Distortionless PAPR Reduction Method for ExistingOFDM Systems

Masato SAITO, Akihiro OKUDA, Minoru OKADA, and Heiichi YAMAMOTO

Nara Institute of Science and Technology (NAIST)8916-5 Takayama-cho, Ikoma-shi, Nara, Japan 630-0192

Tel.: +81-743-72-5342, Fax: +81-743-72-5349Email: saito@is.naistjp

Abstract- In this paper, we propose a distortionless PAPR(Peak-to-Average Power Ratio) reduction method for applying toexisting OFDM systems, for example IEEE 802.11a/g/n wirelessLAN or ADSL and so on. The proposed method estimates thePAPR of output OFDM symbol through the emulation of thelower layer operations. If the estimated PAPR is larger than therequired value, we continue permutes binary data according toprepared mapping functions until the requirement is satisfiedor reach to preset maximum number of iterations. Simulationresults based on the parameters of IEEE 802.11a standard showthat the proposed method can effectively lower the distributionsof PAPR. When nonlinear amplifier is assumed, 2 or 4 timesof iterations are enough to suppress the out-of-band emissioneffectively.

I. INTRODUCTIONOFDM (Orthogonal Frequency Division Multiplexing) sys-

tem is recognized as a promising current and future mobilecommunications technique [1]. By using a large number ofsubcarriers, it can achieve high data rate. Moreover, the longsymbol duration and use of GI (Guard Interval) by cyclic-prefixing can minimize the effect of multipath fading channel.However, a wide range of amplitude fluctuation is an essentialdrawback of multicarrier modulated signals which have a largePAPR (Peak-to-Average Power Ratio). Effectively reducingthe PAPR of OFDM signals has been a challenging problemto minimize the bandwidth expansion and ICI (Inter-CarrierInterference) when a nonlinear amplifier is used.

There are many promising techniques to lower the distri-bution of PAPR of an OFDM signal such as SLM (SelectedMapping), PTS (Partial Transmit Sequences), clipping, etc [1]-[5]. Detailed explanations about other PAPR reduction meth-ods can be found in [5]. Although those techniques capable toreduce PAPR effectively, few techniques have been introducedin existing wireless communications standards. If we applysuch PAPR methods into an existing transmitter, we cansuppress the out-of-band emission which is interferences tothe neighboring channel or boost the transmit power withoutsignal distortion. Many conventional techniques are requiredto touch and control the data symbols or OFDM symbols justbefore or after IFFT operation. However, it is actually andlegally impossible to apply such techniques to existing LSI,for example, WLAN (Wireless LAN) card based on IEEE802.1 1a/g standard.

In this study, we propose a simple method to reducePAPR applicable to an existing OFDM system, that is, thesystem which is already installed inside an LSI. The basicapproach to suppress PAPR is based on SLM [3] which isone of distortionless methods. The conventional SLM needsto change the phase of each subcarrier, however, it is almostimpossible to perform the operation to the transmitter whichis a commercial product. The idea is to change raw binarydata which will be sent from an application software to lowerlayers such as TCP, IP, MAC, and PHY to achieve SLM. Thelower layers are generally implemented in WLAN cards orOS (Operation System). Before sending the binary data intolower layers, we change the binary data into the data whichwill generate an OFDM symbol with low PAPR. To estimatethe prospective PAPR of the OFDM symbol, emulating lowerlayer operations is necessary.

Although random phase rotation of each subcarrier is gen-erally used as a mapping function of SLM, we alternativelyemploy interleaving (permutation). We show the mappingfunction is comparable in the abilities of reducing PAPR.Moreover, as a new point of this study, we use PAPR thresholdand iterative SLM to reduce the computational complexity andtime delay due to calculating PAPR of OFDM symbols withdifferent mapping functions.

II. SYSTEM MODELIn this paper, we evaluate the PAPR performance of an

OFDM system. The OFDM system targeted in this study isan existing system, i.e., the system follows a wireless standardemploying OFDM system, for example, IEEE 802.11 a/g/nWLAN or ADSL, and so on. If some effective PAPR reductionmethods are included in the standards, our method maywork little. Since the transmitter of commercial products isimpossible for users to operate directly, we treat only binarydata sequences.The transmitter model is shown in Fig. 1. The model

consists of three parts, binary data, a block treating the datafor PAPR reduction, and a WLAN transmitter.

If the second part, which is in the middle box in Fig. 1,doesn't exist, the model is the same as a normal WLANtransmitter. The block consists of emulators of first to thirdlayer operations. In this case, we assume that these three layer

0-7803-9206-X/05/$20.00 ©2005 IEEE

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Fig. 1. Transmitter Model.

emulation is required to generate the same OFDM signal withthe signal WLAN transmitter generates.The second to fourth layer (below TCP layer) emulator

operates as the corresponding parts in WLAN transmitter andthe OS. In this study, however, we assume the output ofMAC layer is random data instead of actual data, becauseour objective is to examine the possibility of PAPR reductionby our method.

The binary data from the emulator are encoded by convo-lutional code with rate R and the constraint length K, theninterleaved and modulated into BPSK or M-QAM symbol.The number of parallel data symbols and pilot symbols areJVSD and Nsp, respectively. Scrambler generates randombinary sequence, then mapping block maps the sequence intoBPSK symbol which becomes a pilot symbol.

After the IFFT (Inverse Fast Fourier Transform), GI is addedto the output time sequence, and a windowing function isapplied to the sequence. The resulting baseband OFDM signalduring (O < t < Ts) is given as follows.

NST12 (j2rk (t - TOI)s(t) = W(t) E dkNsTk/2 p ( TFFT )

(1)where NST is the number of total (data and pilot) subcarriers,dk is the k-th modulated data symbol, TGI is GI duration,TFFT is FT1 window duration, TS = TFFT+TGI is an OFDMsymbol duration, and w(t) is a raised cosine windowingfunction defined as follows,

(i 2(7 o5+ t I

W (t) = 1

tsin (r 0O5 _- T)

Ti,....r. t

22r" < t < TS- 2t.r (

TS-1r < t < TS+ 7ir.(2)

where Ttr is transition time.The PAPR of the OFDM symbol is defined as

max IS (t) 12PAPR= O<t<T . (3)

E [Is(t)12]After PAPR calculation, the value is compared to a preset

threshold PAPRth. If the PAPR is less than PAPRth, thebinary data are sent to WLAN transmitter. Otherwise, thenext mapping function is tried whether the OFDM signal

"~-2

-~~~~-4~~p=

6-6 /

O -8 / /IBO=OdB-8

10

-10 -5 0 5Input Amplitude Level [dB]

Fig. 2. AM/AM conversion of an SSPA.

has smaller PAPR than the threshold or not. The iteration iscontinued to reach the maximum number of iterations Nit.To evaluate transmit out-of-band emissions due to nonlinear

amplifier in the WLAN transmitter, we assume an SSPA (SolidState Power Amplifier) is installed in the transmitter. As amodel of SSPA, we use Rapp's model of SSPA nonlinear-ity [1]. The AM/AM conversion can be shown as

9(A)=- A(1±+A21p) 2

(4)

where A is the amplitude of SSPA input signal and p is thesmoothness factor of SSPA. We ignore the effect of AM/PMconversion [1]. The characteristic of AM/AM conversion isshown in Fig. 2. The IBO (Input Back-Off) = 0 dB is definedas the input power with A = 1.

III. SLM (SELECTED MAPPING)

In this section, we briefly introduce conventional SLM andthe proposed method which is iteration based SLM.

The mechanism of reducing PAPR of an OFDM signalby SLM is introduced in the following sentences. A datasymbol sequence is applied to one of Ml mapping functions.The mapping functions are prepared to generate differentsequences. The OFDM signals are generated by IFFT basedon the sequences. If different mapping functions are appliedto the data symbols, usually the shape of the OFDM signalalso becomes different. Therefore, the PAPR value changesaccording to the selected mapping function. By selecting thesignal with minimum PAPR, it is desirable to generate quitedifferent signal shape by different functions to reduce thePAPR effectively.

In conventional SLM methods, a phase rotation is appliedto the modulated symbol. However, as described above, themapping function is impossible to implement. As an alterna-tive mapping function, we propose to use interleavers. Thatis, the order of binary data is changed according to an orderdefined by each interleaver.

405

Although it is crucial to find an optimal interleaver set inthe sense of PAPR reduction, that is beyond the scope of thispaper. A pseudo-random interleaver is considered in this study.The order of the interleaver is determined by the decimal valueconverted from a state of binary shift registers which generatesan m-sequence. As shown in the next section, this pseudo-random interleaver works well in the system model. Althoughthe result is not shown in this paper, PAPR reduction capabilityof the interleaver without coding is a little weaker than pseudo-random phase rotation when the number of mapping functionsis increased.The SLM needs to generate multiple OFDM symbols to

construct an OFDM symbol from a data set. Therefore, ad-ditional computations for PAPR reduction are required. Soft-ware implemented SLM will calculate sequentially estimatedPAPRs. In this case, if the number of mapping functions M1 isfixed, Ml - 1 times of computational effort and time delay arenecessary. Due to the additional computations, the proposedmethod is not suitable for a delay sensitive application.To minimize the total spent time for additional calculations,

we propose iterative SLM with PAPR threshold. At first, Mdifferent mapping functions are prepared, and the maximumnumber of iterations Nit is set as Nit = Ml. When anOFDM symbol whose data are permuted by an interleaver isgenerated, the PAPR is calculated, then the value is comparedwith the threshold PAPRth and the previous values. If thePAPR is lower than PAPRth, the mapping function is selectedas the mapping function for the OFDM symbol. Then theoperation shifts to that for the next OFDM symbol. If not, thePAPR is compared with the PAPR calculated in the previousiteration process. Based on those PAPRs, the mapping functionwhich achieves lower PAPR is selected. These operations arecontinued through OFDM frame. Unfortunately, if adequatemapping function is not found and the number of iterationsreachs to Nit, the OFDM symbol whose PAPR minimumamongst Nit symbols will be transmitted.To reduce the additional computation, Nit must be mini-

mized with keeping the required PAPR. The proposed methoddoesn't always use every mapping function, it can be expectedthat the computational time for SLM dramatically decreases.Although the iterative SLM sometimes generates the signalwith higher PAPR than the threshold, it does not matter if theoccurrence is below some level.

IV. NUMERICAL EXAMPLESIn this section, numerical results of the proposed iterative

SLM are illustrated. The common simulation parameters areshown in Table I.The CCDF (Complementary Cumulative Distribution Func-

tion) of PAPR calculated from COFDM signals using iterativeSLM based on interleaver mapping functions is shown inFig. 3. The number of iterations is set at Nit = 1, 2,4, 8, 16.Here, the CCDF properties of conventional SLM with randomphase rotations as a mapping function for different numberof mapping functions Ml = 2,4,8,16 are also shown bydashed line. In Fig. 3, the worst (right most) curve is the

TABLE ISIMULATION PARAMETERS.

100

0 1(

Number of data subcarriers NSD 48Number of pilot subcarriers NSp 4Number of total subcarriers NST 52

Oversampling factor 4FFT point NFFT 256Modulation scheme 16QAMCoding scheme Convolutional CodingCoding rate R 1/2

Constraint Length K 7#Mapping functions M 16

Maximum number of iterations Niit 16PAPR threshold PAPRth [dB] 7

HPA model SSPA Rapp modelSmoothness factor p 3

8 9PAPR [dB]

Fig. 3. CCDF of PAPR for various number of iterations. Dashed linesare CCDF of PAPR with conventional SLM for various mapping functionsAl' = 2,4,8,16.

PAPR performance of COFDM without PAPR reduction, i.e.,Nit = 1.From the figure, we can see the proposed method sharply

suppress the generation of PAPR larger than the thresholdwhen Nit = 16. If the iteration number decreases, suppressionof PAPR becomes looser in the low probability region. In theregion where PAPR is larger than the threshold (PAPRth =7[dB]), the curves of the iterative SLM and conventional SLMwith Nit = M are similar to each other. This means that theperformance depend almost nothing on differences of mappingfunctions, i.e., pseudo-random interleaver and random phaserotation. On the other hand, if PAPR < PAPRth, thePAPR of conventional SLM distributes lower than that of theproposed method. This is because the conventional methodfinds the minimum PAPR and the mapping function from morecandidates than the proposed method.The CCDF of PAPR of COFDM symbols with threshold

based iterative SLM is shown for various numbers of thresholdin Fig. 4. The number of iterations is Nit = 16 in this figure.PAPR thresholds are set as PAPRth = 5,6,... , 11[dB].

406

-4-- PAPR5h= 10dB

< ~~~~~E3PAPRth= 9dB

/ i PAPRth= 8dB

/i PAPRth= 7dB

i--- PAPRth=6dB-E PAPRh=5dB

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Number of Iterations N.

it

Fig. 4. CCDF of PAPR of COFDM symbols with threshold based SLM.(Nit 16)

Fig. 5. Cumulative distribution of the number of iterations to lower thethreshold

Because Nit is large enough, when PAPRth is larger than

7dB, PAPR is completely suppressed below the threshold. Thethresholds of 5dB and 6dB seem no effect as the iterative SLMin this condition (Nit = 16). However the performance issimilar to that by the conventional SLM. It can be obtained thatthe proposed method can sufficiently suppress the occurrence

of large PAPR..The cumulative distributions of required number of itera-

tions until PAPR by a mapping function lowers the thresholdis shown in Fig. 5. The simulation condition is the same as

Fig. 4. Inadequate selection of threshold values results that a

PAPR lowers the threshold too many or too few times. It iscrucial for the iterative method to select the suitable thresholdconsidering the system specification and allowable computa-tional complexity and delay (Nit). Since the probability cross

0.5 in small number of iterations, we use the threshold of 7dBin this study. SLM is some kind of selection diversity schemeto reduce the PAPR. Therefore, PAPRs by different mappingfunctions should be independent amongst the candidates. Inthe iterative method, the probability of satisfying the thresholdor not should be equivalent to maximize the diversity gain.The relative PSDs (Power Spectrum Density) of transmitted

signal with HPA and without HPA are shown in Figs. 6 and 7.In both figures, thick line shows the transmit spectrum maskregulated in the IEEE 802.1 la standard [6]. PSD of transmittedsignals must be below the mask.When linear amplifier is used (Fig. 6), the curves for

different number of iterations are overlapped each other. Sincethe proposed method changes only binary data, the generatedsignals are never distorted.

If an SSPA is assumed in the transmitter, out-of-bandemission characteristics vary with the IBO values as shownin Fig. 7. Smaller IBO decreases a margin to the spectrummask. In the figure, we set the number of iterations as Nit =1, 2, 4, 8, 16. It is obviously that spectrum emission decreaseswith increase of IBO. Increase of !Vit is effective for the cases

10 15 20Frequency [MHz]

Fig. 6. Power spectrum density (PSD) of OFDM signals after the iterativeSLM for various number of iterations. Thick line shows transmit spectrummask regulated in the IEEE 802. lIa standard.

of Nit = 2 or 4. Additional 2 or 3dB of margin can beobtained by the proposed method when IBO = 7, 9[dB] at thefrequency is around 11MHz. This means that the transmittercan increase the transmit power by 2 or 3 dB without increaseof interferences to neighboring channel. Moreover, largernumber of iterations such as Nit = 8,16 shows almost thesame performance and a gain from Nit = 4 is so little thatexcess iterations are not necessary.

V. CONCLUSION

In this study, we propose a PAPR reduction method forexisting OFDM system. The proposed method interleavesbinary data when an OFDM signal is expected to have largerPAPR than a threshold. The method continues to compare thePAPR by an interleave and the threshold until the requiredPAPR is satisfied or reaching to the maximum iterations. This

407

100

8 9PAPR [dB]

12

10

CA -10

e 20u

; -30C)

0

-40c 0X4 -50'

T 5 ------- ~~~~~~~~~~. .= 1IBO=3dB Nt=l

-/ -N=2

N. =4IBO=5dB N =8

-N.=16

- Linear amp.-Spectrum Mask

IBO=7dB

IBO=9dB

5 10 15 20Frequency [MHz]

25 30

Fig. 7. PSD of OFDM signals with the iterative SLM after SSPA. Theback-off is set at IBO = 3, 5, 7,9 dB. The curves by the same number ofiterations are shown by the same line property for different IBO. The thickblack line shows the PSD of OFDM signals through linear amplifier.

method effectively reduce the additional computations andspent time for PAPR reduction. We have evaluated the effectof the proposed method through computer simulations basedon the parameter of IEEE 802.1 la standard.The interleaver works well as a mapping function of SLM

like conventional random phase rotations. In the thresholdbased SLM, it is crucial to select a suitable PAPR thresholdfor the system specifications and requirements. The evaluationof out-of-band emission of COFDM signals through SSPAindicates that the number of iterations suitable for the systemis 2 to 4 in the system. By the PAPR reduction method, wecan boost the transmit power by 2 to 3 dB without additionalsignal distortion.

As a future work, we would like to compare the proposedmethod to the other PAPR reduction methods applicable toexisting OFDM systems. By considering the spectrum shapeof the transmitting signal, it should be determined an appro-priate threshold value and minimized the number of requiredmapping functions.

ACKNOWLEDGMENTThe authors would like to thank anonymous reviewers for

their useful and helpful comments. Some of them are toughfor us to solve within a limited time. We sincerely would liketo address all the problems.

This research was partially supported by Fujitsu Laborato-ries Limited.

REFERENCES

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[2] X. Li and L.J. Cimini, Jr., "Effects of clipping and filtering on theperformance of OFDM," IEEE Commun. Lett., vol.2, no.5, pp.131-133,May 1998.

[3] R.W. Bauml et al., R.F.H. Fischer, and J.B. Huber, "Reducing the peak-to-average power ratio of multicarrier modulation by selected mapping,"Electron. Lett., vol.32, no.22, pp.2056-2057, Oct. 1996.

[4] S. Muller and J.B. Huber, "OFDM with reduced peak-to-average powerratio by optimum combination of partial transmit sequences," Electron.Lett., vol.33, no.5, pp.368-369, Feb. 1997.

[5] L. Hanzo, M. Munster, B. Choi, and T. Keller, OFDM and MC-CDMAfor Broadband Multi-user Communications, WLANs and Broadcasting,John Wiley & Sons Ltd, Chichester, England, 2003.

[6] IEEE, Supplement to Part 11: Wireless LAN Medium Access Control(MAC) and Physical Layer (PHY) specifications: Higher-speed PhysicalLayer in the 5GHz Band, IEEE Std 802.1 la- 1999, 1999.

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