International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 8- August 2013
Performance Analysis of PAPR Reduction
Techniques Based on PTS and GA-SLM
#1
*2
Prof. Mukesh Tiwari , Prof. Jaikaran Singh , Mr. Lokendra Vishwkarma
#3
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Assoc. Professor, ECE & RGPV
Shri Satya Sai Institute of Science & Technology
Sehore (M.P) India
Abstract— AnSLM (Selective Mapping) is an effective algorithm
to reduce PAPR (Peak to Average Power Ratio) in
OFDM(orthogonal frequency division multiplexing) signal
without distortion. This paper describe, a comparative analysis
of genetically optimized Selective mapping (GA-SLM) and
Partial Transmit Sequence (PTS) techniques.The proposed
algorithm has lower complexity compares with GA-SLM.
Moreover, it has advantages in enhancing the signal transmission
rate and decreasing the PAPR of OFDM signals.
complexity for the SLM scheme. The authors in [7]
reduce the computational complexity for the PTS
scheme. The researches [4]–[7] maintain the
original BER of OFDM systems but require a large
number of computational complexity and side
information.
PAPR of OFDM System
Keywords— SLM, PAPR, PTS, OFDM, Genetic Algorithm.
I. INTRODUCTION
Recently, a global convergence has occurred for the
use of Orthogonal Frequency Division Multiplexing
(OFDM) as an emerging technology for high data
rates. When applied in a wireless environment such
as radio broadcasting, it is usually referred to as
OFDM. In OFDM a large number of parallel
narrow-band subcarriers are used instead of a single
wide-band carrier to transport information, which
makes it robust against large delay spreads by
preserving orthogonality in the frequency domain.
Although coherent addition of multiple
subcarrier amplitudes and phases from the OFDM
system results high Peak-to-Average Power Ratio
(PAPR). The efficiency of system is reduced due to
large PAPR as it limits the range of linear operation
of power amplifiers in transmitters. It also increases
the complexity of analog-to-digital and digital-toanalog converters in wireless digital systems.
Several researches on PAPR reduction
have been published in the literature.In order to
reduce the PAPR of OFDM systems, the authors in
[1] shows a genetically optimized PTS technique to
reduce the PAPR of OFDM signals.Some other
methods [2]–[8] have been studied for a few years.
The researches[4]–[6] reduce the computational
ISSN: 2231-5381
In an OFDM system having N number of
subcarriers, the discrete time transmitted signal is
given by:
(1)
For
Where,
are input symbols modulated
byPSK orQAM, and
is an over-sampling factor
to simulatethe behaviour of continuous signals. The
PAPR of the transmitted signal in (1), defined as
the ratio of the maximum to the average power,
which is expressed as:
PAPR =
=10
dB
(2)
Where
denotes expectation operation.
Selective mapping (SLM)
In the SLM technique, the transmitter generates a
set of sufficiently dissimilar candidate data blocks,
all representing the similar information as the
original data block, and selects the most favourable
for transmission. A block diagram of the SLM
technique is shown in Figure 2. Each data block is
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 8- August 2013
multiplied by U different phase sequences, each of
length N,
= [ , , , …..
]T u = 1,
2, · · · ,U, resulting in U modified data blocks.To
comprise the unmodified data block in the set of
modified data blocks, we set
as the all-one
vector of length N.
B(1)
Data
Source
X
Partitioning
into Blocks
and Serial
to Parallel
Conversion
X(1)
IFFT
B(2)
(2)
X
IFFT
B(U)
X(U)
Select
one
with
the
lowest
PAPR
modified method of SLM. PTS method works
better than SLM method. The main advantage of
this scheme is that there is no need to send any side
information to the receiver of the system, when
differential modulation is applied in all sub blocks.
Transmitting only part of data of varying subcarrier which covers all the information to be sent
in the signal as a whole is called Partial Transmit
Sequence Technique.
Output Data
IFFT
Genetic Algorithm
Figure1: Block Diagram for OFDM transmitter with SLM Technique
A genetic algorithm is a probabilistic search
Let us indicate the modified data block for the u technique that computationally simulates the
phase sequence as:
process of biological evolution. It mimics evolution
in nature by frequently altering a population of
D (u)= [
,
,
, …..
]T
candidate solutions until an optimal solution is
found.
u = 1, 2, · · ·, U, after applying SLM to X, the multicarrier signal becomes
th
Decoded
Strings
Offspring
A
genetic
algorithm is
a
Genetic
Parents
Evaluation
probabilisti
Operations
c
search
technique
that
Selection
computatio
Score
Pairs
nally
simulates
the process
Figure 2: Genetic algorithm evolutionary cycle
of
biological
The GA evolutionaryevolution.
cycle starts with a randomly
selected initial population.
It mimicsThe changes to the
evolution
population occur through
the in
processes of selection
by using crossover and
based on fitness, andnature
alteration
frequently
mutation. The application
of selection and alteration
altering a
leads to a populationpopulation
with a higher proportion of
better solutions. Theofevolutionary cycle continues
candidateis found in the current
until an acceptable solution
solutions
generation of population,
or some control parameter
an
such as the number ofuntil
generations
is exceeded.
optimal
The steps in the typical
genetic
algorithm for
solution is
finding a solution to afound.
problem are listed below:
Po
(3)
Among the modified data blocks D(u), the one with
the lowest PAPR is Selective for transmission.
Information about the Selective phase sequence
needs to be transmitted to the receiver as side
information. Consequently, the reverse operation is
performed to recover the original data block at the
receiver.
Partial Transmit Sequence (PTS)
Partial Transmit Sequence (PTS) technique has
been proposed by Muller and Hubber in 1997 [9].
This proposed method is based on the phase
shifting of sub-blocks of data and multiplication of
data structure by arbitrary vectors. This method is
flexible and effective for OFDM system. The main
purpose behind this method is that the input data
frame is divided into non-overlapping sub blocks
and each sub block is phase shifted by a constant
factor to reduce PAPR.
PTS is probabilistic method for reducing the
PAPR problem. It can be said that PTS method is a
ISSN: 2231-5381
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pulation
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 8- August 2013
 Create an initial solution population of a
certain size randomly
 Evaluate each solution in the current
generation and assign it a fitness value.
 Select ―good‖ solutions based on fitness
value and discard the rest.
 If acceptable solution(s) found in the current
generation or maximum number of
generations is exceeded then stop.
 Alter the solution population using
crossover and mutation to create a new
generation of solutions.
 Go to step 2.
B = (x1, x2, x3,.......,xN)
Where the number of subcarriers is N, xn (1≤ n≤N),
which is either 0 or 1. The BPSK is adopted to
modulate the input signal sequences as:
B = (xn,1, xn,2, xn,3,......., xn,N)(1 ≤ n ≤ U)
Bn is composed of 1 and -1, GA-SLM selects one
sequence which has the best randomness as the
output. In this scheme the key point is judge the
extent in randomness of the sequence:
1.
II.PROPOSED ALGORITHM
GA-SLM
In order to obtain more effective reduction in
PAPR,the SLM scheme would select one sequence
after IFFT modules, thus it need N IFFT modules,
which makes system highly complicated.
According to [10], the more random the sequence is,
the smoother the frequency spectrum will become.
Thus in order to reduce the complexity of this
system, we propose an improved algorithm which is
called Selective Mapping with Genetic Algorithm.
The principle of GA-SLM can be expressed as
followed:
BPSK
B1
Input
Sequences
BPSK
B2
B
..........
BPSK
Sele
ct
the
best
sequ
ence
Bn
with
GA
Judging the nature of randomness of Bn
sequences. The closer the number of 1 and 1 is, the more random the sequence is,
supposing:
Where Sn> 0 represents the numbers of 1 that
is greater than -1, Sn< 0 stands for the
opposite scenario. The Sn approaches 0, the
randomness of the sequence increases.
2.
Judging the numbers of Bn sequence’s
oscillation which is adding the number of
sequence’s transitions first, and then compare
it with half of the sequence’s width. Suppose:
Tn =
Bn
Map
ping
S/p
IFFT
Output
Sequence
s
(1 ≤ n ≤ U)
Sn =
-
(1 ≤ n ≤ U)
Then when the Tn is smaller, the nature of
random of the sequence is better.
3. Removing the sequences that has a smaller
period, As the sequences with short period
usually have a high PAPR, we need to
exclude them, suppose:
BU
Figure3:Block diagram of GA-SLM principle
This scheme selects one sequence with the best
randomness before IFFTmodules, thus only one
IFFT module is necessary, saving the complexity of
the system.
The specific process of the GA-SLM scheme is
represented as followed. Suppose the input random
sequence B is:
ISSN: 2231-5381
Wn,1 =
Wn,2 =
(1 ≤ n ≤ U)
(1 ≤ n ≤ U)
PTS – SLM
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 8- August 2013
In the PTS technique, input data block X is
partitioned
in
M
disjoint
sub-blocks
such that
and the sub – blocks are combined to
minimize the PAPR in the time domain. The times
oversampled
time
domain
signal
of
,
, is obtained by taking the IDFT
of length on
concatenated with
zeros.
These are called the partial transmit sequences.
Complex phase factors
are
introduced to combine the PTSs. The set of phase
factors is denoted a vector
. The
time domain signal after combining is given by
(4)
III. SIMULATION AND RESULTS
Figure 6: PAPR v/s CCDF graph of original signal
Where
.
The objective is to find the set of phase factors that
minimizes the PAPR. Minimization of PAPR is
related to the minimization of:
Partitioni
ng into
Blocks
and
Serial to
Parallel
Conversi
on
Data
Source
X
Divis
ion
into
subbl
ocks
+
IDFT
IDFT
Optimization for b
Figure 7: PAPR v/s CCDF graph in selective mapping method
Figure 4: Block diagram of Partial Transmit Sequence method
B
IFFT
(1
Data
Source
X
Partitioning
into Blocks
and Serial to
Parallel
Conversion
)
B
X
(2)
(2
IFFT
)
B
(
X
(U)
SELE
CTIVE
MAPP
ING
(SLM)
PARTIAL
TRANSMIT
SEQUENCE
IFFT
U
)
Output Data
Figure 5: Block diagram of PTS-SLM scheme
Figure 8: PAPR v/s CCDF graph in RS-SLM
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 8- August 2013
Figure 9: PAPR v/s CCDF graph in GA-RS-SLM
Figure12: Optimization through Genetic Algorithm
IV. CONCLUSION
In this paper, the two PAPR reduction schemes,
GA-SLM and PTS are investigated and their
performance is compared. This algorithm is
implemented and tested in the OFDM transceiver
designed
using
MATLAB.Theperformance
comparison between GA-SLM and PTS is shown in
figures 9&11 which show that GA-SLM is better
than PTS in terms of PAPR reduction capability.
Here, by using SLM hardware cost increased but at
the same time PAPR reduced.
Future research will focus on investigating and
quantifying further the influence of PAPR as a
function of different modulation mapping schemes,
OFDM subcarrier levels, and phasing schemes.
Figure10: Comparison of different schemes (showing PAPR
v/s CCDF)
V=4
0
10
Orignal
PTS
-1
CCDF (Pr[PAPR>PAPR0])
10
REFERENCE
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-2
10
[2] S. H. Han and J. H. Lee, ―An overview of peak-to-average power ratio
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[3] T. Jiang and Y.Wu, ―An overview: Peak-to-average power ratio reduction
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4
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8
PAPR0 [dB]
9
10
11
Figure 11: PAPR v/s CCDF graph in Partial transmit sequence
scheme
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12
[4] C. P. Li, S. H. Wang, and C. L. Wang, ―Novel low-complexity SLM
schemes for PAPR reduction in OFDM systems,‖ IEEE Transaction on
Signal Processing, volume-58, Issue-5, pp. 2916–2921, May 2010.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 8- August 2013
[5] J. H. Wen, S. H. Lee, and C. C. Kung, ―SLM-based data position
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[8] X. B.Wang, T. T. Tjhung, and C. S. Ng, ―Reduction of peak-to-average
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[9] Muller, S. H., and Huber, J.B., ―OFDM Reduced Peak to Average Power
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