A ML-Based High-Accuracy Estimation of Sampling and Carrier Frequency Offsets for OFDM Systems

  • Cang LiuEmail author
  • Luechao Yuan
  • Zuocheng Xing
  • Xiantuo Tang
  • Guitao Fu
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 592)


This paper addresses the problem of acquiring the sampling frequency offset (SFO) and carrier frequency offset (CFO), which severely degrade the performance of orthogonal frequency division multiplexing (OFDM) system. Using two identical frequency domain (FD) long training symbols in preamble, we propose a novel maximum-likelihood (ML) estimation method to simultaneously acquire the values of SFO and CFO, which extend the Kim’s and Wang’s estimation methods. The main contribution of this paper is that the first-order Legendre series expansion is used to obtain the SFO and CFO values in closed-form. For obtaining the performance of the proposed estimation scheme, we built the OFDM system model according to IEEE 802.11a. The results show that the proposed scheme achieves the best performance to the existing schemes.


Sampling frequency offset Carrier frequency offset Orthogonal frequency division multiplexing Legendre series expansion 



This work is supported by National Science Foundation of China (Grant No. 61170083, 61373032) and Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20114307110001).


  1. 1.
    IEEE: Supplement to IEEE standard for information technology - telecommunications and information exchange between systems - local and metropolitan area networks - specific requirements. part 11: Wireless lan medium access control (MAC) and physical layer (PHY) specifications: High-speed physical layer in the 5 GHz band. IEEE Std 802.11a (1999)Google Scholar
  2. 2.
    IEEE: IEEE standard for local and metropolitan area networks part 16: Air interface for fixed broadband wireless access systems draft amendment: Management information base extensions. IEEE Unapproved Draft Std P802.16i/D5 (2007)Google Scholar
  3. 3.
    IEEE: Etsi, digital video broadcasting (DVD): frame structure, channel coding and modulation for digital terrestrial television (DVD-T). ETSI EN 300 744 (2004)Google Scholar
  4. 4.
    IEEE: Digital radio mondiale (DRM): System specification. ETSI ES 201 980 v3.1.1 (2009)Google Scholar
  5. 5.
    Wu, H.-C.: Analysis and characterization of intercarrier and interblock interferences for wireless mobile OFDM systems. IEEE Trans. Broadcast. 52(2), 203–210 (2006)CrossRefGoogle Scholar
  6. 6.
    Ai, B., Yang, Z.-X., Pan, C.-Y., Ge, J.H., Wang, Y., Lu, Z.: On the synchronization techniques for wireless OFDM systems. IEEE Trans. Broadcast. 52(2), 236–244 (2006)CrossRefGoogle Scholar
  7. 7.
    Wang, Y.-Y.: A subspace-based CFO estimation algorithm for general ICI self-cancellation precoded OFDM systems. IEEE Trans. Wirel. Commun. 12(8), 4110–4117 (2013)CrossRefGoogle Scholar
  8. 8.
    Zhang, W., Yin, Q.: Blind maximum likelihood carrier frequency offset estimation for OFDM with multi-antenna receiver. IEEE Trans. Sig. Proces. 61(9), 2295–2307 (2013)CrossRefGoogle Scholar
  9. 9.
    Gul, M.M.U., Lee, S., Ma, X.: Carrier frequency offset estimation for OFDMA uplink using null sub-carriers. Digit. Sig. Proces. 29, 127–137 (2014)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Gault, S., Hachem, W., Ciblat, P.: Joint sampling clock offset and channel estimation for OFDM signals: Crame acute;r-Rao bound and algorithms. IEEE Trans. Sig. Proces. 54(5), 1875–1885 (2006)CrossRefGoogle Scholar
  11. 11.
    You, Y.-H., Kim, S.-T., Lee, K.-T., Song, H.-K.: An improved sampling frequency offset estimator for OFDM-based digital radio mondiale systems. IEEE Trans. Broadcast. 54(2), 283–286 (2008)CrossRefGoogle Scholar
  12. 12.
    Morelli, M., Imbarlina, G., Moretti, M.: Estimation of residual carrier and sampling frequency offsets in OFDM-SDMA uplink transmissions. IEEE Trans. Wirel. Commun. 9(2), 734–744 (2010)CrossRefGoogle Scholar
  13. 13.
    Oberli, C.: ML-based tracking algorithms for MIMO-OFDM. IEEE Trans. Wirel. Commun. 6(7), 2630–2639 (2007)CrossRefGoogle Scholar
  14. 14.
    Speth, M., Fechtel, S., Fock, G., Meyr, H.: Optimum receiver design for OFDM-based broadband transmission.ii. a case study. IEEE Trans. Commun. 49(4), 571–578 (2001)CrossRefGoogle Scholar
  15. 15.
    Freda, M.M., Weng, J., Le-Ngoc, T.: Joint channel estimation and synchronization for OFDM systems. In: 2004 IEEE 60th Vehicular Technology Conference, VTC2004-Fall, vol. 3, pp. 1673–1677 (2004)Google Scholar
  16. 16.
    Nguyen-Le, H., Le-Ngoc, T., Ko, C.-C.: RLS-based joint estimation and tracking of channel response, sampling, and carrier frequency offsets for OFDM. IEEE Trans. Broadcast. 55(1), 84–94 (2009)CrossRefGoogle Scholar
  17. 17.
    Kim, Y.-H., Lee, J.-H.: Joint maximum likelihood estimation of carrier and sampling frequency offsets for OFDM systems. IEEE Trans. Broadcast. 57(2), 277–283 (2011)CrossRefGoogle Scholar
  18. 18.
    Nguyen-Le, H., Le-Ngoc, T., Ko, C.-C.: Joint channel estimation and synchronization for MIMO OFDM in the presence of carrier and sampling frequency offsets. IEEE Trans. Veh. Technol. 58(6), 3075–3081 (2009)CrossRefGoogle Scholar
  19. 19.
    Wang, X., Hu, B.: A low-complexity ML estimator for carrier and sampling frequency offsets in OFDM systems. IEEE Commun. Lett. 18(3), 503–506 (2014)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Cang Liu
    • 1
    Email author
  • Luechao Yuan
    • 1
  • Zuocheng Xing
    • 1
  • Xiantuo Tang
    • 2
  • Guitao Fu
    • 3
  1. 1.National Laboratory for Parallel and Distributed ProcessingNational University of Defense TechnologyChangshaChina
  2. 2.National Digital Switching System Engineering and Technological R&D CenterZhengzhouChina
  3. 3.Beijing Satellite Navigation Center (BSNC)BeijingChina

Personalised recommendations