Peak-to-Average Power Ratio Reduction Method for OFDM

Peak-to-Average Power Ratio Reduction Method for OFDM Signal by Permutation of Subcarriers 29

Peak-to-Average Power Ratio ReductionMethod for OFDM Signal by Permutation of

Subcarriers

Pornpawit Boonsrimuang1 , Kanchana Limwattanacha2 ,

Pisit Boonsrimuang3 , and Hideo Kobayashi4 , Non-members

ABSTRACT

Many PAPR reduction methods for OFDM timedomain signal have been proposed up to today, all ofwhich can be classified into two kinds of methods asthe distortion and distortion-less methods. The mostof distortion-less methods show better PAPR per-formance without degradation of BER performance.However the distortion-less methods are usually re-quired to control the transmission data information soas to minimize the PAPR performance at the trans-mitter. From this fact, the distortion-less methodsare required to inform the controlled information asthe side information to the receiver for the correctdemodulation of data information. The side infor-mation is usually informed to the receiver with thehigher signal quality by using the separate channel orthe embedded in the data information which wouldlead the degradation of transmission efficiency andthe increase of hardware complexity of transmitterand receiver.

This paper proposes a novel distortion-less PAPRreduction method which employs the permutation ofsubcarriers in the frequency domain. The feature ofproposed method is to achieve the better PAPR per-formance with a very few embedded side informationfor the correct demodulation of data information atthe receiver. This paper presents various computersimulation results to verify the effectiveness of pro-posed method as comparing with the conventionalOFDM method in the non-linear channel.

Keywords: PAPR, OFDM, Non-linear Channel

Manuscript received on July 1, 2014 ; revised on September20, 2014.Final manuscript received April 19, 2015.1 The author is with Faculty of Industrial Technology, Suan

Sunandha Rajabhat University, Bangkok, Thailand., E-mail:[email protected],3 The authors are with Telecommunication Engineering De-

partment, Faculty of Engineering, King Mongkut’s Instituteof Technology Ladkrabang, Bangkok, Thailand., E-mail: por-pear [email protected] and [email protected] The author is with Department of Electrical and Electronic

Engineering, Graduate School of Engineering, Mie University,Japan., E-mail: [email protected]

1. INTRODUCTION

The Orthogonal Frequency Division Multiplexing(OFDM) technique has been received a lot of at-tentions especially in the field of wireless commu-nications because of its efficient usage of frequencybandwidth and robustness to the multi-path fading.From these advantages, the OFDM technique hasalready been adopted as the standard transmissiontechniques in the wireless LAN systems [1] and theterrestrial digital TV broadcasting systems [2]. TheOFDM technique is also employed in the next gen-eration mobile communications systems (LTE: LongTerm Evolution) [3]. One of the limitations of usingOFDM technique is the larger peak to average powerratio (PAPR) of its time domain signal [4-6]. TheOFDM signal with larger PAPR would cause the se-vere degradation of bit error rate (BER) performanceand undesirable frequency spectrum regrowth due tothe occurrence of inter-modulation noise at the out-put of non-linear amplifier.

Many PAPR reduction methods have been pro-posed to overcome the above PAPR problem on theOFDM technique up to today. These techniques canbe classified into two kinds of methods as the dis-tortion [7-8] and distortion-less methods [9-15]. Al-though the distortion techniques including the clip-ping and filtering method can improve the PAPR per-formance relatively, it leads the degradation of BERperformance and undesirable spectrum regrowth tothe adjacent channel due to the clipping distortion.The distortion-less techniques including the multiplesignal representation techniques such as the partialtransmit sequence (PTS) [9-10], the selected mapping(SLM) [11-12] and Dummy Sequence Insertion (DSI)[13-14]. Although these techniques can achieve betterPAPR performance without degradation of BER per-formance, the transmitter is required to inform theside information to the receiver for the correct de-modulation of received signal. The side informationis usually informed to the receiver with the highersignal quality by using the separate channel or theembedded in the data information which would leadthe degradation of transmission efficiency and the in-crease of hardware complexity of transmitter and re-ceiver.

To solve the above problem, the PAPR reduction

30 ECTI TRANSACTIONS ON COMPUTER AND INFORMATION TECHNOLOGY VOL.9, NO.1 May 2015

method without requiring the side information wasproposed for the WiMAX system based on the PTSmethod [15]. The phase optimization problem forthe PTS method is solved by using the SequentialQuadratic Programming (SQP), Particle Swarm Op-timization (PSO) and Least Squares Error (LSE) al-gorithms [15]. The proposed algorithms make useof the antenna beamforming weights and dedicatedpilots at the WiMAX transmitter. Although the pro-posed method can achieve better PAPR performancewithout any degradation of signal quality and anyside information, the dedicated pilots are requiredin each cluster which are used in the beamforming.From this fact, the proposed method in [15] is ap-plicable only to the systems of using the dedicatedpilots.

In this paper, we propose a novel distortion-lessPAPR reduction method which employs the permuta-tion of data subcarriers in the frequency domain andpropose the efficient transmission method of side in-formation which employs the embedded side informa-tion in the data information.The feature of proposedmethod is to achieve the better PAPR performancewith a very few embedded side information whichleads the improvement of transmission efficiency witha lower hardware complexity for the transmitter andreceiver.

In the following of this paper, Section II presentsthe system model of OFDM method in the non-linearchannel. Section III presents the proposed methodwith the permutation of subcarriers (PS). Section IVexplains the detection method for embedded side in-formation at the receiver side. V presents the variouscomputer simulation results to verify the performanceof proposed PS method, and Section VI concludes thepaper.

2. SYSTEM MODEL

Figure 1 shows the OFDM system model to beused in the following evaluation. In the figure, Xn

is the modulated signal at the n − th sub-carrier inthe frequency domain and xk is the time domain sig-nal at k − th sample point, which is converted fromthe frequency domain data by using IFFT. The timedomain sampled OFDM signal yk after adding theguard interval (GI) at the start of every OFDM sym-bol to avoid the inert symbol interference (ISI) willbe converted to the analogue signal by the digital-analogue converter (D/A) and then converted to theradio frequency (RF) by the frequency up-converter(U/C) as shown in Fig.1. The output signal of U/Cis inputted to the non-linear amplifier and transmit-ted to the channel. The output signal of non-linearamplifier can be expressed by the following equation.

s(t) = F [|y(t)|]ej{arg[y(t)]+Φ[|y(t)|]} (1)

where, y(t) and s(t) are the input and output RF sig-nal of non-linear amplifier, and F [ ] and Φ[ ] representthe AM/AM and AM/PM conversion characteristicsof non-linear amplifier. The non-linear amplifier as-sumed in this paper is the Solid State Power Am-plifier (SSPA) of which AM/AM and AM/PM con-version characteristics are modeled by the followingequations [16].

F [ρ] =ρ

[1 + (ρ/A)2r]1/2r(2)

Φ[ρ] = αϕ

( ρ

A

)4

(3)

where, ρ is the amplitude of input signal, A is thesaturated output level, r is the parameter to decidethe non-linear level and αϕ is phase displacement. Inthe following evaluations, the values for these param-eters are assumed by A = 1, r = 2 and αϕ = 0.01 ofwhich these parameters can approximate the typicalSSPA [16]. Fig.2 shows the input and output rela-tionships of AM-AM and AM-PM conversion charac-teristics for SSPA when the parameters are given bythe above values.

In the OFDM system, M frequency domain datasymbols {Xn, n = 0 to M − 1} which correspond tosubcarriers, are modulated with a set of orthogonalfrequency {fn, n = 0 to M − 1}.

Fig.1: OFDM system model.

Fig.2: AM/AM and AM/PM input-output relation-ships of SSPA.

The frequency domain M subcarriers are chosen


to be orthogonal, i.e. fn = n∆f , where ∆f = 1/MTand T represents the OFDM data symbol period. Theresulting baseband OFDM signal xk can be expressedby the following equation.

xk =

N−1∑n=0

Xn · ej 2πnkN k = 0 to N − 1. (4)

Where N is the number of IFFT points including(N −M) zero padding added both ends of OFDM Msubcarriers, which enables the usage of simple ana-logue filter to eliminate the alias occurring at theoutput of D/A converter. From (4), it can be seenthat the OFDM time domain signal is generated bythe summation of random data information in thefrequency domain. From this fact, PAPR of OFDMtime domain signal would be relatively larger as com-pared with the conventional single carrier modulationtechniques. The PAPR of OFDM time domain signalis defined by the following equation [5].

PAPR(dB) = 10 log10

max0≤k≤N

|xk|2

E [|xk|2](5)

where E[ ] denotes the expected value. To evaluatethe PAPR performance for OFDM signal from thestatistical point of view, the Complementary Cumu-lative Distribution Function (CCDF) given in (6) isusually used to represent the probability of exceedinga given threshold PAPR0.

CCDF(PAPR0) = Pr(PAPR > PAPR0) (6)

3. PROPOSAL OF PAPR REDUCTIONMETHOD WITH PERMUTATION OFSUBCARRIERS

Figure 3 shows the structure of frequency domainOFDM symbol for the proposed PS method. Thereare two types of permutation methods Type I andType II as shown in Figs.3 (a) and (b), respectively.Type I is to perform the permutation of subcarriersprocess only for the first part of M/2 subcarriers,while Type II is to perform the permutation processboth for the first and the last parts of M/2 subcarri-ers. Although the computational complexity for TypeII is larger than Type I, the improvement of PAPRperformance for the Type II is better than Type I.Because Type II has the larger number of permuta-tion processes and has the potential capability to findthe better PAPR performance than that for Type I.For simple explanation, we only give an example forType I in the following. As for the Type II, the sameprocedures of Type I can be performed both for thefirst and last parts of M/2 subcarriers.

The proposed OFDM symbol in Type I consists of(M−3) data subcarriers, two dummy subcarriers and

one parity subcarrier which can be expressed by thefollowing equation.

X = [D1, D2, P,X0, X1, X2, · · · , XM/2−3, XM/2−2,

· · · , XM−4] (7)

Where D is the dummy sub-carriers with power of 0(Null subcarrier) and P is the parity check subcar-rier with power of α of which power is taken as thesame as the averaged power of data subcarriers. Thedummy (null subcarriers) and parity subcarriers willbe used for the detection of the first data subcarrierX0 at the receiver for the correct demodulation ofdata information. After the insertion of zero paddingto both ends of (7), the first part of M/2 subcarriersas shown in Fig.3 (a) are simply rotated circularlyone by one so as to achieve the better PAPR per-formance. The number of permutation of subcarriersperformed at the transmitter can be detected by us-ing the dummy and parity check subcarriers at thereceiver. When the number of permutation for thefirst part of M/2 subcarriers R is 5 as an example,the resultant ordering of subcarriers is given by thefollowing equation.

XR=5 = [X2, X3, · · · , XM/2−4, D1, D2, P,X0, X1,

XM/2−3, · · · , XM−4] (8)

Figure 4 shows the example of proposed PS methodwhen R = 5. In this example, the location of 1st sub-carrier becomes the data subcarrierX2 and the paritycheck subcarrier P becomes (M/2−R+3)− th sub-carrier in the OFDM symbol after the permutationof subcarriers by R = 5 times. In this case, the signof parity check subcarrier P is set by the followingequation in order to detect the number of permuta-tion for the subcarriers with higher accuracy at thereceiver.

P = (−1)(M/2−R+3) ·√α (9)

The permutation of subcarriers for the first part ofM/2 subcarriers is taken from 1 to M/2. In theproposed method, the best PAPR performance willbe selected from among the permutation of subcar-riers from 1 to M/2. Then the selected ordering ofsubcarriers with the best PAPR performance will beconverted to the time domain signal by using IFFT.The time domain signal can be given by the followingequation

x̃k =1√N

N−1∑n=0

X̃n · ej 2πknN (10)

where x̃n is the frequency domain signal after per-


forming the permutation of subcarriers and x̃k is thetime domain signal with lower PAPR performance.As for Type II, the above procedures are performedboth part of M/2 subcarriers. Fig. 5 shows the struc-ture of transmitter with the proposed PS method.

(a) Type I

(b) Type II

Fig.3: Structure of OFDM system for proposed PSmethod.

Fig.4: Example of Permutation Sequence whenR=5.

Fig.5: Structure of transmitter for the proposed PSmethod with Type I.

4. DETECTION METHOD FOR EMBED-DED SIDE INFORMATION

The first data subcarrier which is moved to thecertain subcarrier number after the permutation ofsubcarriers performed at the transmitter is requiredto detect at the receiver for the correct demodula-tion of data information. The position of first data

subcarrier can be detected by finding the position ofdummy (null subcarriers) and check the sign of paritycheck sub-carriers.

Figure 6 show the detection algorithm for the per-mutation number selected at the transmitter. Theproposed detection method is firstly to replace theconsecutive two subcarriers to zero from the start ofreceived OFDM signal in the frequency domain andcalculate the power of received signal by using thefollowing equation.

Power(ℓ) =

M/2∑n=0

{R(ℓ)n · conj[R(ℓ)

n ]} (11)

ℓ = 0, 1, 2, · · · ,M/2− 1

where R(m)n is the received frequency domain signal

at the n − th subcarrier after replacing two subcar-riers to zero at ℓ − th and (ℓ + 1) − th subcarriersand conj[ ] represents the complex conjugate. From(11), the maximum power could be obtained when ℓis equal to the location of first dummy subcarriers.The detection performance can be improved furtherby checking the sign of parity check subcarrier P forthe next subcarrier which is detected at the ℓ−th and(ℓ+1)− th dummy subcarriers with having the max-imum power given in (11). The sign of parity checksubcarrier given by (9) can be used for assuring thedetection of the first data subcarrier X0. The detec-tion performance can be improved by using both twodummy subcarriers and parity check subcarrier baseon the procedures as show in Fig. 6.

Fig.6: Detection algorithm for permutation number.


The proposed PS method enables the correct de-modulation of data information by using only twodummy and one parity subcarriers, which can achievebetter transmission efficiency and reduce the com-plexity of receiver as compared with the conventionalmethod of using the side information which is in-formed to the receiver through the separate channel.

Figure 7 show the structure of proposed receiver ofusing the above detection algorithm for the embed-ded side information. By using the above method, theoriginal data sequence can be recovered with higheraccuracy and data information can be demodulatedcorrectly. The feature of proposed method is to en-able the detection for the number of permutation pre-cisely by using very few embedded side information.

Fig.7: Structure of receiver for the proposed method.

5. EVALUATION OF PROPOSED PSMETHOD

This section presents the various computer simu-lation results to verify the performance of proposedmethod as comparing with the conventional OFDMby using the M-file script of Matlab program. Ta-ble 1 shows the list of simulation parameters. In thesimulations, the number of FFT points N = 256 istaken by 4 times larger than the number of subcarri-ers M = 64 to evaluate the PAPR performance withhigher accuracy.

Table 2 shows the transmission efficiency for theproposed PS method with Type I and Type II. Fromthe table, it can be observed that the proposedmethod can achieve the higher transmission efficiencybecause the number of permutation selected at thetransmitter can be detected by using only 2 dummysubcarriers and one parity check subcarriers for TypeI and 4 dummy subcarriers and 2 parity check sub-carriers for Type II, respectively.

As the purpose of easy understanding the effective-ness of proposed PS method, Figures 8 and 9 showthe OFDM signals before and after the proposed PSmethod in the frequency and time domains, respec-tively. In the simulations, the modulation methodis 16QAM and the number of data subcarriers (K),dummy subcarriers (D) and parity subcarrier (P) aretaken by 61, 2 and 1 for the PS method with Type I.From Figure 8 which shows the OFDM signals in the

Table 1: Simulation parameters.

Modulation method 6QAM & 64QAMDemodulation method CoherentOFDM bandwidth 5 MHzNumber of FFT points (N=Z+M) 256Number of sub-carriers (M=D+P+K) 64Number of dummy sub-carriers (D) 2Number of parity sub-carriers (P) 1Number of data sub-carriers (K) 61Number of zero padding (Z) 192Symbol duration 12.8 usGuard interval 1.2 usModel of non-linear amplifier SSPANon-linear parameter of Eq. (2) r=2Channel model AWGN

Table 2: Transmission efficiency from proposedmethod.

No. of Transmission efficiency (%)sub-carriers Type I Type II

64 95.3% (61/64 ) 95.6% (58/64 )256 98.8% (253/256 ) 97.7% (250/256 )1024 99.7% (1021/1024 ) 99.4% (1018/1024 )

frequency domain, it can be observed that the loca-tions of two dummy subcarriers and one parity sub-carriers at the 1st to 3rd subcarriers before the pro-posed PS method are moved to the locations of 18-thto 20-th subcarriers after the PS method in which thebest PAPR performance is obtained when the num-ber of permutations R is 15. The frequency domainsignals before and after the PS method as shown inFigure 8 are converted to the time domain signals byIFFT which are shown in Figure 9. From Figure 9, itcan be observed that the amplitude of time domainsignal after proposed PS method is lower than thatbefore the PS method. The PAPR performances be-fore and after the proposed PS method are 7.0dB and5.1dB, respectively. This means that the proposedPS method can achieve better PAPR performance by1.9dB than the conventional OFDM.

Figure 10 shows the PAPR performances both forthe conventional OFDM and proposed PS methodswith Type I and Type II. In the figure, the PAPR per-formance is evaluated by using the ComplementaryCumulative Distribution Function (CCDF). From thefigure, it can be observed that the proposed PSmethod shows better PAPR performance than thatfor the conventional OFDM by 2.2dB for Type I and3 dB for Type II at CCDF=10−1, respectively. Hereit should be noted that the degradation of BER per-formance of OFDM signal in the non-linear channelwould be dominated by the PAPR performance atthe CCDF higher than 10−1. From these results, itcan be expected that the proposed PS method couldachieve the better BER performance than that for theconventional OFDM method in the non-linear chan-nel.

Figures 11 (a) and (b) show the BER performances


(a) OFDM signal before PS method.

(b) OFDM signal after PS method.

Fig.8: Comparison of OFDM frequency domain sig-nals before and after the proposed PS Method.

Fig.9: Comparison of OFDM time domain signalsbefore and after the proposed PS Method.

Fig.10: PAPR performance of proposed method.

in the non-linear channel when changing C/N for theconventional OFDM and the proposed PS method.The modulation method is 16QAM and 64QAM.In the simulation, the number of data subcarriers,dummy subcarriers and parity subcarrier are takenby 61, 2 and 1 for Type I and 58, 4 and 2 for Type II,respectively. The input back-off (IBO) of non-linearamplifier (SSPA) is taken by -2dB, -4dB and -6dB,respectively. From the figures, it can be observedthat the proposed PS method with detection methodfor embedded side information can achieve much bet-ter BER performance than those for the conventionalOFDM in the non-linear channel.

(a) 16 QAM

(b) 64 QAM

Fig.11: BER performance of proposed method inthe non-linear channel.

6. CONCLUSIONS

This paper proposed the distortion-less PAPR re-duction method which employs the permutation ofdata subcarriers in the frequency domain and alsoproposed the efficient transmission method of sideinformation which employs the embedded side infor-mation in the data information. The features of pro-posed method are to enable the reduction of PAPRperformance by rotating the subcarriers in the fre-quency domain and to enable the correct demodula-tion of received signal by using a very few embed-


ded side information which enables the detection ofrotation number precisely at the receiver. The pro-posed method can achieve the better PAPR perfor-mance and higher transmission efficiency with a lowerhardware complexity for the transmitter and receiver.From the computer simulation results, this paper con-firmed that the proposed permutation of subcarriersmethod can achieve the better PAPR performanceand better BER performance in the non-linear chan-nel with keeping the higher transmission efficiency ascomparing with conventional OFDM systems.

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Pornpawit Boonsrimuang receivedthe B.Eng. and M.Eng degreesin telecommunication engineering fromKing Mongkut’s Institute of Technol-ogy Ladkrabang (KMITL), Thailand,in 2003, 2007 and Doctor degrees inTelecommunications Engineering at theMie University, Japan in 2013. He iscurrently a lecturer at the faculty ofindustrial technology, Suan SunandhaRajabhat university, Thailand. His re-

search interests include digital communications for next gener-ation of satellite, mobile and wireless LAN systems.

Kanchana Limwattanachai receivedthe B.Eng. and M.Eng degreesin telecommumication engineering fromKing Mongkut’s Institute of Technol-ogy Ladkrabang (KMITL), Thailand,in 2008 and 2014 respectively. Herresearch interests include transmissiontechniques for mobile, wireless LAN sys-tems and future multimedia.

Pisit Boonsrimuang received theB.Eng, M.Eng,and Doctor degrees inTelecommunications Engineering, in1997,2000,and 2007 respectively.He iscurrently an associate professor at theKing Mongkut’s Institute of TechnologyLadkrabang(KMITL),Thailand. His re-search interests include transmissiontechniques for future multimedia wire-less LAN systems and next generation ofmobile communication systems. He re-

ceived the Student Award of Young Research’s Encouragement


Award from IEICE Tokai branch and Doctor Thesis Award forinformation technology from Nation Research Council of Thai-land(NRCT) in 2005 and 2008,respectively.

Hideo Kobayashi received the B.E.,M.E., and PhD in 1975, 1977 and 1989,respectively from Tohoku University inJapan. He joined KDD in 1977, andengaged in the research and develop-ment of digital fixed satellite and mo-bile satellite communications systems.From 1988 to 1990, he was with Interna-tional Maritime Satellite Organization(INMARSAT) at its London Headquar-ters as the Technical Assignee and in-

volved in the design and development of Inmarsat-M communi-cations system. From 1997 to 1998, he was with the NEC ICOproject office as the technical consultant at its London officeand involved in the development of the ICO personal satellitecommunications system. Since 1998 he has been the Professorof Graduate School of Engineering, Mie University in Japan.His current research interests include mobile communicationsand wireless LAN systems.

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Peak-to-Average Power Ratio Reduction Method for OFDM