Hochwald, Bertrand M. and Marzetta, Thomas L. and Hassibi, Babak (2001) Spacetime autocoding. IEEE Transactions on Information Theory, 47 (7). pp. 27612781. ISSN 00189448. doi:10.1109/18.959258. https://resolver.caltech.edu/CaltechAUTHORS:HOCieeetit01

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Abstract
Prior treatments of spacetime communications in Rayleigh flat fading generally assume that channel coding covers either one fading intervalin which case there is a nonzero “outage capacity”or multiple fading intervalsin 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, spacetime signals are their own channel codes. We call this phenomenon spacetime autocoding, and the accompanying capacity the spacetime autocapacity. Let an Mtransmitter antenna, Nreceiver antenna Rayleigh flat fading channel be characterized by an M×N matrix of independent propagation coefficients, distributed as zeromean, unitvariance complex Gaussian random variables. This propagation matrix is unknown to the transmitter, it remains constant during a Tsymbol 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 matrixvalued signal, associated with R·T bits of information for some rate R is transmitted during the Tsymbol coherence interval. Then there is a positive spacetime 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 signaltonoise ratio (SNR) at each receiver antenna. Lower bounds on the cutoff rate derived from random unitary spacetime 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 18dB 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.
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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, multipleelement antenna arrays, space–time coding, unitary space–time modulation, wireless communications  
Issue or Number:  7  
DOI:  10.1109/18.959258  
Record Number:  CaltechAUTHORS:HOCieeetit01  
Persistent URL:  https://resolver.caltech.edu/CaltechAUTHORS:HOCieeetit01  
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:  08 Nov 2021 19:08 
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