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1 THE ISTITUTE OF ELECTROICS, IEICE Technical Report IFORMATIO AD COMMUICATIO EGIEERS OFDM PAPR (OFDM (PAPR PAPR Tomlinson-Harashima precoding (THP modulo (QAM PAPR PAPR (BER BER OFDM PAPR modulo A study of PAPR reduction scheme for OFDM signal transmission Kazuki TAKEDA and Fumiyuki ADACHI Dept. of Electrical and Communication Engineering, Graduate School of Engineering, Tohoku University , Aza-Aoba, Aramaki, Aoba-ku, Sendai, , Japan kazuki@mobile.ecei.tohoku.ac.jp, adachi@ecei.tohoku.ac.jp Abstract Orthogonal frequency-division multiplexing (OFDM has a problem of its high peak-to-average power ratio (PAPR since the data symbols are multiplexed using a lot of orthogonal subcarrier frequencies. Many works have been done on the PAPR reduction for OFDM signal transmission which are used to re-shape the signal spectrum or waveform such that the different data are not coherently combined at a time. In this paper, we propose a PAPR reduction scheme which exploits the principle of the modulo operation used in Tomlinson-Harashima precoding (THP. A quadrature amplitude modulation (QAM signal is superimposed on the data symbols to reduce the PAPR. We show by computer simulation that the proposed scheme offers a large PAPR reduction without using any side information. Also we discuss the theoretical bit error rate (BER performance of the OFDM transmission using the proposed scheme. Keyword OFDM, PAPR, modulo. (OFDM [,] [3] OFDM OFDM (PAPR [] PAPR PAPR [5]-[] OFDM Clipping&filtering[5,6] OFDM (CT[7] Copyright 00 by IEICE

2 OFDM Selective mapping (SLM[,9] PAPR Active constellation extension (ACE[0] PAPR [] PAPR OFDM PAPR Tomlinson-Harashima precoding (THP[,3] modulo [] (QAM PAPR PAPR QAM modulo PAPR modulo (BER modulo BER modulo BER QAM PAPR 3 BER BER BER 5. QAM PAPR.. THP における modulo 演算 modulo [] THP[,3] THP THP modulo modulo ( y ( y I Q = {( x = {( x ( I ( Q + M modm} M + M modm} M (. (I (. (Q M x y modulo ( x (, y IorQ ( M, M ] ( ( y = x + Mz, z [ L,,0,, L] so that y ( M, M ] M<y (IorQ M z.. QAM 信号重畳型 PAPR 低減法の動作原理 ( z ( M QAM ( QAM PAPR THP modulo PAPR ( QAM THP c IFFT OFDM PAPR QAM.3. QAM Im Re 6QAM data signal constellation 6M M M Im M M ( Re 0 M M 6M M M Superimposed QAM signal constellation (6QAM QAM.3. 送受信信号 (FFT c OFDM PAPR OFDM ( Pure OFDM {D(; k=0~ c } c (IFFT OFDM {d(; t=0~ c } t=0,,, c d( c t d ( = D( exp jπk (3 c k = 0 c {d(} PAPR PAPR [{ d( } ] max [ d( ] t [0, c ] = ( E[ d( ] IFFT PAPR PAPR[{d(}] QAM k D( QAM

3 k S = D( + MZt (5 ( Z IorQ Z t ( t [ L,,0,, L] [{ s( } ] Zt = arg min PAPR (6 Z [...,,0,,...] t {s(; t=0~ c } QAM c t s( = S( exp j k = d( + Mzt ( π c k = 0 c (7 c t Mz t ( = MZt exp jπk ( c k = 0 c {s(} c (FFT {R(; k=0~ c } R( R( = = PH S( + ( PH { D( + MZ } t + ( P QAM H( ( k E[ H( ]= E[ ( ]=σ THP modulo Dˆ = R( / PH + MZ = D( + M{ Z + Z t r r } + ( / PH (9 (0 Z r ( ˆ ( D IorQ ( M, M ] modulo Z r (=Z t (.. 重畳する QAM 信号の選び方. QAM {MZ t (; k=0~ c } PAPR IFFT PAPR Z t (IorQ (>> QAM E[ s( ]>>E[ d( ] PAPR QAM PAPR {MZ t (; k=0~ c } Z t ( {0, 0±j, ±+j0} QAM OFDM Z t ( 0 k M c QAM 0 M 0 Z t ( ±± {Z t (} {D(+MZ t (} 6QAM M = / 0 MZ t ( 0 5 6QAM 5 modulo (0 QAM {MZ t (; k=0~ c } QAM IFFT QAM QAM IFFT PAPR M = IFFT PAPR PAPR PAPR M QAM ± ±j {D(+MZ t (} c IFFT PAPR QAM PAPR G G PAPR Z t (=+j 0 Im Z t (=0+j Z t (=+j 0 Z t (=0+j 0 Z t (=0j Z t ( {D(+MZ t (} 3. BER 3.. チャネル利得が与えられたときの瞬時 BER QAM Re

4 (0 {MZ t (; k=0~ c } modulo [5] THP BER modulo BER BER [5] H( 6QAM 6QAM 56QAM BER p e (γ p e ( γ erfc 3 erfc 7 erfc 6 erfc 65 ( γ / + erfc( γ ( M / ( γ /0 + erfc( γ ( M 3/ 0 ( γ / + erfc( γ ( M 7 / ( γ / 65 + erfc( γ ( M 5/ 70 6 for for for 6QAM, for, 6QAM, 56QAM ( γ = ( P + ΔP/ σ H (ΔP QAM QAM BER modulo BER 3.. 平均 BER H( γ p r (γ [6] γ p r ( γ = exp ( Γ Γ Γ P/σ ( ( BER P = ( γ ( γ γ p p d e 0 e 3 r + + / Γ + + 0/ Γ ( M / ( M / + / Γ for, ( M 3/ 0 ( M 3/ 0 + / Γ for 6QAM, / Γ / Γ 6 ( M 7 / ( M 7 / + / Γ for 6QAM, ( M 5/ 70 ( M 5/ 70 + / Γ for 56QAM (3 β exp( α ( β = x x erf x dx ( 0 α α + β. QAM PAPR 6QAM 6QAM 56QAM M for, / 0 for 6QAM, M = ( / for 6QAM, 6/ 70 for 56QAM.. PAPR の累積分布特性 PAPR (CCDF Pure OFDM CCDF PAPR FFT PAPR CCDF 3 6QAM 6QAM 56QAM CCDF M =0,,,, M =0 Pure OFDM 3 CCDF M PAPR Pure OFDM( M =0 M = Pure OFDM 0% % PAPR.5dB 9.3dB QAM M PAPR 3 M = 0% % PAPR db M PAPR

5 M PAPR M = PAPR PAPR CCDF G=0,, 6, 6, 56 G=0 Pure OFDM G PAPR PAPR PAPR G PAPR 3 M G=6 56 PAPR M = G G PAPR.0E+00.0E-0.0E-0 M = M = 6QAM 6QAM 56QAM Pure OFDM ( M =0 M = M =.0E PAPR CCDF(.0E+00.0E-0 G=6 Pure OFDM (G=0 G= G=56 G=6.0E-0 M = 6QAM 6QAM 56QAM.0E (a M =.0E+00.0E-0.0E-0 G=6 G=56 M = Pure OFDM (G=0 G= G=6 6QAM 6QAM.0E-03 56QAM (b M =.0E+00.0E-0.0E-0 G=6 G=56 G= G=6 6QAM 6QAM 56QAM Pure OFDM (G=0 M =.0E (c M = PAPR CCDF(.. 平均 BER 特性 GI g = L= BER 5 E b / 0 ( BER ( modulo BER M M BER BER modulo BER [5] 5 6QAM QAM PAPR

6 BER BER modulo 5 M modulo BER BER.0E-0.0E-0.0E-03 M =0.0E E-0.0E-0 (a.0e-03 M =0.0E E-0.0E-0 (b 6QAM 6QAM.0E-03 M =0.0E E-0.0E-0 (c 6QAM 6QAM.0E-03 M =0.0E (d 56QAM 5 BER 56QAM 5. OFDM QAM PAPR PAPR CCDF BER QAM PAPR BER BER modulo PAPR QAM QAM modulo BER [] A. Czylwik, Comparison between adaptive OFDM and single carrier modulation with frequency domain equalization, Proc. IEEE Veh. Technol. Conf. (VTC, Vol., pp , Ariz, U.S.A., May 997. [] R. Prasad, OFDM for wireless communications systems, Artech House, 00. [3] 3GPP TR 5., Physical Layer Aspects for Evolved UTRA, v..0.0, June 006. [] H. Han and J. H. Lee, An overview of peak-to-average power ratio reduction techniques for multicarrier transmission, IEEE Wireless Commun. Mag., Vol., o., pp , April 005. [5] H. Ochiai and H. Imai, Performance analysis of deliberately clipped OFDM signals, IEEE Trans. Commun., Vol. 50, o., pp. -, Jan. 00. [6] X. Li and L. J. Cimini, Jr., Effects of clipping and filtering on the performance of OFDM, IEEE Comm. Lett., Vol., o. -, pp. 3-33, May 99. [7] T. Jiang, W. Xiang, P. C. Richardson, D. Qu, and G. Zhu, On the nonlinear companding transform for reduction in PAPR of MCM signals, IEEE Trans. Wireless Comm., Vol. 6, o. 6, pp. 07-0, Jun [] R. W. Bauml, R. F. Fischer and J. B. Huber, Reducing the peak-to-average power ratio of multicarrier modulation by selective mapping, Electronic Letters, Vol. 3, o., October 996. [9] H. Gacanin and F. Adachi, Selective mapping with symbol re-mapping for OFDM/TDM using MMSE-FDE, Proc. IEEE 6th VTC, Calgary, Canada, Sept. 00. [0] B. S. Krongold and D. L. Jones, PAR reduction in OFDM via active constellation extension, IEEE Trans. Broadcasting, Vol. 9, o. 3, pp. 5-6, Sept [] P. Boonsrimuang, K. Mori, T. Paungma, and H. Kobayashi, Proposal of simple PAPR reduction method for OFDM signal by using dummy sub-carriers, IEICE Trans. Commun., Vol. E9-B, Vol. 3, pp. 7-79, Mar. 00. [] M. Tomlinson, ew automatic equalizer employing modulo arithmetic, Electronics Letters, Vol. 7, o. 5/6, pp. 3-39, Mar. 97. [3] H. Harashima and H. Miyakawa, Matched-transmission technique for channels with intersymbol interference, IEEE Trans. Commun., Vol. 0, o., pp , Aug. 97. [] R. Fischer, The modulo-lattice channel: the key feature in precoding schemes, Inter. J. of Elec. and Commun., Vol. 59, o., pp. -53, Jun [5] K. Takeda, H. Tomeba and F. Adachi, Theoretical analysis of joint THP/pre-FDE for single-carrier signal transmissions, Proc. IEEE Wireless Communications and etworking Conference, Hungary, May 009 [6] 996

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