Peak-to-Average Power ratio of IEEE a PHY layer Signals

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1 Peak-to-Averae Power ratio of IEEE 802.a PHY layer Sinals A. D. S. Jayalath and C. Tellambura School of Computer Science and Software Enineerin Monash University, Clayton, VIC, Abstract In this paper, we propose clippin with amplitude and phase chanes of the sinal points to reduce the peak-to-averae power ratio (PAR) of orthoonal frequency division multiplexed (OFDM) sinals in hih-speed wireless local area networks defined in IEEE 802.a physical layer. The proposed technique can be implemented with a small modification at the transmitter and the receiver remains standard compliant. PAR reduction as much as db can be achieved by selectin a suitable clippin ratio and a correction factor dependin on the constellation used. Out of band noise (OB) is also reduced. Key WordsOFDM, Peak-to-averae power ratio, IEEE 802.a PHY. I. ITRODUCTIO With a rapidly rowin demand for wireless communications, much research has been expended on providin efficient and reliable hih-data-rate wireless services. The IEEE 802. standard for wireless local area networks (WLA) was first established in 997, and it supported data rates of Mb/s and 2Mb/s in indoor wireless environments. In comparison to 00Mb/s Ethernet, the 2Mb/s data rate is relatively slow and is not sufficient for most multimedia applications. Recently, the IEEE 802. WLA standard roup finalized the IEEE Standard 802.a, which has an OFDM physical layer for indoor wireless data communications []. The data rates of IEEE 802.a rane from 6Mb/s up to 5Mb/s. This new standard can provide almost all multimedia communication services in indoor wireless environments. However, two limitations of OFDM based systems are often asserted. Firstly, due to the nonlinearities of transmitter power amplifiers, hih PAR values of the OFDM sinal enerates hih OB. There are restrictions imposed by the Federal Communications Commission and other reulatory bodies on the level of these spurious transmissions. These restrictions impose a maximum output power limitation. This output power limitation corresponds to what is known as power amplifier back-off. Further more nonlinearities of amplifier cause inband distortion of the sinal ivin hiher bit error rates (BER). 6-quadrature amplitude modulation (6-QAM) modulation is used in IEEE.a PHY for 8Mb/s and 5Mb/s transmission. This modulation scheme is hihly sensitive to distortions due small Euclidian distances between sinal points. Thus IEEE 802.a WLA devices may need power amplifiers with lare back off, which are inefficient and bulky. Overcomin this problem requires reducin the PAR of OFDM sinals. Secondly, OFDM is hihly sensitive to frequency off-set errors. However, frequency offset due to the mobility of the terminal is neliible in WLA environments, owin to very low speeds of the mobile. Clippin of hih peaks increases the in-band distortion and the OB. In [2] several modulation schemes are examined and effects of amplitude limitin is presented. A controlled amount of limitin is permissible in many cases. Clippin an oversampled sinal produces less in-band noise but the OB will increase [3]. Performance evaluation of clipped OFDM symbol with and without oversamplin is presented in []. Two extra oversampled DFT operation are used in the transmitter to filter the OB due to clippin. Oversamplin is necessary to avoid peak rerowth after filterin. Similar PAR reduction scheme based on clippin and filterin an oversampled sinal is presented in [5]. Two oversampled inverse fast Fourier transform (IFFT) operations are used to interpolate and perform frequency domain filterin after clippin. This reduces the amount of OB. Increased BER due to clippin may be reduced usin forward error correction codin. Thus, a system based on clippin and forward error correction is proposed in [6]. Decision aided reconstruction (DAR) is proposed in [7] for mitiatin the clippin noise. The receiver is assumed to know the clippin level. DAR is an iterative reconstruction technique, which increases the receiver complexity. Several discrete Fourier transform (DFT) operations are performed at the receiver before reconstructin the oriinal sinal. For baseband transmission, an approximation for the resultin increase in BER is iven in [8], but spectral distribution of the distortion is not considered. References [9, 0] consider the spectral spreadin but only for real valued discrete multitone (DMT) sinals. The deradation due to clippin of an OFDM sinal is analyzed in []. Extensive research has been undertaken to understand the effect of hih power amplifier (HPA)

2 G I nonlinear distortion in OFDM systems [2, 3]. Compared to other PAR reduction schemes clippin based techniques are simple to implement. A PAR reduction usin sinal clippin and phase correction at the transmitter is proposed in []. The basic idea is as follows. Let the IFFT of the modu- lated symbol sequence be. Here we assume quadrature phase shift keyin (QPSK). The sequence is clipped to a desired level, and the IDFT is taken. Because "! # of the clippin. The key idea in [] is to apply phase correction to such that both and have identical phases. This is done by multiplyin with $%&('*),+.- '*)0/ where and are the phases of and. The idea of this phase correction is to limit OB and BER deradation. Of course, we cannot make the amplitude equal to the oriinal sinal manitude. Then we would be back to the oriinal input sequence. Finally, the IDFT of the phase-corrected sequence is used to enerate the transmitted sinal. ote that only samples per each OFDM symbols are enerated. Clippin those to a low level does not uarantee that the peaks of the output sinals are reduced to the same level. This paper presents three enhancements to the method proposed in []. First, we oversample the OFDM sinal by a factor of 2. Oversamplin will lead to reater robustness aainst peak rerowth. Oversamplin is implemented usin 2 -lenth IDFTs. Secondly, the phase correction is controlled (additional parameter 3 ) and is applied only if the difference between and exceeds 3. Third, if the amplitude deviates too much from the oriinal sinal amplitude (as measure by a parameter ), an amplitude adjustment is applied. The BER deradation caused is thus neliible and the OB is reduced considerably. This approach is more eneral than []. For instance the special case in our scheme represented by 65 and 3 =0 corresponds to []. We then apply this new scheme in IEEE 802.a PHY transmit sinals and evaluate the performance. II. A OFDM SYSTEM AD PEAK-TO-AVERAGE POWER RATIO (PAR) 7 8 "9 A block of symbols,, is 7 ; 9 formed with each symbol modulatin one of a set of subcarriers with frequency,. The subcarriers are chosen to be orthoonal, that is 8 =< where is the OFDM symbol duration. The complex baseband sinal can be expressed as?bdc E F +H KJML $ %OP*)0Q SR C RT@U () FEC CODER Interleavin + Mappin Oversampled IFFT L ew block AMP and Phase chane A -A Soft limiter (SL) L IFFT Oversampled FFT Symbol Wave Shapin Amplitude and Phase Adjustments Fi.. IEEE 802.a Transmitter. This sinal can be enerated by takin an point V inverse discrete Fourier transform (IDFT) of the block followed by low pass filterin. The actual transmitted sinal is modelled as real W?BDC E $%OP X*QZY, where K[ is the carrier frequency. The PAR of the transmitted sinal in () can be defined as \ ^] c d _0`ba?BDC E a (2) a?bdc E a e c d where e is the expected value of. The PAR of the continuous-time OFDM sinal cannot be computed precisely by the use of the yquist samplin rate [5], which amounts to samples per symbol. In this case, sinal peaks are missed and PAR reduction estimates are unduly optimistic. Oversamplin by a factor of is sufficiently accurate. III. IEEE 802.f SYSTEM DESCRIPTIO The IEEE 802. transmitter with the proposed PAR reduction scheme is presented in Fiure. Input data is first mapped into symbols ( ) and serial to parallel converted. Then a 2 point oversampled IFFT is taken. The output of oversampled IFFT is clipped accordin the clippin ratio selected. A second 2 point fast Fourier transform (FFT) is taken to et the clipped sample points back to frequency domain. We will now select samples correspondin to the oriinal sinals ( ). The clippin of the sinal causes dispersion of the sinal points. If we do not clip the sinal, the oriinal symbols ( ) will be reenerated at this point. ext, we adjust the phase and the amplitude of these sinal points such that they are confined V to a smaller reion around the oriinal sinal points. Let us define an arbitrary sinal point of the iven constellation havin amplitude and phase and as shown in Fiure 2. Then phase, and amplitude of each sinal point is adjusted accordin to the followin rules. If the amplitude of deviates from by more than, the corrected amplitude will be adjusted as follows. ihj k lj bm n n p n else.o.o IQ Mod (3)

3 3 lj L Fi. 2. Amplitude and phase adjustment parameters. where. If the phase of the clipped sinal deviates by 3 or more from the phase of the oriinal sinal points, the phase is also adjusted. 3 is calculated from the iven as follows k hj where _ +H m Vo 3 Vo else () (5). At this point we have a new symbol sequence optimized for lower PAR. This new scheme needs two extra oversampled-ifft operations at the transmitter. However, o modifications are needed at the receiver. TABLE I IEEE 802. PHY PARAMETERS Information data rate 6,9,2,2,36 8 and 5 Mb/s Modulation BPSK-OFDM QPSK-OFDM 6-QAM-OFDM 6-QAM-OFDM FEC code Convolutional rate /2, (K=7) Code rates /2, 2/3,3/ Total umber of sub carriers 52 umber of pilot subcarriers OFDM symbol duration Guard interval 0.8 Sinal bandwidth 6.6 MHz IV. CLIPPIG HIGH PEAKS A soft limiter (SL) described below is used to clip the sinal peaks. The nonlinear characteristics of an SL can Fi. 3. Sinal distortion at db clippin of 8Mb/s Sinals. be written as where $% a a a a R o SR VR ^ (6) is the clippin level and is the phase anle of the sample M and is the clipped output sequence. The clippin ratio is defined as Clippin ratio H V. RESULTS c d a a e db (7) Simulation results were obtained for different transmit sinals. As IEEE 802.a transmit sinals utilize four constellations (binary phase shift keyin (BPSK), QPSK, 6-QAM and 6-QAM), simulations are performed for data rates involvin these constellations except for BPSK. Clippin has little effect on BPSK OFDM. Fiure 3 depicts the constellation of a 8Mb/s transmitted sinal passin throuh a SL with a db back off. The distortion of the sinal is clearly evident. Fiure shows the amplitude and phase corrected sinal after db clippin with correction factor ;. The distortion of the sinal reduces sinificantly dependin on the value of the correction factor. Fiure 5 depicts the complementary cumulative distribution function of the PAR of the 8Mb/s sinal. PAR is reduced by more than db with the db clippin, but with a severely distorted sinal. Phase and amplitude correction reduces the distortion of the sinal points but derades the PAR statistics. A 3dB ain in PAR statistics is obtained when, while this ain is around 2dB when at + of CCDF. Clippin with suitable phase and amplitude correction can achieve a sinificant PAR reduction. We also examined the performance of other schemes. Fiure 6 depicts the 36Mb/s sinal constellation after passin throuh a SL with 2dB clippin. As 6-QAM

4 Fi.. Corrected sinal constellation at db clippin (8Mb/s and ). Fi. 6. Sinal distortion at 2dB clippin of 36Mb/s Sinals Without adjustments Without clippin 0 2 alpha=0.02 fra replacements alpha= Fi. 5. CCDF of the 8Mb/s sinals with db clippin. is less condensed than the constellation for 8Mb/s or 5Mb/s (6-QAM), we can allow for hiher clippin ratios. Fiure 7 shows the amplitude and phase corrected sinal constellation. The amplitude and phase distortion is reatly reduced when the correction factor. Fiure 8 depicts the CCDF of PAR of the transmitted sinals. The PAR statistics improve as before. The correction factor is chosen as and with clippin at 2dB. These parameters correspond to PAR statistics improvements of 3dB and db respectively. When the simulations are performed for 2Mb/s sinals we could observe far better performance improve- ments. The constellation in 2Mb/s sinal is less dense than the two other schemes before and allows reater flexibility in selectin correction factor PSfra. Hih replacements values of ive out hih PAR reduction. When the ; ^ about 5dB ain is observed while this was more than 3dB when. ext we observe the power spectral density (PSD) of the transmitted sinal when passin throuh a non- Fi. 7. Corrected sinal constellation at 2dB clippin (36Mb/s and ) Without adjustments alpha=0.5 alpha=0. Without clippin Fi. 8. CCDF of the 36Mb/s sinals with 2dB clippin.

5 @ 5 e e 0 0 Ordinary Sinals Modified Sinals dB Power spectral density dB 7dB 5dB 5dB 9dB 3dB dB ormalized frequency B n Fi. 9. Sinal distortion at 2dB clippin of 2 Mb/s Sinals. Fi. 2. Power spectral density when passin throuh a non-linear amplifier. fra replacements Fi. 0. Corrected sinal constellation at 2dB clippin (2Mb/s and ) Without adjustments alpha=0.2 alpha=0. Without clippin Fi.. CCDF of the 2 Mb/s sinals with 2dB clippin. linear power amplifier. The input output relationship of power amplifiers can be modelled as d d d m B E e 8 (8) where is the clippin level, is the amplitude of the sinal input and and denote the amplitude and the phase at the output respectively. The parameter controls the smoothness of the transition from the linear reion to the limitin or saturation reion. When, this model approximates the SL characteristics. For PSD results, it is convenient to define the normalized bandwidth B < > where is the OFDM symbol duration. In Fiure 2, 2 Mb/s sinal with 2dB clippin and correction factor is compared with an ordinary transmitted sinal. The back-off of the power amplifier is set at different levels (3dB, 5dB, 7dB and 9dB). When the back off is very low (3dB) very sliht improvement in OB is observed. OB is reduced by about 8dB when the back-off is at 5dB. Similarly, OB reduces sinificantly with the increase in back-off at a faster rate compared to the ordinary sinal. Therefore the back-off of the amplifier can be reduced sinificantly by usin this technique. Selection of initial clippin ratio and the correction factor depends on the sinal constellation bein used. Therefore, by selectin a suitable clippin level and a proper phase an amplitude correction factor sinificant PAR reduction is achieved without causin sinificant BER deradation. This is a desired feature in portable devices in WLAs, where power efficient transmitter power amplifiers are essential.

6 VI. COCLUSIO A technique based on clippin with amplitude and phase chanes to reduce the PAR of OFDM based WLA sinals defined in the IEEE 802.a physical layer is presented in this paper. The proposed technique is capable of reducin the PAR by 3-dB by selectin a suitable clippin level and amplitude and phase correction factor. It can be implemented with a sliht increase in the complexity at the transmitter. This involves with insertion of two additional DFT operations and soft limiter at the transmitter. The receiver remains standard compliant. REFERECES [] IEEE Std 802.a-999 (supplement to IEEE Std , Part II Wireless LA medium access control (MAC) and physical layer PHY specifications Hih speed physical layer in 5 GHz bnad, tech. rep., IEEE, Sept [2] D. W. Bennett, P. B. Keninton, and R. J. Wilkinson, Distortion effects of multicarrier envelope limitin, IEE Proc. Commun., vol., pp , Oct [3] X. Li and L. J. Cimini, Effects of clippin and filterin on the performance of OFDM, IEEE Commun. Lett., vol. 2, pp. 3 33, May 998. [] H. Ochiai and H. Imai, On the clippin for peak power reduction of OFDM sinals, in IEEE GLOBECOM, (San Fracisco, USA), pp , IEEE, [5] J. Armstron, ew OFDM peak-to-averae power reduction scheme, in IEEE Vehicular Technoloy Conference, (http// ja/pubs.htm), IEEE, May 200. [6] D. Wulich and L. Goldfeld, Reduction of peak factor in orthoonal multicarrier modulation by amplitude limittin and codin, IEEE Trans. Commun., vol. 7, pp. 8 2, Jan [7] D. Kim and G. L. Stuber, Clippin noise mitiation for OFDM by decision-aided reconstruction, IEEE Commun. Lett., vol. 3, pp. 6, Jan [8] R. O eill and L. B. Lopes, Performance of amplitude limited multitone sinals, in IEEE Vehicular Technoloy Conference, (ew York, Y, USA), pp , IEEE, 99. [9] D. J. G. Mestdah, P. Spruyt, and B. U. Brain, Analysis of clippin effect in DMT-based ADSL systems, in IEEE ICC, (ew York, Y, USA), pp , IEEE, 99. [0] R. Gross and D. Veeneman, SR and spectral properties for a clipped DMT ADSL sinal, in IEEE ICC, (ew York, Y, USA), pp , IEEE, 99. [] M. Friese, On the deradation of OFDM-sinals due to peakclippin in optimally predistorted power amplifiers, in IEEE GLOBECOM, (Sydney, Australia), pp , IEEE, 998. [2] E. Boenfeld, R. Valentin, K. Metzer, and W. Sauer-Greff, Influence of nonlinear HPA on trellsi-coded OFDM for terrestrial broadcastin of diital HDTV, in IEEE GLOBECOM, (ew York, Y, USA), pp , IEEE, 993. [3] G. Santella and F. Mazzena, A hybrid analytical-simulation procedure for performance evaluation in M-QAM-OFDM schemes in presence of nonlinear distortions, IEEE Trans. Veh. Technol., vol. 7, pp. 2 5, Feb [] M. C. D. Maddocks and P. Shelswell, Shelswell Diital sinal transmission system usin frequency division multiplex. U. S. Patent U. S. Patent US , 997. [5] C. Tellambura, Phase optimization criterion for reducin peakto-averae power ratio in OFDM, IEE Elect. Lett., vol. 3, pp , Jan. 998.