IEEE TRANSACTIONS ON BROADCASTING, VOL. 44, NO. 1, MARCH 1998 12 zy zyx zyxwvutsrqponm IN DIGITAL TV BROADCAST1 FDM MODULATION Ahmad Chini*, Yiyan Wu**, Mohammed El-Tanany* and Samy Mahmoud” Albstract - FFT-based Coded Orthogonal Frequency Division Multiplexing (COFDM) is one of the techniques for digital TV broadcasting over multipath fading channels. A FITbased OFDM signal is subject to various hardware nonlinearities in both the transmitter and receiver. Hardware nonlinearities not only affect the in-band performance of a FFT-based OFDM system but also may affect the system performance of an adjacent channel signal because of regenerated sidelobes of the transmitted signal. The aim of this paper is to investigate the in-band and out-of-band behavior of a 64QAM-OFDM system under various nonlinear devices. It is shown that the inherent signal clipping in the IFFT processors with a limited word length reduces the required RF amplifier output backoff (OBO) where adjacent channel interference is the limiting factor. For 0.25% clipping rate, an additional 2dB O B 0 is required for the COFDM signal to achieve the same level of adjacent channel interference as for the single carrier system. The loss in SNR due to signal clipping is negligible in a coded OFDM system. lobes. A number of researchers have studied the effects of hardware nonlinearities in OFDM systems [12]-[26]. The aim of this paper is to further the knowledge in this area by investigating the in-band and out-of-band behavior of a 64QAMOFDM proposed for digital TV broadcasting under various nonlinear devices. Special consideration is given to the required O B 0 in the RF amplifier. Section I1 describes the system under consideration, Section I11 discusses the signal distribution and is divided in two parts. Part A, discusses the distribution of the discrete signal power at the IFFToutput assuming unlimited word length. Part B, discusses the distribution of the IF signal envelope power for both a single carrier modulated signal and an OFDM 64QAM signal. The effects of clipping of the discrete signal at the IFFT output on the BER performance and also on the IF signal envelope power distribution are discussed in section IVA. The transmit signal power spectrum and BER performance subject to nonlinear RF amplifiers are discussed in sections IVB and IV-C. zyxwvuts zyxw zyxwvutsrqpo zyxwv zyxwvutsr zyxwvutsr I. INTRODUCTION One of the techniques for digital TV broadcasting over multipath fading channels is coded OFDM [l]. OFDM is an effective method to mitigate IS1 in wideband signalling over multipath frequency selective channels. The main idea is to transmit the data in parallel over a number of essentially flat subchannels. This is efficiently achieved by using a set of overlapped orthogonal signals to partition off the channel along the frequency axis [2]. An OFDM system can be realized using a number of Staggered-QAM coherent modems equally spaced in the frequency domain [3]. Due to the level of complexity involved in the design of conventional modulators and demodulators, practical systems use a FFT (Fast Fourier Transform) to implement OFDM modems [4]-[ 111. The OFDM signal is subject to various hardware nonlinearities in both the transmitter and receiver. Examples of these nonlinearities are signal clipping in the A/D convertor, signal clipping in the IFFT and FFT processors with a limited word length, AMIAM and AMIPM distortion in RF amplifiers. Hardware nonlinearities not only affect the performance of a FFT-based OFDM system, but also may affect the system performance of an adjacent channel because of generated side* Department of Systems and Computer Engineering, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada, K I S 586 ** Communications Research Centre, 3701 Carling Avenue, Ottawa, Ontario, Canada K2H 8S2 Publisher Item Identlfier S 0018-9316(98)03639-7 11. SYSTEM DESCRIPTION Fig.1 shows a functional block diagram of the system under consideration. The blocks marked “U@” and “U*#” represent the equivalent baseband frequency responses of the transmitter and the receiver filters respectively. These are considered to be square root Nyquist filters with the Nyquist bandwidth W equal to the transmission symbol rate UT The sampling rate at the receiver is equal to the symbol rate. The block marked “A” represents the equivalent baseband response of the RF amplifier. This in general can be a nonlinear amplifier. The binary information are first coded and mapped to complex-valued QAM symbols in a 2-dimensional signal constellation. These complex-valued symbols are grouped into frames of length N, each called a “data vector” I={&}. The elements of each data vector are processed using an N-point complex IFFT (Inverse FFT) which acts as a discrete frequency synthesizer. The N complex-valued transform coefficients are then followed by a circular prefix which contains the last L-1 transform coefficients ( N 2 L ). Such an OFDM system withstands a total multipath spread of (L-1)T A more detailed block diagram of the transmitter is shown in Fig.2. The complex-valued IFFT outputs are transmitted using a quadrature IF modulator. With no loss in generality, we shall normalize the average signal power to one, i.e.: zyxwvut 0018-9316/98$10.00 0 1998 IEEE 13 ... zyxwvutsrqp zyxwvutsrqponmlkji zyxwvutsrqp zyxwvut zyxwvu zyxwvutsrqponm zyxwvutsr zyxwvut zyxwv Block Diagram of an OFDM System Fig.1: ............................................................................................................ (i,l 2 = I m = 0, I , ..., N - 1 (2.1) and consequently the average noise power is the inverse of the average signal-to-noise ratio y: 2 IzmI zy -1 = Y systems based on computer simulation. It is seen that the power distribution for the OFDM system is exponential (a straight line on the logarithmic scale). This is expected from data with the complex-Gaussian distribution, Le.: 2 Pr(li,l m = 0, 1, ..., N - 1 * 2 (2.2) liml 111. SIGNAL DISTRIBUTION The signal distribution is discussed before and after IF filtering and pulse shaping. The signal is in discrete form before the IF stage. The pdf of the discrete signal is first discussed. > 2x) = e -X where (3.1) =I m = 0, I , ..., N-I The signal power distribution of FFT-based OFDM systems is essentially independent of the number of carriers Nand the signal constellation (QPSK, 64QAM, etc.). B. IF signal envelope power distribution A. Discrete signal power distribution Assuming zero-mean independent data elements {In}, the IFFT coefficients of these data elements {i,} are zero-mean complex-valued elements with a distribution well approximated by a complex-Gaussian distribution' (for large N). Based on a computer simulation of a 1024-carrier 64QAM-OFDM system and a single carrier 64 QAM system, the following observations are made: The real part of {i,} elements for a randomly generated sequence of data in a system with N=1024 carriers, has a noiselike magnitude with a distribution given in Fig.4. The signal power { limI2}has occasional peaks greater than that of a single-carrier 64QAM system. This is expected since a single carrier system has a functional block diagram similar to Fig.1 but without IFFT, FFT and circular prefix blocks. Therefore the complex discrete data elements at the IFFT input (In}are similar in distribution to that of a single carrier signal. Fig.3 shows the block diagram of a quadrature modulator used to transmit complex data elements {},i in a OFDM system or { I , } in a single carrier system (see Fig.1 and Fig.2). The IF signal can be written as: = C a m u ( t - m T ) c o s ( W I F t+ ) S,(t) + b,u( t - m T ) sin( a,#) = A ( t ) cos( wIFt+ O(t ) ) where a, is the real part and b, is the imaginary part of the complex data elements. The signal envelope A(?) as defined in (3.2) can be written as: J + i, Eb,u(t-mT) (3.3) IC ( u m + j b m ) u ( t -mT) .". Therefore, the IF signal envelope power is given by: = The cumulative distribution function (CDF) of the signal power is given in Fig.5 for both the single carrier and OFDM Gaussian for the real and imaginary parts while Rayleigh for the magnitude liml and Exponential for the power limlz. (3.2) m 2 A (t) = Ci,u(t-mmT) lm 2 I 1' OFDM (3.4) Single Currier (3.5) 2 A ( t ) = zZ,u(t-nT) In 14 zyxwvutsrqponmlkjihgfedcba zyxwvutsrqpon zyxwv zyxwvutsrqpo z For the OFDM signal, the distribution of the signal envelope power A2(t) at a given time instant t, is exponential as the inphase and quadrature components of the data elements {},i are Gaussian. The signal Cl,u(t-m~) ond type. The letter 'c' is used denote the clipping power level __ normalized to ( lim12)2. The clipping noise power and the clip rate for the two types of clippers are calculated as: is cyclostationary and 1- Magnitude clippers: m the ~ ~ (average t ) signal power is a periodic function (assuming a nonzero filter roll-off). The overall distribution (over all times) of the signal envelope power A2(t) is well approximated by exponential distribution when { i,} are complex Gaussian and U(R is a square-root raised-cosine filter with a small rolloff.The distribution is exactly exponential for an ideal filter with a roll-off factor of zero. The approximation for nonzero roll-off factor will be verified by computer simulation. Let U(f)be a square-root raised-cosine filter with a roll-off factor' of 11.5%. The envelope power distributions of a 64QAM-OFDM and a 64QAM-SCM signals obtained by computer simulation are depicted in Fig.5. If, for instance, a RF amplifier with an O B 0 of 7dB is used for both the single and the OFDM systems, more frequent and more powerful clipping interferences are generated by the OFDM system compared to the single carrier system. This may not be a problem for the OFDM system itself or an adjacent OFDM system as these systems are robust to impulse interferences. This however may affect the performance of an adjacent channel with a different modulation scheme. A higher O B 0 is therefore required for the OFDM systems compared to the single carrier systems. However the required O B 0 is independent from the number of carriers (N) as the envelope power distribution is not dependent on N . m l~,(c)1~ = j(&- = e-'- & elfc(&) (4.1) C m = 0, I , ...,N - I Clip rate = e-' 2- Baseband clippers: m (4.2) JC m = 0, I , ..., N - I clip rate = 2egi($c)-erjc2(h) The ratio of the signal power to the clipping noise is depicted in Fig.6 for various clipping rates. It is seen that for the same clip rate, both types of clippers have the same signal to the clipping noise ratio. Notice however that for the same clip rate, the clipping levels as given by (4.1) and (4.2) are different for the two types of clippers. The loss in SNR (i.e.The ratio of the transmit symbol energy per noise spectral density) due to the clipping noise is approximated as: zyxwvutsrqpo zyxwvutsrqponm Loss in SNR s 1Olog Original noise power + Clipping noise power Originul noise power ) (4.3) IV. EFFECTS OF HARDWARE NONLINEARITIES A. Clipping the discrete signal In this section, the effects of clipping the discrete signal { i,} prior to the IF stage are discussed. Clipping the discrete data elements {},i has two advantages. First, it substantially reduces the word length required for the IFFT, FFT, D/A and A/D. Second, it reduces the required O B 0 in the RF amplifier when the determining factor for the O B 0 is the adjacent channel interference. The price paid for these advantages is an increase in the noise level. Signal clippers can be divided into two groups. The first group (magnitude clippers) cuts the signal whenever the signal power 2I,il exceeds a certain level. The second group (baseband c1ippers)cuts the signal whenever the real or the imaginary part of the signal ,i exceeds a certain power level. Clipping of the signal in the IFFT processor with a reduced word length (number of bits used for output data) is of the secThe same roll-off for both the single carrier and the OFDM systems has been considered. The OFDM system however can have a smaller roll-off due to the fact that it is less sensitive to the data timing clock mismatch. where y is the SNR value. The loss in SNR versus the clip rate for various values of SNR is depicted in Fig.7. As the loss is higher for larger values of SNR, channel coding can lower the loss by reducing the minimum required SNR. In general, higher level modulations require higher SNR for a given BER performance. This implies that OFDM systems with higher level modulations should be clipped at higher power levels to have the same loss as the lower level modulations. The simulated BER performance of an uncoded 64QAM-OFDM on an AWGN channel is shown in Fig.8 for two cases, no clipping and 1% clipping. It is shown that the loss in SNR is about 0.6dB at SNR of 22dB and about 0.25dB at SNR of 18dB. This agrees well with the theoretical results of Fig.7. Fig.9 shows the distribution of the signal envelope power at the IF output where the discrete data elements are clipped at a rate of 1% and 0.25%. It is seen that with an additional 1.5dB O B 0 in the R F amplifier, the frequency of crossing any power 2 ~ m = 0, I , ..., N - 1 . The real and imaginary parts of the = I signal each have a power equal to 112. 2 Itm/ 15 level for the OFDM signal with 1% clipping is comparable to that of a single carrier signal. The excess O B 0 is less than 2dB for the OFDM signal with 0.25% clipping. With this additional OBO, the adjacent channel interference caused by the OFDM signal will be less than that of the single carrier signal. The relative O B 0 of the single carrier and OFDM systems depends on the clip rate. In general, a higher clip rate results in a lower O B 0 and a higher loss in SNR, while a lower clip rate results in a higher O B 0 and a lower loss in SNR. For a given RF amplifier, one may maximize the transmitter coverage range by minimizing the required O B 0 and the loss in SNR. The degradation in the BER performance due to signal clipping is larger in higher SNRs (see Fig.8). As systems with higher level modulations require higher SNRs, OFDM signals with higher level modulations should be clipped at rates less than that of OFDM signals with lower level modulations. As lower clip rates require higher OBOs, an O B 0 set for a QPSKOFDM may not be adequate for a 64QAM-OFDM. zyx the BER of the OFDM system is only about 0.3dB worse than the single carrier system with the same OBO. If the adjacent channel uses the same type of modulation and the same power level, one may set the amplifier O B 0 to 7dB accounting for the small loss in the SNR. If the adjacent channel uses another modulation scheme or a different power level, the interference caused by the sidelobes of the OFDM signal may play the main role in determining the required OBO. An additional 2.7dB O B 0 for the OFDM signal results in the same sidelobes level as the single carrier signal (Fig.14), and the loss in SNR is negligible as indicated by curve 2 of Fig.lO. For a clip rate of 0.25% and an excess O B 0 of 2dB the SNR degradation, at BER of is only 0.2dB (curve 3, Fig.10). With 1% signal clipping and excess O B 0 of 1.5dB, the SNR degradation at BER of is increased to 0.9dB (curve 5 in Fig.10). zyxwvutsr zyx B. Transmit signal power spectrum and BER performance in the presence of a nonlinear RF amplifier In this section, the effects of amplitude nonlinearities (AM/AM) of the RF amplifier are discussed. The effects of phase nonlinearities (AMEM) are discussed in the following section. The RF amplifier model is presented in Appendix A. The power spectral densities of the single carrier and OFDM signals are compared with and without prior clipping of the discrete data elements. Appendix B discusses the details of simulation and the method used for spectrum analysis. Fig.14a shows the power spectrum of a 64QAM single carrier signal at the RF amplifier output. The amplifier O B 0 is set to 7dB. The sidelobes levels are less than -56dB. The power spectrum of a 64QAM OFDM signal is shown in Fig.14b through Fig.14f. For an O B 0 of 7 dB, the sidelobes levels are close to -36dB. When the signal is clipped at 1% rate prior to the IF stage, and by increasing the O B 0 to 8.5dB the sidelobe levels for the OFDM signal are lowered below -56 dB (Fig.14~).When the O B 0 for the OFDM signal is 8.5dB, and in the absence of amplitude clipping the sidelobes levels for the OFDM signal will still be higher than the single carrier signal (Fig. 14d). Without signal clipping, the OFDM signal requires 2.7dB extra O B 0 to have the same sidelobes levels as the single carrier signal (Fig.14e). With 0.25% clipping, the OFDM signal requires 2dB extra O B 0 to have the same sidelobes level as the single carrier signal (Fig. 140. C. Effects of RF amplifier phase distortions (AM/PM) on the transmit signal spectrum and BER performance Fig. 15a to Fig. 15f show the transmit signal power spectrum subject to the phase as well as amplitude (s=O) distortions as described in Appendix A. The signal spectrum is given for both the single-carrier and OFDM- 64QAM signals. The amplifier O B 0 for the single carrier signal is fixed at 7dB and for the OFDM signal the O B 0 is set to 9dB. The OFDM signal is clipped at a rate of 0.25% prior to the IF stage where the signal is still in the discrete form. Comparing the various results given in Fig.15, it is seen that phase distortions of up to 5' cause sidelobes levels to increase by about 14dB . The sidelobes levels are reduced as the phase distortions decrease . Fig.15e and Fig.15f show the signal spectrum when the phase distortions are present only in the nonlinear part of the amplifier . It is seen that even with phase distortions of up to 45', the sidelobes levels are less than those in F i g . 1 5 ~and Fig.15d where the phase distortion of up to 3'was extended to the linear part of the amplifier. Fig. 1I shows the BER performance of an OFDM 64QAM system over an AWGN channel and in the presence of phase as well as amplitude distortions'. It is clear that the loss in SNR due to phase distortions is not noticeable for three of the four phase distortion models. For the model with up to 10' phase distortions , the SNR degradation is about 0.3dB at SNWsymbo1 of 23dB. Note that phase distortions of up to 45' in the nonlinear part of the amplifier have no noticeable effect on the performance of neither the single-carrier nor the OFDM64QAM systems. zyxwvutsrq Fig.10 shows the effect of the nonlinear RF amplifier on the BER performance of uncoded single carrier and OFDM64QAM systems. The results are based on computer simulations oyer an AWGN channel. Curve 1 shows the BER of both the single and OFDM systems using a linear RF amplifier and also the BER of the single carrier system using the nonlinear RF amplifier with O B 0 of 7dB. The BER performance of the OFDM system with amplifier O B 0 of 7dB is shown by curve 4. Comparing curve 1 and curve 4 at BER of it is seen that V. SUMMARY AND CONCLUSION The distribution of the discrete OFDM signal was discussed. It was shown that the OFDM signal has a complex Gaussian distribution with an exponential distribution for the signal power. The distribution is essentially independent of the number of carriers and the signal constellation (QPSK, I. The average phase shift is measured and removed in the receiver 16 zyxwvutsrqponmlkjihg 64QAM, etc.). The distribution of the IF signal envelope power was given for both the single-carrier and OFDM-64QAM signals based on computer simulation. The OFDM signal has a distribution well approximated by an exponential distribution. [5] S. B. Weinstein, and P. M. Ebert, “Data Transmission by Frequency Division Multiplexing using the Discrete Fourier Transform”, IEEE Trans. Comm., Vol. COM-19, pp. 628-634, Oct. 1971 [6] A. Peled, and A. Ruiz, “Frequency Domain Data Transmission using Reduced Computational Complexity Algorithms”, Proc. IEEE-ICASSP, Denver, CO., pp. 964-967, Apr. 1980 [7] B. Hirosaki, “A 19.2 Kbps Voiceband Data Modem based on Orthogonally Multiplexed QAM Techniques”, IEEE Int. Con$ Comm., Chicago, IL., pp. 661-665, June 23-26, 1985 [8] B. Le Floch, R. Halbert, and D. Castelain, “Digital Sound Broadcasting To Mobile Receivers”, IEEE Trans. Consumer Electronics,Vol. 35, No. 3, pp. 493-503, Aug. 1989 [9] J. S. Chow, J. C. Tu, and J. M. Cioffi, “A Discrete Multitone Transceiver System for HDSL Application”, IEEE-JSAC, Vol. 9, No. 6, pp. 895-908, Aug. 1991 [10]A. Chini, M. S. El-Tanany, and S. A. Mahmoud, “Multi Carrier Modulation for Indoor Wireless Communications”, Proc. of IEEE-ICUPC 93, pp. 674-678, Oct. 1993 [11]A. Chini, Multi Carrier Modulation in Frequency Selective Fading Channels, Ph.D. dissertation, Carleton University, Canada, 1994 [ 12lE. Feig, “Fourier Transform Coding for Peak Limited Channel”, Proc. Twenty Sixth Annu. Allerton Con$ Comm., Contl: Comput., PP. 473-479, Sept. 1988 [13]E. Feig, and A. Nadas, “The Performance of Fourier Transform Division Multiplexing Schemes on Peak Limited Channels”, GlOBECOM88, pp. 1141-1144, Dec. 1988 [14]E. Feig, F. Mintzer, and A. Nadas, “Digital Implementation of Frequency Division Multiplexing on Peak Limited Channels”, Proc. IEEE-ICASSP, Scotland, pp. 1364-1367, 1989 [15lE. Feig, “Practical, Aspects of FFT-Based Frequency Division Multiplexing for Data Transmission”, IEEE Trans. Comm., Vol. 38, NO7, pp. 929-932, July 1990 [16]C. Rapp, “Effects of HPA-Nonlinearity on a 4-DPS/OFDM Signal for a Digital Sound Broadcasting System”, Proc. Second European Con$ on Satellite Comm., Belgium, ESA SP-332, pp. 178184,22-24 Oct. 1991 [ 171C. W. Rhodes, “Transmitter Linearity Considerations for Digital TV Broadcasting”, IEEE Trans. on Broadcasting, Vol. 39, pp. 345-349, Dec. 1993 [18]D. J. G. Mestdagh, P. M. P. Spruyt, and B. Brian, “Effect of Amplitude Clipping in DMT-ADSL Transceivers”, Electronics Letters, Vol. 29, No. 15, pp. 1354-1355,22nd July 1993 [19]R. Gross and D. Veeneman, “Clipping distortion in DMT ADSL systems”, Electronics Letters, Vol. 29, No. 24, pp. 2080-2081, 25th Nov. 1993 [20]E. Bogenfeld, R. Valentin, K. Metzger, W. Sauer-Greff, “Influence of Nonlinear HPA on Trellis-Coded OFDM for Terrestrial Broadcasting of Digital HDTV”, IEEE-GLOBECOM 93, pp. 1433-1438, 1993 [21]D. W. Burke, The Effect of Non-Ideal Filtering and Nonlinear Amplification on the BER performance of a COFDMbased Digital Audio Broadcasting System, M. Eng. thesis, zyxwvuts z zyxwvutsrqp zyxwvu zyxwvutsrq Clipping the OFDM signal prior to the IF stage where the signal is still in the discrete form has a number of advantages. The word lengths of the IFFT, FFT, D/A and A/D processors are substantially reduced by signal clipping. The required O B 0 in the R F amplifier is also reduced if the adjacent channel interference is the determining factor. The effect of signal clipping on the BER performance was also discussed. The distribution of the IF signal envelope power for a OFDM 64QAM signal with 0.25% clip rate was compared with that of a single carrier 64QAM signal. It was shown that an extra 2dB O B 0 for the OFDM signal guaranties the same level of adjacent channel interference as the single carrier signal in the presence of amplitude nonlinearities. The loss in SNR due to signal clipping at 0.25% rate is negligible in a coded OFDM system. The transmit signal power spectrum in the presence of a nonlinear R F amplifier was discussed for both the single-carrier and OFDM 64QAM systems. A higher O B 0 is required for the OFDM signals to have the same power spectrum sidelobe levels as the single carrier signals. With an O B 0 of 7dB, the single carrier signal has spectrum sidelobes below -56dB provided that the amplifier has no phase distortion. The sidelobe level is increased in the presence of phase distortions specially if they are extended into the linear part of the amplifier. Almost the same sidelobe level is obtained for the OFDM signal with an O B 0 of 9dB and a clip rate of 0.25% as for a SCM system with an O B 0 of 7dB. The BER performance of both the single and OFDM 64QAM systems over an AWGN channel was investigated in the presence of the nonlinear R F amplifier. With an O B 0 of 7dB and no phase distortion, the single carrier system shows no noticeable loss in SNR. For the same R F amplifier, the OFDM system shows about 0.2dB loss at the SNWsymbol23dB where the O B 0 is set to 9dB and the signal is clipped at a rate of 0.25%. Phase distortions have no noticeable effect on the BER performance of neither the single-carrier nor the OFDM systems as long as the distortions within the linear part of the amplifier is less than 5’. zyxwvutsrq zyxw REFERENCES Mike Sablatash, “Transmission of All-digital Advanced Television: State of The Art and Future Directions”, IEEE Trans. on Broadcasting, Vol. 40, pp. 102-121, June 1994 R. W. Chang, “Synthesis of Band-limited Orthogonal Signals for Multichannel Data Transmission”, The Bell System Tech. Journal, pp. 1775-1796, Dec. 1966 B. R. Saltzberg, “Performance of an Efficient Parallel Data Transmission System”, IEEE Trans. Comm. Tech., Vol. COM-15, No, 6, pp. 805-811, Dec. 1967 M. S. Zimmerman, and A.L. Kirsch, “The AN/GSC-10 (KATHRYN) Variable Rate Data Modem for HF Radio”, IEEE Trans. Comm. Tech., Vol. COM-15, pp.197-204, Apr. 1967 Carleton University, Canada, 1994 [22]Y. Wu, B. Ledoux, A. Bergeron, and B. Caron, “OFDM for Digital Television Terrestrial Distribution over channels with Multipath and Non-linear Distortions”,Proceedings of the international workshop on HDTV’94, Turin, Italy, October, 1994. [23]J. Rinne, M. Renfors, “The Behavior of Orthogonal Frequency Division Multiplexing- Signals in an Amplitude Limiting Channel”, IEEE-ICC 94, pp. 381-385, 1994 [24]A. Brajal and Antoine Chouly, “Compensation of nonlinear distortions for orthogonal multicarrier schemes using predistortion”, IEEE-GLOBECOM 94, pp. 1909-1914,1994 [25]A. E. Jones, T. A. Wilkinson, and S. K. Barton, “Block coding scheme for reduction of peak to mean envelope power ratio of multicarrier transmission schemes”, Electronics Letters, Vol. zyx zyxwvutsrqpo zyxwvutsrq zyxwvutsrq zyxw 17 30, No. 25, pp. 2098-2099, 8th Dec. 1994 [26]R. O’Neill, L. B. Lopes, “Performance of Amplitude Limited Multitone Signals”, IEEE-VTC94, pp. 1675-1679, 1994 [27]M. C. Jeruchim, P. Balaban, K. S. Shanmugan, Simulation of Communication Systems, Plenum Press, New York, 1992 This function was used to represent the RF amplifier in our simulations. The amplifier O B 0 was measured from 1dB compression point. The equivalent band-limited baseband responses of the limiting amplifiers of the form given by (A.l) have no phase distortions. As some nonlinear amplifiers have phase as well as amplitude distortions, phase distortions were represented by the following hypothetical function: APPENDIX A : A MODEL FOR THE NONLINEAR RF AMPLIFIER The general model given in [27]: Q 1 ( A ) = $tunh(A) can be used to represent a non-linear amplifier where x is the instantaneous input signal amplitude and s is a parameter. The equivalent band-limited baseband response of the amplifier is given in [27]: (A.4) where @ is a parameter which indicates the maximum phase distortion. zyxwvutsr zyxwvutsrqp zyxwvu APPENDIX B : SPECTRAL ANALYSIS LR F(A) = 7c1 j F(Acose)eiede The transmit and receive filters are set to be square root raised cosine filters with a 11.5% roll-off. The signals are oversampled with a rate of 8 and truncated at 532 T , With this precision it is possible to to examine the signal sidelobes of down to -60dB. A frame of M=1024*8 samples is formed and weighted using a modified Hamming window: (A.2) 0 where A is the signal envelope. Equations (A.l) and (A.2) are depicted in Fig. 12 and Fig.13 for various values of the parameter s. For s=O, the equivalent band-limited baseband response of the amplifier is given by: z W , = 0.47-0.46cos(2nm/(M- I)) m = O , l , ..., M - I (B.1) The IFFT algorithm is used to analyze the signal spectrum. The signal spectrum is averaged out over 100 frames of independently generated data. Binary ~ Modulation Fig.2: Circular Prefix 3 DIA IF VQ Modul. , OFDM transmitter with a quadrature IF modulator Fig.3: IF VQ modulator channel RF Amp. & Filter 18 zyxwvutsrqponmlkjihgfe zyxwvutsrq 100 lo-' . . . . . . . . . . ...................... zyxwvutsrqp zyx zyxwvuts zyxwvutsr 10-3 1o -~ Signal level (normalized to the rms value) , 1 [dBl 2 I l I 4 3 l I 3 5 I I 6 7 8 I 9 I 6 Signal power (normalized to the average power) Fig.4: Distribution of data in a frame of 1024 elements, real part of the IDFT output signal; 64QAM-1024 Carriers Fig.5: Power distribution for the single-carrier and OFDM signals, with filtering 1 oo zyxwv ............... lo-' 3 E 10-2 zyxwvuts 1o Clip rate -~ 0 0.5 1 2 1.5 2.5 3 3.5 4 . 4.5 Loss in SNR [dB] Fig.6: Clipping noise power Fig.7: Clipping loss for OFDM-64QAM systems 10" I 16 17 18 I I 19 20 21 22 23 24 SNR per transmit symbol Fig& BER of a OFDM-64QAM with and without amplitude clipping on an AWGN channel 5 zyxwvutsrqponmlkji 19 1oo lo-' lo-' 1o-2 1o-2 m 1o .......... . -~ zyx zyxwvutsrqp ................ I . . 1 o-< 16 17 18 19 20 21 22 23 24 Signal power (normalized to the average power) [dB] SNR per transmit symbol [dB] IF signal envelope power distribution Fig.10: BER performance of OFDM-64QAM subject to signal clipping and a nonlinear RF amplifier Fig.9: zyxwvutsrqponm 1o-2 @m 1o -~ zyx zyxwvutsrqponmlkj 1o -~ 16 17 18 19 20 21 23 22 24 SNR per transmit symbol [dB] Fig.11: Effects of A M P M conversion on the BER performance of a OFDM-64QAM system 0 5, 2.1 dB -2 -4 0 -6 z x -8 -10 -12 zyxwvutsrqponmlk -5 n s -1 0 L4 -14 -1 5 -1 6 8 -20 -20 -15 -10 -5 10 x [dBl Fig.12: A parametric model for non-linear amplifiers 15 -20 -20 -15 -10 -5 0 5 10 A tdB1 Fig.13: The equivalent band-limited baseband response of the non-linear amplifiers 20 zy zyxwvutsrqponmlkji zyxwvutsrq 0, , , , , , , , , zyx zyxwvutsrq Fig.14: Transmit signal power spectral density. Single carrier and OFDM-64QAM modulation. 10 , Fig.15: Impact of amplifier A M P M distortion on the power spectral density of single-carrier 64 QAM and OFDM-64QAM Dr. Mohammed El-Tanany: Biography zyxwvutsrq Mohammed El-Tanany obtained the B.Sc. and M.Sc. in Electrical Engineering in 1974 and 1978 respectively, both from Cairo University in Giza, Egypt, and the Ph.D. in Electrical Engineering from Carleton University, Ottawa, ON, Canada in 1983. He worked with the Advanced Systems division of Miller Communications in Kanata, ON from 1982 to 1985 with principal involvement in the research and development of digital transmission equipment for mobile satellite type of applications and also for VHF airborne high-speed down links. He joined Carleton University in 1985, initially as a research associate in the area of wireless communications for mobile and indoor communications. He is currently a professor with the Department of Systems and Computer Engineering where he is actively involved in several research programs that deal with broadband digital transmission in the PCS and millimeter wave frequency bands, HDTV transmission over terrestrial channels, and LMDS transmission in the 28 and 40 GHZ bands. Dr. Yiyan Wu: biography Dr. Yiyan Wu received the M. Eng. and Ph.D. Degrees in electrical engineering from Carleton University, Ottawa, Canada, in 1986 and 1990 respectively. He was a satellite communication systems engineer with Telesat Canada in 1990-1992. He is now a research scientist with the Communications Research Centre, Ottawa, Canada. His research interests include digital video compression and transmission, high definition television, satellite and mobile communications. He was involved in the North American HDTV standard development and ITU-R digital television study. He is an adjunct professor of Carleton University and a member of the Administrative Committee of the IEEE Broadcasting Technology Society. He is advisors/ consultants to many international institutions and industries on digital television broadcasting and wideband wireless communications. Dr. Samy A. Mahmoud: Biography Professor S.A. Mahmoud obtained the M.Eng. and Ph.D. degrees in Electrical Engineering, Carleton University, in 1971 and 1974, respectively. He joined theFaculty of Engineering at Carleton University in 1975 where at present, he is Professor .His main academic and professional research interests are in the areas of Computer Networks, Mobile and Personal Communication Systems and Distributed Computing. He has directed several large R&D projects in theses areas, involving joint universityhndustry research work. He served as a member of the founding Executive Committee which was tasked with the responsibility of drafting the technical architecture and business plans for CANARIE. In the past 15 years he published over 100 archival and conference papers in the areas of computer networks and wireless communication systems. Recently he has led a research project dealing with developing system architectures for the transmission of multi-media infor- mation over frame relay networks. He won several recognition awards in recent years for pioneering research work leading to universityhndustry technology transfer. He is also co-recipient of the Stentor 1993 National Telecommunications award. Dr. Ahmad Chini: biography Dr. Chini's biography is not available for publication