Partial Transmit Sequences for PAPR Reduction Using Parallel Tabu Search Algorithm in OFDM Systems

Abstract

In this letter, partial transmit sequences (PTS) based on parallel tabu search (Parallel TS-PTS) scheme is proposed to reduce the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals. PTS is a distortionless PAPR reduction technique, but its high search complexity for finding optimal phase factors must be reduced for usable applications. Parallel TS-PTS is compared to different PTS schemes for PAPR reduction and search complexity performances. The simulation results show that the proposed parallel TS-PTS method provides good PAPR reduction and bit- error-rate (BER) performances. Index Terms—OFDM, PAPR, PTS, parallel tabu search, tabu search, high power amplifier (HPA).

Full text

974 IEEE COMMUNICATIONS LETTERS, VOL. 15, NO. 9, SEPTEMBER 2011
Partial Transmit Sequences for PAPR Reduction
Using Parallel Tabu Search Algorithm in OFDM Systems
Necmi Tas¸pınar, Adem Kalınlı, and Mahmut Yıldırım, Member, IEEE
Abstract—In this letter, partial transmit sequences (PTS)
based on parallel tabu search (Parallel TS-PTS) scheme is
proposed to reduce the peak-to-average power ratio (PAPR)
of orthogonal frequency division multiplexing (OFDM) signals.
PTS is a distortionless PAPR reduction technique, but its high
search complexity for finding optimal phase factors must be
reduced for usable applications. Parallel TS-PTS is compared to
different PTS schemes for PAPR reduction and search complexity
performances. The simulation results show that the proposed
parallel TS-PTS method provides good PAPR reduction and bit-
error-rate (BER) performances.
Index Terms—OFDM, PAPR, PTS, parallel tabu search, tabu
search, high power amplifier (HPA).
I. INTRODUCTION
ORTHOGONAL frequency division multiplexing
(OFDM) is a very attractive multicarrier modulation
technique for various wireless communication standards [1].
Despite the advantages, high PAPR value of the signals is
a major drawback of the OFDM systems. The high PAPR
value causes in-band distortion and out-of-band radiation due
to unwanted saturation in the high power amplifier (HPA)
[2], and this leads to performance degradation of the OFDM
systems. In order to eliminate degradation of the high PAPR
of the OFDM signals, many PAPR reduction methods have
been proposed [1]. From these methods, partial transmit
sequences (PTS) is the most popular technique because
of good PAPR reduction performance and distortionless
structure [1]. However, the conventional PTS requires an
exhaustive search, which causes high search complexity
to find the optimal phase factors. In the literature, there
are some recently proposed methods to reduce PAPR with
low complexity in OFDM systems [3-5]. Among these
methods, we compared the improved discrete particle swarm
optimization (IDPSO) [4] and artificial bee colony (ABC)
algorithm [5] with our proposed method to reduce the PAPR.
In this letter, a hybrid method based on the PTS technique
and parallel tabu search (parallel TS) algorithm is introduced
to reduce the PAPR of the OFDM signals with low search
complexity. The parallelism helps the TS algorithm to find the
promising regions of the search space very quickly [6-7]. The
simulation results show that the parallel TS-PTS gives better
Manuscript received May 13, 2011. The associate editor coordinating the
review of this letter and approving it for publication was A. Panagopoulos.
N. Tas¸pınar is with the Department of Electrical and Electronics Engineer-
ing, Erciyes University, Kayseri, Turkey (e-mail: taspinar@erciyes.edu.tr).
A. Kalınlıis with the Kayseri Vocational Technical School, Erciyes Univer-
sity, Kayseri, Turkey (e-mail: kalinlia@erciyes.edu.tr).
M. Yıldırım is with the Department of Electrical and Electronics
Engineering, Bozok University, Yozgat, Turkey (e-mail: mah-
mut.yildirim@bozok.edu.tr).
Digital Object Identifier 10.1109/LCOMM.2011.072911.110999
PAPR reduction performance compared to conventional PTS,
TS-PTS, ABC-PTS and IDPSO-PTS. In addition, parallel TS-
PTS is compared with original OFDM signals, ABC-PTS and
optimum-PTS for bit-error-rate (BER) performances of the
OFDM system using the HPA. In the simulations, solid-state
power amplifier (SSPA), which is a kind of HPA, was used.
II. SYSTEM MODEL
A. PAPR of the OFDM Signal
The discrete-time transmitted OFDM signal with 𝑁subcar-
riersisgivenby
𝑥𝑘=1
√𝑁
𝑁−1
∑
𝑛=1
𝑋𝑛𝑒𝑗2𝜋𝑛𝑘/𝐿𝑁 ,𝑘=0,1,⋅⋅⋅,𝐿𝑁 −1,(1)
where X=[𝑋0,𝑋
1,...,𝑋
𝑁−1]𝑇is the input signal vector
with each symbol modulated by PSK or QAM, and 𝐿is the
oversampling factor where 𝐿=4, which is enough to provide
an accurate approximation of the PAPR [1]. The PAPR of the
discrete-time OFDM signal 𝑥𝑘is defined as
𝑃𝐴𝑃𝑅(𝑥)=
max
0≤𝑘≤𝐿𝑁−1∣𝑥𝑘∣2
𝐸[∣𝑥𝑘∣2](dB),(2)
B. PTS for PAPR reduction
In the PTS, input signal vector 𝑿is partitioned into 𝑀
disjoint sub-blocks, and oversampled by inserting (𝐿−1) ⋅𝑁
zeros, such that
𝑿(𝑚)=⎡
⎣𝑋(𝑚)
0,...,𝑋(𝑚)
𝑁╱2−1,0⋅⋅⋅0
 
(𝐿−1)⋅𝑁
,𝑋(𝑚)
𝑁╱2,...,𝑋(𝑚)
𝑁−1
⎤
⎦,
(3)
where 𝑚=0,1,...,𝑀 −1; therefore,
𝑿=
𝑀−1
∑
𝑚=0
𝑿(𝑚).(4)
Next, sub-blocks are transformed from the frequency do-
main to the time domain by inverse fast Fourier transform
(IFFT) with 𝐿𝑁 point. Then, each sub-block is rotated to
minimize the value of the PAPR by phase factors 𝒃=
[𝑏0,𝑏
1,...,𝑏
𝑀−1],where𝑏𝑚=𝑒𝑗𝜙,and𝜙∈[0,2𝜋).Finally,
the sub-blocks are summed up. After the PTS optimization,
the OFDM signal is given by
𝑥
′
𝑘=
𝑀−1
∑
𝑚=0
𝑏𝑚𝐼𝐹𝐹𝑇 {𝑿(𝑚)}.(5)
1089-7798/11$25.00 c
⃝2011 IEEE

TAS¸PINAR et al.: PARTIAL TRANSMIT SEQUENCES FOR PAPR REDUCTION USING PARALLEL TABU SEARCH ALGORITHM IN OFDM SYSTEMS 975
III. PARALLEL TS-PTS TECHNIQUE FOR PAP R
REDUCTION
The TS algorithm is a form of iterative heuristic search
based on intelligent problem solving principles. In this letter,
the parallel TS algorithm is used to find the phase factors with
the aim of minimizing the PAPR of the OFDM signals. The
problem of searching the optimal phase factors 𝒃that makes
𝑃𝐴𝑃𝑅(𝒃)minimum is called the optimization problem of
the 𝑃𝐴𝑃𝑅(𝒃)and can be mathematically expressed as
𝑚𝑖𝑛𝑖𝑚𝑖𝑠𝑒 𝑃 𝐴𝑃 𝑅 (𝒃)
𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝒃∈{+1,−1}(6)
TS has a flexible memory that retains the information about
previous steps of the search, and uses it to create and exploit
new solutions in the search space. Main steps of the TS
algorithm are described as follows:
Step 1:Get a randomly generated initial solution 𝒃𝑛𝑜𝑤 .
Step 2:Select the best admissible solution:𝒃𝑏𝑒𝑠𝑡 (𝒃𝑏𝑒𝑠𝑡 is the
best of all 𝒃∗∈𝐴(𝒃𝑛𝑜𝑤):𝒃∗is not in tabu list).
Step 3:Update the current solution 𝒃𝑛𝑜𝑤 ←− 𝒃𝑏𝑒𝑠𝑡, and
update the tabu list.
Step 4:Repeat Step 2 and Step 3 until a stopping criterion
(𝑚𝑎𝑥𝑖𝑡)is satisfied.
A step of the TS starts with a present solution 𝒃𝑛𝑜𝑤 .𝒃𝑛𝑜𝑤
has an associated set of feasible solutions 𝐴which can be
obtained by applying a simple modification to 𝒃𝑛𝑜𝑤 .This
modification is called a move. In order to be able to get rid
of a local minima, a move to the neighbor 𝒃∗, is created even
if 𝒃is worse than 𝒃𝑛𝑜𝑤 . This would cause the cycling of
the search. In order to avoid the cycling problem, a tabu list
𝑇is introduced. The tabu list stores all the tabu moves that
can not be applied to the present solution, 𝒃𝑛𝑜𝑤 . The moves
stored in the tabu list are those carried out most frequently and
recently, according to certain criteria called tabu restrictions.
The use of tabu list decreases the possibility of cycling because
it prevents returning, in a certain number of iterations, to a
solution visited recently. After a subset of feasible solutions
𝐴∗is produced according to the tabu list and evaluated for
𝑃𝐴𝑃𝑅(𝒃), the next solution is selected from it. The highest
evaluation solution is selected as the next solution 𝒃𝑛𝑒𝑥𝑡.This
loop is repeated until a stopping criterion is satisfied.
In the parallel TS approach considered in this letter, the
information exchange process between the basic TS algorithms
executed in parallel is based on the crossover operation used in
genetic algorithm (GA). The crossover operator employed by
GA is used to create two new solutions (children) from two
existing solutions (parents) in the population formed by the
selection operation. The potential phase factors solutions are
represented with binary strings in the parallel TS algorithm.
Therefore, a solution is created from the binary string by
changing the value of a bit, 0to −1and 1to 1.Since
the problem is represented in the binary string form, the
crossover operation is applied as follows: Two solutions are
selected as parent solutions from the population and cut at
a randomly selected point. The tails, which are the parts
after the cutting point, are swapped and two new solutions
are produced. A crossover operation can thus yield better
solutions by combining the good features of parent solutions.
The flowchart of the parallel TS is depicted in Fig. 1.
Fig. 1. Flowchart of the parallel TS algorithm for phase factors optimization.
IV. SIMULATION RESULTS
In the simulations, we consider an OFDM system with
𝑁= 256 subcarriers, and data symbols are modu-
lated using the 16 QAM constellation. In order to gen-
erate the complementary cumulative distribution function
(𝐶𝐶𝐷𝐹 =Pr[𝑃𝐴𝑃𝑅 > 𝑃𝐴𝑃𝑅
0]) of the 𝑃𝐴𝑃𝑅,104
OFDM blocks are generated randomly, where the transmitted
signal is oversampled by a factor of 𝐿=4.InthePTS
optimization, the 256 subcarriers are divided into 𝑀=16
sub-blocks, and two allowed phase factors 𝑏𝑚∈{+1,−1}
(𝑊=2) are used. The SSPA is used with input back-offs
𝐼𝐵𝑂 =0,1,...,12 dB and smoothness factor 𝑝=0.5,2[2].
Fig. 2(a) and 2(b) compare the PAPR reduction performance
of the parallel TS-PTS with the conventional PTS, TS-PTS,
IDPSO-PTS [4] and ABC-PTS [5]. The PAPR value of the
original OFDM signal is measured before the PTS optimiza-
tion so its search number (𝑆)is0. The optimum-PTS tests all
the phase factors, and requires 𝑊𝑀=2
16 = 65536 search
numbers. Parallel TS-PTS is composed of parallel structures of
the TS algorithms and crossover operator. The number of TS
algorithms running in parallel is ℎ=4and each TS algorithm
searches the phase factors until the 𝑚𝑎𝑥𝑖𝑡 as mentioned in
the main steps of the TS-PTS algorithm. Parallel TS-PTS
uses 𝑚𝑎𝑥𝑖𝑡 =11. Therefore, the search cost of parallel
structures of the TS algorithms is 𝑚𝑎𝑥𝑖𝑡 ×ℎ. Crossover
is applied for all candidate solutions of the TS algorithms
with each other. Therefore, the search cost of the crossover
is 𝑐=(4
2)=6,where4and 2are equal to ℎand the
number of phase factors to which the crossover operation is
applied, respectively. The total search cost of the parallel TS-
PTS for one cycle is equal to (𝑚𝑎𝑥𝑖𝑡 ×ℎ)+𝑐. The cycles
are repeated until they reach the search number 𝑆.Inthe
ABC-PTS, the search number is equal to 𝑆=𝑀𝐶𝑁 ⋅𝑆𝑁,
where 𝑀𝐶𝑁 is the maximum cycle number and 𝑆𝑁 is the
size of the population. ABC-PTS uses 𝑀𝐶𝑁 ⋅𝑆𝑁 =5⋅10
and 𝑀𝐶𝑁 ⋅𝑆𝑁 = 100 ⋅10 for 𝑆=50and 𝑆= 1000,
respectively with limit value 𝐿𝑉 = 10. In the IDPSO-PTS,
the search number is equal to 𝑆=𝐾0⋅𝑄,where𝐾0is

976 IEEE COMMUNICATIONS LETTERS, VOL. 15, NO. 9, SEPTEMBER 2011
Fig. 2. PAPR reduction performances of the PTS schemes: (a) parallel TS-
PTS, ABC-PTS and IDPSO-PTS; (b) parallel TS-PTS, TS-PTS and RS-PTS.
TAB L E I
COMPUTATI ONAL COMPLEXITY OF THE PTS SCHEMES
Methods Number of Searches (𝑆)PA P R [ d B]
Original 011.26
Optimum-PTS 𝑊𝑀=2
16 = 65536 6.74
Parallel TS-PTS [(𝑚𝑎𝑥𝑖𝑡 ×ℎ)+𝑐]⋅𝑐𝑦𝑐𝑙𝑒
=[(11×4) + 6]⋅20 = 1000 6.93
ABC-PTS 𝑀𝐶𝑁 ⋅𝑆𝑁 = 100 ⋅10 = 1000 6.98
TS-PTS 𝑚𝑎𝑥𝑖𝑡 = 1000 7.06
IDPSO-PTS 𝐾0⋅𝑄= 100 ⋅10 = 1000 7.09
RS-PTS number of randomly selected
phase factors = 1000 7.13
the maximum number of iterations and 𝑄is the number of
particles. IDPSO-PTS uses 𝐾0⋅𝑄=5⋅10 and 𝐾0⋅𝑄= 100⋅10
for 𝑆=50and 𝑆= 1000, respectively. As shown in Fig. 2(a),
parallel TS-PTS shows better PAPR reduction performance
than IDPSO-PTS and ABC-PTS. In the random search (RS)-
PTS [8], the search number is equal to the number of randomly
selected phase factors. The search number of the TS-PTS is
equal to the number of 𝑚𝑎𝑥𝑖𝑡 =𝑆. As shown in Fig. 2(b),
parallel TS-PTS with 𝑆= 250 and RS-PTS with 𝑆= 1000
show the nearly same PAPR performance. Therefore, parallel
TS-PTS has about 1∖4search complexity of the RS-PTS.
Computational complexity and PAPR reduction performances
of the PTS schemes at 𝐶𝐶𝐷𝐹 =10
−3are shown in Table I.
Fig. 3(a) shows effect of the SNR on the BER performance
of the OFDM system using the ABC-PTS with 𝑆= 1000,
parallel TS-PTS with 𝑆= 1000, optimum-PTS and original
OFDM signal on AWGN channel. BER performance of the
system with linear amplifier, which does not cause any signal
distortion, is 𝐵𝐸𝑅 =10
−5when 𝑆𝑁𝑅 = 13.5dB. In
the case of high values of the IBO, SSPA works near the
linear region of the amplification. But in the case of low
values of the 𝐼𝐵𝑂, SSPA works near the nonlinear region
of the amplification. At 𝐵𝐸𝑅 =10
−5, parallel TS-PTS needs
𝑆𝑁𝑅 = 17.54 dB for 𝐼𝐵𝑂 =6dB, and this value is only
0.18 dB higher than the optimum-PTS. In addition, as it can be
Fig. 3. BER performances of the OFDM system using linear amplifier and
SSPA (a): effect of SNR with 𝑝=2;(b):effectof𝐼𝐵𝑂.
seen from the zoom window in Fig. 3(a), parallel TS-PTS has
better performance than ABC-PTS for 𝐼𝐵𝑂 =6dB. Fig. 3(b)
shows effect of the 𝐼𝐵𝑂 on the BER performance using the
parallel TS-PTS with 𝑆= 1000 and the original OFDM signal
with 𝑝=0.5,2on AWGN channel. As shown in Fig. 3(b),
𝐼𝐵𝑂 and 𝑝must be increased for better BER performance of
the OFDM system. As expected, parallel TS-PTS shows better
BER performance compared to the original OFDM signal.
V. C ONCLUSION
In this letter, we propose a parallel TS-PTS scheme to
improve the PAPR reduction performance with low search
complexity for the OFDM signals. The proposed method is
compared with the conventional PTS, IDPSO-PTS, TS-PTS
and ABC-PTS. The simulation results show that the proposed
parallel TS-PTS method provides good PAPR reduction and
bit-error-rate (BER) performances.
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