
radio communication because of OFDM’s capability
to convert a frequency selective fading channel to
multiple flat fading channels. Thus, there is no need
to implement any equalizers in the receiver.
However, multi-carrier signals such as OFDM
inherently have a high peak-to-average power ratio
/PAPR/ problem. Transmitting the OFDM signals
without any distortion requires a sufficient back-off
of power amplifiers. This property is not acceptable
for handsets with limited resources. Many proposals
to reduce the PAPR of OFDM signals have been
presented. Amplitude clipping and filtering /ACF/ is
a simple and effective method. However, clipping
causes signal distortion and degrades detection
performance in specific to QAM. Selective mapping
/SLM/ (Ib. Abdullah, 2011) and partial transmit
sequence /PTS/ are based on the same idea that the
PAPR of an OFDM symbol can be reduced by
applying a certain phase rotation to a part of the
transmit data or sequence. In general, SLM needs
more IFFT operations but provides better PAPR
reduction. Both SLM and PTS are distortionless
unlike ACF. However, side information on the phase
rotation pattern must be transmitted besides the main
data. The side information requirement slightly
decreases the transmission efficiency and impacts on
the standardization defining the transmitted signal
design.
In the paper, we propose a novel scheme for
partial transmit sequence, which is based on finding
the lowest PAPR from all binary weighting factors
combinations.
The paper is organized as follows: In Section 2,
the principle of PTS is described. In Section 3
ordinal PTS and a novel PTS technique is presented.
In Section 4, the simulation results are given.
Finally, we conclude the paper in Section 5.
2 PRINCIPLE OF PTS /PARTIAL
TRANSMIT SEQUENCE/
Partial Transmit Sequence /PTS/ algorithm was first
proposed by Müller S. H., Huber J. B., (S. H.
Muller, 1997) which is a technique for improving
the statistics of a multi-carrier signal. The basic idea
of partial transmit sequences algorithm is to divide
the original OFDM sequence into several sub-
sequences, and for each sub-sequence, multiplied by
different weights until an optimum value is chosen.
Fig. 1 is the block diagram of PTS algorithm. We
have added Hadamard transform to reduce the
occurrence of the high peaks comparing the original
OFDM system. The idea to use the hadamard
170
Iliev M. and Hadzhivasilev V.
A NOVEL PTS SCHEME FOR PAPR REDUCTION IN OFDM SYSTEMS.
DOI: 10.5220/0005415501700174
In Proceedings of the First International Conference on Telecommunications and Remote Sensing (ICTRS 2012), pages 170-174
ISBN: 978-989-8565-28-0
Copyright
c
 2012 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

Figure 1: Block diagram of PTS algorithm.
transform is to reduce the autoc
orrelation of the
input sequence to reduce the peak to average power
problem and it requires no side information to be
transmitted to the receiver.
From the left side of diagram, we see that the
data information in frequency domain X is separated
into V non-overlapping sub-blocks and each sub-
block vectors has the same size N. Hence, we know
that for every sub-block, it contains N/V nonzero
elements and set the rest part to zero. Assume that
these sub-blocks have the same size and no gap
between each other, the sub-block vector is given by
(1)
where is a
wei
ghting factor been used for phase rotation.
},...,2,1]){2,0[( Vveb
v
j
v
v
 

The si
gnal in time domain is obtained by
applying IFFT operation on , that is
v
X
(2
)
Select one suitable factor combination
which makes the result achieve
opt
imum. The combination can be given by
],...,,[
21 v
bbbb 
(3
)
where argmin (·) is the judgment condition tat
output the minimum value of function. In this way
we can find the best b so as to optimize the PAPR
performance. The additional cost we have to pay is
the extra V-1 times IFFTs operation.
In conventional PTS approach, it requires the
PAPR value to be calculated at each step of the
optimization algorithm, which will introduce
tremendous trials to achieve the optimum value.
Furthermore, in order to enable the receiver to
identify different phases, phase factor b is required
to send to the receiver as sideband information
(usually the first sub-block b1, is set to 1). So the
redundancy bits account for , in which
V rep
resents the number of sub-block, W indicates
possible variations of the phase. This causes a huge
burden for OFDM system, so studying on how to
reduce the computational complexity of PTS has
drawn more attentions, nowadays.
WV
2
log)1( 
Th
e optimization is achieved by searching
thoroughly for the best phase factor. Theoretically,
],...,,[
21 v
bbbb

is a set of discrete values, and
numerous computation will be required for the
system when this phase collection is very large. For
example, if
v

contains W possible values,
theoretically, b will have different
co
mbinations, therefore, a total of IFFTs
w
ill be introduced.
v
W
V *
v
W



v
v
b
ˆ
By increasing
the V, W, the computational cost
of PTS algorithm will increase exponentially. For
instance, define phase factor contains only four
pos
sible values, that means , then for
each OFDM s
ymbol, 2*(
V-1) bits are transmitted as
side information. Therefore, in practical
applications, computation burden can be reduced by
limiting the value range of phase factor
v
b
b
v
 ],1[ j
],...,,[
21 v
bbbb

to a proper level. At the same time,
it can also be changed by different sub-block
partition schemes.
3 ORDINAL PTS TECHNIQUE
Cimini and Sollenberger’s (L. J. Cimini, 2000)
ordinal technique is developed as a sub-optimal
technique for the PTS algorithm. In their original
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xbXIFFTx
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)()
ˆ
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ˆ
(
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)2
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
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vvvbv
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v
V
v
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(maxminarg],...,,[
1,...,,(1
1


Nbb
bbbb
A Novel PTS Scheme for PAPR Reduction in OFDM Systems
171

paper, they only use binary weighting factors. That
is
b
v
= 1 or b
v
= −1. These can be expanded to more
phase factors. The algorithm is as follows. After
dividing the data block into V
disjoint sub-blocks,
one assumes that
b
v
= 1, (v = 1, 2, … ,V) for all of
sub-blocks and calculates PAPR of the OFDM
signal. Then one changes the sign of the first sub-
block phase factor from 1 to -1 (
b
1
=
−1), and
calculates the PAPR of the signal again. If the PAPR
of the previously calculated signal is larger than that
of the current signal, keep
b
1
=
−1. Otherwise,
revert to the previous phase factor,
b
1
= 1. Suppose
one chooses
b
1
=
−1. Then the first phase factor is
decided, and thus kept fixed for the remaining part
of the algorithm. Next, we follow the same
procedure for the second sub-block. Since one
assumed all of the phase factors were 1, in the
second sub-block, one also changes
b
2
= 1 to
b
2
=
−1, and calculates the PAPR of the OFDM signal. If
the PAPR of the previously calculated signal is
larger than that of the current signal, keep
b
2
=
−1.
Otherwise, revert to the previous phase factor,
b
2
=
1. This means the procedure with the second sub-
block is the same as that with the first sub-block.
One continues performing this procedure iteratively
until one reaches the end of sub-blocks (V
th sub-
block and phase factor
b
v
).
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
 1
 1...11...
21

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









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min
SPmeanSPPAPR
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4 MODIFIED PTS TECHNIQUE
Fi
gure 2: Block scheme of proposed PTS algorithm.
In this section, we present a modified PTS technique
wh
ich is similar to Cimini and Sollenberger’s
technique. We made simulation with 4 and 8 phase
factors to reduce the PAPR of the OFDM signal:
And
The basic idea of the proposed algorithm is first
to find and use this combination of binary weighting
factors, which gives the lowest PAPR. Secondly we
can repeat the process using changed matrix in first
step. The result phase factor will be
m
ultiplication from all found binary weighting
factors. We can reduce all possible combinations,
using only this binary weighting factors which
begun with 1. The process is repeated
P times,
where
P is an adjustable parameter.
],...,,[
21 v
bbbb 
There i
s and another feature – when finding the
lowest PAPR, we first chose this sub-block which
gives minimum PAPR and then we try to find next
sub-block, which will reduces mostly PAPR. If there
is no one /no further improvement is possible/, we
may try next binary combinations. Finally we
choose this combination of binary weighting factors,
which gives lowest PAPR.
]11[4 jjbW
v



2/2/12/2/112/2/12/2/118 jjjjjjb
The basic st
ructure of the modified PTS
technique is illustrated in Fig 2. For the clarity we
choose
P=2 and W=4. In this case we will have only
three /k=3/ binary combinations: (1, -1), (1, j), (1,-j)
we are interested in.
After dividing the data block into V
disjoint sub-
blocks, let one choose first combination
k=1 and
X
k,v
=1, (v=1, 2, … ,V) for all sub-blocks and
calculates PAPR of the OFDM signal. Then one
changes the first sub-block /
v=1/ phase factor from 1
to
W
k
= -1 /X
k,v
= -1/, and calculates the PAPR of
W
v

First International Conference on Telecommunications and Remote Sensing
172

the signal again. If PAPR of the current signal is
lower than previously calculated signal, remember
index /
ind=v/ and PAPR minimum. Restore current
phase factor to 1 /X
k,v
= 1/. Repeat this procedure
until the end of the sub-blocks. Then if there is a
PAPR improvement, change sub-block with the
remembered index to
W
k
/X
k,ind
= -1/. One
continues performing this algorithm iteratively until
there is a PAPR improvement for those sub-blocks,
which has phase factor set to 1.
If there is no further improvement, we can try
next binary combination
k=2 /W
k
=j/ and so on, until
the end of all possible combinations.
Finally, we choose these binary weighting
factors X
k,v
, (v=1, 2, … ,V) which gives the lowest
PAPR.
At last, if we multiply the input matrix with the
chosen weighting factors, we can repeat the entire
process /
P=2/. The result phase factor
will be multiplication from all
fo
und binary weighting factors X
k,v
, (v=1, 2, … ,V).
],...,,[
21 v
bbbb 
5 SIMULATION RESULTS
3 4 5 6 7 8 9 10 11 12 13
10
-3
10
-2
10
-1
10
0
PAPR0 (dB)
P(PAPR>PAPR0)
OFDM 64Sc 4QAM
PTS 4QAM V8 W4 org
PTS 4QAM V8 W4 new
PTS 4QAM V16 W4 org
PTS 4QAM V16 W4 new
Figure 3: Comparison between ordinal and a novel
PTS technique of PAPR reduction performances
with different values of V.
From Fig. 3, it can be seen that a novel PTS
algorithm undeniably improve the performance of
OFDM system, moreover, with the increasing of
V,
the improvement of PAPR reduction performance
becomes better and better. Assume that we fix the
probability of PAPR at 0.1% and compare the CCDF
curve with different values of
V. Form the figure, we
notice that the CCDF curve has nearly 1.5dB
improvement when
V=8, compared to the ordinal
PTS algorithm. When
V=16, the 0.1% PAPR is
about 6dB, so an optimization of 1dB is achieved. If
we compare PAPR reduction to the conventional
OFDM system, we can observe that an improvement
of nearly 5dB is reached.
However, the downward trend of CCDF curve is
tended to be slow when we keep on increasing
V,
which means too large sub-block numbers
V will
result in small improvement of PAPR reduction
performance, but anyway we have to increase sub-
block numbers
V, if we have a many of sub-curriers.
Therefore, practically, we prefer to choose a
suitable value of
V.
The simulation result in Fig. 4 shows the varying
PAPR reduction performance with different
W,
when using ordinal and modified PTS reduction
scheme. Simulation specific parameters are: the
number of sub-carriers N=64, 4-QAM constellation
modulation, the number of sub-blocks
V=8. From
the figure we notice that the CCDF curve has al least
1/3dB improvement when
W=8, compared to W=4.
We can conclude that the larger
W value takes, the
better PAPR performance will be obtained when the
number of sub-block
V is fixed, but pay for the
enormous computation time. Therefore, practically,
we prefer to fix
W=4.
3 4 5 6 7 8 9 10 11 12 13
10
-3
10
-2
10
-1
10
0
PAPR0 (dB)
P(PAPR>PAPR0)
OFDM 64Sc 4QAM
PTS 4QAM V8 W4 org
PTS 4QAM V8 W4 new
PTS 4QAM V8 W8 org
PTS 4QAM V8 W8 new
Figure 4: Comparison between ordinal and modified
PTS technique of PAPR reduction performances
with different values of
W.
On the next scheme, shown on Fig. 5, we
compare PAPR reduction performances with
different number of sub-carriers, when
W is fixed
/four phase rotations/ and modulation is 4-QAM. We
observe that if the number of sub-curries is increased
A Novel PTS Scheme for PAPR Reduction in OFDM Systems
173

the PAPR reduction performance has been slowed
down.
3 4 5 6 7 8 9 10 11 12 13
10
-3
10
-2
10
-1
10
0
PAPR0 (dB)
P(PAPR>PAPR0)
OFDM 128Sc 4QAM
PTS Sc32 V8 W4
PTS Sc32 V16 W4
PTS Sc128 V8 W4
PTS Sc128 V16 W4
Fi
gure 5: Comparison of PAPR reduction
performances with different values of
V and number
of sub-curriers.
The simulation results in Fig. 6 compares PAPR
reduction performances with different modulation
schemes /4-QAM and 16-QAM/ and fixed values of
V, W and number of sub-curriers. We may notice
that the number of constellation points almost has no
effect of PAPR characteristics.
3 4 5 6 7 8 9 10 11 12 13
10
-3
10
-2
10
-1
10
0
PAPR0 (dB)
P(PAPR>PAPR0)
OFDM 64Sc 4QAM
PTS 4QAM V8 W4
PTS 4QAM V16 W4
PTS 16QAM V8 W4
PTS 16QAM V16 W4
Figure 6: Comparison of PAPR reduction
performances with different values of V and variable
QAM size.
Finally, on the Fig. 7 we made comparison
between different number of sub-blocks and an
adjustable parameter -
P. We can see that the trend
of CCDF curve is tended quickly to be slow-down
when we keep on increasing
P. Therefore,
practically it is suitable to choose
P=2 and to
determinate the number of sub-blocks on
dependency of sub-curriers, as we discuss above -
see Fig. 3.
3 4 5 6 7 8 9 10 11 12 13
10
-3
10
-2
10
-1
10
0
PAPR0 (dB)
P(PAPR>PAPR0)
OFDM 64Sc 4QAM
PTS V8 W4 P1
PTS V8 W4 P2
PTS V8 W4 P4
PTS V16 W4 P1
PTS V16 W4 P2
PTS V16 W4 P4
Figure 7: Comparison of PAPR reduction
performances with different values of
P and number
of sub-blocks.
6 CONCLUSION
One of the major problems associated with OFDM is
its high PAPR. In this chapter, we proposed a novel
PTS algorithm to reduce efficiently the PAPR of
OFDM signal. There is an adjustable parameter,
which enables us to be able to obtain the best
performance.
Simulation results show that the proposed novel
algorithm can yield good PAPR reduction with low
computational complexity.
REFERENCES
Ib. Abdullah, Z. Mahamud, Sh. Hossain, “Reduction of
PAPR in OFDM using SLM for different route
number”, IJRRCS, June 2011
S. H. Muller, J. B. Huber, “OFDM with reduced peak-to-
average power ratio by optimum combination of
partial transmit sequence,” IEEE Electronic Letters,
Vol. 33, No. 5, Feb. 1997
L. J. Cimini, Jr. and N.R. Sollenberger, “Peak-to-average
power ratio reduction of an OFDM signal using partial
transmit sequences,” IEEE Communication Letters,
vol. 4, Mart 2000
Y. Cho, J. Kim, W. Yang, Ch. Kang, “MIMO-OFDM
Wireless Communications With MATLAB”, John
Wiley & Sons, Singapore, 2010
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174