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Space-time autocoding

Hochwald, Bertrand M. and Marzetta, Thomas L. and Hassibi, Babak (2001) Space-time autocoding. IEEE Transactions on Information Theory, 47 (7). pp. 2761-2781. ISSN 0018-9448. http://resolver.caltech.edu/CaltechAUTHORS:HOCieeetit01

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Abstract

Prior treatments of space-time communications in Rayleigh flat fading generally assume that channel coding covers either one fading interval-in which case there is a nonzero “outage capacity”-or multiple fading intervals-in which case there is a nonzero Shannon capacity. However, we establish conditions under which channel codes span only one fading interval and yet are arbitrarily reliable. In short, space-time signals are their own channel codes. We call this phenomenon space-time autocoding, and the accompanying capacity the space-time autocapacity. Let an M-transmitter antenna, N-receiver antenna Rayleigh flat fading channel be characterized by an M×N matrix of independent propagation coefficients, distributed as zero-mean, unit-variance complex Gaussian random variables. This propagation matrix is unknown to the transmitter, it remains constant during a T-symbol coherence interval, and there is a fixed total transmit power. Let the coherence interval and number of transmitter antennas be related as T=βM for some constant β. A T×M matrix-valued signal, associated with R·T bits of information for some rate R is transmitted during the T-symbol coherence interval. Then there is a positive space-time autocapacity Ca such that for all R<Ca, the block probability of error goes to zero as the pair (T, M)→∞ such that T/M=β. The autocoding effect occurs whether or not the propagation matrix is known to the receiver, and Ca=Nlog(1+ρ) in either case, independently of β, where ρ is the expected signal-to-noise ratio (SNR) at each receiver antenna. Lower bounds on the cutoff rate derived from random unitary space-time signals suggest that the autocoding effect manifests itself for relatively small values of T and M. For example, within a single coherence interval of duration T=16, for M=7 transmitter antennas and N=4 receiver antennas, and an 18-dB expected SNR, a total of 80 bits (corresponding to rate R=5) can theoretically be transmitted with a block probability of error less than 10^-9, all without any training or knowledge of the propagation matrix.


Item Type:Article
Additional Information:“©2001 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.” Manuscript received December 22, 1999; revised November 1, 2000. Communicated by M. L. Honig, Associate Editor for Communications. The authors wish to thank A. O. Hero, J. E. Mazo, S. Shamai, and J. Ziv for helpful comments during this research.
Subject Keywords:Eigenvalues of random matrices, multiple-element antenna arrays, space–time coding, unitary space–time modulation, wireless communications
Record Number:CaltechAUTHORS:HOCieeetit01
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:HOCieeetit01
Alternative URL:http://dx.doi.org/10.1109/18.959258
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1171
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:02 Jan 2006
Last Modified:26 Dec 2012 08:43

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