### 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) |
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Title of host publication | Proceedings - 2007 IEEE International Symposium on Information Theory, ISIT 2007 |

Pages | 2316-2320 |

Number of pages | 5 |

DOIs | |

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 |
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ISSN (Print) | 2157-8101 |

### Other

Other | 2007 IEEE International Symposium on Information Theory, ISIT 2007 |
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Country | France |

City | Nice |

Period | 6/24/07 → 6/29/07 |

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

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## Cite this

*Proceedings - 2007 IEEE International Symposium on Information Theory, ISIT 2007*(pp. 2316-2320). [4557565] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2007.4557565