On Limits of Wireless Communications in a Fading Environment when UsingMultiple Antennas

  • Authors:
  • G. J. Foschini;M. J. Gans

  • Affiliations:
  • Lucent Technologies, Bell Labs. Innovations, Crawford Hill Laboratory – R137, 791 Holmdel-Keyport Road, Holmdel, New Jersey 07733-0400, U.S.A.;Lucent Technologies, Bell Labs. Innovations, Crawford Hill Laboratory – R137, 791 Holmdel-Keyport Road, Holmdel, New Jersey 07733-0400, U.S.A.

  • Venue:
  • Wireless Personal Communications: An International Journal
  • Year:
  • 1998

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This paper is motivated by the need for fundamental understanding ofultimate limits of bandwidth efficient delivery of higher bit-rates indigital wireless communications and to also begin to look into how theselimits might be approached. We examine exploitation of multi-element array(MEA) technology, that is processing the spatial dimension (not just thetime dimension) to improve wireless capacities in certain applications.Specifically, we present some basic information theory results that promisegreat advantages of using MEAs in wireless LANs and building to buildingwireless communication links. We explore the important case when the channelcharacteristic is not available at the transmitter but the receiver knows(tracks) the characteristic which is subject to Rayleigh fading. Fixing theoverall transmitted power, we express the capacity offered by MEA technologyand we see how the capacity scales with increasing SNR for a large butpractical number, n, of antenna elements at both transmitter and receiver.We investigate the case of independent Rayleigh faded paths between antennaelements and find that with high probability extraordinary capacity isavailable. Compared to the baseline n = 1 case, which by Shannon‘s classicalformula 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 morebits/cycle for each 3 dB increase in SNR. To illustrate how great thiscapacity is, even for small n, take the cases n = 2, 4 and 16 at an averagereceived SNR of 21 dB. For over 99% of the channels the capacity isabout 7, 19 and 88 bits/cycle respectively, while if n = 1 there is onlyabout 1.2 bit/cycle at the 99% level. For say a symbol rate equal tothe channel bandwith, since it is the bits/symbol/dimension that is relevantfor signal constellations, these higher capacities are not unreasonable. The19 bits/cycle for n = 4 amounts to 4.75 bits/symbol/dimension while 88bits/cycle for n = 16 amounts to 5.5 bits/symbol/dimension. Standardapproaches such as selection and optimum combining are seen to be deficientwhen compared to what will ultimately be possible. New codecs need to beinvented to realize a hefty portion of the great capacity promised.