Efficient Cross-Correlation Algorithm for Correction of Common Phase Error Employing Preamble for Orthogonal Frequency Division Multiplexing (OFDM) Receivers

Abstract

In this paper, we propose a cross-correlation algorithm for correction of common phase error (CPE) in orthogonal frequency division multiplexing (OFDM) systems with high implementation efficiency. CPE resulting from the impairment of orthogonality among subcarriers is due to phase noise. It leads to the offset of demodulated data and increases the bit error rate (BER) of the receivers. As a result, it significantly degrades the performance of wireless communication systems that use OFDM. Therefore, offset compensation algorithm must be adopted in the OFDM system. The phase offset is traditionally estimated and compensated by introducing pilots in each OFDM symbol. However, the BER performance of the traditional algorithm PCP is poor because it is limited by the quantity of the pilot constraints of the wireless communication standard. A novel CPE correction algorithm involved in time and frequency domain can be developed to solve this problem. The proposed algorithm takes advantage of preamble sequences to remove the limitation of the pilots and improve the BER performance. Numerical analyses show that the proposed algorithm presents better estimation performance in additive white Gaussian noise (AWGN) channel. And the mean square error (MSE) is reduced to 10−3, which is lower than that of the traditional algorithm (10−2) at 10 dB signal-to-noise ratio (SNR). The BER is approximately down to10−5 at 12 dB SNR. The proposed algorithm can be easily implemented with low complexity of hardware for practical applications.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

References

  1. 1.

    Lim, B., & Ko, Y. (2017). SIR Analysis of OFDM and GFDM Waveforms With Timing Offset, CFO, and Phase Noise. IEEE Transactions on Wireless Communications, 16(10), 6979–6990.

    Article  Google Scholar 

  2. 2.

    Miriyala, G., Kakumanu, A., Swapna, M. P., et al. (2018). Joint estimation of channel response, frequency offset and phase noise in OFDM systems. In Second international conference on intelligent computing and control systems (ICICCS) (pp. 1299–1303). Madurai.

  3. 3.

    Rha, H. Y., Youn, C. J., Jeon, B. G., et al. (2015). Efficient Chromatic Dispersion Precompensation for Coherent Optical OFDM. IEEE Photonics Technology Letters, 27(1), 30–33.

    Article  Google Scholar 

  4. 4.

    Wang, R., Mehrpouyan, H., Tao, M., et al. (2016). Channel Estimation, Carrier Recovery, and Data Detection in the Presence of Phase Noise in OFDM Relay Systems. IEEE Transactions on Wireless Communications, 15(2), 1186–1205.

    Article  Google Scholar 

  5. 5.

    Lu, H., Zhang, L., Chen, X., et al. (2019). Recursive carrier interferometry aided high data rate OFDM systems With PAPR suppression, phase noise rejection, and carrier frequency offsets compensation. IEEE Transactions on Vehicular Technology, 68(4), 3655–3671.

    Article  Google Scholar 

  6. 6.

    Salim, O. H., Nasir, A. A., Mehrpouyan, H., et al. (2014). Channel, Phase Noise, and Frequency Offset in OFDM Systems: Joint estimation, data detection, and hybrid Cramér-Rao lower bound. IEEE Transactions on Communications, 62(9), 3311–3325.

    Article  Google Scholar 

  7. 7.

    Stefanatos, S., Foukalas, F., & Khattab, T. (2017). On the achievable rates of OFDM with common phase error compensation in phase noise channels. IEEE Transactions on Communications, 65(8), 3509–3521.

    Google Scholar 

  8. 8.

    Ngebani, I., Li, Y., Xia, X., et al. (2016). EM-Based Phase Noise Estimation in Vector OFDM Systems Using Linear MMSE Receivers. IEEE Transactions on Vehicular Technology, 65(1), 110–122.

  9. 9.

    Yan, Q., Hong, X., & Hong, X. (2018). Low-complexity residual carrier frequency offset mitigation based on spectrum symmetry for CO-OFDM systems. Journal of Lightwave Technology, 36(22), 5210–5217.

    Article  Google Scholar 

  10. 10.

    Bo, T., Huang, L., & Chan, C. (2015). Common phase estimation in coherent OFDM system using image processing technique. IEEE Photonics Technology Letters, 27(15), 1597–1600.

    Article  Google Scholar 

  11. 11.

    Leshem, A., & Yemini, M. (2017). Phase noise compensation for OFDM systems. IEEE Transactions on Signal Processing, 65(21), 5675–5686.

    MathSciNet  Article  Google Scholar 

  12. 12.

    Wang, Z., Babu, P., & Palomar, D. P. (2017). Effective low-complexity optimization methods for joint phase noise and channel estimation in OFDM. IEEE Transactions on Signal Processing, 65(12), 3247–3260.

    MathSciNet  Article  Google Scholar 

  13. 13.

    Mathecken, P., Riihonen, T., Werner, S., et al. (2017). Constrained phase noise estimation in OFDM using scattered pilots without decision feedback. IEEE Transactions on Signal Processing, 65(9), 2348–2362.

    MathSciNet  Article  Google Scholar 

  14. 14.

    Wang, C., Cui, G., Wang, W., et al. (2017). Joint estimation of carrier frequency and phase offset based on pilot symbols in quasi-constant envelope OFDM satellite systems. China Communications, 14(7), 1–11.

    Google Scholar 

  15. 15.

    Wu, S., & Bar-Ness, Y. (2004). OFDM systems in the presence of phase noise: consequences and solutions. IEEE Transactions on Communications, 52(11), 1988–1996.

    Article  Google Scholar 

  16. 16.

    McKilliam, R. G., Pollok, A. É., Cowley, W., et al. (2014). Carrier phase and amplitude estimation for phase shift keying using pilots and data. IEEE Transactions on Signal Processing, 62(15), 3976–3989.

    MathSciNet  Article  Google Scholar 

  17. 17.

    Ngebani, I., Li, Y., Xia, X., et al. (2014). Analysis and compensation of phase noise in vector OFDM systems. IEEE Transactions on Signal Processing, 62(23), 6143–6157.

    MathSciNet  Article  Google Scholar 

  18. 18.

    Ma, X., Zhang, H., Yao, X., et al. (2017). Pilot-based phase noise, IQ mismatch, and channel distortion estimation for PDM CO-OFDM system. IEEE Photonics Technology Letters, 29(22), 1947–1950.

    Article  Google Scholar 

  19. 19.

    Gao, Z., Zhang, C., & Wang, Z. (2015). Robust preamble design for synchronization, signalling transmission, and channel estimation. IEEE Transactions on Broadcasting, 61(1), 98–104.

    Article  Google Scholar 

  20. 20.

    Mathecken, P., Riihonen, T., Werner, S., et al. (2016). Phase noise estimation in OFDM: utilizing its associated spectral geometry. IEEE Transactions on Signal Processing, 64(8), 1999–2012.

    MathSciNet  Article  Google Scholar 

  21. 21.

    Syrjälä, V., Levanen, T., Ihalainen, T., et al. (2019). Pilot allocation and computationally efficient non-iterative estimation of phase noise in OFDM. IEEE Wireless Communications Letters, 8(2), 640–643.

    Article  Google Scholar 

  22. 22.

    Zhang, Y., Feng, X., He, G., et al. (2009). Design considerations for the compensation of phase noise in OFDM systems. International SoC Design Conference (ISOCC) (pp. 266–269). Busan.

  23. 23.

    Liu, T., Chung, W., Yuan, S., et al. (2015). ICI self-cancellation with cosine windowing in OFDM transmitters over fast time-varying channels. IEEE Transactions on Wireless Communications, 14(7), 3559–3570.

    Article  Google Scholar 

  24. 24.

    Garcia Armada, A. (2001). Understanding the effects of phase noise in orthogonal frequency division multiplexing (OFDM). IEEE Transactions on Broadcasting, 47(2), 153–159.

    Article  Google Scholar 

  25. 25.

    Shukla, R., & Ray, K. C. (2014). Low latency hybrid CORDIC algorithm. IEEE Transactions on Computers, 63(12), 3066–3078.

    MathSciNet  Article  Google Scholar 

  26. 26.

    Ramadoss, R., Mozaffari Kermani, M., & Azarderakhsh, R. (2017). Reliable hardware architectures of the cordic algorithm with a fixed angle of rotations. IEEE Transactions on Circuits and Systems II: Express Briefs, 64(8), 972–976.

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the financial support of the Key Projects of R&D and Achievement Transformation in Qinghai Province (Grant: 2018-NN-151), the National Natural Science Foundation of China (Grant: 61761040 and 61771363), and the ChunHui Project of Education Ministry (Grant: Z2016108).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Lingfei Zhang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhang, L., Ma, J., Wu, Z. et al. Efficient Cross-Correlation Algorithm for Correction of Common Phase Error Employing Preamble for Orthogonal Frequency Division Multiplexing (OFDM) Receivers. Wireless Pers Commun (2021). https://doi.org/10.1007/s11277-020-08030-6

Download citation

Keywords

  • Orthogonal frequency division multiplexing (OFDM)
  • Common phase error estimation
  • Preamble
  • IEEE 802.11ac- standard