Skip to main content
SpringerLink
Log in

Multiple antennas

  • Chapter
Coding for Wireless Channels

  • 1283 Accesses

Abstract

This chapter focuses on the main theoretical aspects of transmission systems where more than one antenna is used at both ends of a radio link and hence where one channel use involves sending signals simultaneously through several propagation paths. The use of multiple transmit and receive antennas allows one to reach capacities that cannot be obtained with any other technique using present-day technology, and is expected to make it possible to increase the data rates in wireless networks by orders of magnitude. After describing system and channel models, we compute the capacities that can be achieved, and we show how “space-time” codes can be designed and how suboptimum architectures can be employed to simplify the receiver. Finally, we examine the basic trade-off between the data-rate gain, made possible by simultaneous transmission by several antennas, and the diversity gain, achieved by sending the same signal through several independently faded paths.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Select. Areas Commun., Vol. 16, No. 8, pp. 1451–1458, October 1998.

    Article  Google Scholar 

  2. S. L. Ariyavisitakul, “Turbo space-time processing to improve wireless channel capacity,” IEEE Trans. Commun., Vol. 48, No. 8, pp. 1347–1359, Aug. 2000.

    Article  Google Scholar 

  3. Z. D. Bai and J. W. Silverstein, “CLT for linear spectral statistics of large dimensional sample covariance matrices,” Ann. Probabil., Vol. 32, No. 1A, pp. 553–605, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  4. S. Benedetto and E. Biglieri, Principles of Digital Transmission with Wireless Applications. New York: Kluwer/Plenum, 1999.

    MATH  Google Scholar 

  5. E. Biglieri and G. Taricco, “Transmission and reception with multiple antennas: Theoretical foundations,” Foundations and Trends in Communications and Information Theory, Vol. 1, No. 2, 2004.

    Google Scholar 

  6. E. Biglieri, G. Caire, and G. Taricco, “Limiting performance of block-fading channels with multiple antennas,” IEEE Trans. Inform. Theory, Vol. 47, No. 4, pp. 1273–1289, May 2001.

    Article  MATH  MathSciNet  Google Scholar 

  7. E. Biglieri, A. Nordio, and G. Taricco, “Suboptimum receiver interfaces and space-time codes,” IEEE Trans. Sig. Proc, Vol. 51, No. 11, pp. 2720–2728, November 2003.

    Article  MathSciNet  Google Scholar 

  8. E. Biglieri, A. Nordio, and G. Taricco, “Doubly-iterative decoding of space-time turbo codes with a large number of antennas,” Proc. 2004 IEEE Int. Conf. Communications (ICC 2004), Paris, France, June 20–24, 2004.

    Google Scholar 

  9. E. Biglieri, G. Taricco, and A. Tulino, “Performance of space-time codes for a large number of antennas,” IEEE Trans. Inform. Theory, Vol. 48, No. 7, pp. 1794–1803, July 2002.

    Article  MATH  MathSciNet  Google Scholar 

  10. E. Biglieri, G. Taricco, and A. Tulino, “Decoding space-time codes with BLAST architectures,” IEEE Trans. Sig. Proc, Vol. 50, No. 10, pp. 2547–2552, October 2002.

    Article  Google Scholar 

  11. M. Bilodeau and D. Brenner, Theory of Multivariate Statistics. New York: Springer, 1999.

    MATH  Google Scholar 

  12. N. Bleistein and R.A. Handelsman, Asymptotic Expansions of Integrals. Dover, 1986

    Google Scholar 

  13. H. Boelcskei, D. Gesbert, and A. J. Paulraj, “On the capacity of OFDM-based spatial multiplexing systems,” IEEE Trans. Commun., Vol. 50, No. 2, pp. 225–234, February 2002.

    Article  Google Scholar 

  14. J. K. Cavers and P. Ho, “Analysis of the Error Performance of Trellis-Coded Modulations in Rayleigh Fading Channels,” IEEE Trans. Commun., Vol. 40, No. 1, pp. 74–83, January 1992.

    Article  MATH  Google Scholar 

  15. J.-J. Chang, D.-J. Hwang, and M.-C. Lin, “Some extended results on the search for good convolutional codes,” IEEE Trans. Inform. Theory, Vol. 43, No. 5, pp. 1682–1697, September 1997.

    Article  MATH  MathSciNet  Google Scholar 

  16. N. Chiurtu, B. Rimoldi, and E. Telatar, “Dense multiple antenna systems,” Proc. IEEE Information Theory Workshop ITW2001, Cairns, Australia, pp. 108–109, September 2–7, 2001.

    Google Scholar 

  17. D. Chizhik, G.J. Foschini, M.J. Gans, and R.A. Valenzuela, “Keyholes, correlations, and capacities of multielement transmit and receive antennas,” IEEE Trans. Wireless Commun., Vol. 1, No. 2, pp. 361–368, April 2002

    Article  Google Scholar 

  18. C.-N. Chuah, D. N. C. Tse, J. M. Kahn, and R. A. Valenzuela, “Capacity bounds via duality with applications to multiple-antenna systems on flat-fading channels,” IEEE Trans. Inform. Theory, Vol. 48, No. 3, pp. 637–650, March 2002.

    Article  MATH  MathSciNet  Google Scholar 

  19. H. El-Gamal and A. R. Hammons, Jr., “A new approach to layered space-time coding and signal processing,” IEEE Trans. Inform. Theory, Vol. 47, No. 6, pp. 2321–2334, September 2001.

    Article  MATH  MathSciNet  Google Scholar 

  20. G. J. Foschini, “Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas,” Bell Labs Tech. J., Vol. 1, No. 2, pp. 41–59, Autumn 1996.

    Article  Google Scholar 

  21. G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Personal Commun., Vol. 6, No. 3, pp. 311–335, March 1998.

    Article  Google Scholar 

  22. G. J. Foschini, G. D. Golden, R. A. Valenzuela, and P. W. Wolniansky, “Simplified processing for high spectral efficiency wireless communication employing multielement arrays,” IEEE J. Select. Areas Commun., Vol. 17, No. 11, pp. 1841–1852, November 1999.

    Article  Google Scholar 

  23. G. J. Foschini and R. A. Valenzuela, “Initial estimation of communication efficiency of indoor wireless channels,” Wireless Networks, Vol. 3, No. 2, pp. 141–154, 1997.

    Article  Google Scholar 

  24. D. Gesbert, H. Bölcskei, D. Gore, and A. Paulraj, “Outdoor MIMO wireless channels: Models and performance prediction,” IEEE Trans. Commun., Vol. 50, No. 12, pp. 1926–1934, December 2002.

    Article  Google Scholar 

  25. V. L. Girko, “A refinement of the central limit theorem for random determinants,” Theory Probab. Appl., Vol. 42, No. 1, pp. 121–129, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  26. A. Goldsmith, S. A. Jafar, N. Jindal, and S. Vishwanath, “Capacity limits of MIMO channels,” IEEE J. Select. Areas Commun., Vol. 21, No. 5, pp. 684–702, June 2003.

    Article  Google Scholar 

  27. A. R. Hammons, Jr., and H. El Gamal, “On the theory of space-time codes for PSK modulation,” IEEE Trans. Inform. Theory, Vol. 46, No. 2, pp. 524–542, March 2000.

    Article  MATH  MathSciNet  Google Scholar 

  28. B. Hassibi and B. M. Hochwald, “High-rate codes that are linear in space and time,” IEEE Trans. Inform. Theory, Vol. 48, No. 7, pp. 1804–1824, July 2002.

    Article  MATH  MathSciNet  Google Scholar 

  29. B. Hassibi, B. M. Hochwald, A. Shokrollahi, and W. Sweldens, “Representation theory for high-rate multiple-antenna code design,” IEEE Trans. Inform. Theory, Vol. 47, No. 6, pp. 2335–2367, September 2001.

    Article  MATH  MathSciNet  Google Scholar 

  30. B. Hochwald and T. Marzetta, “Unitary space-time modulation for multiple-antenna communication in Rayleigh flat-fading,” IEEE Trans. Inform. Theory, Vol. 46, No. 2, pp. 543–564, March 2000.

    Article  MATH  MathSciNet  Google Scholar 

  31. B. M. Hochwald, T. L. Marzetta, and V. Tarokh, “Multi-antenna channel-hardening and its implications for rate feedback and scheduling,” IEEE Trans. Inform. Theory, Vol. 50, No. 9, pp. 1893–1909, September 2004.

    Article  MathSciNet  Google Scholar 

  32. B. Hochwald and W. Sweldens, “Differential unitary space-time modulation,” IEEE Trans. Commun., Vol. 48, No. 12, pp. 2041–2052, December 2000.

    Article  Google Scholar 

  33. B. L. Hughes, “Differential space-time modulation,” IEEE Trans. Inform. Theory, Vol. 46, No. 11, pp. 2567–2578, November 2000.

    Article  MATH  Google Scholar 

  34. A. Lapidoth and S. M. Moser, “Capacity bounds via duality with applications to multiple-antenna systems on flat-fading channels,” IEEE Trans. Inform. Theory, Vol. 49, No. 10, pp. 2426–2467, October 2003.

    Article  MathSciNet  Google Scholar 

  35. E.G. Larsson and P. Stoica, Space-Time Block Coding for Wireless Communications. Cambridge, UK: Cambridge University Press, 2003.

    MATH  Google Scholar 

  36. X. Ma and G. B. Giannakis, “Full-diversity full-rate complex-field space-time coding,” IEEE Trans. Sig. Proc., Vol. 51, No. 11, pp. 2917–2930, November 2003.

    Article  MathSciNet  Google Scholar 

  37. T. L. Marzetta and B. M. Hochwald, “Capacity of a mobile multiple-antenna communication link in Rayleigh flat fading,” IEEE Trans. Inform. Theory, Vol. 45, No. 1, pp. 139–157, January 1999.

    Article  MATH  MathSciNet  Google Scholar 

  38. T. L. Marzetta, B. M. Hochwald, and B. Hassibi, “New approach to single-user multiple-antenna wireless communication,” Proc. 2000 Conference on Information Sciences and Systems, Princeton University, pp. WA4-16–WA4-21, March 15–17, 2000.

    Google Scholar 

  39. A. F. Molish, M. Z. Win, and J. H. Winters, “Capacity of MIMO systems with antenna selection,” Proc. IEEE International Conference on Communications (ICC 2001), Helsinki, Finland, June 11–14, 2001.

    Google Scholar 

  40. A. L. Moustakas, H. U. Baranger, L. Balents, A. M. Sengupta, and S.H. Simon, “Communication through a diffusive medium: Coherence and capacity,” Science, Vol. 287, pp. 287–290, January 2000.

    Article  Google Scholar 

  41. A. L. Moustakas, S. H. Simon, A. M. Sengupta, “MIMO capacity through correlated channels in the presence of correlated interferers and noise: A (not so) large N analysis,” IEEE Trans. Inform. Theory Vol. 49, No. 10, pp. 2545–2561, October 2003.

    Article  MathSciNet  Google Scholar 

  42. A. Paulraj, R. Nabar, and D. Gore, Introduction to Space-Time Wireless Communications. Cambridge, UK: Cambridge University Press, 2003.

    Google Scholar 

  43. P. B. Rapajic and D. Popescu, “Information capacity of a random signature multiple-input multiple-output channel,” IEEE Trans. Commun., Vol. 48, No. 8, pp. 1245–1248, August 2000.

    Article  MATH  Google Scholar 

  44. M. Schwartz, W. R. Bennett, and S. Stein, Communications Systems and Techniques. New York: McGraw-Hill, 1966.

    Google Scholar 

  45. M. Sellathurai and S. Haykin, “Turbo-BLAST for wireless communications: Theory and experiments,” IEEE Trans. Sig. Proc, Vol. 50, No. 10, pp. 2538–2546, October 2002.

    Article  Google Scholar 

  46. M. Sellathurai and S. Haykin, “Turbo-BLAST: Performance evaluation in correlated Rayleigh-fading environment,”IEEE J. Select. Areas Commun., Vol. 21, No. 3, pp. 340–349, April 2003.

    Article  Google Scholar 

  47. M. Sellathurai and S. Haykin, “T-BLAST for wireless communications: First experimental results,” IEEE Trans. Vehicular Technology, Vol. 52, No. 3, pp. 530–535, May 2003.

    Article  Google Scholar 

  48. A. M. Sengupta and P. P. Mitra, “Capacity of multivariate channels with multiplicative noise: Random matrix techniques and large-N expansions for full transfer matrices,” LANL arXiv:physics, 31 October 2000.

    Google Scholar 

  49. N. Seshadri and J. H. Winters, “Two signaling schemes for improving the error performance of frequency-division duplex (FDD) transmission systems using transmitter antenna diversity,” Proc. 43rd IEEE Vehicular Technology Conference (VTC 1993), pp. 508–511, May 18–20, 1993.

    Google Scholar 

  50. H. Shin and J. H. Lee, “Capacity of multiple-antenna fading channels: Spatial fading correlation, double scattering, and keyhole,” IEEE Trans. Inform. Theory, Vol. 49, No. 10, pp. 2636–2647, October 2003.

    Article  MathSciNet  Google Scholar 

  51. D. Shiu, G. Foschini, M. J. Gans, and J. M. Kahn, “Fading correlation and its effect on the capacity of multielement antenna systems”, IEEE Trans. Commun., Vol. 48, No. 3, pp. 502–513, March 2000.

    Article  Google Scholar 

  52. P. J. Smith and M. Shafi, “On a Gaussian approximation to the capacity of wireless MIMO systems,” Proc. IEEE International Conference on Communications (ICC 2002), pp. 406–410, New York, April 28–May 2, 2002.

    Google Scholar 

  53. P. Soma, D. S. Baum, V. Erceg, R. Krishnamoorty, and A. J. Paulraj, “Analysis and modeling of multiple-input multiple-output (MIMO) radio channel based on outdoor measurements conducted at 2.5 GHz for fixed BWA applications,” in Proc. IEEE ICC 2002, Vol. 1, pp. 212–216, New York, NY, May 28–April 2, 2002.

    Google Scholar 

  54. G. Szegö, Orthogonal Polynomials. Providence, RI: American Mathematical Society, 1939.

    Google Scholar 

  55. G. Taricco and E. Biglieri, “Space-time decoding with imperfect channel estimation,” IEEE Trans. Wireless Commun., in press, 2005.

    Google Scholar 

  56. V. Tarokh and T. K. Y. Lo, “Principal ratio combining for fixed wireless applications when transmitter diversity is employed,” IEEE Commun. Lett., Vol. 2, No. 8, pp. 223–225, August 1998.

    Article  Google Scholar 

  57. V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high data rate wireless communication: Performance criterion and code construction,” IEEE Trans. Inform. Theory Vol. 44, No. 2, pp. 744–765, March 1998.

    Article  MATH  MathSciNet  Google Scholar 

  58. E. Telatar, “Capacity of multi-antenna Gaussian channels,” Eur. Trans. Telecomm., Vol. 10, No. 6, pp. 585–595, November–December 1999.

    Article  Google Scholar 

  59. D. Tse and V. Hanly, “Multi-access fading channels—Part I: Polymatroid structure, optimal resource allocation and throughput capacities,” IEEE Trans. Inform. Theory, Vol. 44, No. 7, pp. 2796–2815, November 1998.

    Article  MATH  MathSciNet  Google Scholar 

  60. D. Tse and P. Viswanath, Fundamentals of Wireless Communication. Cambridge, UK: Cambridge University Press, 2005, to be published.

    MATH  Google Scholar 

  61. S. Verdü, Multiuser Detection. Cambridge, UK: Cambridge University Press, 1998.

    Google Scholar 

  62. S. Verdú and S. Shamai (Shitz), “Spectral efficiency of CDMA with random spreading,” IEEE Trans. Inform. Theory, Vol. 45, No. 2, pp. 622–640, March 1999.

    Article  MATH  MathSciNet  Google Scholar 

  63. H. Wang and X.-G. Xia, “Upper bounds of rates of complex orthogonal space-time block codes,” IEEE Trans. Inform. Theory, Vol. 49, No. 10, pp. 2788–2796, October 2003.

    Article  MathSciNet  Google Scholar 

  64. A. Wittneben, “Basestation modulation diversity for digital SIMULCAST,” Proc. 41st Vehicular Technology Conference (VTC 1991), pp. 848–853, May 19–22, 1991.

    Google Scholar 

  65. D. Wuebben, R. Boehnke, J. Rinas, V. Kuehn, and K. D. Kammeyer, “Efficient algorithm for decoding layered space-time codes,” Electron. Lett., Vol. 37, No. 22, pp. 1348–1349, 25 October 2001.

    Article  Google Scholar 

  66. L. Zheng and D. N. C. Tse, “Communication on the Grassman manifold: A geometric approach to the noncoherent multiple-antenna channel,” IEEE Trans. Inform. Theory, Vol. 48, No. 2, pp. 359–383, February 2002.

    Article  MATH  MathSciNet  Google Scholar 

  67. L. Zheng and D. N. C. Tse, “Diversity and multiplexing: A fundamental tradeoff in multiple antenna channels,” IEEE Trans. Inform. Theory, Vol. 49, No. 5, pp. 1073–1096, May 2003.

    Article  MATH  Google Scholar 

Download references

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer Science+Business Media, Inc.

About this chapter

Cite this chapter

(2005). Multiple antennas. In: Coding for Wireless Channels. Information Technology: Transmission, Processing and Storage. Springer, Boston, MA. https://doi.org/10.1007/1-4020-8084-0_10

Download citation

  • DOI: https://doi.org/10.1007/1-4020-8084-0_10

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4020-8083-8

  • Online ISBN: 978-1-4020-8084-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation