Artificial signals add'ition for reducing PAPR ofOFDM systems

Desire GUEL, Jacques PALICOTSUPELEC/IETR,

Avenue de la Boulaie CS 47601F-35576 Cesson-Sevigne cedex

E.mail: desire.guel,jacques.palicot} @supelec.fr

Abstract One of the major drawbacks of OFDM modulation is the effects but, unfortunately, they would increase the costthe large envelopefluctuations which either result in an inefficient ise of the system [8]. Some probabilistic schemes such as se-of high power amnplifers (HPA) or decreased transmission system lective mapping (SLM) scheme [9], partial transmit sequenceperformance. Peak-to-Ayerage Power Ratio (PAPR) is a very wellknown measure of the envelope fluctuations and has become the cost (PTS) [10] bave also been proposed, to reduce PAPR. Thesefinctiown sed to evlluateatnd design OFDM systemsc techniques require side information to be transmitted from the

In this poper, we propose a PAPR reduction scheme known as transmitter to the receiver to recover the original data blockadding signal methodfor which the principle is to reduice the PAPR from the received signal. Another class of methods knownof the OFDM signals by adding several artificial signals. It is an as adding signal technique has also been proposed to reduceextension of the method that we have proposed in [1i. The major PAPR and seems to be promising. Its techniques include toneadvantages of this technique include downward compatibility no reevtion (TR) [I

be sin g Itcarrier rdctonperformance degradation and no transmission of side information. A reservation (TR) [11] using ghost carriers for PAPR reductionmethod is said to be downward compatibility if its implementation in [12]. A classification of methods that have been proposed toa transmitter does not imply modifications in the associated receiver address nonlinear power amplification of highly fluctuatingAccording to simulation results, the method outperforms the PAPR- signals in telecommunications is presented [13].reduction Performance presented in [f!-For example, at 102 Of In [], we have proposed. a technique for PAPR reduc-the Complen entary Cuimulative Distribuition Function (CCDF), thePAPR is reduced about 3. dB for 5 artificial signals addition tion of the OFDM signals known as adding signal principlewhereas this reduiction is about 1.5 dB for method [1] which is the whose major advantages include downward compatibility, lowcase of one artificial signal addition. complexity, no performance degradation (no degradation of

Keywords Orthogonal Frequency Division Multiplexing the BER) and, no transmission of side information. In order(OFDMI), Peak-to-Averalge Power Ratio (PAPR), Artificiazl Signalls. to outperform the PAPR-reduction performance of [1], we

I. INTRODUCTION propose, in this article, a PAPR-reduction method based onan iterative process of [1]. Thus, for k-iterations, the iterative

The demand for high data-rate services over wireless process generates k-artificial signals, added to OFDM signalcommunications has been increasing very rapidly in recent to reduce its PAPR.decades. These services require reliable data transmission over The paper is structured as follows. In section II, a briefwireless channels which are subjected to many degradations description of the PAPR of OFDM signals is given. In sectionsuch as noise, multipath fading and interference. Orthogonal III, the proposed, PAPR-reduction scheme is described andfrequency division multiplexing (OFDM) [2] is a transmission the PAPR-reduction algorithm is given. In section IV, thetechnique that offers robustness with respect to multipath complexity of the method is evaluated in terms of additions,fading. Because of its many advantages, OFDM has gained multiplications and divisions number. Section V describes themuch popularity and has been used, widely in variety of simulation results. Conclusions are drawn in section VI.communication systems. Well-known examples include digital II. PAPR Or OFDM SIGNALSaudio broadcasting [3], digital video broadcasting [4], theIEEE 802.1L la and IEEE 802. 1lg standards for wireless local Several notations are employed to define the power ratioarea networks [5]. (PR) of a signal. Let us denote the data block of length NDue to the large number of subcarriers, the OFDM signal as a vector X = [ XO, Xl, , XN-1 T

, where Nhas a high Peak-to-Average Power Ratio (PAPR) which makes is the number of subcarriers. The duration of the block X issystem performance very sensitive to distortion introduced by Ts. Each symbol in X modulates one of a set of subcarriersnonlinear devices such as high power amplifiers (HPA) [6]. L fo, fi, fN 1 ]. The N subcarriers are chosen to

In an attempt to reduce the distortions caused by the be orthogonal, that is fr = NITS. The complex envelope of thenonlinear HPA, several techniques have been proposed to transmitted OFDM signal is given by:reduce the PA:PR of O:FDM; signals. These techniqu.es includ.e N-1ampltudciping cl.ipping_ is at_nonlinea pro es.s, itdgades (t). .................=>wN#et . . 0 <tT . (Ithe 'bit-error-rate (:B:ER) of the system and increases the ou.t-of- =band radiation [7]. Coding and bandpass filtering can reduce The PAPR of the trans:mitted signal in (1) is defined as:

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2 magnitude of the time-domain OFDM symbol exceeds themax Jr (t) magnitude threshold, (Ck), an artificial signal is created and

A te[OT~]PAPR[,T] , (2) filtered, by the digital passband filter, it is then carried by anX intermediate frequency Afk and finally added to the time-

where £-= E X (t) 2 } is the OFDM signal power and. domain OFDM symbol. The digital filter based on FFT/IFFT£ f.} is the statistical expectation operator. pair, mitigates the part of artificial signals generated in the

Usually, the continuous time PAPR of (t) is approximated OFDM signal bandwidth so that there is no transmission,. . .... -I . . | . o~~erformance degradatilon (BER degrad.ation).using the discrete time PAPR, which is obtained from the fio

samples of the OFDM signal. In r14], it is shown that an B. Principle of PAPR Reductionoversampling factor of 4 is enough to estimate the continuous Let (t) be an OFDM baseband complex signal during aPAPR given in equation (2). block period in continuous time-domain. It can be expressed

III. CONCEPT OF REDUCING PAPR VIA SEVERAL below.ARTIFICIAL SIGNALS

The PAPR reduction scheme proposed in this paper is to (t) I (t) iQ (t), (3)restrict the envelope of OFDM baseband signal by adding where I (t) is the inphase signal and Q (t) the quadratureseveral artificial signals. This scheme uses the principle of phase signal. The corresponding passband signal 5 (t) carriedthe method proposed in1l], unlike this method, the technique by ft is given by:proposes to iteratively apply L1], which leads to the adding ofseveral artificial signals for PAPR reduction. x (t) = I (t) cos t2ftt} - Q (t) sin {2ftft}. (4)

A. Description of the technique Let us suppose the detailed block diagram of the artificialThe reduction technique consists of reducing the complex signal generator shown in the Fig.2.

envelope of the OFDM signal just before the HPA. The idea isto generate some artificial signals at different carrier frequen- Ck Afkcies so that, added with OFDM signal, decreases considerablyits PAPR. In contrast to the method that we have proposedin [l], the new technique allows to add P-artificial signals for Qk-l QakPAPR-reduction, where P is the iterations number. For P =1 hk-i akF

the PAPR-reduction scheme generates one artificial signal and - I Xin this scenario, it is equivalent to the PAPR-reduction scheme F3proposed in [1] The PAPR-reduction scheme becomes moreinteresting for P > 2.

Fig. 2: The System of generating artificial signal.k-iteration

Let us suppose Yk (t), the resulting baseband signal after k-iterations. Obviously, Q0 (t) = (t), where x (t) is the OFDM

~ IFFT X 'IPA baseband signal given in (3). It can be expressed by:ADDING DIGITAL

Ck SIGNAL f k (t) = (t) + - t (s)Afk GENERATOR FILTER k

where aik (t) is the baseband. artificial signal generated, fromFig. 1: The OFDM Transmitter. the multicarrier signal Pk- (t) to the k-th iteration and given

by:Fig. 1 illustrates the transmission system block including

mainly an artificial (adding) signal generator and a digital ak (t) = -a, (t) + JQak (t) (6)filter. The OFDM transmitter receives framed data at the According to the generating system of a ificial signal, thesymbol generator (modulation scheme/IFFT) and generates multicarrier signal Yk-1 (t) is written as:a time-domain OFDM symbol based on the framed data.The IFFT block transforms the frequency-domain vectors-to time-domailn, resulting in a time-domain OFDM symbol.Y-i()mc k(t+jQit)The artificial signal generator includes a magnitude threshold. and its complex elnve:lope is written as fo:lLlows:comparator. fLet us suppose that the system is at the k-th

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The parameters Iaa (t) and Qak2 (t) are determined in [L] where DF {.} is the filtering function.according to the following principle: The Table 1 shows the algorithm of PAPR reduction scheme.

Let Ck, the maximum permissible magnitude at the k-thiteration. Step 1

Set the number of iterations P.(i) If 7Zk-1 (t) > Ck, the adding signal ak (t) iS Input Ck and Afkt for k 6 I= {1, P}.

generated such as Input the OFDM baseband symbol F.Step 2

gYF-i (t) + Clk (t) = c2 (8) for k C-I compute lZk-1 using (7).(t) k (t) 2 If (Rk-1 ._ COO-lOn the contrary, i.e for lkl? (t) < Ck, the adding Compute first "Iakand Qak using (10),then &k using (6),

a k .

) Otherwise set aik = 0.Compute bk using (13).

Let a time t such as: JRk-l (t) > Ck, the problem lies in Compute_ , using (5).finding the parameters 'Ik (t) and Qk (t) which check (8). Table 1: The proposed algorithm for PAPR reduction.Developing (8), we obtain:

(t)]2+ (t)]2 2 IV. COMPLEXITY ANALYSIS OF THE PROPOSED[Ik-1 (t) +I(t)a + [Qk-1 (t) + Qa (t)] C. (9) ALGORITHM

In Li], the equation (9) is solved and the solution is given We now evaluate the complexity of the algorithm usingby (10). the number of real additions, real multiplications and real

divisions.Ia k F (Ik-1, Ck) Ik - Ik) 1 Let us consider the L-times oversampled time-domain sam-

'(10) ples &k,n, Yk-1,n and Rk-l,n defined as

{Qak aF(Qk- ,Ck)aa(lk Qk_F)~~~~~~~~~~~~~~~~~~~s Tnrr5,k,nz =ak -yl) Yik-1,n = Yk-1 NLs)Now let us suppose that the iterations number is P, then kL k Y

zn i\ > t n r7n \~~~~n

the system generates P-artificial signals and the resulting kk-1,n lZk-1 (NLT )multicarrier baseband signal fjp (t) can be expressed as: In step 2, using (6) and (10), dk,n is calculated as

ak,n = Yk-1,n 1 hr } with the probability vkyp (t) =~S(t) + Z t?tk (t) e2iAfkt (11) Pr {Rk-1,n > Ck and k0n = 0 with the probability 1 - k.

k=1 Let us denote k = ft : Rk-1,n > Ck} and Nk theThe radio frequency signal yp (t) associated with the base- size Of 0k. So, NZk = VkNL. To simplify the calculations,

band multicarrier signal fip (t) is written as follows: let us suppose that Ck is the same in all iterations, i.e.Ck = C, Vk c [1, P] . Only the runtime complexity is con-

P sidered, and the complexity of the initialization stage can beyp (t) = (t) + R Idk (t) e2j7fktX (1L2)yp (t) _ (t) + =iv {ak (t) e2ofk}, (12) omitted since it occurs only once.

k=1 At the first iteration,where fk -f + Afk is the carrier frequency of the basebandartificial signal alk (t) generated at the k-th iteration and x (t) :-= fn Rn,0n> Cl and N< = v,NL.is the OFDM radio frequency signal given by (4). _ 2

Let DF f{. be the filtering function, and, let ak and, bk to As R0,n is a Rayleigh random variable, so vi = 1- 6 P. In

- ~~~~ ~ ~ ~ ~ ~~~~~~~N* -g- NL Vk > -1beo inptlhaan output f the digita file respectively, then the 15] it iS shlown thlat, N1v iS roughlyl constant in all iterations.signlszl ak and bk are 1ll ed y the flJlowingrlab11tion:. 7 c2

bk =1DF{-k}(13)NNL Vk>1Note that, the digital filter is based on FFT/IFFT pair and it Now, let us evaluate the complexity of the algorithm in themitigates the part of artificial signals generated in the OFDM case of using digital filtering and in the case without usingsignal bandwidth so that there is no BER degradation. digital filtering.

Using the digital filter for which the filtering function is A. Case without digital filteringgiven in (13), the radio frequency signal yp (t) after P-

itera: In this case, only the complexi of calculating k isconsidered. fFor P iterations, we estimate that the compXlexitof the a:lgorithm as

yp (t) =xs (t) + El? {DF {ak} (t e J fkt}, (14) . 3N4 P real additions,k~~~~~~1~~~~~.2N' P realL mlultiplilcations,

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* 2NrP real divisions. A. Effect of digital filtering on the BER peiformance andAs the number of iterations P does not depend on L and PAPR-reduction performance

N, the complexity of the algorithm without digital filtering is In order to explore the effect of the digital filtering on the( ). Forexample, N1 P=.95NLP 0.96NLP and quality of transmission and on the PAPR-reduction perfor-

0.72NLP for C 5 d;B, 3 dB and 1 dB respectively. mance, the PAPR-reduction algorithm is investigated without

B.Case with digital fiterPing digital filter; we used equation (12) and with digital filter; weIn this case, in addition to the complexi of calculating used equation (14), and the uncoded BER over an additive

Gaussian noise (AWGN) channel at the output of a conven-ak,, we have the complexity of calculating bk,n. The samplesbk, are the result of digital filtering Of k and are obtained tional OFDM receiver is simulated.by using NL-point DFT/IDFT pair. o

Using the decimation-in-time (DIT) radix-2 FFT algorithm Original OFDM[16], the complexity of a NL-point DFT with N,* nonzero L---------- PAPR-reduction (eq.14)inputs can be calculated as - PAPR-reduction (eq.12)

ADFT 3N* log 2 (Nl*) -3N* + 4,1 oX I ~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~I I(15) ->

M"DFT 2Nj* log2(N*) -7N + 12 10 -------

i~~~~~~~~~~~~~~~~~~~~--------

where ADFT and MDFT denote the number of real additionsand real multiplications for calculating a DFT respectively. z -------------

As the digital filter mitigates the pa of k,, generated in the <OFDM signal bandwidth, thus the NL-point IDFT has N --------------.--N (L -1) nonzero inputs, its complexity can be calculated I \using (15) with replacing N< by N, -2------

AIDFT 3Nr log 2 (Nr) 3Nr - -4 ------- ----------(16) ---

.M1DFT 2N* log2 (N )7Nr +12 \WM - 2N l 2tN 0 7N 12t 8 _ --------F--t-----9------t- ---------lWith the above discussion, the complexity of the algorithm I

with digital filtering for P iterations is: 3 -. . .. . * 10 l l 1?> S~~~1. Real additions: 4 6 8 10 12 143N*Plog (N1) + 3Nr log2 (Nr- 3NrP + 8P, X (in dB)

* Real multiplications:2N*PPlog2 (Nj) + 2N Plog2 (N Fg. 3 CC s ofthe OFDM system.- 5NP - 7NrP + 24P,

* Real divisions: 2N1 P . Fig.3 shows the effect of the digital filtering on the PAPRP does not depend on L and N, the complexity of the reduction performance for one artificial signal of PAPR-

algorithm is mainly linked to the complexity of the NL-point reduction. For example, at 10-2 of the CCDF, without digitalDFT/IDFT pair. filtering the PAPR of OFDM signal is reduced by 2.75 dB,

In practice, N > N4i.e. c > in (L), the complexity whereas with digital filtering the PAPR is reduced by 1.50r : r 47 Q1V r r 9is then approximated as 0 (N P log 2 (N y) dB. It can be concluded in view of the results that the digitalAbove complexity analysis shows that in the both cases ( filter creates a loss of performance in terms of PAPR reduction,

case of using digital filtering and, case without using digital but it guarantees a good, quality of transmission. Indeed, withfiltering), the complexity grows linearly with the number of the digital filtering there is no degradation of BER as showniterations P. in Fig.4.

V. SIMULATIONS B. The number of iterations P effect on the PAPR-reductionThe proposed technique was applied to an OFDM system performance

with 64-subcarriers and 16-QAM symbol mapping. The signal In this section, we study the PAPR-reduction as a functionwas oversampled by a factor of 4uAsing zero padding i fre- of the number of iterations P; P is also the number of arificialquency domain before the app:lication of the VPAPRlE-reduction signalLs. For the simrulation results, we use the digital filter toalgorithm. We apply the algorithm for VPAPR reduction of make sure that the fBER is not degraded..Tal... wit C 1 dBand.,.... .. _0 25 riteration, where BW is lbandwidth of the OFDM signal. reduction method at different P over an OFDM system with

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64-subcarriers and 16-QAM symbol mapping. As it mightbe expected, the PAPR reduction increases as the number of

Conventional BER artificial signals P increases. However, for P > 5, there is1o-17 r -BER(P=1) w/o Filter no significant reduction of the PAPR compared, to P = 5. At

BER(P=1) with Filter 102 of the CCDF, a PAPR reduction of 3.5 dB is obtained for5-artificial signals addition, whereas for 6-artificial signals ad-

X t dition, this reduction is 3.75 dB. According to the complexityanalysis in section IV, the system complexity grows linearly

1o02 L ---- , , . .. . L ...:! 2 .with P and as the PAPR reduction is not linearly dependent onU) P thus further increase in P does not improve PAPR reduction

± ~~~~significantly but increases linearly the system complexity. We17- ----- .have chosen P 5 as optimal value for further experiments.

i-3 L L Conventional BER_0 ---___

------ 10 ' - - -BER (P=1), with Filter---- - ---- >- - BER (P=3), with Filter

---- BER (P=5), with Filter-~~-~~-~~-~~r~~-~~-~~-~r~-~-~~~~~~ - ------------ --- --v-BER (P=6), with Filter

-4%1i0 i__ _-

0 2 4 6 8 10 12Eb/No (in dB) -2

10 ------

- R . .: - lSl-l .:-:fr i :-:fr ~~~~a:°-t-- -----0- - - 1- ------

0 _ _ _ _ = PAPR-reduction (eq.14), P=5 ------------t------------!-------------f--- ------------- ------

* PAPR reduction (eq 14) P-i ---~~~~~~~~~~---------PAPR reduction(eq 14) P 3 --~~~~~~~~~------------

PAPR reduction(eql4) P5 ~~~:L- --------------

_ _ _ W£1 PAPR-reduction (eq.14),P=6

I ~~~~~~~~~~10

i 0 2 4 6 8 10 12101 EbNo (in dB)

11111 Fig. 6BERialOFD----perormnce for-----P--36---i- asgnl

PAPR-red -to (eq. 4-, P= ___L_ _-- ------of PAPR reduction.

L ----------- ;--------- 4.\--------0\-----------2Fig.6shows the BER performnances over an additiveGaus-PAPRreductin\ 4 sian noise (AWGN) channel for P 1, P 3, P 5 and

-02 _____L_____ __ ___ _____ P= 6. fIt shows that for each situation, fBER is not degraded._ _ ___PLPRreductiont (eq14, __ by the PAPR reduction scheme.

F~~~~~~ Ct Effect o .-,:-f'P ove th spectra regowt

,tf t,* Fig.7 shows the effect of the artificial signals nu.mber on the

- t .>X-- r--------,----- l tpower spectral d.ensit (:PS:D) for aln O:FDM: system with 64-T 0 | # . \ ~~suhcarriers employing 16 QAXM. The simu.lation results show

0-4o

1 2 that larger the number of artificial signals, la.rger will be the4 6in 8d10B) spectral 2reg1rowth.2. (in dB) Table 2 shows the average power increase of the transmitted

Fig. 5: CCDFs for adding of P =1, 3, 5, 6-artificial signals s;igal when the peak power is redu.ced lby the addition of F-of PAPR reduction. artificia:l signals for PAPR reduction. It can be appreciated

that a flower increase of the signafl power is olbtained at largervalLues of P. Therefore, the choice of the nppropriate P wilul

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l-l0 1) According the simulation results shown by Fig.7: larger

the number of artificial signals, larger will be the spectral---------- ----------- -------=I-------------------------- regrowth. In further work,weplantofindtheoptimal

thresholds that minimize both the PAPR and the spectralP=3:SPECTRAL ~~regrowth.

RSPEGROWA 2) Using the Cognitive Radio (CR) approach, we plan tom~L 1V.4 X 1apply this technique of PAPR reduction in software radiosignals. The idea is to exploit the free bands (unlicensedbands) to carry artificial signals in order to reduce the

= -20 _ _PAPR of the software radio signals.S ~0 Y _ 1ELREFERENCES

[1] D. Guelo J. Palicot and Y Louet, "'A Geometric Method for PAPR* Reduction in a Signal Adding Context for OFDM Signals, DSP 2007",

-30 - . - pp. 347-350, 1-4 July 2007.

A____ ORIGINAL \ 9[2] J. Bingham, 'Multicarrier modulation for data transmission: an ideaOFDM whose time has come", IEEE Commun. Mag.,pp. 5-14, May 1990.

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[6] C. Rapp "'Effects of HPA-nonlinearity on a 4-DPSK/OFDM signalfor digital sound broadcasting system"' Proc. Second Euro. SatelliteCommun., pp. 179-184, Oct. 1991.

[7] X. Li and L. J. Cimini7 Jr., "Effects of clipping and filtering on thestrongly depend on the wireless system scenario because the performance of OFDM", IEEE Commun. Lett., vol. 2, pp. 131-133, Maysystem complexity grows with P. 1998.

[8] H. Ochiai and H. Imai, "Performance analysis of deliberately clippedP I1 3 5 6 OFDM signals", IEEE Trans. Commun., vol. 50, pp. 89-101, Jan. 2002.

[9] R. W Bauml, R. F. H. Fisher and J. B. Huber, "Reducing the Peak-to-Average Power Average Power Ratio of Multicarrier Modulation by Selected Mapping"increase (in dB) 0.030 0.097 0.147 0.170 Elect. Lett., vol. 32, no. 22, pp. 2056-57, Oct. 1996.

[10] A. D. S. Jayalath and C. Tellambura, "Adaptive PTS Approach forTalblLe 2: Power increase dB of a 64-subcarriers OFDM Reduction of Peak-to-Average Power Ratio of OFDM Signal", Elect.system due to the addition of P-artificial signals for PAPR Lett., vol. 36, no. 14, pp. 1226-1228, July 2000.

reduction. [11] J. Tellado, "Peak to Average Power Reduction for Multicarrier Modu-lation", Ph.D. dissertation, Stanford Univ., 2000.

[12] S. Zabre, J. Palicot, Y. Louet and C. Lereau, "Reduction ofOFDM Peak-to-mean envelope power ratio using ghost carriers', Wireless and Mobile

VI. CONCLUSION Communications, ICWMC, pp. 37-42, March 2007.[13] Yves Louet and Jacques Palicot, "A classification ofmethods for efficient

power amplification of signals', Annals of Telecom, to be published inIn this paper, a new technique for reducinag the PAPR of 2008.

OFDM systems via addition of several artificial signals in [14] C. Tellambura, "Improved phase factor computation for the PAPRorder to enhance the power amplifier efficiency is presented. reduction of an OFDM signal using PTS'" IEEE Commun., Lett., vol.5,no.4, pp,1135-1137, Apr, 2001,The major advantages of this technique include downward [15] L. Wang and C. Tellambura "Analysis of Clipping Noise and Tone-compatibility, good quali of transmission (no BER degra- Reservation Algorithms for Peak Reduction in OFDM Systems"', IEEE

dation) and no transmission of side information. For P > Transactions on Vehicular Technology, Volume 57, Issue 3, pp. 1675 -- 1694, May 2008.2, the method, outperforms the PAPR-reduction performance [16] Douglas L. Jones Decimation-in-Frequency Radix-2 FET'presented in [1], where P is the number of artificial signals. http://cnx.org/content/ml201l8/latest.Simulation results show that the PAPR reduction increasesas the number of artificial signals P increases. However, forP > 5, there is no significant reduction of the PA PR comparedto P = 5. As the system complexity increases linearly with Pand furher increase of P does not improve -PAPR signficantly,we have chosen P =5 as optimal value.

T:he work carried out iln this paper has generated someareas of possible future study. Some suggested extensions andadditio:ns are given below.

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