Skip to content


  • Research Article
  • Open Access

A Hub Matrix Theory and Applications to Wireless Communications

EURASIP Journal on Advances in Signal Processing20072007:013659

  • Received: 24 July 2006
  • Accepted: 22 January 2007
  • Published:


This paper considers communications and network systems whose properties are characterized by the gaps of the leading eigenvalues of for a matrix . It is shown that a sufficient and necessary condition for a large eigen-gap is that is a "hub" matrix in the sense that it has dominant columns. Some applications of this hub theory in multiple-input and multiple-output (MIMO) wireless systems are presented.


  • Information Technology
  • Wireless Communication
  • Quantum Information
  • Matrix Theory
  • Network System

Authors’ Affiliations

Harvard School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
US Air Force Research Laboratory, Rome, NY 13440, USA


  1. Tse D, Viswanath P: Fundamentals of Wireless Communication. Cambridge University Press, Cambridge, UK; 2005.View ArticleGoogle Scholar
  2. Kleinberg JM: Authoritative sources in a hyperlinked environment. Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms, January 1998, San Francisco, Calif, USA 668–677.Google Scholar
  3. Kung HT, Wu C-H: Differentiated admission for peer-to-peer systems: incentivizing peers to contribute their resources. Workshop on Economics of Peer-to-Peer Systems, June 2003, Berkeley, Calif, USAGoogle Scholar
  4. O'Leary DP, Stewart GW: Computing the eigenvalues and eigenvectors of symmetric arrowhead matrices. Journal of Computational Physics 1990,90(2):497-505. 10.1016/0021-9991(90)90177-3MathSciNetView ArticleGoogle Scholar
  5. Horn RA, Johnson CR: Matrix Analysis. Cambridge University Press, Cambridge, UK; 1985.View ArticleGoogle Scholar
  6. Love DJ, Heath RW Jr.: Equal gain transmission in multiple-input multiple-output wireless systems. IEEE Transactions on Communications 2003,51(7):1102-1110. 10.1109/TCOMM.2003.814195View ArticleGoogle Scholar
  7. Love DJ, Heath RW Jr.: Corrections to "Equal gain transmission in multiple-input multiple-output wireless systems". IEEE Transactions on Communications 2003,51(9):1613. 10.1109/TCOMM.2003.818386View ArticleGoogle Scholar
  8. Meyer CD: Matrix Analysis and Applied Linear Algebra. SIAM, Philadelphia, Pa, USA; 2000.View ArticleGoogle Scholar
  9. Tse C-H, Yip K-W, Ng T-S: Performance tradeoffs between maximum ratio transmission and switched-transmit diversity. Proceedings of the 11th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC '00), September 2000, London, UK 2: 1485–1489.Google Scholar
  10. Love DJ, Heath RW Jr., Strohmer T: Grassmannian beamforming for multiple-input multiple-output wireless systems. IEEE Transactions on Information Theory 2003,49(10):2735-2747. 10.1109/TIT.2003.817466MathSciNetView ArticleGoogle Scholar
  11. Murthy C, Rao BD: On antenna selection with maximum ratio transmission. Conference Record of the 37th Asilomar Conference on Signals, Systems and Computers, November 2003, Pacific Grove, Calif, USA 1: 228–232.Google Scholar
  12. Molisch AF, Win MZ, Winter JH: Reduced-complexity transmit/receive-diversity systems. IEEE Transactions on Signal Processing 2003,51(11):2729-2738. 10.1109/TSP.2003.818211MathSciNetView ArticleGoogle Scholar
  13. Young RM: An Introduction to Nonharmonic Fourier Series. Academic Press, New York, NY, USA; 1980.MATHGoogle Scholar
  14. Sebe N: Diagonal dominance and integrity. Proceedings of the 35th IEEE Conference on Decision and Control, December 1996, Kobe, Japan 2: 1904–1909.View ArticleGoogle Scholar


© H. T. Kung and B.W. Suter. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.