Skip to main content
SpringerLink
Log in

Achievable degrees of freedom of MIMO two-way X relay channel with delayed CSIT

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

The previous work on interference alignment for multiple-input-multiple-output (MIMO) two-way X relay channel assumes perfect channel state information at the transmitter (CSIT), which is reasonable in slow fading channel. However, in fast fading scenario, this assumption is impractical. In this paper, assuming that each node has delayed CSIT, we study the achievable degrees of freedom (DOF) for MIMO two-way X relay channel in frequency division duplex (FDD) systems. Specifically, in the broadcast (BC) phase, we propose a new multiple-stage transmission (MST) scheme, which utilizes retrospective interference alignment for physical layer network coding (PLNC). We show that MST can achieve significant DOF gain and tremendous power gain over other schemes. When the number of antennas for each user, N, is smaller than the number of the relays, M, the time division multiple access (TDMA) scheme can only achieve an ergodic sum-rate increase by N bps/Hz for every increasing of 3 dB of signal-to-noise power ratio (SNR), while the proposed MST scheme can achieve an ergodic sum-rate increase by M bps/Hz.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hossain E, Rasti M, Tabassum H, et al. Evolution toward 5G multi-tier cellular wireless networks: an interference management perspective. IEEE Wirel Commun, 2014, 21: 118–127

    Article  Google Scholar 

  2. Vander Meulen E. Three-terminal communication channels. Adv Appl Prob, 1974, 3: 120–154

    Article  MathSciNet  MATH  Google Scholar 

  3. Vander Meulen E. A survey of multi-way channels in information theory: 1961–1976. IEEE Trans Inf Theory, 1977, 23: 1–37

    Article  MathSciNet  MATH  Google Scholar 

  4. Cover T, Gamal A. Capacity theorems for the relay channel. IEEE Trans Inf Theory, 1979, 25: 572–584

    Article  MathSciNet  MATH  Google Scholar 

  5. Xing C W, Li S, Fei Z S, et al. How to understand linear minimum-mean-square-error transceiver design for multipleinput multiple-output systems from quadratic matrix programming. IET Commun, 2013, 7: 1231–1242

    Article  Google Scholar 

  6. Xing C W, Ma S D, Fei Z S, et al. General robust linear transceiver design for multi-hop amplify-and-forward MIMO relaying systems. IEEE Trans Signal Proc, 2013, 61: 1196–1209

    Article  MathSciNet  Google Scholar 

  7. Jafar S A, Shamai S S. Degrees of freedom region of the MIMO x channel. IEEE Trans Inf Theory, 2008, 54: 151–170

    Article  MathSciNet  MATH  Google Scholar 

  8. Maddah-Ali M, Motahari A, Khandani A. Communication over MIMO x channels: interference alignment, decomposition, and performance analysis. IEEE Trans Inf Theory, 2008, 54: 3457–3470

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhang S L, Liew S C, Lam P P. Hot topic: physical-layer network coding. In: Proceedings of the 12th Annual International Conference on Mobile Computing and Networking. New York: ACM, 2006. 358–365

    Google Scholar 

  10. Xiang Z Z, Tao M X, Mo J H, et al. Degrees of freedom for MIMO two-way x relay channel. IEEE Trans Signal Proc, 2013, 61: 1711–1720

    Article  MathSciNet  Google Scholar 

  11. Maddah-Ali M, Tse D. Completely stale transmitter channel state information is still very useful. IEEE Trans Inf Theory, 2012, 58: 4418–4431

    Article  MathSciNet  Google Scholar 

  12. Maleki H, Jafar S A, Shamai S S. Retrospective interference alignment over interference networks. IEEE J Sel Topic Signal Proc, 2012, 6: 228–240

    Article  Google Scholar 

  13. Abdoli M, Ghasemi A, Khandani A. On the degrees of freedom of K-user SISO interference and x channels with delayed CSIT. IEEE Trans Inf Theory, 2013, 10: 6542–6561

    Article  MathSciNet  Google Scholar 

  14. Vaze C, Varanasi M. The degrees of freedom region of the two-user MIMO broadcast channel with delayed CSIT. In: Proceedings of IEEE International Symposium on Information Theory (ISIT), Saint Petersburg, 2011. 199–203

    Google Scholar 

  15. Yi X P, Yang S, Gesbert D, et al. The degrees of freedom region of temporally correlated MIMO networks with delayed CSIT. IEEE Trans Inf Theory, 2014, 60: 494–514

    Article  MathSciNet  Google Scholar 

  16. Abdoli M, Ghasemi A, Khandani A. On the degrees of freedom of three-user MIMO broadcast channel with delayed CSIT. In: Proceedings of IEEE International Symposium on Information Theory, Saint Petersburg, 2011. 209–213

    Google Scholar 

  17. Wang I H, Diggavi S. On degrees of freedom of layered two-unicast networks with delayed CSIT. In: Proceedings of IEEE International Symposium on Information Theory, Cambridge, 2012. 46–50

    Google Scholar 

  18. Tandon R, Mohajer S, Poor H, et al. On x channels with feedback and delayed CSI. In: Proceedings of IEEE International Symposium on Information Theory, Cambridge, 2012. 1877–1881

    Google Scholar 

  19. Li Q Y, Li H X, Wu G, et al. Achievable degrees of freedom of MIMO y channel with delayed CSIT. IEEE Commun Lett, 2014, 18: 1583–1586

    Article  Google Scholar 

  20. Li Q Y, Li H X, Wu G, et al. Retrospective network coding alignment over K-user MIMO y channel. IEEE Commun Lett, 2016, 20: 502–505

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Qingyun Li, Gang Wu & Shaoqian Li

  2. Department of Electrical and Computer Engineering, University of Louisville, Louisville, KY, 40292, USA

    Hongxiang Li

Authors
  1. Qingyun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gang Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hongxiang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shaoqian Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gang Wu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Q., Wu, G., Li, H. et al. Achievable degrees of freedom of MIMO two-way X relay channel with delayed CSIT. Sci. China Inf. Sci. 59, 082306 (2016). https://doi.org/10.1007/s11432-015-0772-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-015-0772-6

Keywords

Search

Navigation