Skip to main content
SpringerLink
Log in

Spatial Degrees of Freedom for MIMO Interference Channel with Local Channel State Information at Transmitters

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

This paper discusses inner bound and outer bound for the total number of spatial degrees of freedom (DoF) of the K-user MIMO interference channel with only local channel state information at each transmitter when channel extensions are disabled over time and frequency dimensions. We firstly provide a constructive proof of the achievability of the DoF based on zero forcing for two-user MIMO interference channel with \(M_{1},M_{2}\) antennas at transmitter 1, 2 and \(N_{1},N_{2}\) antennas at the corresponding receivers when only local channel state information (CSI) is available at the transmitters. Then the total achievable DoF and interference management scheme for 3-user interference channel with specific antenna configuration is presented by comparing the number of equations and the number of variables. We apply interference zero-forcing scheme and signal subspace analysis on the generalization of the interference management for this special case to the common 3-user and K-user MIMO symmetric interference channel and establish that the the inner bound on total spatial DoF \(\min ({K\min (M_{t}, N_{r}), \max (M_{t}, N_{r})})\) is achievable in K-user MIMO symmetric interference channel with \(M_{t}\) transmitter antennas and \(N_{r}\) receiver antennas. We also provide the proof of an outer bound on spatial DoF for the K-user MIMO symmetric interference channel with only local CSI at each transmitter and indicate that the inner bound and outer bound are tight when the number of receiver antennas is not less than the number of transmitter antennas.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Tse, D. N. C., Viswanath, P., & Lizhong, Z. (2004). Communication on the Grassmann manifold: A geometric approach to the noncoherent multiple-antenna channel. IEEE Transactions on Information Theory, 50(9), 1859–2004. doi:10.1109/TIT.2004.833347.

    Article  MATH  Google Scholar 

  2. Telatar, E. (2002). Capacity of multi-antenna Gaussian channel. European Transactions on Telecommunications (ETT), 10(6), 585–596. doi:10.1002/ett.4460100604.

    Article  MathSciNet  Google Scholar 

  3. Lizhong, Z., & Tse, D. N. C. (2002). Communication on the Grassmann manifold: A geometric approach to the noncoherent multiple-antenna channel. IEEE Transactions on Information Theory, 48(2), 359–383. doi:10.1109/18.978730.

    Article  MathSciNet  MATH  Google Scholar 

  4. Jafar, S. A., & Fakhereddin, M. J. (2007). Degrees of freedom for the MIMO interference channel. IEEE Transactions on Information Theory, 53(7), 2637–2642. doi:10.1109/TIT.2007.899557.

    Article  MathSciNet  MATH  Google Scholar 

  5. Cadambe, V. R., & Jafar, S. A. (2008). Interference alignment and degrees of freedom of the K-user interference channel. IEEE Transactions on Information Theory, 54(8), 3425–3441.10. doi:1109/TIT.2008.926344.

    Article  MathSciNet  MATH  Google Scholar 

  6. Jun, S., Yingzhuang, L., & Guangxi, Z. (2010) On the degrees of freedom of the cellular network. In 2010 IEEE International Conference on Communications (ICC), 23–27 May 2010 (pp. 1–5). doi:10.1109/ICC.2010.5502363.

  7. Chiachi, H., Jafar, S. A., Shamai, S., & Vishwanath, S. (2012). On degrees of freedom region of MIMO networks without channel state information at transmitters. IEEE Transactions on Information Theory, 58(2), 849–857. doi:10.1109/tit.2011.2173615.

    Article  MathSciNet  Google Scholar 

  8. Zhu, Y., & Guo, D. (2010). The degrees of freedom of MIMO interference channels without state information at transmitters. arXiv:1008.5196.

  9. Yan, Z., & Dongning, G. (2012). The degrees of freedom of isotropic MIMO interference channels without state information at the transmitters. IEEE Transactions on Information Theory, 58(1), 341–352. doi:10.1109/tit.2011.2167314.

    Article  MathSciNet  Google Scholar 

  10. Tiangao, G., Chenwei, W., & Jafar, S. A. (2011). Aiming perfectly in the dark-blind interference alignment through staggered antenna switching. IEEE Transactions on Signal Processing, 59(6), 2734–2744. doi:10.1109/TSP.2011.2129517.

    Article  MathSciNet  Google Scholar 

  11. Jafar, S.A. (2010). Exploiting channel correlations—simple interference alignment schemes with no CSIT. In Global Telecommunications Conference (GLOBECOM 2010), 2010 IEEE, 6–10 December 2010 (pp. 1–5). doi:10.1109/GLOCOM.2010.5683592.

  12. Gomadam, K., Cadambe, V. R., & Jafar, S. A. (2011). A distributed numerical approach to interference alignment and applications to wireless interference networks. IEEE Transactions on Information Theory, 57(6), 3309–3322. doi:10.1109/TIT.2011.2142270.

    Article  MathSciNet  Google Scholar 

  13. Peters, S. W., & Heath, R. W. (2009) Interference alignment via alternating minimization. In IEEE international conference on acoustics, speech and signal processing, 2009. ICASSP 2009, 19–24 April 2009 (pp. 2445–2448). doi:10.1109/ICASSP.2009.4960116.

  14. Santamaria, I., Gonzalez, O., Heath, R.W., & Peters, S.W. ( 2010). Maximum sum-rate interference alignment algorithms for MIMO channels. In Global Telecommunications Conference (GLOBECOM 2010), 2010 IEEE, 6–10 December 2010 (pp. 1–6). doi:10.1109/GLOCOM.2010.5683919.

  15. Hakjea, S., Seok-Hwan, P., Kyoung-Jae, L., & Inkyu, L. (2010). Linear precoder designs for K-user interference channels. IEEE Transactions on Wireless Communications, 9(1), 291–301. doi:10.1109/TWC.2010.01.090221.

    Article  Google Scholar 

  16. Shen, H., Li, B., Tao, M. X., & Wang, X. D. (2010). MSE-based transceiver designs for the MIMO interference channel. IEEE Transactions on Wireless Communications, 9(11), 3480–3489. doi:10.1109/twc.2010.091510.091836.

    Article  Google Scholar 

  17. Ho, Z.K.M., & Gesbert, D. (2010) Balancing egoism and altruism on interference channel: The MIMO case. In 2010 IEEE international conference on communications (ICC), 23–27 May 2010 (pp. 1–5). doi:10.1109/ICC.2010.5501882

  18. Yetis, C. M., Tiangao, G., Jafar, S. A., & Kayran, A. H. (2010). On feasibility of interference alignment in MIMO interference networks. IEEE Transactions on Signal Processing, 58(9), 4771–4782. doi:10.1109/TSP.2010.2050480.

    Article  MathSciNet  Google Scholar 

  19. Bresler, G., Cartwright, D., & Tse, D. (2011). Settling the feasibility of interference alignment for the MIMO interference channel: The symmetric square case. arXiv:1104.0888.

  20. Razaviyayn, M., Lyubeznik, G., & Zhi-Quan, L. (2012). On the degrees of freedom achievable through interference alignment in a MIMO interference channel. IEEE Transactions on Signal Processing, 60(2), 812–821. doi:10.1109/tsp.2011.2173683.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work was supported in part by the Key Project of National Natural Science Foundation of China under grant 61231007, the National Science and Technology Major Project of the Ministry of Science and Technology of China under grant 2011ZX03003-001-04 and 2013ZX03003015-005, the National High Technology Research and Development Program of China (863 Program) under grant 2012AA121604 and 2014AA01A702, the Fundamental Research Funds for the Central Universities under grant 2042014kf0041, the International Science and Technology Cooperation Program of China under grant 2012DFG12010. Zhengmin Kong should be considered co-corresponding author.

Author information

Authors and Affiliations

  1. State Grid Information and Communication Company of Hunan Electric Power Corp, Changsha, China

    Shixin Peng

  2. Department of Electronics and Information Engineering, Huazhong University of Science and Technology, Wuhan National Laboratory for Optoelectronics, Wuhan, China

    Yingzhuang Liu

  3. Automation Department, Wuhan University, Wuhan, China

    Zhengmin Kong

  4. Air Force Early Warning Acedemy, Wuhan, China

    Wei Lv

Authors
  1. Shixin Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yingzhuang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhengmin Kong
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wei Lv
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shixin Peng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Peng, S., Liu, Y., Kong, Z. et al. Spatial Degrees of Freedom for MIMO Interference Channel with Local Channel State Information at Transmitters. Wireless Pers Commun 89, 639–662 (2016). https://doi.org/10.1007/s11277-016-3300-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-016-3300-2

Keywords

Search

Navigation