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Performance of OFDM Systems with Adaptive Nonlinear Ampli ers Je-hong Jong, Kyounghoon Yang , Wayne E. Stark, and George I. Haddad Department of Electrical Engineering and Computer Science The University of Michigan, Ann Arbor, Michigan, U.S.A. Department of Electrical Engineering Korea Advanced Institute of Science and Technology KAIST, Taejon, Korea Abstract | Orthogonal frequency division multiplexing OFDM is known for its high peak-to-mean-envelope- ej 2fc t power ratio. This requires a large ampli er power output dt bt At si t so t backo , when linear ampli cation is needed, resulting in low dc to RF power conversion e ciency of the ampli er. IFFT ht Ref g AMP Recently, adaptive dc bias controlled ampli ers were pro- posed, which achieve both high power e ciency and linear- ity. In this paper, we quantify and optimize the power con- Fig. 1. Transmitter sumption of OFDM systems when the proposed ampli ers are used. The bit error rate BER and adjacent channel power ratio ACPR are obtained through computer sim- achieves both high e ciency and linearity. In this pa- ulation to help quantifying the ampli er nonlinear e ects. per, we quantify and optimize the power consumption It is found that power consumption can be greatly mini- mized by using adaptive ampli ers, especially with highly of OFDM systems when the proposed ampli ers are nonconstant envelope modulated signals such as OFDM. used. Pulse shaped QPSK modulation scheme, which has smaller envelope variations, is also considered as a special I. Introduction case of OFDM when the number of subcarrier is one. The need for low power and high speed transmission The paper is organized as follows. In Section II, the is well recognized in current and future mobile personal communication system and channel model considered are communications. Battery life now becomes one of the given. In addition, three di erent types of dc bias con- most important factors determining the size and weight trolled ampli er are described: 1 xed, 2 single, and of portable terminals, such as mobile phones and note- 3 dual dc bias controlled ampli ers. In Section III, a books 1 , 2 . Besides voice communication, high speed performance measure to optimize power consumption is data transmission e.g. images and videos is also required de ned. Also a simpli ed asymptotic analysis of the per- to meet expected future needs. formance measure with OFDM is performed to help gain Orthogonal frequency division multiplexing OFDM is some insight into the performance measure and dc bias an e ective multicarrier modulation technique for such schemes. In Section IV, the bit error rate BER and ad- high speed data applications, especially in an interfer- jacent channel power ratio ACPR are obtained through ence limited environment such as a multipath fading computer simulation. Moreover, optimum ampli er out- channel 3 . However, because of its high peak-to-mean- put backo s are obtained. Section V nally concludes the envelope-power ratio PMEPR 4 when linear ampli ca- paper. tion is required, the ampli er average output power has to be backed o . This results in low dc to RF power II. System and Channel Model conversion e ciency for conventional xed dc bias power A. Modulation ampli ers. Even for single carrier systems, this low con- version e ciency usually happens when bandwidth e - A block diagram of the transmitter is shown in Fig. 1. cient modulation schemes are used, such as pulse shaped The basic principle behind OFDM is to split a data stream quadrature phase shift keying QPSK and quadrature dt into M streams serial to parallel process, each of amplitude modulation QAM, because of their envelope which is transmitted on a separate carrier. In our OFDM variations. system, the number of carriers, M , is 64 and each car- Recently, a technique for adaptively controlling the rier is modulated with QPSK. This modulation scheme is dc bias of a power ampli er was proposed in 5 , which implemented by the inverse fast Fourier transform tech- nique IFFT which eliminates the complexity involved This research is supported by the Department of Defense Research in using a large number of oscillators. This scheme oper- & Engineering Multidisciplinary University Research Initiative on ates block-wise every MT seconds. That is M symbols Low Power Low Noise Devices" and managed by the Army Re- s search O ce ARO under grant ARO DAAH04-96-1-0001. are transmitted every MTs and each symbol constitutes 0-7803-5538-5/99/$10.00 (c) 1999 IEEE 2 information bits. The modulated signal TABLE I Parameters for different dc bias schemes si t = RefAtej 2fc tg = Vi t cos2fc t + t 1 Bias scheme CV;0 CI;0 CV;1 CI;1 Fixed bias 1 1 0 0 where Vi t = jAtj is the voltage envelope of the signal, Single bias 1 0 0 1 t = 6 At is the phase, and fc is the carrier frequency. Dual bias 0 0 1 1 The complex signal At bt ht is the output signal of the square root raised cosine transmitter lter ht with which is denoted by Vo t, is obtained by the Fourier series roll-o factor , and bt is the parallel to serial processed expansion or so called Chebyshev transform 6 , 9 of output of the IFFT, given by the instantaneous voltage characteristics which are those M ,1 X of ideal soft-limiter in 5 at the fundamental carrier fre- bt = bc;l t , lTs for t 2 0; MTs 2 quency fc . This is l=0 et; for et 1 where t is the Dirac delta function and Vo t = 2 et asin 1 + 1 , 21 1 ; for et 1 5 et e t 2 M ,1 X bc;l = p1 fdi k + jdq kge j2M lk 3 where et is the normalized input voltage envelope, de- M k=0 ned as et = Vi t=Vi;m : 6 where dik 2 f,1; 1g and dq k 2 f,1; 1g are informa- tion bits. In a QPSK transmitter, M is simply set to The value Vi;m is the maximum sinusoid input envelope 1 in 2 and 3. As can be seen in 3, the amplitude voltage that can be ampli ed linearly. distribution becomes complex Gaussian from the central The signal power is related to the envelope voltage by limit theorem as M increases, resulting in higher enve- lope variations. Pi t = Vi2t=2 and Po t = Vo2 t=2 7 B. Ampli er and channel model and the power output backo OBO of the ampli er is The modulated signal, si t, is rst ampli ed and then de ned as corrupted by additive white Gaussian noise AWGN with OBO = Psat=Po = Vsat=Vo2 2 8 two sided power spectral density N0 =2. which is the ratio of saturation power Psat to average out- B.1 Ampli er input and output characteristics put power Po . Note that the averagings over-bars are done over the input envelope variations, i.e., over et. The ampli er model considered in this paper is a band- The saturation voltage V is set to be the asymptotic pass memoryless nonlinear model. In this model, the re- output voltage, i.e., maxsat t = limet!1 Vo t = 4 . Vo lationship between the input and output signal of the For a given saturation power, smaller OBO gives larger ampli er is described by the two memoryless functions, average output power resulting in more power e ciency; namely amplitude AM AM and phase AM PM non- however, it gives more signal distortion resulting in more linearities 6 . In this model, when the input to the am- required received power for a given BER for nonconstant pli er is the modulated signal in 1, the output of the envelope signals. The goal of this paper is to nd an op- ampli er is expressed as timum OBO which minimizes the average power required so t = F Vi t cosf2fc t + t + Vi tg: 4 for reliable communications. The functions F Vi t and Vi t denote AM AM and B.2 Ampli er dc bias schemes AM PM, respectively. In a bandpass model, it is assumed Based on the model presented in 5 , three di erent dc that the harmonics spectral component centered around bias controlled schemes are considered: 1 xed, 2 sin- nfc ; n = 0; 2; 3; 4; :: : generated by nonlinearities are re- gle, and 3 dual. The xed bias scheme is used in con- jected by an ideal zonal lter around the carrier frequency ventional class A ampli ers, where dc power is constant fc . In this paper, we assume no AM PM e ects. This regardless of the magnitude of the input power. In the dc is because a solid state power ampli er SSPA usually bias controlled schemes, when the dc power dotted line has negligible AM PM Vi t 0, and it is found, in Fig. 2 changes according to the input signal power by computer simulation, that the e ects of AM AM are level as opposed to a xed dc power dashed line. This much more signi cant than AM PM 7 , 8 . reduces dc power consumption especially in the low input The relationship AM AM between the input voltage power levels which are more predominant than high input envelope Vi t and the output voltage envelope F Vi t, power levels. A detailed description of these schemes can 0-7803-5538-5/99/$10.00 (c) 1999 IEEE be found in 5 . The mathematical relationship between Pdc( t ) for a fixed dc bias dc power, Pdc t and normalized input voltage envelope, Pdc,m et, is as follows: dc power Pdc( t ) Pdc( t ) Po ( t ) Pdc t= CV;0 + CV;1etCI;0 + CI;1et; for et 1 Pdc;m ; for et 1 Pi ( t ) AMP Po ( t ) Psat Pdc;m = 1 Pi ( t ) The parameters CV;0, CV;1, CI;0, and CI;1 depend on the con guration of dc bias controlled schemes, and are listed in Table 1. Notice that the dc power is a linear function Fig. 2. Ampli er characteristics of normalized input et for the single bias scheme and a quadratic function for the dual bias scheme. We note that the input signal power is neglected in this TDD, assuming the ampli er gain output power input III. Performance Measures power is high. The detailed explanation is given in 10 . In this section, we rst brie y describe the objective function, total dc power degradation TDD, which will B. Implications of TDD be used to optimize system power consumption. Then we In this subsection, we discuss the asymptotic behavior discuss some insight we have gained from the simpli ed of OBO dB , SOBO dB when OBO is large, with asymptotic analysis of TDD with OFDM. Finally, we close the three ampli er models given in Section II. B. From the this section with a discussion of the performance measure simpli ed asymptotic analysis, we will gain some insight for out-of-band interference, ACPR. into TDD and show the potential power saving that can be realized with dc bias controlled ampli ers. A. Objective function, TDD Since the output power increases monotonically with To optimize power consumption of the systems, we the input power in our ampli er model, large OBO means adopt TDD which is proposed in 10 . The de nition of small normalized input power, i.e., e2 1. In this case, TDD is as follows: the probability that et is greater than one is small, and let's assume TDD dB = OBO dB , S OBO dB Z1 Z1 + Eb =N0 OBO dB 9 e efe e de and e2 e2 fe e de 11 0 0 where E b =N0 OBO is called E b =N0 degradation given where fe e is the probability density function of et. by From this, when OBO is large E b =N0OBO dB , E b =N0linear dB 10 4=2 Vo;m 4= 12 2 2 OBO = 2 R 1 2 R1 2 and E b =N0OBO is the required average received signal Vo;m 0 e fe e de + 1 Vo efe e de e2 energy per bit to noise density ratio to meet a target BER and, similarly, e.g. 10,4 at a given OBO, which is greater than or equal to that with a linear ampli er E b=N0 Linear. The 8 1; for xed bias increase, Eb =N0 OBO, results from the signal wave- SOBO : 1=e; for single bias 13 form distortion of the nonlinear ampli cationlow OBOs. 1=e2 ; for dual bias: The second term in 9, S OBO = Pdc;m =P dc , denot- ing a dc power saving or a correction term that can be Hence, when OBO is large, the power ampli er ine - achieved by using a dc bias controlled ampli er or that is ciency term OBO dB , SOBO dB needed for any ampli er which has a non- xed dc power; 8 S OBO 1, and equality holds for the xed bias scheme OBO dB; for xed bias for all OBOs : 20 log4= + 10 loge=e2 ; for single bias 14 In summary, the rst two terms in 9 represent the am- 20 log4= 2:1 dB; for dual bias: pli er ine ciency and the last term denotes the receiver performance degradation from the nonlinear signal distor- If we assume that Eb =N0 OBO 0 dB for large OBO, tion. We want to minimize degradations from both ampli- the above result implies that the TDD can be nite even er ine ciency and the signal distortion. It can be shown for in nite OBO in the dual bias scheme, whereas it can that an optimum OBO to minimize the required P dc to be in nite for the xed bias ampli er. For dual bias, when meet target BER also gives the minimum value of TDD. OBO is large, OBO dB , SOBO dB has a constant 0-7803-5538-5/99/$10.00 (c) 1999 IEEE value of 2.1 dB, regardless of the statistics of the modu- lated signal envelope. Since the envelope of the OFDM 12 signal assuming the number of subcarriers is larger than Fixed Bias Single Bias 10 can be wellp approximated by the Rayleigh random 10 Dual Bias variable, e = e2 =2 in this case. Thus, from 12 and 14, for single bias in OFDM, 8 OBO dB , SOBO dB 5 log + 1 OBO dB: 4 TDD (dB) 2 6 The single bias scheme reduces the slope of OBO dB 4 by a factor of half. These observations can help de- signing power e cient ampli ers jointly with modulation schemes, since di erent modulation schemes have di er- 2 ent envelope statistics 0 1 2 3 4 5 6 7 8 9 10 C. Out-of-band interference OBO (dB) The out-of-band interference power is usually quanti ed by the ACPR, which is de ned as a ratio of the out-of- a band signal power in the adjacent channel to the in-band signal power, given as 6 Fixed Bias R fc ,B R fc +3B Single Bias fc ,3B So f df + fc +B So f df ; 15 5 Dual Bias ACPRB = R fc +B fc ,B So f df 4 where ,B; B is the desired in-band, and So f is the TDD (dB) power spectral density of the ampli ed signal so t. 3 IV. Simulation Results and Discussions 2 A Monte Carlo method is used in the simulation. The signals are oversampled with a rate of 16 16 samples are taken in each Ts seconds for the BER calculation and 1 with a rate of 32 for the ACPR calculation. For accurate results, a higher sampling rate is needed for the ACPR cal- 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 culation than for the BER. The square root raised cosine OBO (dB) lter with roll-o factor of 0.35 is used for the transmit- ter and receiver lters with a nite impulse length of 96Ts, b which is enough for ACPR calculation down to ,50 dB at BTs = 2:0. Fig. 3. TDD dB for three di erent ideal dc bias schemes: a OFDM b QPSK Fig. 3 shows the TDD for the three di erent adaptive dc bias ampli ers, when the target BER is 10,4. The solid lines in the plots are the power ampli er ine ciency TDD for OBO 8 dB is too small to be seen in the plot. terms OBO dB , SOBO dB for each scheme, and Optimum OBOs for QPSK in Fig. 3b are all no larger the di erence between the solid line and curve for a given than 0.5 dB for all three bias schemes. Hence, in terms scheme is the E b=N0 degradation. As expected, E b =N0 of reducing dc power consumption, it is desirable to drive increases as the OBO becomes smaller, and for OFDM, the ampli er hard for QPSK modulation. However, these the E b =N0 degradation is about 6.2 dB when OBO = 2 low output backo s increase spectral regrowth, and when dB. However, E b=N0 degradation is very small for QPSK out-of-band interference is a major concern, OBO must due to its small envelope variations. Note that E b =N0 be larger. This issue will be discussed again when we degradation is same for all the bias schemes, since the examine ACPR. bias schemes do not change the signal waveform. Fig. 4a shows ACPR dB at BTs = 1:35=2 of OFDM Optimum OBOs of OFDM in Fig. 3a, which give the and QPSK. The ACPR of OFDM decays slowly approxi- minimum values of the TDDs, are found to be 4, 5, and mately piece-wise inverse linear with OBO, and is about 8 dB for the xed, single, and dual dc bias schemes, re- -15 dB when OBO = 1 dB. The ACPR of QPSK is smaller spectively. For the dual bias scheme, the increase in the than that of OFDM, and the slope is sharper than that 0-7803-5538-5/99/$10.00 (c) 1999 IEEE −10 −10 −15 OFDM OBO=1 dB OBO=1 dB QPSK OBO=2 dB OBO=2 dB −15 −15 −20 OBO=3 dB OBO=3 dB OBO=4 dB OBO=4 dB −20 OBO=5 dB OBO=5 dB −25 −20 OBO=7 dB OBO=7 dB ACPR(B) (dB) ACPR(B) (dB) −25 ACPR (dB) −30 −25 −30 −35 −30 −35 −40 −35 −40 −45 −45 −40 −50 −50 1 2 3 4 5 6 7 8 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.6 0.8 1 1.2 1.4 1.6 1.8 2 OBO (dB) Normalized frequency BT Normalized frequency BT s s a b c Fig. 4. a ACPR at B Ts =1 35 2; ACPR vs. normalized frequency : = BTs : b OFDM and c QPSK of OFDM. Above OBO = 5 dB, QPSK is almost linearly the dual bias scheme is used. This is especially desirable ampli ed, resulting in constant residual ACPR in theory when the adjacent channel interference ACPR from the it should be zero, which is from the truncation of lter nonlinear ampli cation is a major concern, requiring a time response in the simulation. Figs. 4b and c show large ampli er backo . ACPR versus B in OFDM and QPSK, respectively. The ACPR still decays slowly with B . References We note that E b=N0 degradation decays relatively fast 1 L. E. Larson, Radio frequency integrated circuit technology for low-power wireless communications," IEEE Personal Com- with OBOs, as seen in Fig 3. This degradation can be mun., vol. 5, pp. 11 19, June 1998. further reduced by channel coding and spread spectrum 2 E. Biglieri, G. Caire, and G. Taricco, Coding and modulation techniques, whereas the ACPR can not be reduced with under power constraints," IEEE Personal Commun., vol. 5, pp. 32 39, June 1998. these techniques, unless envelope variations become very 3 J. A. C. Bingham, Multicarrier modulation for data trans- small. Although the optimum OBO for QPSK, in terms mission: An idea whose time has come," in IEEE Commun. of minimizing dc consumption, is found to be less than Mag., pp. 5 14. May 1990. 4 Simon Shepherd, John Orriss, and Stephen Barton, Asymp- 0.5 dB from Fig. 3b, the OBO, required to meet for totic limits in peak envelopepower reductionby redundantcod- example ACPR of -38 dB or less at BTs = 1:35=2, is ing in orthogonal frequency-division multiplex modulation," found to be at least 4 dB 8 dB for OFDM from Fig. 4a. IEEE Trans. Commun., vol. 46, no. 1, pp. 5 10, Jan. 1998. 5 K. Yang, J. R. East, and G. I. Haddad, Automatic control of When the ACPR need to be -38 dB, the dual bias scheme e ciency and linearity in power ampli ers," in Topical Meeting has TDD of 2 dB less than the xed bias scheme in QPSK. on Silicon Monolithic Integrated Circuits in RF Systems, Sept. 1998, pp. 113 118, and in IEEE Trans. on Microwave Theory This saving for OFDM is about 2.3 dB for single bias and and Techniques, in press. 6 dB for dual bias. A dc bias controlled scheme provides 6 M. C. Jeruchim, P. Balaban, and K. S. Shanmugan, Simula- one solution for using a linear ampli er without sacri cing tions of Communication Systems, Plenum, 1992. 7 M. T.Le and L. Thibault, Performance evaluation of COFDM power consumption, especially with highly nonconstant for digital audio broadcasting part II: E ects of HPA nonlin- envelope modulated signals. earities," IEEE Trans. on Broadcasting, vol. 44, no. 2, pp. 165 171, June 1998. V. Conclusion 8 J. Boccuzzi, Performance evaluation of non-linear transmit power ampli ers for North American digital cellular portables," The performance and power consumption of OFDM IEEE Trans. Veh. Technol., vol. 44, no. 2, pp. 220 228, May 1995. systems are quanti ed and optimized when the adaptive 9 N. M. Blachman, Detectors, bandpass nonlinearities, and ampli er is adopted. The obtained results suggest a signif- their optimization: Inversion of the Chebyshev transform," IEEE Trans. Inform. Theory, vol. IT-17, no. 4, pp. 398 404, icant power reduction from the adaptive dc bias ampli ers July 1971. for the OFDM systems. Even with linear ampli cations 10 J. Jong, K. Yang, W. E. Stark, and G. I. Haddad, Power op- high OBOs the power loss from the ine ciency of the timization of OFDM systems with dc bias controlled nonlinear ampli er, compared to the power loss at the ampli er's ampli ers," in Proceedings of the IEEE Vehicular Technology Conference, Sept. 1999. operating saturation region low OBOs, is minimal when 0-7803-5538-5/99/$10.00 (c) 1999 IEEE