Vector precoding in high dimensions: A replica analysis

Ralf R. Müller; Dongning Guo; Aris L. Moustakas

doi:10.1109/ISIT.2007.4557565

Vector precoding in high dimensions: A replica analysis

Ralf R. Müller, Dongning Guo, Aris L. Moustakas

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

Abstract

We apply the replica method to analyze vector pre-coding, a method to reduce transmit power in antenna array communications, in the limit of an infinite number of dimensions of the signal vector. The analysis applies to a very general class of channel matrices. The statistics of the channel matrix enter the transmitted energy per symbol via its R-transform. We specialize our result to inversion of an i.i.d. channel and two cases of signal point optimization i) 2-point lattice pre-coding and ii) compact relaxation. In the two cases the replica symmetric transmitted energy is found to be 4.3 dB and 9.6 dB above the orthogonal case for a square channel matrix, respectively.

Original language	English (US)
Title of host publication	Proceedings - 2007 IEEE International Symposium on Information Theory, ISIT 2007
Pages	2316-2320
Number of pages	5
DOIs	https://doi.org/10.1109/ISIT.2007.4557565
State	Published - Dec 1 2007
Event	2007 IEEE International Symposium on Information Theory, ISIT 2007 - Nice, France Duration: Jun 24 2007 → Jun 29 2007

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
ISSN (Print)	2157-8101

Other

Other	2007 IEEE International Symposium on Information Theory, ISIT 2007
Country/Territory	France
City	Nice
Period	6/24/07 → 6/29/07

ASJC Scopus subject areas

Electrical and Electronic Engineering

Access to Document

10.1109/ISIT.2007.4557565

Cite this

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title = "Vector precoding in high dimensions: A replica analysis",

abstract = "We apply the replica method to analyze vector pre-coding, a method to reduce transmit power in antenna array communications, in the limit of an infinite number of dimensions of the signal vector. The analysis applies to a very general class of channel matrices. The statistics of the channel matrix enter the transmitted energy per symbol via its R-transform. We specialize our result to inversion of an i.i.d. channel and two cases of signal point optimization i) 2-point lattice pre-coding and ii) compact relaxation. In the two cases the replica symmetric transmitted energy is found to be 4.3 dB and 9.6 dB above the orthogonal case for a square channel matrix, respectively.",

author = "M{\"u}ller, {Ralf R.} and Dongning Guo and Moustakas, {Aris L.}",

year = "2007",

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doi = "10.1109/ISIT.2007.4557565",

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Müller, RR, Guo, D & Moustakas, AL 2007, Vector precoding in high dimensions: A replica analysis. in Proceedings - 2007 IEEE International Symposium on Information Theory, ISIT 2007., 4557565, IEEE International Symposium on Information Theory - Proceedings, pp. 2316-2320, 2007 IEEE International Symposium on Information Theory, ISIT 2007, Nice, France, 6/24/07. https://doi.org/10.1109/ISIT.2007.4557565

Vector precoding in high dimensions: A replica analysis. / Müller, Ralf R.; Guo, Dongning; Moustakas, Aris L.
Proceedings - 2007 IEEE International Symposium on Information Theory, ISIT 2007. 2007. p. 2316-2320 4557565 (IEEE International Symposium on Information Theory - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Vector precoding in high dimensions

T2 - 2007 IEEE International Symposium on Information Theory, ISIT 2007

AU - Müller, Ralf R.

AU - Guo, Dongning

AU - Moustakas, Aris L.

PY - 2007/12/1

Y1 - 2007/12/1

N2 - We apply the replica method to analyze vector pre-coding, a method to reduce transmit power in antenna array communications, in the limit of an infinite number of dimensions of the signal vector. The analysis applies to a very general class of channel matrices. The statistics of the channel matrix enter the transmitted energy per symbol via its R-transform. We specialize our result to inversion of an i.i.d. channel and two cases of signal point optimization i) 2-point lattice pre-coding and ii) compact relaxation. In the two cases the replica symmetric transmitted energy is found to be 4.3 dB and 9.6 dB above the orthogonal case for a square channel matrix, respectively.

AB - We apply the replica method to analyze vector pre-coding, a method to reduce transmit power in antenna array communications, in the limit of an infinite number of dimensions of the signal vector. The analysis applies to a very general class of channel matrices. The statistics of the channel matrix enter the transmitted energy per symbol via its R-transform. We specialize our result to inversion of an i.i.d. channel and two cases of signal point optimization i) 2-point lattice pre-coding and ii) compact relaxation. In the two cases the replica symmetric transmitted energy is found to be 4.3 dB and 9.6 dB above the orthogonal case for a square channel matrix, respectively.

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M3 - Conference contribution

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SN - 9781424414291

T3 - IEEE International Symposium on Information Theory - Proceedings

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BT - Proceedings - 2007 IEEE International Symposium on Information Theory, ISIT 2007

Y2 - 24 June 2007 through 29 June 2007

ER -

Vector precoding in high dimensions: A replica analysis

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