ISSN 0253-2778

CN 34-1054/N

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Open AccessOpen Access JUSTC Original Paper

Subspace interference alignment on Grassmann manifold for cellular networks

  • WINLab, University of Science and Technology of China, Hefei 230027, China

Funds:  Supported by National Natural Science Foundation of China (61171112), MIIT of China (2010ZX03005-001-02, 2012ZX03001037, 2010ZX03002-010-02).
Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2014.01.006
More Information
  • Author Bio:

    ZHANG Chen, male, born in 1985，博士生. Research field: 多用户干扰对齐技术. E-mail: zhangzc@mail.ustc.edu.cn

  • Corresponding author: WEI Guo
  • Received Date: 06 March 2013
  • Accepted Date: 18 April 2013
  • Rev Recd Date: 18 April 2013
  • Publish Date: 30 January 2014
    Abstract

  • Abstract

    The subspace interference alignment for multi-cell and multi-user cellular networks was focused. Different from most previous algorithms that are based on a joint design of precoder and receive filter, the proposed method achieves interference alignment with precoder design only. This means our algorithm only requires the participation of transmitters, which will alleviate significantly the overhead induced by alternation between the up and down links. More importantly, varying from the traditional constrained optimization method, the precoder design on complex Grassmann manifold with lower dimensions was reformulated and a novel steepest descent algorithm was derived to achieve perfect subspace interference alignment. Simulation results suggest that the proposed algorithm has better convergence performance and higher system capacity compared with previous methods.

    Abstract

    The subspace interference alignment for multi-cell and multi-user cellular networks was focused. Different from most previous algorithms that are based on a joint design of precoder and receive filter, the proposed method achieves interference alignment with precoder design only. This means our algorithm only requires the participation of transmitters, which will alleviate significantly the overhead induced by alternation between the up and down links. More importantly, varying from the traditional constrained optimization method, the precoder design on complex Grassmann manifold with lower dimensions was reformulated and a novel steepest descent algorithm was derived to achieve perfect subspace interference alignment. Simulation results suggest that the proposed algorithm has better convergence performance and higher system capacity compared with previous methods.
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    • References(25)
  • [1]
    Cadambe V R, Jafar S A. Interference alignment and degrees of freedom of the K-user interference channel[J]. IEEE Transactions on Information Theory, 2008, 54(8): 3 425-3 441.
    [2]
    Maddah-Ali M A, Motahari A S, Khandani A K. Signaling over MIMO multi-base systems: Combination of multi-access and broadcast schemes[C]// IEEE International Symposium on Information Theory. Seattle, USA: IEEE Press, 2006: 2 104-2 108.
    [3]
    Jafar S A. Interference alignment: A new look at signal dimensions in a communication network[J]. Foundations and Trends in Communications and Information Theory, 2011, 7(1): 1-136.
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    [5]
    Suh C, Ho M, Tse D. Downlink interference alignment[J]. IEEE Transactions on Communications, 2011, 59(9): 2 616-2 626.
    [6]
    Yin H R, Ke L, WangZ D. Interference alignment and degrees of freedom region of cellular sigma channel[C]// Proceedings of the IEEE International Symposium on Information Theory. Petersburg, Russia: IEEE Press, 2011: 21-25.
    [7]
    Zhang C, Li X, Yin H R, et al. Interference alignment precoder design on Grassmann manifold for cellular system[C]// First IEEE International Conference on Communications. Beijing, China: IEEE Press, 2012: 568-572.
    [8]
    Gomadam K S, Cadambe V R, Jafar S A. Approaching the capacity of wireless networks through distributed interference alignment[C]// IEEE Global Telecommunications Conference. New Orleans, USA: IEEE Press, 2008: 1-6.
    [9]
    Peters S W, Heath R W. Interference alignment via alternating minimization[C]// IEEE International Conference on Acoustics, Speech, and Signal Processing. TaiPei, China: IEEE Press, 2009: 2 445-2 448.
    [10]
    Kumar K R, Xue F. An iterative algorithm for joint signal and interference alignment[C]// IEEE International Symposium on Information Theory. Austin, USA: IEEE Press, 2010: 2 293-2 297.
    [11]
    Liu S, Du Y G, Zhao M. A new joint iterative transceiver design with interference alignment method[C]// 19th Annual Wireless and Optical Communications Conference. Shanghai, China: IEEE Press, 2010: 1-5.
    [12]
    Shen H, Li B. A novel iterative interference alignment scheme via convex optimization for the MIMO interference channel[C]// Vehicular Technology Conference. Ottawa, Canada: IEEE Press, 2010: 1-5.
    [13]
    Shen H, Li B, Tao M X, et al. The new interference alignment scheme for the MIMO interference channe[C]// Wireless Communications and Networking Conference. Sydney, Australia: IEEE Press, 2010: 1-6.
    [14]
    Ghauch H G, Papadias C B. Interference alignment: A one-sided approach[C]// IEEE Global Telecommunications Conference. Texas, USA: IEEE Press, 2011: 1-5.
    [15]
    Santamaria I, Gonzalez O, Heath R W, et al. Maximum sum-rate interference alignment algorithms for MIMO channels[C]// IEEE Global Telecommunications Conference. Miami, USA: IEEE Press, 2010: 1-6.
    [16]
    Edelman A, Arias T A, Smith S T. The geometry of algorithms with orthogonality constraints[J]. SIAM Journal on Matrix Analysis and Applications, 1999, 20(2): 303-353.
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    Abrudan T E, Eriksson J, Koivunen V. Steepest descent algorithms for optimization under unitary matrix constraint[J]. IEEE Transaction on Signal Processing, 2008, 56(3): 1 134-1 147.
    [18]
    张贤达. 矩阵分析与应用[M]. 北京: 清华大学出版社, 2004.
    [19]
    Hjrungnes A. Complex-Valued Matrix Derivatives: With Applications in Signal Processing and Communications[M]. Cambridge, UK: Cambridge University Press, 2011.
    [20]
    AbsilP A, Mahony R, Sepulchre R. Optimization Algorithms on Matrix Manifolds[M]. New Jersey: Princeton University Press, 2008.
    [21]
    Zhang C, Yin H R, Wei G. One-sided precoder designs for interference alignment[C]// IEEE Vehicular Technology Conference. Quebec, Canada: IEEE Press, 2012: 1-5.
    [22]
    Manton J H. Optimization algorithms exploiting unitary constraints[J]. IEEE Transaction on Signal Processing. 2002, 50(3): 635-650.
    [23]
    Boyd S, Vandenberghe L. Convex Optimization[M]. Cambridge, UK: Cambridge University Press, 2004.
    [24]
    Polak E. Optimization: Algorithms and Consistent Approximations[M]. New York: Springer-Verlag, 1997.
    [25]
    王存祥, 邱玲. 协作多点传输中一种基于特征子信道的干扰对齐预编码矩阵优化方案[J]. 信号处理, 2011, 27(3): 395-399.
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    [1]
    Cadambe V R, Jafar S A. Interference alignment and degrees of freedom of the K-user interference channel[J]. IEEE Transactions on Information Theory, 2008, 54(8): 3 425-3 441.
    [2]
    Maddah-Ali M A, Motahari A S, Khandani A K. Signaling over MIMO multi-base systems: Combination of multi-access and broadcast schemes[C]// IEEE International Symposium on Information Theory. Seattle, USA: IEEE Press, 2006: 2 104-2 108.
    [3]
    Jafar S A. Interference alignment: A new look at signal dimensions in a communication network[J]. Foundations and Trends in Communications and Information Theory, 2011, 7(1): 1-136.
    [4]
    Suh C, Tse D. Interference alignment for cellular networks[EB/OL]. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.172.5552&rep=rep1&type=pdf.
    [5]
    Suh C, Ho M, Tse D. Downlink interference alignment[J]. IEEE Transactions on Communications, 2011, 59(9): 2 616-2 626.
    [6]
    Yin H R, Ke L, WangZ D. Interference alignment and degrees of freedom region of cellular sigma channel[C]// Proceedings of the IEEE International Symposium on Information Theory. Petersburg, Russia: IEEE Press, 2011: 21-25.
    [7]
    Zhang C, Li X, Yin H R, et al. Interference alignment precoder design on Grassmann manifold for cellular system[C]// First IEEE International Conference on Communications. Beijing, China: IEEE Press, 2012: 568-572.
    [8]
    Gomadam K S, Cadambe V R, Jafar S A. Approaching the capacity of wireless networks through distributed interference alignment[C]// IEEE Global Telecommunications Conference. New Orleans, USA: IEEE Press, 2008: 1-6.
    [9]
    Peters S W, Heath R W. Interference alignment via alternating minimization[C]// IEEE International Conference on Acoustics, Speech, and Signal Processing. TaiPei, China: IEEE Press, 2009: 2 445-2 448.
    [10]
    Kumar K R, Xue F. An iterative algorithm for joint signal and interference alignment[C]// IEEE International Symposium on Information Theory. Austin, USA: IEEE Press, 2010: 2 293-2 297.
    [11]
    Liu S, Du Y G, Zhao M. A new joint iterative transceiver design with interference alignment method[C]// 19th Annual Wireless and Optical Communications Conference. Shanghai, China: IEEE Press, 2010: 1-5.
    [12]
    Shen H, Li B. A novel iterative interference alignment scheme via convex optimization for the MIMO interference channel[C]// Vehicular Technology Conference. Ottawa, Canada: IEEE Press, 2010: 1-5.
    [13]
    Shen H, Li B, Tao M X, et al. The new interference alignment scheme for the MIMO interference channe[C]// Wireless Communications and Networking Conference. Sydney, Australia: IEEE Press, 2010: 1-6.
    [14]
    Ghauch H G, Papadias C B. Interference alignment: A one-sided approach[C]// IEEE Global Telecommunications Conference. Texas, USA: IEEE Press, 2011: 1-5.
    [15]
    Santamaria I, Gonzalez O, Heath R W, et al. Maximum sum-rate interference alignment algorithms for MIMO channels[C]// IEEE Global Telecommunications Conference. Miami, USA: IEEE Press, 2010: 1-6.
    [16]
    Edelman A, Arias T A, Smith S T. The geometry of algorithms with orthogonality constraints[J]. SIAM Journal on Matrix Analysis and Applications, 1999, 20(2): 303-353.
    [17]
    Abrudan T E, Eriksson J, Koivunen V. Steepest descent algorithms for optimization under unitary matrix constraint[J]. IEEE Transaction on Signal Processing, 2008, 56(3): 1 134-1 147.
    [18]
    张贤达. 矩阵分析与应用[M]. 北京: 清华大学出版社, 2004.
    [19]
    Hjrungnes A. Complex-Valued Matrix Derivatives: With Applications in Signal Processing and Communications[M]. Cambridge, UK: Cambridge University Press, 2011.
    [20]
    AbsilP A, Mahony R, Sepulchre R. Optimization Algorithms on Matrix Manifolds[M]. New Jersey: Princeton University Press, 2008.
    [21]
    Zhang C, Yin H R, Wei G. One-sided precoder designs for interference alignment[C]// IEEE Vehicular Technology Conference. Quebec, Canada: IEEE Press, 2012: 1-5.
    [22]
    Manton J H. Optimization algorithms exploiting unitary constraints[J]. IEEE Transaction on Signal Processing. 2002, 50(3): 635-650.
    [23]
    Boyd S, Vandenberghe L. Convex Optimization[M]. Cambridge, UK: Cambridge University Press, 2004.
    [24]
    Polak E. Optimization: Algorithms and Consistent Approximations[M]. New York: Springer-Verlag, 1997.
    [25]
    王存祥, 邱玲. 协作多点传输中一种基于特征子信道的干扰对齐预编码矩阵优化方案[J]. 信号处理, 2011, 27(3): 395-399.
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