# Lund University Publications

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### Optimal Lattices for MIMO Precoding

; ; and (2011) IEEE International Symposium on Information Theory, 2011 p.2924-2928
Abstract
Consider the communication model (y) over bar = H F (x) over bar + (n) over bar, where H; F are real-valued matrices, (x) over bar is a data vector drawn from some real-valued lattice (e.g. M-PAM), (n) over bar is additive white Gaussian noise and (y) over bar is the received vector. It is assumed that the transmitter and the receiver have perfect knowledge of the channel matrix H (perfect CSI) and that the transmitted signal F (x) over bar is subject to an average energy constraint. The columns of the matrix H F can be viewed as basis vectors that span a lattice, and we are interested in the minimum distance of this lattice. More precisely, for a given H, which F under an average energy constraint will maximize the minimum distance of the... (More)
Consider the communication model (y) over bar = H F (x) over bar + (n) over bar, where H; F are real-valued matrices, (x) over bar is a data vector drawn from some real-valued lattice (e.g. M-PAM), (n) over bar is additive white Gaussian noise and (y) over bar is the received vector. It is assumed that the transmitter and the receiver have perfect knowledge of the channel matrix H (perfect CSI) and that the transmitted signal F (x) over bar is subject to an average energy constraint. The columns of the matrix H F can be viewed as basis vectors that span a lattice, and we are interested in the minimum distance of this lattice. More precisely, for a given H, which F under an average energy constraint will maximize the minimum distance of the lattice H F ? This particular question remains open within the theory of lattices. This work provides the solution for 2 x 2 matrices H; F. The answer is an F such that H F is a hexagonal lattice. (Less)
author
; ; and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
2011 IEEE International Symposium on Information Theory Proceedings (ISIT)
pages
2924 - 2928
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
IEEE International Symposium on Information Theory, 2011
conference location
Saint Petersburg, Russian Federation
conference dates
2011-07-31 - 2011-08-05
external identifiers
• wos:000297465103062
• scopus:80054811284
ISBN
978-1-4577-0595-3
DOI
10.1109/ISIT.2011.6034112
language
English
LU publication?
yes
id
2016-04-04 10:29:39
date last changed
2021-09-29 04:03:41
```@inproceedings{7a35dda4-1c0b-4ef1-afa9-32b0cb2adc02,
abstract     = {Consider the communication model (y) over bar = H F (x) over bar + (n) over bar, where H; F are real-valued matrices, (x) over bar is a data vector drawn from some real-valued lattice (e.g. M-PAM), (n) over bar is additive white Gaussian noise and (y) over bar is the received vector. It is assumed that the transmitter and the receiver have perfect knowledge of the channel matrix H (perfect CSI) and that the transmitted signal F (x) over bar is subject to an average energy constraint. The columns of the matrix H F can be viewed as basis vectors that span a lattice, and we are interested in the minimum distance of this lattice. More precisely, for a given H, which F under an average energy constraint will maximize the minimum distance of the lattice H F ? This particular question remains open within the theory of lattices. This work provides the solution for 2 x 2 matrices H; F. The answer is an F such that H F is a hexagonal lattice.},
author       = {Kapetanovic, Dzevdan and Cheng, Hei Victor and Mow, Wai Ho and Rusek, Fredrik},
booktitle    = {2011 IEEE International Symposium on Information Theory Proceedings (ISIT)},
isbn         = {978-1-4577-0595-3},
language     = {eng},
pages        = {2924--2928},
publisher    = {IEEE - Institute of Electrical and Electronics Engineers Inc.},
title        = {Optimal Lattices for MIMO Precoding},
url          = {http://dx.doi.org/10.1109/ISIT.2011.6034112},
doi          = {10.1109/ISIT.2011.6034112},
year         = {2011},
}

```