Skip to main content
Springer Nature Link
Log in

Pilot Contamination Reduction in Multi-cell TDD Systems with Very Large MIMO Arrays

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

Very large multiple-input multiple-output (MIMO) technology has a potential of significantly improving the system performance of multi-cell time-division duplexing (TDD) networks, but in practice it is limited by pilot contamination. Different from the traditional channel estimation mean square error (MSE) expressions, the expressions that we derived have algebraic form, which no longer need hard matrix inversion as M, the number of the base station (BS) antennas, increasing. From them, we also found that the average transmitted power and length of training sequence almost does not help in enhancing the performance of MSE as \(M\rightarrow \infty \). Based on this, two pilot contamination reduction methods for the very large MIMO multi-cell TDD system were proposed. One is realized by grouping all the cells into two categories, using orthogonal pilots between these two types of cells or aligning the uplink pilot time slot of the cells in one category with the downlink data time slot of those cells in the neighboring categories. The other is to find the optimal division of pilot sequence length and the set of all users’s pilot transmission slots allocation through BSs’s coordination. The effectiveness of our proposed methods are verified via both theoretical analysis and numerical results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Notes

  1. If \(L=3\), \(K=2\), this system needs only 6 orthogonal pilot sequences. Here, limited by the simulation complexity, we can only select smaller L and K, which just for verification.

References

  1. Wang, H., Yang, L., Zhu, H., & Fu, Y. (2015). Pilot contamination reduction based on MSE performance of channel estimation. In International conference on IEEE wireless communications and signal processing (WCSP) (pp. 1–5). Nanjing, China.

  2. Gesbert, D., Kountouris, M., Heath, R. W, Jr., Chae, C.-B., & Salzer, T. (2007). Shifting the MIMO paradigm. IEEE Signal Processing Magazine, 24(5), 36–46.

    Article  Google Scholar 

  3. Costa, M. H. M. (1983). Writing on dirty paper. IEEE Transactions on Information Theory, 29(3), 439–441.

    Article  MathSciNet  MATH  Google Scholar 

  4. Caire, G., & Shamai, S. (2003). On the achievable throughput of a multiantenna Gaussian broadcast channel. IEEE Transactions on Information Theory, 49(7), 1691–1706.

    Article  MathSciNet  MATH  Google Scholar 

  5. Viswanath, P., & Tse, D. N. C. (2003). Sum capacity of the vector Gaussian broadcast channel and uplink-downlink duality. IEEE Transactions on Information Theory, 49(8), 1912–1921.

    Article  MathSciNet  MATH  Google Scholar 

  6. Yu, W., & Cioffi, J. M. (2004). Sum capacity of Gaussian vector broadcast channels. IEEE Transactions on Information Theory, 50(9), 1875–1892.

    Article  MathSciNet  MATH  Google Scholar 

  7. Rusek, F., Persson, D., Lau, B. K., Larsson, E. G., Marzetta, T. L., & Edfors, O., et al. (2013). Scaling up MIMO: Opportunities and challenges with very large arrays. IEEE Signal Processing Magazine, 30(1), 40–60.

    Article  Google Scholar 

  8. Huang, Y., Yang, L., Bengtsson, M., & Ottersten, B. (2011). Exploiting longterm channel correlation in limited feedback SDMA through channel phase codebook. IEEE Transactions on Signal Processing, 59(3), 1217–1228.

    Article  MathSciNet  Google Scholar 

  9. Marzetta, T. L. (2010). Noncooperative cellular wireless with unlimited numbers of base station antennas. IEEE Transactions on Wireless Communications, 9(11), 3590–3600.

    Article  Google Scholar 

  10. Hoydis, J., ten Brink, S., & Debbah, M. (2013). Massive MIMO in the UL/DL of cellular networks: How many antennas do we need? IEEE Journal on Selected Areas in Communications, 31(2), 160–171.

    Article  Google Scholar 

  11. Li, G. Y., Xu, Z., Xiong, C., Yang, C., Zhang, S., Chen, Y., et al. (2011). Energy-efficient wireless communications: Tutorial, survey, and open issues. IEEE Wireless Communications, 18(6), 28–35.

    Article  Google Scholar 

  12. Ngo, H. Q., Larsson, E. G., & Marzetta, T. L. (2013). Energy and spectral efficiency of very large multiuser MIMO systems. IEEE Transactions on Communications, 61(4), 1436–1449.

    Article  Google Scholar 

  13. Marzetta, T. L. (2006). How much training is required for multiuser MIMO? In Proceedings of Fortieth Asilomar conference on signals, systems and computers (ACSSC’06), pp. 359–363.

  14. Ngo, H. Q., Marzetta, T. L., & Larsson, E. G. (2011). Analysis of the pilot contamination effect in very large multicell multiuser MIMO systems for physical channel models. In Proceedings of speech and signal processing (ICASSP) IEEE Int’l conference on acoustics. Prague, Czech.

  15. Larsson, E. G. (2012). Very large MIMO systems part I: Theory and analysis. IEEE ICASSP tutorial on very large MIMO, March, 2012.

  16. Krishnan, N., Yates, R. D., Mandayam, N. B. (2012). Cellular systems with many antennas: Large system analysis under pilot contamination. In 50th Annual allert on conference on communication, control, and computing (Allerton), pp. 1220–1224.

  17. Fernandes, F., Ashikhmin, A. E., & Marzetta, T. L. (2013). Inter-cell interference in noncooperative TDD large scale antenna systems. IEEE Journal on Selected Areas in Communications, 31(2), 192–201.

    Article  Google Scholar 

  18. Jose, J., Ashikhmin, A., Marzetta, T., & Vishwanath, S. (2011). Pilot contamination and precoding in multi-cell TDD systems. IEEE Transactions on Wireless Communications, 10(8), 2640–2651.

    Article  Google Scholar 

  19. Appaiah, K., Ashikhmin, A., & Marzetta, T. L. (2010). Pilot contamination reduction in multi-user TDD systems. In Proceedings of IEEE international conference on communications (ICC’10) (pp. 1–5). CapeTown, South Africa.

  20. Fernandes, F., Ashikhmin, A., & Marzetta, T. L. (2012). Interference reduction on cellular networks with large antenna arrays. In Proceedings of IEEE international conference on communications (ICC’12), Ottawa, Canada.

  21. Ashikhmin, A., & Marzetta, T. L. (2012). Pilot contamination precoding in multi-cell large scale antenna systems. In Proceedings of IEEE information theory proceedings (ISIT) (pp. 1137–1141), Cambridge, MA.

  22. Mazrouei-Sebdani, M., & Krzymien, W. A. (2013). Massive MIMO with clustered pilot contamination precoding, 2013. In Asilomar conference on signals, systems and computers (pp. 1218–1222).

  23. Yin, H., Gesbert, D., Filippou, M., & Liu, Y. (2013). A coordinated approach to channel estimation in large-scale multiple-antenna systems. IEEE Journal on Selected Areas in Communications, 31(2), 264–273.

    Article  Google Scholar 

  24. Kailath, T., Sayed, A. H., & Hassibi, B. (2000). Linear estimation. Upper Saddle River: Prentice Hall.

    MATH  Google Scholar 

  25. Wang, H., Huang, Y., Jin, S., Fei, Y., & Yang, L. (2013). Performance analysis on precoding and pilot scheduling in very large MIMO multi-cell systems. In IEEE wireless communications and networking conference (WCNC’13), Shanghai, China.

Download references

Acknowledgements

This work was supported by the National High Technology Research and Development Program of China (863 Program) (2014AA01A705), the National Natural Science Foundation of China under Grants 61071113, 61201172 and 61201176, The Project of Nanjing University of Posts and Telecommunications (NY213072).

Author information

Authors and Affiliations

  1. College of Telecommunications and Information Engineering, University of Post and Telecommunications, Nanjing, 210003, China

    Hairong Wang

  2. School of Information Science and Engineering, Southeast University, Nanjing, 210096, China

    Yongming Huang, Shi Jin & Luxi Yang

  3. Communication Technology Research Department, Huawei Technologies Co. Ltd., Shenzhen, 518129, China

    Yinggang Du

Authors
  1. Hairong Wang
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Yongming Huang
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Shi Jin
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Yinggang Du
    View author publications

    You can also search for this author inPubMed Google Scholar

  5. Luxi Yang
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Hairong Wang.

Additional information

Part of this work was presented at the 2015 IEEE International Conference on Wireless Communications and Signal Processing (WCSP) [1]. This work was supported by the National High Technology Research and Development Program of China (863 Program) (2014AA01A705), the National Natural Science Foundation of China under Grants 61671251, Natural Science Foundation of Jiangsu Province of China under Grants BK20130874, BK20140881, The Project of Nanjing University of Posts and Telecommunications (NY213072).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, H., Huang, Y., Jin, S. et al. Pilot Contamination Reduction in Multi-cell TDD Systems with Very Large MIMO Arrays. Wireless Pers Commun 96, 5785–5808 (2017). https://doi.org/10.1007/s11277-017-4447-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-017-4447-1

Keywords