From frequency domain to time domain: performance analysis on cyclic prefixed multi-user single-carrier transmission


This paper analyzes the performance of cyclic prefixed single-carrier transmission under multiuser interference (MUI). For multi-user receivers using single carrier frequency domain adaptive antenna array, we derive the signal to interference plus noise ratio by analyzing the time domain estimated signal after the transformation from frequency domain to time domain. By assuming the MUI follows the Gaussian distribution, we can derive the analytical expression for the bit error rate (BER) performance. The analytical result is verified by the numerical results generated by Monte Carlo method. It is concluded from the analytical results that if the number of receive antennas goes to infinity as assumed in massive multiple input multiple output (MIMO) system, the BER performance will be determined by two ratios: signal to noise ratio as well as the N r to U ratio, where N r is the number of receive antennas and U is the number of users.

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  1. 1

    Proakis J. Digital Communications. 4th ed. New York: McGraw-Hill, 2001

    MATH  Google Scholar 

  2. 2

    Wang Z, Giannakis G B. Wireless multicarrier communications: where Fourier meets Shannon. IEEE Signal Process Mag, 2000, 47: 29–48

    Article  Google Scholar 

  3. 3

    Zhu H L, Wang J Z. Chunk-based resource allocation in OFDMA systems—Part I: chunk allocation. IEEE Trans Commun, 2009, 57: 2734–2744

    Article  Google Scholar 

  4. 4

    Zhu H L, Wang J Z. Chunk-based resource allocation in OFDMA systems—Part II: joint chunk, power and bit allocation. IEEE Trans Commun, 2012, 60: 499–509

    Article  Google Scholar 

  5. 5

    Zhu H L. Radio resource allocation for OFDMA systems in high speed environments. IEEE J Sel Areas Commun, 2012, 30: 748–759

    Article  Google Scholar 

  6. 6

    Li M Q, Rui Y. Analysis of CFO effects and phase compensation method for SC-FDMA systems. Sci China Ser-F: Inf Sci, 2009, 52: 2397–2405

    Article  MATH  Google Scholar 

  7. 7

    Wang Z D, Ma X L, Giannakis G B. OFDM or single-carrier block transmissions? IEEE Trans Commun, 2004, 52: 380–394

  8. 8

    Ohno S. Performance of single-carrier block transmissions over multipath fading channels with linear equalization. IEEE Trans Signal Process, 2006, 54: 3678–3687

    Article  Google Scholar 

  9. 9

    Muquet B, Wang Z D, Giannakis G B, et al. Cyclic prefixed or zero padded multicarrier transmissions? IEEE Trans Commun, 2002, 50: 2136–2148

  10. 10

    Kaleh G K. Channel equalization for block transmission systems. IEEE J Sel Areas Commun, 1995, 13: 110–121

    Article  Google Scholar 

  11. 11

    Qureshi S U H. Adaptive equalization. Proc IEEE, 1985, 73: 1349–1387

    Article  Google Scholar 

  12. 12

    Forney G D. Maximum-likelihood sequence estimation of digital sequences in the presence of inter-symbol interference. IEEE Trans Inform Theory, 1972, 18: 363–378

    MathSciNet  Article  MATH  Google Scholar 

  13. 13

    Falconer D, Ariyavisitakul S L, Benyamin-Seeyar A, et al. Frequency domain equalization for single-carrier broadband wireless systems. IEEE Commun Mag, 2002, 40: 58–66

    Article  Google Scholar 

  14. 14

    Liu R, Gao X Q, Wang W J. A Sub-block orthogonal single carrier frequency domain equalization system in fast Rayleigh fading channel. Sci China Inf Sci, 2010, 53: 1833–1847

    MathSciNet  Article  Google Scholar 

  15. 15

    Peng W, Adachi F. Frequency domain adaptive antenna array for broadband single-carrier uplink transmission. IEICE Trans Commun, 2011, E94-B: 2003–2012

    Article  Google Scholar 

  16. 16

    Peng W, Adachi F, Wang X D, et al. Spectrum efficiency analysis and adaptive transceiver design for single-carrier multi-user transmission. IEEE Trans Veh Technol, 2015, 64: 3566–3577

    Article  Google Scholar 

  17. 17

    Ghosh A, Ratasuk R, Mondal B, et al. LTE-advanced: next-generation wireless broadband technology. IEEE Trans Wirel Commun, 2010, 17: 10–12

    Article  Google Scholar 

  18. 18

    Prasad N, Wang S Q, Wang X D. Efficient receiver algorithms for DFT-spread OFDM systems. IEEE Trans Wirel Commun, 2009, 8: 3216–3225

    Article  Google Scholar 

  19. 19

    Myung H G, Lim J, Goodman D J. Single carrier FDMA for uplink wireless transmission. IEEE Veh Technol Mag, 2006, 1: 30–38

    Article  Google Scholar 

  20. 20

    Iwamura M, Etemad K, Fong M, et al. Carrier aggregation framework in 3GPP LTE-Advanced. IEEE Commun Mag, 2010, 48: 60–67

    Article  Google Scholar 

  21. 21

    Mendicute M, Altuna J, Atxa V, et al. Performance comparison of OFDM and FDE single-carrier modulation for spatial multiplexing MIMO systems. In: Proceedings of IEEE 5thWorkshop on Signal Processing Advances in Wireless Communications, Lisbon, 2004. 532–535

    Google Scholar 

  22. 22

    Khan U, Baig S, Mughal M J. Performance comparison of single carrier modulation with frequency domain equalization and OFDM for wireless communications. In: Proceedings of International Conference on Emerging Technologies, Islamabad, 2009. 297–300

    Google Scholar 

  23. 23

    Kim K J, Tsiftsis T A. Performance analysis of QRD-based cyclically prefixed single-carrier transmissions with opportunistic scheduling. IEEE Trans Veh Technol, 2011, 60: 328–333

    Article  Google Scholar 

  24. 24

    Adachi F, Takeda K. Bit error rate analysis of DS-CDMA with joint frequency-domain equalization and antenna diversity combining. IEICE Trans Commun, 2004, E87-B: 2991–3002

    Google Scholar 

  25. 25

    Kelkar S S, Grigsby L L, Langsner J. An extension of Parseval’s theorem and its use in calculating transient energy in the frequency domain. IEEE Trans Ind Electron, 1993, IE-30: 42–45

    Article  Google Scholar 

  26. 26

    Haykin S. Adaptive Filter Theory. 4th ed. Englewood Cliffs: Prentice-Hall, 2000

    MATH  Google Scholar 

  27. 27

    Franklin M. Matrix Theory. New York: Dover, 2000

    Google Scholar 

  28. 28

    Marzetta T L. Noncooperative cellular wireless with unlimited number of base station antennas. IEEE Trans Wirel Commun, 2010, 9: 3590–3600

    Article  Google Scholar 

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Correspondence to Qing F. Zhou.

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Peng, W., Zhou, Q.F., Huang, A. et al. From frequency domain to time domain: performance analysis on cyclic prefixed multi-user single-carrier transmission. Sci. China Inf. Sci. 59, 082302 (2016).

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  • single-carrier transmission
  • multi-user interference
  • frequency domain processing
  • MIMO