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Wireless Personal Communications

, Volume 6, Issue 3, pp 311–335 | Cite as

On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas

  • G.J. Foschini
  • M.J. Gans
Article

Abstract

This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bit-rates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multi-element array (MEA) technology, that is processing the spatial dimension (not just the time dimension) to improve wireless capacities in certain applications. Specifically, we present some basic information theory results that promise great advantages of using MEAs in wireless LANs and building to building wireless communication links. We explore the important case when the channel characteristic is not available at the transmitter but the receiver knows (tracks) the characteristic which is subject to Rayleigh fading. Fixing the overall transmitted power, we express the capacity offered by MEA technology and we see how the capacity scales with increasing SNR for a large but practical number, n, of antenna elements at both transmitter and receiver.

We investigate the case of independent Rayleigh faded paths between antenna elements and find that with high probability extraordinary capacity is available. Compared to the baseline n = 1 case, which by Shannon's classical formula scales as one more bit/cycle for every 3 dB of signal-to-noise ratio (SNR) increase, remarkably with MEAs, the scaling is almost like n more bits/cycle for each 3 dB increase in SNR. To illustrate how great this capacity is, even for small n, take the cases n = 2, 4 and 16 at an average received SNR of 21 dB. For over 99% of the channels the capacity is about 7, 19 and 88 bits/cycle respectively, while if n = 1 there is only about 1.2 bit/cycle at the 99% level. For say a symbol rate equal to the channel bandwith, since it is the bits/symbol/dimension that is relevant for signal constellations, these higher capacities are not unreasonable. The 19 bits/cycle for n = 4 amounts to 4.75 bits/symbol/dimension while 88 bits/cycle for n = 16 amounts to 5.5 bits/symbol/dimension. Standard approaches such as selection and optimum combining are seen to be deficient when compared to what will ultimately be possible. New codecs need to be invented to realize a hefty portion of the great capacity promised.

capacity information theory diversity matrix channel array 

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References

  1. 1.
    W.C. Jakes, Jr., “Microwave Mobile Communications”, John Wiley and Sons, New York, Chapters 1 and 5, 1974.Google Scholar
  2. 2.
    B.J. Tuch, “An ISM Band Local Area Network: WaveLAN”, IEEE Workshop on Local Area Networks, Worcester Polytechnic Institute, Worcester Massachusetts, pp. 103–111, 1991.Google Scholar
  3. 3.
    W. Diepstraten and H.J.M. Stevens, “WaveLAN Systems Test Report”, NCR Corporation TR No. 407–0023871 rev A.Google Scholar
  4. 4.
    J. Kruys, “HiperLAN, Applications and Requirements”, PIMRC’ 92, Boston Massachusetts, pp. 133–135, 1992.Google Scholar
  5. 5.
    M.V. Clark, L.J. Greenstein, W.K. Kennedy and M. Shafi, “Matched Filter Performance Bounds for Diversity Combining Receivers in Digital Mobile Radio”, IEEE Trans. Veh. Technol., Vol. 41, No.4, pp. 356–362, 1992.Google Scholar
  6. 6.
    M.V. Clark, M. Shafi, W.K. Kennedy and L.J. Greenstein, “Optimum Linear Diversity Receivers for Mobile Communications”, IEEE Trans. Veh. Technol., Vol. 43, No.1, pp. 47–56, 1994.Google Scholar
  7. 7.
    M.V. Clark, M. Shafi, W.K. Kennedy and L.J. Greenstein, “MMSE Diversity Combining for Wide-Band Digital Cellular Radio”, IEEE Trans. Commun., Vol. 40, No.6, pp. 1128–1135, 1992.Google Scholar
  8. 8.
    M.V. Clark, L.J. Greenstein, W.K. Kennedy and M. Shafi, “Optimum Linear Diversity Receivers in Digital Cellular Radio”, PIMRC’ 92, Conference Proceedings, IEEE Communications Society, Boston Massachusetts, pp. 174–178, 1992.Google Scholar
  9. 9.
    D.L. Noneaker and M.B. Pursley, “Error Probability Bounds for M-PSK and M-DPSK nd Selective Fading Diversity Channels”, IEEE Trans. Veh. Technol., Vol. 43, No.4, pp. 997–1005.Google Scholar
  10. 10.
    J.H. Winters, “On the Capacity of Radio Communications Systems with Diversity in a Rayleigh Fading Environment”, IEEE J. Select. Areas Communic., pp. 871–878, 1987.Google Scholar
  11. 11.
    J.H. Winters, “The Diversity Gain of Transmit Diversity in Wireless Systems with Rayleigh Fading”, ICC’ 94, pp. 1121–1125, 1994.Google Scholar
  12. 12.
    J. Salz and P. Balaban, “Optimum Diversity Combining and Equalization in Digital Data Transmission with Applications to Cellular Mobile Radio - Part I: Theoretical Considerations”, IEEE Trans. Communic., Vol. 40, No.5, pp. 885–894, 1992.Google Scholar
  13. 13.
    J. Salz and P. Balaban, “Optimum Diversity Combining and Equalization in Digital Data Transmission with Applications to Cellular Mobile Radio - Part II: Numerical Results”, IEEE Trans. Communic., Vol. 40, No.5, pp. 895–907, 1992.Google Scholar
  14. 14.
    R.D. Gitlin, J. Salz and J.H. Winters, “The Impact of Antenna Diversity on the Capacity of Wireless Communication Systems”, IEEE Trans. Commun., Vol. 42, No.4, pp. 1740–1751, 1994.Google Scholar
  15. 15.
    J. Salz and J.H. Winters, “Effects of Fading Correlation on Adaptive Arrays in Digital Mobile Radio”, IEEE Trans. Veh. Technol., Vol. 43, No.4, pp. 1049–1057, 1994.Google Scholar
  16. 16.
    P.C.F. Eggers, J. Toftgard and A. Oprea, “Antenna Systems for Base Station Diversity in Urban Small and Micro Cells”, IEEE J. Select. Areas Communc., Vol. 11, No.7, pp. 1046–1047, 1993.Google Scholar
  17. 17.
    P. Dent, B. Gudmundson and M. Ewerbring, “CDMA-IC: Novel Code Division Multiple Access Scheme Based on Interference Cancellation”, PIMRC 1992, pp. 98–102, 1992.Google Scholar
  18. 18.
    B. Suard, A. Naguib, G. Xu and A. Paulraj, “Performance Analysis of CDMA Mobile Communication Systems Using Antenna Arrays”, Proc. ICASSP 93, Vol. VI, Minneapolis, MN, pp. 153–156, 1993.Google Scholar
  19. 19.
    S. Talwar, A. Paulraj and M. Viberg, “Reception of Multiple Co-Channel Digital Signals Using Antenna Arrays with Applications to PCS”, Proc. ICC 94, Vol. II, pp. 700–794, 1994.Google Scholar
  20. 20.
    J. Blanz, A. Klein, M. Nasshan and A. Steil, “Performance of a Cellular Hybrid C/TDMA Mobile Radio System Applying Joint Detection and Coherent Receiver Antenna Diversity”, IEEE J. Select. Areas Communic., Vol. 12, No.4, pp. 568–574, 1994.Google Scholar
  21. 21.
    W. Honcharenko, H.L. Bertoni and J.L. Dailing, “Bilateral Averaging over Receiving and Transmitting Areas for Accurate Measurements of Sector Average Signal Strength Inside Buildings”, IEEE Trans. Antennas Propag., Vol. 43, No.5, pp. 508–511, 1995.Google Scholar
  22. 22.
    J.R. Pierce and E.C. Posner, “Introduction to Communication Science and Systems”, Plenum Press, New York, Chapter 11, 1980.Google Scholar
  23. 23.
    R.M. Fano, “Transmission of Information”, John Wiley and Sons, New York, pp. 168–178, 1961.Google Scholar
  24. 24.
    R.G. Gallager, “Information Theory and Reliable Communcation”, J.Wiley and Sons, New York, Chapter IV, 1968.Google Scholar
  25. 25.
    M.S. Pinsker, “Information and Information Stability of Random Processes”, Holden Bay, San Francisco, Chapter 10, 1964.Google Scholar
  26. 26.
    G.J. Foschini and R.K. Mueller, “The Capacity of Linear Channels with Additive Gaussian Noise”, Bell Syst. Tech. J., pp. 81–94, 1970.Google Scholar
  27. 27.
    R.E. Blahut, “Digital Transmission of Information”, Addison Wesley, New York, p. 503, 1990.Google Scholar
  28. 28.
    J. Wolfowitz, “Coding Theorems of Information Theory”, Springer-Verlag, New York, 1978.Google Scholar
  29. 29.
    A. Edelman, “Eigenvalues and Condition Numbers of Random Matrices”, M.I.T. Doctoral Dissertation, Mathematics Department, 1989.Google Scholar
  30. 30.
    T.W. Anderson (ed.) and S.S. Wilks, “Collected Papers Contributions to Mathematical Statistics”, JohnWiley and Sons, New York, 1967.Google Scholar
  31. 31.
    P. Lancaster and M. Tismenetsky, “The Theory of Matrices”, Academic Press, p. 46, 1985.Google Scholar
  32. 32.
    J.M. Wozencraft and I.M. Jacobs, “Principles of Communication Engineering”, John Wiley and Sons, New York, pp. 106–111, 1965.Google Scholar
  33. 33.
    B. Hajek and E. Wong, “Stochastic Processes in Information and Dynamical Systems”, McGraw Hill, New York, 1989.Google Scholar
  34. 34.
    E. Csiszar and J. Korner, “Information Theory: Coding Theorems for Discrete Memoryless Systems”, Academic Press, New York, 1981.Google Scholar
  35. 35.
    Fortran Library Mark 16, “Introductory Guide”, The Numerical Algorithms Group Limited, Downers Grove, Illinois, 1993.Google Scholar
  36. 36.
    R.D. Gitlin, J.F. Hayes and S. Weinstein, “Data Communication Principles”, Plenum Press, New York, Chapters 5 and 7, 1992.Google Scholar
  37. 37.
    G. Ungerboeck, “Channel Coding with Multilevel/Phase Signals”, IEEE Trans. Inform. Theory, Vol. IT-28, No.1, pp. 55–67, 1982.Google Scholar
  38. 38.
    G.D. Forney, Jr., R.G. Gallager, G.R. Lang, F.M. Longstaff and S.U. Qureshi, “Efficient Modulation for Band-Limited Channels”, Vol. SAC-2, No.5, pp. 632–647, 1984.Google Scholar
  39. 39.
    C. Berrou, A. Glavieux and P. Thitimajshima, “Near Shannon Limit Error-Correcting Coding and Decoding: Turbocodes”, ICC’ 93, Conference Record, Geneva, pp. 1064–1070, 1993.Google Scholar
  40. 40.
    G.J. Foschini and A.C. Salazar, “Data Pulse Design - Intersymbol Interference Aspects”, J. Institute Mathem. Applic., pp. 225–237, 1975.Google Scholar
  41. 41.
    J.A. Stratton, “Electromagnetic Theory”, McGraw-Hill Book Company, Inc., New York, 1941.Google Scholar
  42. 42.
    K.S. Miller, “Complex Stochastic Processes”, Addison-Wesley, Massachusetts, 1974.Google Scholar
  43. 43.
    S. Kullback, “Information Theory and Statistics”, John Wiley and Sons, New York, 1959.Google Scholar
  44. 44.
    D.B. Osteyee and I.J. Good, “Information Weight of Evidence, the Singularity between Probability Measures and Signal Detection”, Springer-Verlag, New York, 1970.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • G.J. Foschini
    • 1
  • M.J. Gans
    • 1
  1. 1.Lucent TechnologiesBell Labs. Innovations, Crawford Hill Laboratory – R137HolmdelU.S.A

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