A PAPR Reduction Method Based on Harmony
Search Optimization for OFDM Signals
Renu Verma
Electronics & Telecommunication
Engineering
Chhatarpati Shivaji Institute of
Technology, Durg (C.G.) India
renu02v@gmail.com
Mr.Mangal Singh
Neelam Dewangan
Electronics & Telecommunication
Engineering
Chhatarpati Shivaji Institute of
Technology, Durg (C.G.) India
Mangalsingh.@csitdurg.in
Electronics & Telecommunication
Engineering
Chhatarpati Shivaji Institute of
Technology, Durg (C.G.) India
neelamdewangan@csitdurg.in
Abstract — As one of the popular scheme, partial transmit
sequence (PTS) is able to provide the reduce peak to average
power ratio (PAPR) of orthogonal frequency division
multiplexing (OFDM) signal successfully. However when
traditional partial transmit sequence perform their function it
have to search the optimum phase factor from all the possible
combinations to provide the reduce PAPR of OFDM signal. This
searching complexity increases, when the number of sub-blocks
and phase factor increase. In this paper we illustrate the metaheuristic (harmony search) optimization method along with PTS
to find optimal phase factor which gives the improve PAPR
performance & reduce searching complexity of phase factors.
Index Terms—Harmony Search (HS), Orthogonal Frequency
Division Multiplexing (OFDM), Partial Transmit Sequence
(PTS), Peak to Average Power Ratio (PAPR), Traditional PTS
(T-PTS).
I.
INTRODUCTION
Orthogonal frequency division multiplexing is broadly used
wireless communication system that requires a high bit rate &
high capacity transmission. Beside the advantages of an OFDM
system, one of the biggest challenging issues of OFDM is its
high peak power compare to its calculated average power. This
high PAPR of OFDM degraded the performance of bit error
rate Vs signal to noise ratio. In addition, the PAPR should be
reduced for removal of non-linear distortion effects and for
power efficiency of high power amplifier [1].
In the past, number of authors proposed various PAPR
reduction techniques for solving the most challenging issue of
OFDM signals which is high PAPR [2]. Among various
schemes partial transmit sequence technique is popular one. In
which first the input binary data is divided into sub-blocks by
using various sub-block partition mechanism. After taking its
IFFT each sub-blocks are multiplied by phase factors. At last
the summation of all signals gives the OFDM signal having
reduced PAPR [3].
However when traditional partial transmit sequence
perform their function, it have to search the optimum phase
factor from all the possible combinations to provide the reduce
PAPR of OFDM signal. This searching complexity increases,
when the number of sub-blocks and phase factor increase [4].
So to overcome this problem variant of PTS has been
developed. One of the variants is iterative flipping algorithm
based PTS. In this algorithm the computational complexity is
directly related to the number of sub-blocks of binary input
data [5]. The sub optimal PTS algorithms based on particle
swarm optimization, Cross entropy optimization, Genetic
Algorithm & Artificial Bee Colony algorithm is also proposed
in literature.
In this paper, a sub optimal phase optimization scheme
based on harmony search algorithm which can effectively
reduce the PAPR of OFDM signals is analyzed. The proposed
method can investigate the better combination of phase factor
with less searching complexity for PTS scheme. Simulation
results show that the Harmony Search-PTS phase optimization
scheme can achieve the superior PAPR reduction performance
and at the same time it requires far less searching complexity
of phase factor than the traditional PTS techniques [5].
The rest of this paper is organized as follows. In section II,
the OFDM signal is analyzed in terms of PAPR & CCDF. In
section III, Traditional PTS technique is discussed. Then in
section IV harmony search optimization PTS is described .The
performance of new PTS is evaluated by Simulation result in
section V, conclusion is also given in this section
II.
PEAK TO AVERAGE POWER RATIO OF OFDM
SIGNAL
An OFDM system is parallel transmission scheme in
which N orthogonal sub-carrier is modulated with a
modulation schemes, like Quadrature Amplitude Modulation
(QAM) or Phase Shift Keying (PSK) at a low symbol
rate as shown in Fig.1 .
The discrete time OFDM signal is given by
𝑥(𝑛) =
1
𝑁−1
𝑘
∑ 𝑋𝑛 𝑒 𝑗2𝜋𝐿𝑁𝑛 ,
√𝑁 𝑘=0
(1)
Where N is number of sub carrier & L is oversampling factor
[6].The high peak to average power ratio of OFDM is one of
the biggest challenge in front of users & is given by equation
is
𝑃𝐴𝑃𝑅 =
max |𝑥𝑛 |2
|]2
(2)
IFFT
S/P
Converter &
Modulation
Guard
Interval
Insertion
P/S
Converter
BER Calculation
AWGN
Channel
Output
P/S Converter
&
Demodulation
FFT
S/P
Converter
Guard
Interval
Removal
∑𝑉𝑣=1 𝑠 𝑣 𝑏 𝑣
(6)
Where s v is the partial transmit sequence (PTS). The selection
of phase factor is done vigilantly so that, the PAPR can be
minimized. Then the recognized signal with lowest PAPR can
be given as
(7)
LPF
Pr(PAPR> PAPR o) = 1- (1-e-PAPRo )N
(3)
The CCDF of original OFDM signal is shown in Fig.2. The
PAPR of original OFDM signal is 11.8 db with CCDF of 10 -2.
PAPR Vs CCDF of Original OFDM Signal
10
The PTS simulation outcome for different number of sub
blocks shows that, the PAPR is reduced when we increased
the number of sub blocks but at the same time searching
complexity is increased exponentially with sub blocks as
shown in Fig.3. On the other hand in the optimization
methods, which are used in PTS the excellent transmit signal
is stored until better one is found .For selecting the best
possible phase weighting factor for each input series we have
to go with verification of WV-1 possible combination.[10]
In PTS method, three sub block partition scheme is used
that are pseudo-random, adjacent & interleaved. Pseudo
random sub block partition scheme gives the best result
compared to other two methods. But in terms of hardware
complexity pseudo random scheme is very complex compared
to other two schemes [12, 13].
In literature we have different sort of optimization used to
optimize the phase factor in PTS scheme like Particle Swarm
optimization [9,10], Cross Entropy [20,21] Artificial Bee
Colony[22,23] etc. These sub optimal schemes present the
best collection of phase factor with very less computational
complexity& at the same time it gives the better PAPR
performance.
16-QAM CCDF of OFDMA signal with PTS
0
10
original
PTS N=1
N=2
N=4
N=8
N=16
-1
10
-1
10
0
<--------------------- CCDF --------------------->
x=IFFT{∑𝑉𝑣=1 𝑆 𝑣 𝑏𝑣 }=
(5)
𝑠̃ =∑𝑉𝑣=1 𝑠 𝑣 𝑏̃ v
Figure.1 Block Diagram of an OFDM System
Where PAPR is Peak-to-Average Power Ratio
xn – Oversampled OFDM signal
max 0≤n≤N-1 - Peak Power
[│xn│]2 – Average Power
E{.} denotes the expected value.[7]
Complementary cumulative density function (CCDF) is
commonly used performance criterion to show the PAPR
reduction, and it is described as [1]
0
bv= ejϕv
Where v= 1 2 3….V
Subsequently taking its IFFT it gives
Pr(PAPR>PAPR )
Input
(4)
Each sub block is of identical size. Let phase factor is
0≤𝑛≤𝑁−1
𝐸[|𝑥𝑛
S= [S0 S1 …….SV-1] T
Original OFDM Signal
-2
10
0
2
4
6
8
<------------------ PAPR in dB ------------------>
10
12
-2
10
Figure.2 PAPR Vs CCDF of Original OFDM Signal
III.
TRADITIONAL PARTIAL TRANSMIT SEQUENCE
TECHNIQUE
-3
In partial transmit sequence approach; the input
message block is partitioned into sub-blocks by using different
sub-block partition mechanism. Each sub block is multiplied
by a phase factor [3]. The input data block S is defined as
10
4
5
6
7
8
PAPR0[dB]
9
10
11
Figure.3 PAPR Performance of a 16 QAM/OFDM System
with PTS Technique When the Number of Sub block Varies
IV.
HARMONY SEARCH OPTIMIZATION WITH PTS
Searching of a perfect state of harmony for a perfect tune or
music was motivated the various researcher to propose a new
optimization algorithm that is HSA as a metaheuristic
optimization method [8].The HSA benefit versus traditional
optimization technique is, its simplicity. The mathematical
requirement and the decision variable initialization is also very
less in HAS as compared to other optimization methods [2].
The search of optimum phase factor in PTS can be defined as a
combinatorial optimization problem with a few variables and
constrains .Then; an optimization method based on harmony
search algorithm used in PTS is proposed to realize the OFDM
signal, which improves the PAPR performances with less
searching complexity [4].
S1
SK
Serial to
Parallel
Converter
&
Division
into Sub
block
f (b) = ∑ bm xm 2
s1
IDFT
b1
s2
∑
IDFT
S
b2
S2
IDFT
SV
terms of fitness function, replace the worst Harmony
from HM with new one.
 Step 5: Check for stopping criterion, if not reached
then repeat the improvisation step.
When the HSA is applied in PTS to investigate the better
arrangement of phase factor for reducing the PAPR of OFDM
signal, first the harmony memory is defined with all possible
phase factor combinations..
In PTS if the binary weighting factor is defined as bm
Є{=1,-1}(W=2),then the minimization of PAPR as fitness
function for possible phase factor is formulated as:
Minimize b f (b)
Subject to: bmЄ{=1,-1}M
With the objective function
sV
bV
HS Optimization of phase
Figure.4 Block Diagram of HS- PTS Technique of PAPR
Reduction
In harmony search algorithm the steps involve are as
follows [28-31]:
 Step1: Defining the Algorithm Parameters- In this
step the parameters used in HAS are defined. They
are; Harmony Memory, Harmony Memory Size
(HMS), Harmony memory Consideration Rate
(HMCR), Pitch Adjustment Rate (PAR), adjustment
bandwidth BW & stopping criterion K.
 Step 2: Harmony Memory Initialization-The each row
of HM matrix represents a set of possible solutions of
optimization problem (In PTS-it is phase factors).
Step 3: Improvisation process of New Harmony from
HM- A New Harmony vector x’ is determined by
three parameters consideration, i.e. Harmony memory
consideration rate, pitch adjustment rate & random
selection
 If r is random number [0,1] is less then HMCR then
select the new phase factor by considering HMCR &
Pitch adjustment using equation
x’ = x ± (r* BW),where r is [0,1]. Otherwise it is
selected randomly.
 Step 4: If the New Harmony vector or solution is
viable and better than the worst harmony in HM in
for 0≤ m ≤M-1
(8)
Firstly the phase factor is generated arbitrarily & fitness
function is defined as PAPR of OFDM signal which has to be
minimized. The each row of HM shows the one of the possible
solution of phase factors. The improvisation of phase factor is
performed on basis of three considerations as mentioned above
in step 3.
If the PAPR of new phase factor is less than the PAPR
calculated by old phase factor then the old one is replaced by
new phase factor or we can say that the harmony memory is
updated. This improvisation process is performed till the
stopping criterion is reached. In HS-PTS algorithm the
searching complexity of optimum phase factor is proportional
to MK, where M= number of phase factor & K is stopping
criterion [4].
The performance of harmony search optimization method
is enhanced when the PAR & BW is dynamically updated
(IHS). These parameters are very important. The convergence
rate of optimization can be adjusted by changing the values of
both parameters. The combination of Large PAR values with
small bandwidth values in HSA provides the best solutions at
last iterations. Both parameters are updated by using equations
[31]
PAR (i) = PARmin + (PARmax- PARmin ). i
(9)
NI
BW(i) = BWmax e(ki)
(10)
K =
(11)
ln (BWmin/BWmax)
NI
Where PARmin, BWmin & PARmax, BWmax are the minimum &
maximum values of PAR and bandwidth respectively. Here i is
the current generation number. This improved HS algorithm
based PTS gives the better PAPR performance compare to HSPTS.
V.
SIMULATION RESULT & CONCLUSION
Simulation parameters are shown in table I. From the
simulation result shown in Fig.6, we can see that for original
OFDM signal the PAPR is around 10.2 dB with CCDF of 10-2
which is very high. For 8 sub-blocks when we perform PTS
method of PAPR reduction the PAPR is 7.8 dB with CCDF 102
. After applying the harmony search optimization to search the
optimum phase factor for PTS, the PAPR is reduced which is
around 7.1 dB with CCDF of 10-2.When the improved harmony
search is used with PTS the PAPR is 6.3 dB which
Start
Initialize the Harmony Search algorithm parameters
(PAR, HMS, and HMCR)
Initialize the HM with randomly generated phase
factor
Generate random number, r [0,1]
r < HMCR
No
Yes
Select the new phase factor by
memory consideration
New phase factor is selected
randomly
Pitch adjustment rate
The new phase factor is
better than a stored one in
terms of PAPR or fitness
function
No
Yes
Refresh the harmony memory
NO
Stopping criterion is
checked
Yes
End
Figure.5 Flow Chart of HS- PTS Technique of PAPR Reduction
is less than the PAPR obtained in the case of T-PTS & HSPTS. The searching complexity of phase factor in T-PTS is 2 8
= 256 for 8 sub-blocks. But the searching complexity is same
in IHS-PTS & HS-PTS, M x K= 8 x 10=80 which is less than
the T-PTS. So we can conclude that in Harmony Search based
partial transmit sequence method & improved HS-PTS, the
good trade off is achieved between the PAPR performance &
computational complexity compare to traditional PTS. All
results are tabulated & well compared in terms of PAPR
reduction & computational complexity in table II. The
controlling parameters requirement is very less in HS –PTS, so
it is easy to be adjusted & gives the improvement in PAPR
performance.
ACKNOWLEDGMENT
TABLE I. SIMULATION PARAMETERS
S.No.
1
Parameters
For QAM- OFDM
No. of Sub-carriers
256
2
No. of Sub-blocks
8
3
No. of Phase Factors
2 (1, -1)
4
No. of OFDM Blocks for Iteration
1000
5
HMCR
0.95
6
PAR
0.20
7
HMS
16
8
Stopping criterion K
10
REFERENCES
Comparison of PAPR prformance of OFDM
0
10
CCDF
HS-PTS
IHS-PTS
Original OFDM
T-PTS
-1
10
-2
10
2
4
6
8
10
PAPR in dB
12
14
Figure.6 Comparison of PAPR performance of HS- PTS,
IHS-PTS, & original PTS Technique of PAPR Reduction
TABLE II. COMPARISON OF PERFORMANCE OF PTS TECHNIQUE
WITHOUT OPTIMIZATION & WITH HARMONY SEARCH AND IMPROVED HS
OPTIMIZATION FOR PAPR REDUCTION OF OFDM SIGNAL
S.No.
Technique Used
PAPR of
OFDM
signal
Computational
Complexity
1
T-PTS
7.8 dB
28=256
2
HS-PTS
7.1 dB
10x8=80
IHS-PTS
6.3dB
10x 8=80
3
I am very grateful to Chhatarpati Shivaji Institute of
Technology, Durg. And I would like to thank my guide Mr.
Mangal Singh and Neelam Dewangan for providing me the
necessary support & their valuable suggestions to improve my
work.
[1] Taspinar, Necmi, et al. "PAPR reduction using artificial bee
colony algorithm in OFDM systems." Turk J Electr Eng Comput
Sci 19.1 ,2011,pp. 47-58.
[2] Kermani, Emad Meimand, and Sedigheh Aflaki. "PAPR
Reduction of OFDM Signals: A Global Harmony Search
Approach."Broadcasting, IEEE Transactions on 57.2 ,2011.
[3] Wen, Jyh-Horng, et al. "A suboptimal PTS algorithm based on
particle swarm optimization technique for PAPR reduction in
OFDM
systems." EURASIP
journal
on
wireless
communications and networking vol.14,2008
[4] Gao, Jing, et al. "A Papr Reduction Algorithm Based on
Harmony
Research
for
Ofdm
Systems." Procedia
Engineering 15 2011,pp. 2665-2669.
[5] Yajun Wang & Wen Chen , “A PAPR reduction method based
on Artificial Bee Colony algorithm for OFDM signals,” IEEE
transactions on wireless communication signal Processing vol.
9, no. 10, Oct. 2010
[6] Jiang T., Wu Y., “An Overview: Peak-to-average power ratio
reduction techniques for
OFDM signals”, IEEE Trans.
Broadcasting, vol. 54, No. 2, Jun. 2008, pp. 257–268.
[7] Guan, Lili, et al. "Joint channel estimation and PTS to reduce
peak-to-average-power radio in OFDM systems without side
information." Signal Processing Letters, IEEE 17.10, 2010, pp
883-886
[8] Salehinejad, Hojjat, and Siamak Talebi. "PAPR Reduction of
OFDM Signals by Novel Global Harmony Search in PTS
Scheme."International Journal of Digital Multimedia
Broadcasting 2012
[9] Hung, Ho-Lung, et al. "Performance of particle swarm
optimization techniques on PAPR reduction for OFDM
systems." Systems, Man and Cybernetics, 2008. SMC 2008.
IEEE International Conference on. IEEE, 2008.
[10] Wen, Jyh-Horng, et al. "A suboptimal PTS algorithm based on
particle swarm optimization technique for PAPR reduction in
OFDM
systems." EURASIP
journal
on
wireless
communications and networking vol.14,2008.
[11] Han, SeungHee, and Jae Hong Lee. "An overview of peak-toaverage power ratio reduction techniques for multicarrier
transmission." Wireless Communications, IEEE 12.2, 2005.
[12] Vinayaka, V., P. Elavarasan, and G. Nagarajan. "Reduction of
PAPR in OFDM signals using Fountain
coded
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
PTS." Communications and Signal Processing (ICCSP), 2013
International Conference on. IEEE,2013.
Hou, Jun, Jianhua Ge, and Jing Li. "Peak-to-average power ratio
reduction of OFDM
signals using PTS scheme with low
computational complexity." Broadcasting, IEEE Transactions
on 57.1 ,2011,pp. 143-148.
Jiang T., Wu Y., “An Overview: Peak-to-average power ratio
reduction techniques for
OFDM signals”, IEEE Trans.
Broadcasting, vol. 54, No. 2, Jun. 2008, pp. 257–268.
Guan, Lili, et al. "Joint channel estimation and PTS to reduce
peak-to-average-power radio in OFDM systems without side
information." Signal Processing Letters, IEEE 17.10, 2010, pp
883-886.
Lingyin Wang &JuLiu , “PAPR reduction of OFDM signals by
PTS with grouping & recursive phase weighting method,” IEEE
transactions on broadcasting comm..vol. 57,June. 2011
Armstrong, J., “Peak-to-average power reduction for OFDM by
repeated clipping and frequency domain filtering,” Electronics
Letters, vol. 38, No. 5, Feb. 2002, pp. 246–247.
Wang X. B., Tjhung T. T., Ng C. S., “Reduction of peak-toaverage power ratio of OFDM system using a companding
technique”, IEEE Transaction on Broadcasting, vol. 45, No. 3,
Sept. 1999, pp. 303–307.
Ankita, Er, and Anand Nayyar. "Review of various PTS (Partial
Transmit Sequence) techniques of PAPR (Peak to Average
Power Ratio) reduction in MIMO-OFDM." IEEE transactions
on wireless communication signal Processing vol. 9, no. 10,
Oct. 2010
Ku, Sheng-Ju, Chin-Liang Wang, and Chiuan-Hsu Chen. "A
reduced-complexity PTS-based PAPR reduction scheme for
OFDM systems."Wireless Communications, IEEE Transactions
on 9.8 2010,pp. 2455-2460.
Jung Chein Chen , “Partial transmit sequence for PAPR
reduction of OFDM signals with the cross entropy methods,”
IEEE signal Processing vol. 16, no. 6, June. 2009
Yajun Wang & Wen Chen, “PAPR reduction method based on
parametric minimum cross entropy for OFDM Signal,” IEEE
communication letter vol. 14, no. 6, June. 2010
[23] Yajun Wang & Wen Chen , “A PAPR reduction method based
on Artificial Bee Colony algorithm for OFDM signals,” IEEE
transactions on wireless communication signal Processing vol.
9, no. 10, Oct. 2010
[24] Taspinar, Necmi, et al. "PAPR reduction using artificial bee
colony algorithm in OFDM systems." Turk J Electr Eng Comput
Sci 19.1 ,2011,pp. 47-58.
[25] Wen, Jyh-Horng, et al. "A suboptimal PTS algorithm based on
particle swarm optimization technique for PAPR reduction in
OFDM
systems." EURASIP
journal
on
wireless
communications and networking vol.14,2008.
[26] Yang, L., et al. "PAPR reduction using low complexity PTS to
construct of OFDM signals
without side information."
Broadcasting, IEEE Transactions on 57.2 ,2011,pp. 284-290.
[27] Gupta, Ishita, and Sarat Kumar Patra. "Single IFFT block based
reduced complexity Partial Transmit Sequence technique for
PAPR reduction in OFDM."Communications, Devices and
Intelligent Systems (CODIS), 2012 International Conference on.
IEEE, 2012.
[28] Gao, Jing, et al. "A Papr Reduction Algorithm Based on
Harmony
Research
for
Ofdm
Systems." Procedia
Engineering 15 2011,pp. 2665-2669.
[29] Kermani, Emad Meimand, and Sedigheh Aflaki. "PAPR
Reduction of OFDM Signals: A Global Harmony Search
Approach."Broadcasting, IEEE Transactions on 57.2 ,2011.
[30] Omran, Mahamed GH, and MehrdadMahdavi. "Global-best
harmony search."Applied Mathematics and Computation 198.2
2008,pp. 643-656.
[31] Salehinejad, Hojjat, and Siamak Talebi. "PAPR Reduction of
OFDM Signals by Novel Global Harmony Search in PTS
Scheme."International Journal of Digital Multimedia
Broadcasting 2012