A low complexity partial transmit sequence scheme for better papr reduction in ofdm systems

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 02 Issue: 10 | Oct-2013, Available @ http://www.ijret.org 127
A LOW COMPLEXITY PARTIAL TRANSMIT SEQUENCE SCHEME FOR
BETTER PAPR REDUCTION IN OFDM SYSTEMS
Amrutha.V.Nair1
, T.Sudha2
1
M tech Student, 2
Professor, Department of Electronics and Communication Engineering, N.S.S. College of Engineering,
Palakkad, Kerala, India,
amrutha.vnair@gmail.com, sudha.thiyyakat@gmail.com
Abstract
The main drawback of OFDM system is the high Peak to Average Power Ratio (PAPR) of the transmitted signals. Partial transmit
sequence scheme is a promising algorithm to reduce the peak-to-average power ratio (PAPR) in orthogonal frequency division
multiplexing (OFDM). The Partial Transmit Sequence (PTS) consist of several inverse fast Fourier transform (IFFT) operations and
complicated calculations to obtain optimum phase sequence which results in increasing the computational complexity of PTS. A phase
sequence applied to the PTS Scheme reduces its complexity but at the expense of slight degradation in PAPR reduction. In this paper,
for further reduction of PAPR the peak clipping of the OFDM signal is introduced along with the PTS with new phase sequence
scheme. Since clipping is one of the simplest techniques of PAPR reduction, it does not increase the complexity of the system much
and a better PAPR reduction is obtained with the combined effect of clipping and PTS with New Phase Sequence. But the clipping
technique introduce some distortion in the signal, however peak clipping of signal below a particular threshold can maintain the BER
in the tolerable range. The clipping threshold selected will be different for different OFDM systems.
Index Terms: OFDM, Peak to Average Power Ratio (PAPR), Partial Transmit Sequence (PTS), Clipping.
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1. INTRODUCTION
Orthogonal Frequency Division Multiplexing (OFDM) is one
of the prominent multicarrier modulation technique used for
high speed data transmission in communication system.
Immunity to Interferences and fading makes it a more
promising method for next generation communication
systems. But the major problem one faces, while
implementing an OFDM system, is the high peak to average
power ratio (PAPR) of the system. OFDM consist of large
number of independent sub carriers, as a result of which the
amplitude of such a signal can have high peak values. To
transmit signals with such high PAPR, power amplifiers with
very high power scope is required. These kinds of amplifiers
are very expensive and have low efficiency cost. Hence PAPR
reduction is necessary for an efficient OFDM system [1], [2],
[3].
Previous works in this field results in many PAPR reduction
schemes to overcome this problem [1],[4].The various PAPR
reduction techniques are Peak Windowing, Scaling, Clipping
and Filtering, Block Coding, Block Coding with error
correction, Selective Mapping (SLM), Interleaving, Tone
Reservation, Tone injection, PTS etc. [1].
Peak windowing, scaling and clipping are simple methods of
PAPR reduction but at the cost of slight interference. These
methods introduce distortion in the OFDM signal. To reduce
the interference, the clipped signal undergoes filtering. Block
coding technique reduces PAPR without any distortion of
OFDM signal and Block coding with error correction
technique provide error correction capability in addition to
PAPR reduction, but these methods are suitable for short code
words [1],[4]. The SLM scheme performs well with any
number of sub carriers and the major drawback with this
scheme is that the overheads of the side information should be
transmitted to the receiver but the interleaving is a simple
method of PAPR reduction which does not induce any signal
distortion, however this method does not give any assurance
on the result [3],[5],[6]. Tone reservation is a less complex
method but it can result in data rate reduction whereas Tone
injection method achieves PAPR reduction of OFDM signals
with no data rate loss [7]. Requirement of side information for
decoding signal at the receiver side and causes complex extra
IFFT operation are the drawbacks of this method [1],[4].
The concentration of this paper is the Partial transmit
Sequence (PTS) scheme, which is one of the most efficient
methods for PAPR reduction and is much better than SLM and
other techniques [7]. However the computational complexity
of this method is very high and also phase sequence applied to
the PTS scheme reduces its complexity but the PAPR
reduction degrades slightly [2],[3]. This paper introduces a
combination of PTS scheme with new phase sequence and the
clipping technique. As the clipping technique is a simple
method of PAPR reduction, the introduction of this technique

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to the system of PTS with new phase sequence does not
increase the complexity. But the application of peak clipping
technique introduces some distortion in the signal. However
the slight clipping of peak of the signal at a particular value
gives better PAPR reduction at the cost of small distortion of
signal.
Simulations are performed with QPSK modulation with
OFDM signal. The tool used for the simulation is Matlab
R2012a. PAPR is described by its complementary cumulative
distribution function (CCDF). OFDM system with QPSK
modulation is implemented to plot the Bit Error Rate Vs SNR
of the original OFDM signal and the clipped OFDM signal.
Also the PAPR of the OFDM system before and after the
application of the PAPR reduction techniques are analyzed.
This paper is organized as follows. Section II includes the
OFDM system and signals generation, Section III presents the
PAPR, its causes and effects. Section IV presents the PTS,
PTS with new phase sequence and low complexity PTS with
clipping schemes. Section V and VI discuss the simulation
results and conclusions respectively.
2. OFDM
OFDM is an efficient method of high data rate transmission in
communication systems. OFDM system consists of large
number of independent sub carriers. These closely spaced
orthogonal sub carriers are used to carry data.
Fig -1: Block Diagram of an OFDM system
At the transmitter section the data is divided into several
parallel streams of channels, one for each sub carriers. These
sub carriers are modulated by phase-shift keying (PSK) or
quadrature amplitude modulation (QAM) mapping techniques.
Transfer of signal over a channel is only possible in its time-
domain. For which IFFT is performed on this modulated
signal, to convert the OFDM signal in frequency domain to
time domain. Then cyclic prefix is inserted. The cyclic prefix
is a periodic extension of the last part of an OFDM symbol
that is added to the front of the symbol in the transmitter, and
is removed at the receiver before demodulation. The different
sub carriers are added up to form the OFDM signal.
The signal is amplified using a power amplifier to overcome
the fading effects and passed through the AWGN channel
where the signal undergoes distortion from white Gaussian
noise and multipath effects. At the receiver section the vice
versa of the operations at transmitter side is performed.
An OFDM symbol is made of sub-carriers modulated by
constellations mapping. For an OFDM system with N sub-
carriers, the high-speed binary serial input stream is denoted
as{ai}. After serial to parallel (S/P) conversion and
constellation mapping, a new parallel signal sequence
{d0,d1,d2,….di,…dN-1} is obtained, di is a discrete complex-
valued signal. When QPSK mapping is used, di {±1, ±i} and
when BPSK is used di {±1}. Each element of parallel signal
sequence is supplied to N orthogonal sub-carriers for
modulation, respectively. Finally, modulated signals are added
together to form an OFDM symbol. Use of discrete Fourier
transform simplifies the OFDM system structure. The
complex envelope of the transmitted OFDM signals can be
written as:
𝑥 𝑡 =
1
𝑁
𝑋(𝑘)𝑒 𝑗2𝜋𝑘 ∆𝑓𝑡𝑁−1
𝑘=0 , 0 ≤ 𝑡 ≤ 𝑇 (1)
where X(k) is the data symbol of k-th sub carrier, N is the
number of sub carriers, ∆f is the frequency difference between
sub carriers and T is the OFDM symbol duration [8].
3. PEAK TO AVERAGE POWER RATIO
The PAPR of OFDM signals x(t) is defined as the ratio
between the maximum instantaneous power and its average
power [4]. The PAPR (in dB) of the transmitted OFDM signal
can be defined as:
𝑃𝐴𝑃𝑅 =
max 0≤𝑡≤𝑇 𝑥(𝑡) 2
𝐸 𝑥(𝑡) 2 (2)
Where E[.] is the expected value operator. In an OFDM
system the different sub carriers are added together to form the
OFDM symbol. That is the system output is the superposition
of multiple sub-carriers. In this case some instantaneous power
output might increase greatly and become far higher than the
mean power of system. This causes high PAPR in an OFDM
system. High PAPR signals would require a large range of
dynamic linearity from the analog circuits which usually
results in expensive devices and high power consumption with
lower efficiency. If no measure is taken to reduce the high
PAPR, OFDM system could face serious restriction for
practical applications.
PAPR is a random variable because it is a function of the input
data, and the input data are random variable. Therefore PAPR
can be calculated by using level crossing rate theorem that
calculates the average number of times that the envelope of a
signal crosses a given level. Knowing the amplitude
distribution of the OFDM output signals, it is easy to compute
the probability that the instantaneous amplitude will be above
a given threshold and the same goes for power. This is

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performed by calculating the complementary cumulative
distribution function (CCDF) for different PAPR values as
follows
𝐶𝐶𝐷𝐹 = Pr⁡(𝑃𝐴𝑃𝑅 > 𝑃𝐴𝑃𝑅0) (3)
The Cumulative Distribution Function (CDF) is one of the
most regularly used parameters, which is used to measure the
efficiency of any PAPR technique. The CCDF helps us to
measure the probability that the PAPR of a certain data block
exceeds the given threshold.
4. LOW COMPLEXITY PTS WITH CLIPPING
The PTS, PTS with new phase sequence schemes and the
computational complexity equations are based on paper [2].
4.1 Partial Transmit Sequence Scheme (PTS)
The basic idea of partial transmit sequence scheme 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 [3],[9]. For implementing PTS
scheme possible phase factors or weights are to be generated
depending on the mapping used. Every subsequence is
multiplied with every weights generated and PAPR is
calculated each time. The phase factors for which
subsequence-weight product signals with minimum PAPR is
obtained is chosen as the optimum values for weight. Thus the
signals with low PAPR is obtained.
Fig -2: Block Diagram of PTS Scheme
Let X is the random input signal in frequency domain with a
length of N. X is divided into V disjoint sub blocks.
𝑋𝑣 = 𝑋𝑣,0, 𝑋𝑣,1, … . . , 𝑋𝑣,𝑁−1
𝑇
(4)
Where . The partitioning of input signal in
to sub blocks is such that the summation of these sub blocks
gives the input signal X, ie.
𝑋𝑣 = 𝑋𝑉
𝑣=1 (5)
Then these sub blocks are combined in time domain. The sub
block partition is based on interleaving in which the
computational complexity is less compared to adjacent and
Pseudo-random, however it has the worst PAPR performance
among them. Then apply the phase rotation factor ‘bv’ to the
IFFT of each of the sub blocks.
𝑏 𝑣 = 𝑒 𝑗 𝜃 𝑣 (6)
Where v=1,2,…, V. The time domain signal after combining is
given by:
𝑥′
𝑏 = 𝑏 𝑣 𝑥 𝑣
𝑉
𝑣=1 (7)
Where 𝑥′
𝑏 = [𝑥′
0 𝑏 , 𝑥′
1 𝑏 , … . . 𝑥′
𝑁𝐿−1 𝑏 ] 𝑇
and L is
the over sampling factor. The optimum signal 𝑥′
𝑏 with the
lowest PAPR is to be found out.
Both b and x can be shown in matrix form as follows:
𝑏 =
𝑏1, 𝑏1, … . . , 𝑏1
⋮ ⋮ ⋮
𝑏 𝑉, 𝑏 𝑉, … . . 𝑏 𝑉 𝑉𝑋 𝑁
(8)
𝑥 =
𝑥1,0, 𝑥1,1, … . . , 𝑥1,𝑁𝐿−1
⋮ ⋮ ⋮
𝑥 𝑉,0, 𝑥 𝑉,1, … . . 𝑥 𝑉,𝑁𝐿−1 𝑉𝑋 𝑁𝐿
(9)
It should be noted that all the elements of each row of matrix b
are of the same values in this method. In order to have exact
PAPR calculation, at least 4 times over sampling is necessary.
As the over sampling of x, add zeros to the vector, hence the
number of phase sequence to multiply to matrix x will remain
the same.
The PTS consist of several inverse fast Fourier transform
(IFFT) operations and complicated calculations to obtain
optimum phase sequence which results in increasing the
computational complexity of PTS.
4.2 PTS with New Phase Sequence
Fig -3: Block Diagram of PTS with new phase sequence

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In this scheme, new phase sequence is generated from the
possible phase factors. The possible phase factors or weights
depend on the mapping used as in PTS. For example in the
case of number of allowed phase factors W=4(QPSK), then
phase sequence can be chosen from {1,j,-1,-j} and let the
phase sequence consist of N random values. The phase
sequences can be random, adjacent or interleaved [10]. The
random phase sequence provides better PAPR reduction
compared to the adjacent and interleaved phase sequences
[1],[4]. The new phase sequences form the phase sequence
matrix. Thus the new phase sequence matrix has different
values in each row.
The phase sequence matrix can be as follows
𝑏 =
𝑏1,1, 𝑏1,2, … . . , 𝑏1,𝑁
⋮ ⋮ ⋮
𝑏 𝑉,1, 𝑏 𝑉,2, … . . 𝑏,𝑁
(𝑉𝑋 𝑁)
(10)
Where N is the number of sub carriers and V is the number of
sub blocks. The matrix ‘x’ has ‘V x NL’ elements and each
row consists of NL elements.
𝑥 =
𝑥1,0, 𝑥1,1, … . . , 𝑥1,𝑁𝐿−1
⋮ ⋮ ⋮
𝑥 𝑉,0, 𝑥 𝑉,1, … . . 𝑥 𝑉,𝑁𝐿−1 (𝑉𝑋 𝑁𝐿)
(11)
The new phase sequences are multiplied with each of the sub
sequences correspondingly to obtain the time domain signal.
The phase factors from the phase sequences which produce the
signals with smallest PAPR is chosen as the optimum values.
Instead of an exhaustive search for phase factors here phase
sequence matrix is applied to PTS, hence the complexity of
this method is lower than that PTS but as the optimum weight
selection is restricted from the generated phase sequence
matrix, there is slight degradation in performance [2].
For comparison with the PTS, the phase sequence matrix of
this scheme can be extended as
𝑏 =
𝑏1,1 … . . 𝑏1,𝑁
⋮ ⋮ ⋮
𝑏 𝑃,1 … . . 𝑏 𝑃,𝑁
(𝑃 𝑋 𝑁)
(12)
Where P>V and is the number of iterations that should be set
in accordance with the number of iterations of the PTS.
The value of P can be calculated as follows:
𝑃 = 𝐷𝑊 𝑉−1
(13)
where D=1,2,…DN. D is the coefficient that can be specified
based on the PAPR reduction and complexity and DN is the
amount that is specified by the user. The value of P depends
on the number of sub blocks V if the number of allowed phase
factor is assumed to be constant. There is a tradeoff for
choosing the value of D, the higher D leads to higher PAPR
reduction but at the expense of higher complexity; while lower
D gives smaller PAPR reduction but with less complexity.
4.3 Computational Complexity
The total complexity of the PTS is given by,
𝐶 𝑃𝑇𝑆 =
3𝑉𝑁
2 log 𝑁
+ 2𝑉𝐼𝑁 (14)
Where I=𝑊 𝑉−1
and I is the number of iterations required for
searching the optimum phase factor. The total complexity of
the PTS with New Phase Sequence is given by,
𝐶 𝑁𝑒𝑤𝑃𝑇𝑆 =
3𝑉𝑁
4𝑉𝑁 log 𝑁
+ 𝑃𝑉𝑁 (15)
where P is the number of iterations and V is the number of sub
blocks. It can be observed that the complexity equations
consist of two parts; the first part is actually the complexity of
the IFFT itself and the second part is the complexity of the
searching algorithm [2],[11].
4.4 Low Complexity PTS with Clipping
In this method, the OFDM symbols are divided in to number
of sub blocks and the signals corresponding to IFFT of each
sub block is clipped. This method provide better PAPR
reduction than the PTS scheme with new phase sequence but
the clipping introduces slight distortion in the signal.
As the PTS with new phase sequence offers less complexity
than conventional PTS, it is considered as the low complexity
PTS throughout this paper.
Fig -4: Block Diagram of Low complexity PTS with clipping
Here, the OFDM sequence is divided in to several (V) sub
blocks as in PTS and new phase sequence applied to PTS
schemes. In this method separate clipping is done on each

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block. The peak clipping can be performed only on time
domain signal. Hence clipping is introduced in the new phase
sequence applied to PTS scheme after the IFFT operation in
each block.
The advantages of this scheme are:
 Low complexity: As clipping is a PAPR reduction
technique which is simple in implementation, the
introduction of clipping to a low complexity PTS
scheme does not increase the complexity of the
system.
 Better PAPR reduction: The combined effect of
clipping and PTS with new phase sequence scheme
reduces PAPR considerably.
 Enhancement of power efficiency and therefore less
power consumption and more battery life.
But the clipping technique introduces distortion in the signal
[12],[13]. However peak clipping of signal below a particular
threshold can maintain the BER in the tolerable range.
Therefore the system can be used only where the OFDM
system can tolerate slight reduction in performance, ie less
power consumption and more battery life are the major
concern.
5. SIMULATION RESULTS & OBSERVATIONS
The simulation is performed with 64 sub band OFDM
symbols. PAPR reduction of OFDM with QPSK and BPSK
mapping and the computational complexity of PTS scheme
with different number of sub blocks in [2] are examined. Over
sampling factor selected for the various PAPR reduction
simulations is, L=4.
As the clipping technique causes distortion of the signal, the
clipping technique has to be implemented such that it does not
degrade the performance of the OFDM system below the
tolerable range. The threshold value set for peak clipping
depends on the OFDM system and the input signal. The
clipping at an amplitude of 0.2 strictly depends on the OFDM
system and input signal used in this work. The test is achieved
on 10000 OFDM symbols and the following results are
obtained.
Table -1: Computational Complexity of PTS Scheme for
Different Number of Sub Blocks
Number of
Sub Blocks
Number of
Sub carriers
Complexity
2 256 1.0702e+03
4 256 3.2860e+04
8 256 1.6777e+07
From Table -1it is clear that as the number of sub blocks
increases the complexity increases as in [2].
Fig -5: PAPR reduction of PTS Scheme with BPSK and
QPSK modulation
Fig. 5 shows the PAPR of original OFDM system, the PAPR
of OFDM system which has undergone the Partial Transmit
Sequence Scheme with QPSK and BPSK modulation. The
PAPR of original OFDM system lies near to 11dB whereas the
PAPR of PTS system with QPSK modulation lies near to 6 dB
and the PAPR of PTS system with BPSK modulation lies near
to 7 dB. From Fig. 5 it is clear that PTS method provides a
better PAPR reduction performance with QPSK mapping than
with BPSK mapping. Based on the simulation results obtained
in Fig. 5 and TABLE I, the QPSK mapping and number of sub
blocks, V=4 are used in the rest of the simulations.
Fig -6: BER Vs SNR of OFDM system with and without
clipping of peak of OFDM signal.
Fig. 6 shows the BER Vs SNR plot of OFDM system with and
without clipping of the OFDM signal peak. From the figure it

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can be observed that the BER is slightly increased for the
OFDM system when the peak of the OFDM signal is clipped,
ie the clipping at amplitude of 0.2 introduced slight distortion
in the OFDM signal. However as this value of clipping
threshold introduces only slight performance degradation this
value can be used for clipping of in the input signal in the
OFDM system for PAPR reduction.
Fig -7: PAPR Reduction of PTS scheme, New phase sequence
applied to PTS Scheme and PTS Scheme with both New
Phase Sequence and clipping
Fig.7 shows the PAPR of original OFDM system, the PAPR
of OFDM system which has undergone the Partial Transmit
Sequence Scheme, PTS with New Phase sequence scheme and
PTS Scheme with both New Phase Sequence and clipping. It
can be observed that the PAPR reduction of the PTS Scheme
with both New Phase Sequence and clipping scheme offers
better PAPR reduction than the Partial Transmit Sequence
Scheme and the PTS with New Phase sequence scheme at the
expense of slight reduction in system performance.
CONCLUSIONS AND FUTURE WORKS
The major difficulty one faces in the practical implementation
of the Orthogonal Frequency Division Multiplexing is its high
PAPR. To transmit signals with large PAPR, expensive wide
range power amplifiers are required. One of the effective
methods of PAPR reduction is Partial Transmit Sequence
scheme. The complexity of this scheme can be reduced by the
application of a new phase sequence but the PAPR reduction
is slightly reduced. A scheme comprising of the PTS with both
the new phase sequence and the clipping has been introduced
in this paper. As clipping of peak of signal is simple in
implementation, it does not increase the complexity of the
system and a better PAPR reduction can be achieved. The
BER Vs SNR of the OFDM system with and without clipping
of peak signal is examined. By applying the scheme the PAPR
is reduced further. There exist a trade off for choosing the
threshold for clipping, greater the clipping greater will be the
distortion but better PAPR reduction , while lower clipping
gives low distortion of the signal and lower the PAPR
reduction achieved. Since clipping causes degradation in the
system performance, this scheme can be used where less
power consumption and more battery life are our primary
concern.
The filtering of a clipped signal reduces the distortion
introduced due to clipping. Hence by introducing the clipping
in the proposed scheme is expected to reduce the signal
distortion due to clipping and provide better PAPR reduction.
This can be a scope of future work as it enhances the system
performance.
REFERENCES
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