WIMAX, New Developments 2011 Part 5 pptx

TheApplicationofµ-LawCompandingtoMobileWiMax 101 (a) QPSK Veh A (b) QPSK Veh A Equalised Power (c) 16QAM Veh A (d) 16QAM Veh A Equalised Power (e) 64QAM Veh A (f) 64QAM Veh A Equalised Power Fig. 15. QPSK, 16QAM and 64QAM Veh A BER probability curves as a function of  for situations of companded and equalised power companded WiMax (a) QPSK Ped B (b) QPSK Ped B Equalised Power (c) 16QAM Ped B (d) 16QAM Ped B Equalised Power (e) 64QAM Ped B (f) 64QAM Ped B Equalised Power Fig. 16. QPSK, 16QAM and 64QAM Ped B BER probability curves as a function of  for situations of companded and equalised power companded WiMax WIMAX,NewDevelopments102 The significant observations regarding mobility are as follows. The BER depreciates significantly for Veh A and Ped B channels as  increases for both companded and equalised power companded situations. It can also be seen that for each value of , as the SNR increases, the BER flattens off to an asymptotic optimum value. This asymptotic value decreases with increasing , and also with increased data modulation on the subcarriers i.e. the performance is best for QPSK, deteriorates for 16QAM and further deteriorates for 64QAM. Thus a general conclusion is that increased companding will always degrade the performance of WiMax systems for larger SNR in the mobile channels considered. It may also be noted that for very small values of , the BER performance in the asymptotic region is comparable to the asymptotic value associated with standard WiMax. The main reason for the depreciated BER performance is clearly a combination of the companding profile, the modulation and also the affects of the channel. Interestingly, for the direct companding situations, there is a marginal improvement in BER rate over WiMax at lower SNR values across a range of  values. An improvement in BER with companding is expected due to the inherent increased average power provided through the companding process itself. However, the BER is still poor over the regions where the improvement over WiMax occurs. For the Veh A scenarios in Figure 15(a), (b) and (c), the value of  which optimises the BER varies over the lower SNR range under consideration. The optimised  values over the lower SNR range is also nearly independent of the modulation employed. For example, for QPSK, 16QAM and 64QAM, for SNR < 4dB the curve for  ≈ 3 provides the best BER performance. For the approximate range 4dB < SNR < 11dB, the curve for  ≈ 1 is best, and for 11dB < SNR < 16dB,  ≈ 0.1 is optimum. Above 16dB WiMax provides the best BER performance, although there is minimal difference for values of  around 1 or less than 1 and WiMax as the BER levels off. For the Ped B channel in Figures 16(a), (c) and (e), the best performance of companding for lower values of SNR appears to be more dependent on the modulation. For the QPSK BER curves evaluated, for SNR < 8dB,  ≈ 3 is preferred, for SNR > 8,  ≤ 1 is best, though values of  around 1 provide similar results to WiMax in this situation. For 16QAM, µ ≈ 3 is preferred for SNR < 10dB, and for 10 dB < SNR > 18dB  ≈ 1 is preferred and for SNR > 18dB  ≈ 0.1 is best. For 64QAM,  ≈ 3 is preferred for SNR < 11dB, whilst for the range 11dB < SNR < 20dB  ≈ 1 produces the best BER, and for SNR > 20dB,  ≤ 0.1 is the best. Again for increasing SNR WiMax produces the best asymptotic BER performance, though there is little difference in BER performance between WiMax and very small values of  as the BER levels off. Clearly, the BER performance in lower SNR values, when mobility is present, depends not just on the companding profile, but on the modulation and the nature of the multipath channel. As discussed previously, the raw companding BER curves may be slightly misleading due to the fact that real transmitters may be required to work on power limitations in which case the equalised symbol power curves are important. For the equalised power situations, as expected, as  increases, the BER performance depreciates. However, for very small values of  in all situations, the companded performance is similar or close to the general WiMax situation. The reason for the rapid deterioration in BER with increasing  can be explained again as a consequence of the nature of the companding profiles, i.e. large peak amplitude signals can have significant decompanding bit errors at a receiver for larger  values when noise is present. This, mixed with the problems of a mobile channel, accentuates the deterioration in BER. However, for some situations the increased BER may be acceptable within some mobile channels when a significant improvement in PAPR is desired. But perhaps the most important result is that the asymptotic BER values for the equalised power companded situations are nearly identical to the raw companded asymptotic BER values. These asymptotic values are plotted in Figure 17 and indicate that for large SNR values, when  is applied, the influence of the multipath channel is the overwhelming limiting factor on the BER performance. Figure 17 is therefore useful to precisely quantify the optimum BERs achievable for the Veh A and Ped B channels when companding is applied. (a) Veh A 60kmh -1 (b) Ped B 3kmh -1 Fig 17. Variation of the asymptotic BER values as a function of  for QPSK, 16QAM and 64QAM for (a) Veh A 60km -1 and (b) Ped B 3kmh -1 10. Conclusions This chapter has presented and discussed the principles of PAPR reduction and the principles of -Law companding. The application of -Law compounding was applied to one implementation of mobile WiMax using an FFT/IFFT of 1024. The main conclusions are as follows. Companding using -Law profiles has the potential to reduce significantly the PAPR of WiMax. For straight companded WiMax the average power increases and as a consequence the BER performance can be improved. For direct companding the optimum BER performance occurs for  = 8, which produces a PAPR of approximately 6.6dB at the 0.001 probability level, i.e. a reduction of 5.1 dB. However an increase in frequency spectral energy splatter occurs which must be addressed to minimise inter channel interference. For equalised symbol power companded transmissions, the BER performance is actually shown to deteriorate for all values of . However, for small values of , the BER degradation is not severe. This is advantageous as a balance between cost in terms of BER and PAPR reduction can now be quantified along with the expected out-of-band PSD for any chosen value of . The figures produced in this chapter will allow an engineer to take informed decisions on these issues. In relation to mobility, the influence of companding on performance is more complex and appears to depend on the modulation, mobile speed and more importantly the nature of the channel itself. It was shown that for straight companding the optimum BER performance at low values of SNR was dependent on the value of  as well as the nature of the channel. Different ranges of lower SNR values defined different optimum values of . TheApplicationofµ-LawCompandingtoMobileWiMax 103 The significant observations regarding mobility are as follows. The BER depreciates significantly for Veh A and Ped B channels as  increases for both companded and equalised power companded situations. It can also be seen that for each value of , as the SNR increases, the BER flattens off to an asymptotic optimum value. This asymptotic value decreases with increasing , and also with increased data modulation on the subcarriers i.e. the performance is best for QPSK, deteriorates for 16QAM and further deteriorates for 64QAM. Thus a general conclusion is that increased companding will always degrade the performance of WiMax systems for larger SNR in the mobile channels considered. It may also be noted that for very small values of , the BER performance in the asymptotic region is comparable to the asymptotic value associated with standard WiMax. The main reason for the depreciated BER performance is clearly a combination of the companding profile, the modulation and also the affects of the channel. Interestingly, for the direct companding situations, there is a marginal improvement in BER rate over WiMax at lower SNR values across a range of  values. An improvement in BER with companding is expected due to the inherent increased average power provided through the companding process itself. However, the BER is still poor over the regions where the improvement over WiMax occurs. For the Veh A scenarios in Figure 15(a), (b) and (c), the value of  which optimises the BER varies over the lower SNR range under consideration. The optimised  values over the lower SNR range is also nearly independent of the modulation employed. For example, for QPSK, 16QAM and 64QAM, for SNR < 4dB the curve for  ≈ 3 provides the best BER performance. For the approximate range 4dB < SNR < 11dB, the curve for  ≈ 1 is best, and for 11dB < SNR < 16dB,  ≈ 0.1 is optimum. Above 16dB WiMax provides the best BER performance, although there is minimal difference for values of  around 1 or less than 1 and WiMax as the BER levels off. For the Ped B channel in Figures 16(a), (c) and (e), the best performance of companding for lower values of SNR appears to be more dependent on the modulation. For the QPSK BER curves evaluated, for SNR < 8dB,  ≈ 3 is preferred, for SNR > 8,  ≤ 1 is best, though values of  around 1 provide similar results to WiMax in this situation. For 16QAM, µ ≈ 3 is preferred for SNR < 10dB, and for 10 dB < SNR > 18dB  ≈ 1 is preferred and for SNR > 18dB  ≈ 0.1 is best. For 64QAM,  ≈ 3 is preferred for SNR < 11dB, whilst for the range 11dB < SNR < 20dB  ≈ 1 produces the best BER, and for SNR > 20dB,  ≤ 0.1 is the best. Again for increasing SNR WiMax produces the best asymptotic BER performance, though there is little difference in BER performance between WiMax and very small values of  as the BER levels off. Clearly, the BER performance in lower SNR values, when mobility is present, depends not just on the companding profile, but on the modulation and the nature of the multipath channel. As discussed previously, the raw companding BER curves may be slightly misleading due to the fact that real transmitters may be required to work on power limitations in which case the equalised symbol power curves are important. For the equalised power situations, as expected, as  increases, the BER performance depreciates. However, for very small values of  in all situations, the companded performance is similar or close to the general WiMax situation. The reason for the rapid deterioration in BER with increasing  can be explained again as a consequence of the nature of the companding profiles, i.e. large peak amplitude signals can have significant decompanding bit errors at a receiver for larger  values when noise is present. This, mixed with the problems of a mobile channel, accentuates the deterioration in BER. However, for some situations the increased BER may be acceptable within some mobile channels when a significant improvement in PAPR is desired. But perhaps the most important result is that the asymptotic BER values for the equalised power companded situations are nearly identical to the raw companded asymptotic BER values. These asymptotic values are plotted in Figure 17 and indicate that for large SNR values, when  is applied, the influence of the multipath channel is the overwhelming limiting factor on the BER performance. Figure 17 is therefore useful to precisely quantify the optimum BERs achievable for the Veh A and Ped B channels when companding is applied. (a) Veh A 60kmh -1 (b) Ped B 3kmh -1 Fig 17. Variation of the asymptotic BER values as a function of  for QPSK, 16QAM and 64QAM for (a) Veh A 60km -1 and (b) Ped B 3kmh -1 10. Conclusions This chapter has presented and discussed the principles of PAPR reduction and the principles of -Law companding. The application of -Law compounding was applied to one implementation of mobile WiMax using an FFT/IFFT of 1024. The main conclusions are as follows. Companding using -Law profiles has the potential to reduce significantly the PAPR of WiMax. For straight companded WiMax the average power increases and as a consequence the BER performance can be improved. For direct companding the optimum BER performance occurs for  = 8, which produces a PAPR of approximately 6.6dB at the 0.001 probability level, i.e. a reduction of 5.1 dB. However an increase in frequency spectral energy splatter occurs which must be addressed to minimise inter channel interference. For equalised symbol power companded transmissions, the BER performance is actually shown to deteriorate for all values of . However, for small values of , the BER degradation is not severe. This is advantageous as a balance between cost in terms of BER and PAPR reduction can now be quantified along with the expected out-of-band PSD for any chosen value of . The figures produced in this chapter will allow an engineer to take informed decisions on these issues. In relation to mobility, the influence of companding on performance is more complex and appears to depend on the modulation, mobile speed and more importantly the nature of the channel itself. It was shown that for straight companding the optimum BER performance at low values of SNR was dependent on the value of  as well as the nature of the channel. Different ranges of lower SNR values defined different optimum values of . WIMAX,NewDevelopments104 Generally, for larger SNR values the BER performance degraded as  was increased and became asymptotic with increasing SNR. For the equalised power companding situation, WiMax always produces best BER performance. However, for very small values of , there is very little difference between companded WiMax and WiMax. A compromise may also be reached in relation to a reduced BER performance in mobility versus a required PAPR level. It was also discovered that the companded and equalised power companded BER optimised asymptotic values for mobility were approximately the same indicating that the best BER performance for the minimum SNR requirements can be quantified for any design value of . This is also helpful in understanding the anticipated best BER performance available in mobile channels when companding is chosen to provide a reduced PAPR level. Further work in relation to the results presented in this chapter may be carried out. This includes an investigation of the BER performance for companded WiMax when channel coding is incorporated, i.e. convolution and turbo coding, when Reed-Solomon coding is employed, and when other more advanced channel estimation techniques are considered. The importance of filtering or innovative techniques for reducing the spectral splatter should also be explored. Other areas for investigation also include quantifying the influence on BER for a larger range of different mobile channels as a function of . 11. References Armstrong, J. (2001). New OFDM Peak-to-Average Power Reduction Scheme, Proc. IEEE, VTC2001 Spring, Rhodes, Greece, pp. 756-760 Armstrong, J. (2002). Peak-to-average power reduction for OFDM by repeated clipping and frequency domain filtering, Electronics Letters, Vol.38, No.5, pp.246-247, Feb. 2002. Bäuml, R.W.; Fisher, R.F.H. & Huber, J.B. (1996). Reducing the peak-to-average power ratio of multicarrier modulation by selected mapping, IEE Electronics Letters, Vol.32, No.22, pp. 2056-2057 Boyd, S. (1986). Multitone Signal with Low Crest Factor, IEEE Transactions on Circuits and Systems, Vol. CAS-33, No.10, pp. 1018-1022 Breiling, M.; Müller-Weinfurtner, S.H. & Huber, J.B. (2001). SLM Peak-Power Reduction Without Explicit Side Information, IEEE Communications Letters, Vol.5, No.6, pp. 239- 241 Cimini, L.J.,Jr.; & Sollenberger, N.R. (2000). Peak-to-Average Power Ratio Reduction of an OFDM Signal Using Partial Transmit Sequences, IEEE Communications Letters, Vol.4, No.3, pp. 86-88 Davis, J.A. & Jedwab, J. (1999). Peak-to-Mean Power Control in OFDM, Golay Complementary Sequences, and Reed-Muller Codes, IEEE Transactions on Information Theory, Vol. 45, No.7, pp. 2397-2417 De Wild, A. (1997). The Peak-to-Average Power Ratio of OFDM, MSc Thesis, Delft University of Technology, Delft, The Netherlands, 1997 Golay, M. (1961). Complementary Series, IEEE Transactions on Information Theory, Vol.7, No.2, pp. 82-87 Hanzo, L.; Münster, M; Choi, B.J. & Keller, T. (2003). OFDM and MC-CDMA for Broadcasting Multi-User Communications, WLANS and Broadcasting, Wiley-IEEE Press, ISBN 0470858796 Han, S.H. & Lee, J.H. (2005). An Overview of Peak-to-Average Power Ratio Reduction Techniques for Multicarrier Transmission, IEEE Wireless Communications, Vol.12, Issue 2, pp. 56-65, April 2005 Hill, G.R.; Faulkner, M. & Singh, J. (2000). Reducing the peak-to-average power ratio in OFDM by cyclically shifting partial transmit sequences, IEE Electronics Letters, Vol.33, No.6, pp. 560-561 Huang, X.; Lu, J., Chang, J. & Zheng, J. (2001). Companding Transform for the Reduction of Peak- to-Average Power Ratio of OFDM Signals, Proc. IEEE Vehicular Technology Conference 2001, pp. 835-839 IEEE Std. 802.16e. (2005). Air Interface for Fixed and Mobile Broadband Wireless Access Systems: Amendment for Physical and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed Bands, IEEE, New York, 2005. Jayalath, A.D.S. & Tellambura, C. (2000). Reducing the Peak-to-Average Power Ratio of Orthogonal Frequency Division Multiplexing Signal Through Bit or Symbol Interleaving, IEE Electronics Letters, Vol.36, No.13, pp. 1161-1163 Jiang, T. & Song, Y-H. (2005). Exponential Companding Technique for PAPR Reduction in OFDM Systems, IEEE Trans. Broadcasting, Vol. 51(2), pp. 244-248 Jones, A.E, & Wilkinson, T.A. (1995). Minimization of the Peak to Mean Envelope Power Ratio in Multicarrier Transmission Schemes by Block Coding, Proc. IEEE VTC’95, Chicago, pp. 825-831 Jones, A.E. & Wilkinson, T.A (1996). Combined Coding for Error Control and Increased Robustness to System Nonlinearities in OFDM, Proc. IEEE VTC’96, Atlanta, GA, pp. 904-908 Jones, A.E.; Wilkinson, T.A. & Barton, S.K. (1994). Block coding scheme for the reduction of peak to mean envelope power ratio of multicarrier transmission schemes, Electronics Letters, Vol.30, No.25, pp. 2098-2099 Kang, S.G. (2006). The Minimum PAPR Code for OFDM Systems, ETRI Journal, Vol.28, No.2, pp. 235-238 Lathi, B.P. (1998). Modern Digital and Analog Communication Systems, 3rd Ed., pp. 262-278, Oxford University Press, ISBN 0195110099 Li, X. & Cimini Jr, L.J. (1997). Effects of Clipping and Filtering on the Performance of OFDM, Proc. IEEE VTC 1997, pp. 1634-1638 Lloyd, S. (2006). Challenges of Mobile WiMAX RF Transceivers, Proceedings of the 8th International Conference on Solid-State and Integrated Circuit Technology, pp. 1821– 1824, ISBN 1424401607, October, 2006, Shanghai May, T. & Rohling, H. (1998). Reducing the Peak-to-Average Power Ratio in OFDM Radio Transmission Systems, Proc. IEEE Vehicular Technology Conf. (VTC’98), pp.2774- 2778 Mattsson, A.; Mendenhall, G. & Dittmer, T. (1999). Comments on “Reduction of peak-to- average power ratio of OFDM systems using a companding technique”, IEEE Transactions on Broadcasting, Vol. 45, No. 4, pp. 418-419 Müller, S.H. & Huber, J.B. (1997a). OFDM with Reduced Peak-to-Average Power Ratio by Optimum Combination of Partial Transmit Sequences, Electronics Letters, Vol.33, No.5, pp.368-369 Müller, S.H. & Huber, J.B. (1997b). A Novel Peak Power Reduction Scheme for OFDM, Proc. IEEE PIMRC ’97, Helsinki, Finland, pp.1090-1094 TheApplicationofµ-LawCompandingtoMobileWiMax 105 Generally, for larger SNR values the BER performance degraded as  was increased and became asymptotic with increasing SNR. For the equalised power companding situation, WiMax always produces best BER performance. However, for very small values of , there is very little difference between companded WiMax and WiMax. A compromise may also be reached in relation to a reduced BER performance in mobility versus a required PAPR level. It was also discovered that the companded and equalised power companded BER optimised asymptotic values for mobility were approximately the same indicating that the best BER performance for the minimum SNR requirements can be quantified for any design value of . This is also helpful in understanding the anticipated best BER performance available in mobile channels when companding is chosen to provide a reduced PAPR level. Further work in relation to the results presented in this chapter may be carried out. This includes an investigation of the BER performance for companded WiMax when channel coding is incorporated, i.e. convolution and turbo coding, when Reed-Solomon coding is employed, and when other more advanced channel estimation techniques are considered. The importance of filtering or innovative techniques for reducing the spectral splatter should also be explored. Other areas for investigation also include quantifying the influence on BER for a larger range of different mobile channels as a function of . 11. References Armstrong, J. (2001). New OFDM Peak-to-Average Power Reduction Scheme, Proc. IEEE, VTC2001 Spring, Rhodes, Greece, pp. 756-760 Armstrong, J. (2002). Peak-to-average power reduction for OFDM by repeated clipping and frequency domain filtering, Electronics Letters, Vol.38, No.5, pp.246-247, Feb. 2002. Bäuml, R.W.; Fisher, R.F.H. & Huber, J.B. (1996). Reducing the peak-to-average power ratio of multicarrier modulation by selected mapping, IEE Electronics Letters, Vol.32, No.22, pp. 2056-2057 Boyd, S. (1986). Multitone Signal with Low Crest Factor, IEEE Transactions on Circuits and Systems, Vol. CAS-33, No.10, pp. 1018-1022 Breiling, M.; Müller-Weinfurtner, S.H. & Huber, J.B. (2001). SLM Peak-Power Reduction Without Explicit Side Information, IEEE Communications Letters, Vol.5, No.6, pp. 239- 241 Cimini, L.J.,Jr.; & Sollenberger, N.R. (2000). Peak-to-Average Power Ratio Reduction of an OFDM Signal Using Partial Transmit Sequences, IEEE Communications Letters, Vol.4, No.3, pp. 86-88 Davis, J.A. & Jedwab, J. (1999). Peak-to-Mean Power Control in OFDM, Golay Complementary Sequences, and Reed-Muller Codes, IEEE Transactions on Information Theory, Vol. 45, No.7, pp. 2397-2417 De Wild, A. (1997). The Peak-to-Average Power Ratio of OFDM, MSc Thesis, Delft University of Technology, Delft, The Netherlands, 1997 Golay, M. (1961). Complementary Series, IEEE Transactions on Information Theory, Vol.7, No.2, pp. 82-87 Hanzo, L.; Münster, M; Choi, B.J. & Keller, T. (2003). OFDM and MC-CDMA for Broadcasting Multi-User Communications, WLANS and Broadcasting, Wiley-IEEE Press, ISBN 0470858796 Han, S.H. & Lee, J.H. (2005). An Overview of Peak-to-Average Power Ratio Reduction Techniques for Multicarrier Transmission, IEEE Wireless Communications, Vol.12, Issue 2, pp. 56-65, April 2005 Hill, G.R.; Faulkner, M. & Singh, J. (2000). Reducing the peak-to-average power ratio in OFDM by cyclically shifting partial transmit sequences, IEE Electronics Letters, Vol.33, No.6, pp. 560-561 Huang, X.; Lu, J., Chang, J. & Zheng, J. (2001). Companding Transform for the Reduction of Peak- to-Average Power Ratio of OFDM Signals, Proc. IEEE Vehicular Technology Conference 2001, pp. 835-839 IEEE Std. 802.16e. (2005). Air Interface for Fixed and Mobile Broadband Wireless Access Systems: Amendment for Physical and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed Bands, IEEE, New York, 2005. Jayalath, A.D.S. & Tellambura, C. (2000). Reducing the Peak-to-Average Power Ratio of Orthogonal Frequency Division Multiplexing Signal Through Bit or Symbol Interleaving, IEE Electronics Letters, Vol.36, No.13, pp. 1161-1163 Jiang, T. & Song, Y-H. (2005). Exponential Companding Technique for PAPR Reduction in OFDM Systems, IEEE Trans. Broadcasting, Vol. 51(2), pp. 244-248 Jones, A.E, & Wilkinson, T.A. (1995). Minimization of the Peak to Mean Envelope Power Ratio in Multicarrier Transmission Schemes by Block Coding, Proc. IEEE VTC’95, Chicago, pp. 825-831 Jones, A.E. & Wilkinson, T.A (1996). Combined Coding for Error Control and Increased Robustness to System Nonlinearities in OFDM, Proc. IEEE VTC’96, Atlanta, GA, pp. 904-908 Jones, A.E.; Wilkinson, T.A. & Barton, S.K. (1994). Block coding scheme for the reduction of peak to mean envelope power ratio of multicarrier transmission schemes, Electronics Letters, Vol.30, No.25, pp. 2098-2099 Kang, S.G. (2006). The Minimum PAPR Code for OFDM Systems, ETRI Journal, Vol.28, No.2, pp. 235-238 Lathi, B.P. (1998). Modern Digital and Analog Communication Systems, 3rd Ed., pp. 262-278, Oxford University Press, ISBN 0195110099 Li, X. & Cimini Jr, L.J. (1997). Effects of Clipping and Filtering on the Performance of OFDM, Proc. IEEE VTC 1997, pp. 1634-1638 Lloyd, S. (2006). Challenges of Mobile WiMAX RF Transceivers, Proceedings of the 8th International Conference on Solid-State and Integrated Circuit Technology, pp. 1821– 1824, ISBN 1424401607, October, 2006, Shanghai May, T. & Rohling, H. (1998). Reducing the Peak-to-Average Power Ratio in OFDM Radio Transmission Systems, Proc. IEEE Vehicular Technology Conf. (VTC’98), pp.2774- 2778 Mattsson, A.; Mendenhall, G. & Dittmer, T. (1999). Comments on “Reduction of peak-to- average power ratio of OFDM systems using a companding technique”, IEEE Transactions on Broadcasting, Vol. 45, No. 4, pp. 418-419 Müller, S.H. & Huber, J.B. (1997a). OFDM with Reduced Peak-to-Average Power Ratio by Optimum Combination of Partial Transmit Sequences, Electronics Letters, Vol.33, No.5, pp.368-369 Müller, S.H. & Huber, J.B. (1997b). A Novel Peak Power Reduction Scheme for OFDM, Proc. IEEE PIMRC ’97, Helsinki, Finland, pp.1090-1094 WIMAX,NewDevelopments106 O’Neill, R. & Lopes, L.B. (1995). Envelope variations and Spectral Splatter in Clipped Multicarrier signals, Proc. IEEE PIMRC ’95, Toronto, Canada. pp. 71-75 Paterson, G.K. and Tarokh, V. (2000). On the Existence and Construction of Good Codes with Low Peak-to-Average Power Ratios, IEEE Transactions on Information Theory, Vol.46, No.6, pp. 1974-1987 Pauli, M & Kuchenbecker, H.P. (1996). Minimization of the Intermodulation Distortion of a Nonlinearly Amplified OFDM Signal, Wireless Personal Communications, Vol.4, No.1, pp. 93-101 Sklar, B. (2001). Digital Communications – Fundamentals and Applications, 2nd Ed, Pearson Education, pp. 851-854 Stewart, B.G. & Vallavaraj, A. 2008. The Application of μ-Law Companding to the WiMax IEEE802.16e Down Link PUSC, 14th IEEE International Conference on Parallel and Distributed Systems, (ICPADS’08), pp. 896-901, Melbourne, December, 2008 Tarokh, V. & Jafarkhani, H. (2000). On the computation and Reduction of the Peak-to-Average Power Ratio in Multicarrier Communications, IEEE Transactions on Communications, Vol.48, No.1, pp. 37-44 Tellambura, C. & Jayalath, A.D.S. (2001). PAR reduction of an OFDM signal using partial transmit sequences, Proc. VTC 2001, Atlanta City, NJ, pp.465-469 Vallavaraj, A. (2008). An Investigation into the Application of Companding to Wireless OFDM Systems, PhD Thesis, Glasgow Caledonian University, 2008 Vallavaraj, A.; Stewart, B.G.; Harrison, D.K. & McIntosh, F.G. (2004). Reduction of Peak-to- Average Power Ratio of OFDM Signals Using Companding, 9th Int. Conf. Commun. Systems (ICCS), Singapore, pp. 160-164 Van Eetvelt, P.; Wade, G. & Tomlinson, M. (1996). Peak to average power reduction for OFDM schemes by selective scrambling, IEE Electronics Letters, Vol.32, No.21, pp. 1963-1964 Van Nee, R. & De Wild, A. (1998). Reducing the peak-to-average power ratio of OFDM, Proc. IEEE Vehicular Technology Conf. (VTC’98), pp. 2072–2076 Van Nee, R. & Prasad, R. (2000). OFDM for Wireless Multimedia Communications, Artech House, London, pp. 241-243 Wang, L. & Tellambura, C. (2005). A Simplified Clipping and Filtering Technique for PAR Reduction in OFDM Systems, IEEE Signal Processing Letters, Vol.12, No.6, pp. 453- 456 Wang, L. & Tellambura, C. (2006). An Overview of Peak-to-Average Power Ratio Reduction Techniques for OFDM Systems, Proc. IEEE International Symposium on Signal Processing and Information Technology, ISSPIT-2006, pp. 840-845 Wang, X., Tjhung, T.T. and Ng, C.S. (1999). Reduction of Peak-to-Average Power Ratio of OFDM System Using a Companding Technique, IEEE Transactions on Broadcasting, Vol.45, No.3, pp. 303-307 Yang, K. & Chang, S II. (2003). Peak-to-Average Power Control in OFDM Using Standard Arrays of Linear Block Codes, IEEE Communications Letters, Vol.7, No.4, pp. 174-176 VLSIArchitecturesforWIMAXChannelDecoders 107 VLSIArchitecturesforWIMAXChannelDecoders MaurizioMartinaandGuidoMasera X VLSI Architectures for WIMAX Channel Decoders Maurizio Martina and Guido Masera Politecnico di Torino Italy 1. Introduction WIMAX has gained a wide popularity due to the growing interest and diffusion of broadband wireless access systems. In order to be flexible and reliable WIMAX adopts several different channel codes, namely convolutional-codes (CC), convolutional-turbo- codes (CTC), block-turbo-codes (BTC) and low-density-parity-check (LDPC) codes, that are able to cope with different channel conditions and application needs. On the other hand, high performance digital CMOS technologies have reached such a development that very complex algorithms can be implemented in low cost chips. Moreover, embedded processors, digital signal processors, programmable devices, as FPGAs, application specific instruction-set processors and VLSI technologies have come to the point where the computing power and the memory required to execute several real time applications can be incorporated even in cheap portable devices. Among the several application fields that have been strongly reinforced by this technology progress, channel decoding is one of the most significant and interesting ones. In fact, it is known that the design of efficient architectures to implement such channel decoders is a hard task, hardened by the high throughput required by WIMAX systems, which is up to about 75 Mb/s per channel. In particular, CTC and LDPC codes, whose decoding algorithms are iterative, are still a major topic of interest in the scientific literature and the design of efficient architectures is still fostering several research efforts both in industry and academy. In this Chapter, the design of VLSI architectures for WIMAX channel decoders will be analyzed with emphasis on three main aspects: performance, complexity and flexibility. The chapter will be divided into two main parts; the first part will deal with the impact of system requirements on the decoder design with emphasis on memory requirements, the structure of the key components of the decoders and the need for parallel architectures. To that purpose a quantitative approach will be adopted to derive from system specifications key architectural choices; most important architectures available in the literature will be also described and compared. The second part will concentrate on a significant case of study: the design of a complete CTC decoder architecture for WIMAX, including also hardware units for depuncturing (bit- deselection) and external deinterleaving (sub-block deinterleaver) functions. 5 WIMAX,NewDevelopments108 2. From system specifications to architectural choices The system specifications and in particular the requirement of a peak throughput of about 75 Mb/s per channel imposed by the WIMAX standard have a significant impact on the decoder architecture. In the following sections we analyze the most significant architectures proposed in the literature to implement CC decoders (Viterbi decoders), BTC, CTC and LDPC decoders. 2.1 Viterbi decoders The most widely used algorithm to decode CCs is the Viterbi algorithm [Viterbi, 1967], which is based on finding the shortest path along a graph that represents the CC trellis. As an example in Fig. 1 a binary 4-states CC is shown as a feedback shift register (a) together with the corresponding state diagram (b) and trellis (c) representations. (c) 0/00 1/11 0/10 0/10 1/01 1/01 00 00 01 01 10 10 11 11 1/11 0/10 0/00 1/01 1/11 1/01 0/10 0/00 (a) (b) e2 e1 c1 u c2 e1 e2 u/c2c1 00 01 10 11 1/11 0/00 Fig. 1. Binary 4-state CC example: shift register (a), state diagram (b) and trellis (c) representations In the given example, the feedback shift register implementation of the encoder generates two output bits, c 1 and c 2 for each received information bit, u; c 1 is the systematic bit. The state diagram basically is a Mealy finite state machine describing the encoder behaviour in a time independent way: each node corresponds to a valid encoder state, represented by means of the flip flop content, e 1 and e 2 , while edges are labelled with input and output bits. The trellis representation also provides time information, explicitly showing the evolution from one state to another in different time steps (one single step is drawn in the picture). At each trellis step n, the Viterbi algorithm associates to each trellis state S a state metric Γ S n that is calculated along the shortest path and stores a decision d S n , which identifies the entering transition on the shortest path. First, the decoder computes the branch metrics (γ n ), that are the distances from the metrics labelling each edge on the trellis and the actual received soft symbols. In the case of a binary CC with rate 0.5 the soft symbols are λ1 n and λ2 n and the branch metrics γ n (c2,c1) (see Fig. 2 (a)). Starting from these values, the state metrics are updated by selecting the larger metric among the metrics related to each incoming edge of a trellis state and storing the corresponding decision d S n . Finally, decoded bits are obtained by means of a recursive procedure usually referred to as trace-back. In order to estimate the sequence of bits that were encoded for transmission, a state is first selected at the end of the trellis portion to be decoded, then the decoder iteratively goes backward through the state history memory where decisions d S n have been previously stored: this allows one to select, for current state, a new state, which is listed in the state history trace as being the predecessor to that state. Different implementation methods are available to make the initial state choice and to size the portion of trellis where the trace back operation is performed: these methods affect both decoder complexity and error correcting capability. For further details on the algorithm the reader can refer to [Viterbi, 1967]; [Forney, 1973]. Looking at the global architecture, the main blocks required in a Viterbi decoder are the branch metric unit (BMU) devoted to compute γ n , the state metric unit (SMU) to calculate Γ S n and the trace-back unit (TBU) to obtain the decoded sequence. The BMU is made of adders and subtracters to properly combine the input soft symbols (see Fig. 2 (a)). The SMU is based on the so called add-compare select structure (ACS) as shown in Fig.2 (b). Said i the i-th starting state that is connected to an arriving state S by an edge whose branch metric is γ i n-1 , then Γ S n is calculated as in (1). }{max 11   n i n i i n S  (1) γ (01) n γ (10) n γ (11) n Γ S n d S n Γ j n −1 γ j n−1 γ i n−1 Γ i − − − + + − + + λ2 λ1 γ (00) n n n (a) (b) n−1 Fig. 2. BMU and ACS architectures for a rate 0.5 CC As it can be inferred from (1) Γ S n is obtained by adding branch metrics with state metrics, comparing and selecting the higher metric that represents the shortest incoming path. The corresponding decision d S n is stored in a memory that is later read by the TBU to reconstruct the survived path. Due to the recursive form of (1), as long as n increases, the number of bits to represent Γ S n tends to become larger. This problem can be solved by normalizing the state metrics at each step. However, this solution requires to add a normalization stage increasing both the SMU complexity and critical path. An effective technique, based on two complement representation, helps limiting the growth of state metrics, as described in [Hekstra, 1989]. u c1 c2 Fig. 3. WIMAX binary 64-state CC with rate 0.5 shift register representation VLSIArchitecturesforWIMAXChannelDecoders 109 2. From system specifications to architectural choices The system specifications and in particular the requirement of a peak throughput of about 75 Mb/s per channel imposed by the WIMAX standard have a significant impact on the decoder architecture. In the following sections we analyze the most significant architectures proposed in the literature to implement CC decoders (Viterbi decoders), BTC, CTC and LDPC decoders. 2.1 Viterbi decoders The most widely used algorithm to decode CCs is the Viterbi algorithm [Viterbi, 1967], which is based on finding the shortest path along a graph that represents the CC trellis. As an example in Fig. 1 a binary 4-states CC is shown as a feedback shift register (a) together with the corresponding state diagram (b) and trellis (c) representations. (c) 0/00 1/11 0/10 0/10 1/01 1/01 00 00 01 01 10 10 11 11 1/11 0/10 0/00 1/01 1/11 1/01 0/10 0/00 (a) (b) e2 e1 c1 u c2 e1 e2 u/c2c1 00 01 10 11 1/11 0/00 Fig. 1. Binary 4-state CC example: shift register (a), state diagram (b) and trellis (c) representations In the given example, the feedback shift register implementation of the encoder generates two output bits, c 1 and c 2 for each received information bit, u; c 1 is the systematic bit. The state diagram basically is a Mealy finite state machine describing the encoder behaviour in a time independent way: each node corresponds to a valid encoder state, represented by means of the flip flop content, e 1 and e 2 , while edges are labelled with input and output bits. The trellis representation also provides time information, explicitly showing the evolution from one state to another in different time steps (one single step is drawn in the picture). At each trellis step n, the Viterbi algorithm associates to each trellis state S a state metric Γ S n that is calculated along the shortest path and stores a decision d S n , which identifies the entering transition on the shortest path. First, the decoder computes the branch metrics (γ n ), that are the distances from the metrics labelling each edge on the trellis and the actual received soft symbols. In the case of a binary CC with rate 0.5 the soft symbols are λ1 n and λ2 n and the branch metrics γ n (c2,c1) (see Fig. 2 (a)). Starting from these values, the state metrics are updated by selecting the larger metric among the metrics related to each incoming edge of a trellis state and storing the corresponding decision d S n . Finally, decoded bits are obtained by means of a recursive procedure usually referred to as trace-back. In order to estimate the sequence of bits that were encoded for transmission, a state is first selected at the end of the trellis portion to be decoded, then the decoder iteratively goes backward through the state history memory where decisions d S n have been previously stored: this allows one to select, for current state, a new state, which is listed in the state history trace as being the predecessor to that state. Different implementation methods are available to make the initial state choice and to size the portion of trellis where the trace back operation is performed: these methods affect both decoder complexity and error correcting capability. For further details on the algorithm the reader can refer to [Viterbi, 1967]; [Forney, 1973]. Looking at the global architecture, the main blocks required in a Viterbi decoder are the branch metric unit (BMU) devoted to compute γ n , the state metric unit (SMU) to calculate Γ S n and the trace-back unit (TBU) to obtain the decoded sequence. The BMU is made of adders and subtracters to properly combine the input soft symbols (see Fig. 2 (a)). The SMU is based on the so called add-compare select structure (ACS) as shown in Fig.2 (b). Said i the i-th starting state that is connected to an arriving state S by an edge whose branch metric is γ i n-1 , then Γ S n is calculated as in (1). }{max 11   n i n i i n S  (1) γ (01) n γ (10) n γ (11) n Γ S n d S n Γ j n −1 γ j n−1 γ i n−1 Γ i − − − + + − + + λ2 λ1 γ (00) n n n (a) (b) n−1 Fig. 2. BMU and ACS architectures for a rate 0.5 CC As it can be inferred from (1) Γ S n is obtained by adding branch metrics with state metrics, comparing and selecting the higher metric that represents the shortest incoming path. The corresponding decision d S n is stored in a memory that is later read by the TBU to reconstruct the survived path. Due to the recursive form of (1), as long as n increases, the number of bits to represent Γ S n tends to become larger. This problem can be solved by normalizing the state metrics at each step. However, this solution requires to add a normalization stage increasing both the SMU complexity and critical path. An effective technique, based on two complement representation, helps limiting the growth of state metrics, as described in [Hekstra, 1989]. u c1 c2 Fig. 3. WIMAX binary 64-state CC with rate 0.5 shift register representation WIMAX,NewDevelopments110 The WIMAX standard specifies a binary 64 states CC with rate 0.5, whose shift register representation is shown in Fig. 3. Usually Viterbi decoder architectures exploit the trellis intrinsic parallelism to simultaneously compute at each trellis step all the branch metrics and update all the state metrics. Thus, said n the number of states of a CC, a parallel architecture employs a BMU and n ACS modules. Moreover, to reduce the decoding latency, the trace-back is performed as a sliding-window process [Radar, 1981] on portions of trellis of width W. This approach not only reduces the latency, but also the size of the decision memory that depending on the TBU radix requires usually 3W or 4W cells [Black & Meng, 1992]. To improve the decoder throughput, two [Black & Meng, 1992] or more [Fettweis & Meyr, 1989]; [Kong & Parhi, 2004]; [Cheng & Parhi, 2008] trellis steps can be processed concurrently. These solutions lead to the so called higher radix or M-look-ahead step architectures. According to [Kong & Parhi, 2004], the throughput sustained by an M-look- ahead step architecture, defined as the number of decoded bits over the decoding time is kMf WMN fNk T clk T clkT     / (2) where f clk is the clock frequency, N T is the number of trellis steps, k=1 for a binary CC, k=2 for a double binary CC and the right most expression is obtained under the condition W << N T that is a reasonable assumption in real cases. Thus, to achieve the throughput required by the WIMAX standard with a clock frequency limited to tens to few thousands of MHz, M=1 (radix-2) or M=2 (radix-4) is a reasonable choice. However, since CCs are widely used in many communication systems, some recent works as [Batcha & Shameri, 2007] and [Kamuf et al., 2008] address the design of flexible Viterbi decoders that are able to support different CCs. As a further step [Vogt & When, 2008] proposed a multi-code decoder architecture, able to support both CCs and CTCs. 2.2 BTC decoders Block Turbo Codes or product codes are serially concatenated block codes. Given two block codes C 1 =(n 1 ,k 1 ,δ 1 ) and C 2 =(n 2 ,k 2 ,δ 2 ) where n i , k i and δ i represent the code-word length, the number of information bits, and the minimum Hamming distance, respectively, the corresponding product code is obtained according to [Pyndiah, 1998] as an array with k 1 rows and k 2 columns containing the information bits. Then coding is performed on the k 1 rows with C 2 and on the n 2 obtained columns with C 1 . The decoding of BTC codes can be performed iteratively row-wise and column-wise by using the sub-optimal algorithm detailed in [Pyndiah, 1998]. The basic idea relies on using the Chase search [Chase, 1972] a near-maximum-likelihood (near-ML) searching strategy to find a list of code-words and an ML decided code-word d ={d 0 ,…, d n-1 } with d j  {-1,+1}. According to the notation used in [Vanstraceele et al., 2008], decision reliabilities are computed as 4 |||| )( 2 )(1 2 )(1 jj j crcr d     (3) where r={r 0 ,…r n-1 } is the received code-word and c -1(j) and c +1(j) are the code-words in the Chase list at minimum Euclidean distance from r such that the j-th bit of the code-word is -1 and +1 respectively. Then one decoder sends to the other the extrinsic information jj out j rdw  )(  (4) If the Chase search fails the extrinsic information is approximated as j out j dw   (5) where β is a weight factor increasing with the number of iterations. The decoder that receives the extrinsic information uses an updated version of r obtained as in j old j new j wrr   (6) where  is a weight factor increasing with the number of iterations. A scheme of the elementary block turbo decoder is shown in Fig. 4 where the block named “decoder” is a Soft-In-Soft-out (SISO) module that performs the Chase search and implements (3), (4) and (5). An effective solution to implement the SISO module is based on a three pipelined stage architecture where the three stages are identified as reception, processing, and transmission units [Kerouedan & Adde, 2000]. As detailed in [LeBidan et al., 2008], during each stage, the N soft values of the received word r are processed sequentially in N clock periods. The reception stage is devoted to find the least reliable bits in the received code-word. The processing stage performs the Chase search and the transmission stage calculates λ(d j ), w j and r j new . Another solution is proposed in [Goubier et al. 2008] where the elementary decoder is implemented as a pipeline resorting to the mini-maxi algorithm, namely by using mini-maxi arrays to store the best metrics of all decoded code-words in the Chase list. w j r j new w j o ut r r j old α delay delay in decoder r j new β r Fig. 4. Elementary block turbo decoder scheme Several works in the literature deal with BTC complexity reduction. As an example [Adde & Pyndiah, 2000] suggests to compute β in (5) on a per-code-word basis, whereas in [Chi et al., [...]... deal with BTC complexity reduction As an example [Adde & Pyndiah, 2000] suggests to compute β in (5) on a per-code-word basis, whereas in [Chi et al., 112 WIMAX, New Developments 2004] the dependency on  in (6) is solved by replacing the term ·wj with tanh(wj/2) In [Le et al 20 05] both  in (6) and β in (5) are avoided by exploiting Euclidean distance property Due to its row-column structure, the block... the ones show in Table 1 N 15 31 63 k 11 26 57 Table 1 WIMAX binary extended Hamming codes (H(n,k)) used for BTC Considering the interleaved architecture described in [Goubier et al 2008] where a fully decoded block is output every 4 .5 half iterations, we obtain that 75 Mb/s can be obtained with a clock frequency of 84 MHz, 31 MHz and 14 MHz for H( 15, 11), H(31,26) and H(63 ,57 ) respectively 2.3 CTC decoders... received from connected bit nodes and generate new messages to be sent back to variable nodes In message passing decoders, messages are exchanged along the edges of the Tanner graph, and computations are performed at the nodes To avoid multiplications and divisions, the decoder usually works in the logarithmic domain 118 WIMAX, New Developments B1 B2 2 B3 4 1 5 3 6 C1 C2 C3 Fig 8 Example Tanner graph The... Lk and Fk are 122 WIMAX, New Developments computed As a consequence, about two clock cycles per sample are required to complete the symbol deselection, namely 6N LLRs are output in 12N clock cycles So that the symbol deselection throughput can be estimated as TSD  f 6N f clk  clk 12 N 2 (27) As it can be observed, to sustain 2 25 millions of LLRs per second a clock frequency of 450 MHz is required... each single bit and check node and all messages are passed in parallel on dedicated routes Partially parallel architectures: more processing units work in parallel, serving all bit and check nodes within a number of cycles; suitable organization and hardware support is required to exchange messages 120 WIMAX, New Developments For most codes and applications, the first approach results in slow implementations,... SCHk Fk  ( SPIDk  Lk ) mod 6 N (23) (24) Since NSCHk[1, 480] and mk{2, 4, 6} we can rewrite (23) as (2 N SCHk  N SCHk )  25  Lk  (2 N SCHk  N SCHk )  26 5  (8 N SCHk  N SCHk )  2  when mk  2 when mk  4 ( 25) when mk  6 The efficient implementation of ( 25) is obtained with an adder whose inputs are NSCHk and the selection between two hardwired left shifted versions of NSCHk (one position... the border metric inheritance strategy [Abbasfar & Yao 2003]; [Zhan et al 2006] we obtain SISOcyclat≈SP·W and so ( 15) can be rewritten as (16), where the rightmost expression is obtained considering W . functions. 5 WIMAX, New Developments1 08 2. From system specifications to architectural choices The system specifications and in particular the requirement of a peak throughput of about 75 Mb/s. WIMAX binary 64-state CC with rate 0 .5 shift register representation WIMAX, New Developments1 10 The WIMAX standard specifies a binary 64 states CC with rate 0 .5, whose shift register representation. Vol.33, No .5, pp.368-369 Müller, S.H. & Huber, J.B. (1997b). A Novel Peak Power Reduction Scheme for OFDM, Proc. IEEE PIMRC ’97, Helsinki, Finland, pp.1090-1094 WIMAX, New Developments1 06