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Optimal Two-Dimensional Lattices for Precoding of Linear Channels

Kapetanovic, Dzevdan; Cheng, Hei Victor; Mow, Wai Ho and Rusek, Fredrik LU (2013) In IEEE Transactions on Wireless Communications 12(5). p.2104-2113
Abstract
Consider the communication system model y = HFx+n, where H and F are the channel and precoder matrices, x is a vector of data symbols drawn from some lattice-type constellation, such as M-QAM, n is an additive white Gaussian noise vector and y is the received vector. It is assumed that both the transmitter and the receiver have perfect knowledge of the channel matrix H and that the transmitted signal Fx is subject to an average energy constraint. The columns of the matrix HF can be viewed as the basis vectors that span a lattice, and we are interested in the precoder F that maximizes the minimum distance of this lattice. This particular problem remains open within the theory of lattices and the communication theory. This paper provides the... (More)
Consider the communication system model y = HFx+n, where H and F are the channel and precoder matrices, x is a vector of data symbols drawn from some lattice-type constellation, such as M-QAM, n is an additive white Gaussian noise vector and y is the received vector. It is assumed that both the transmitter and the receiver have perfect knowledge of the channel matrix H and that the transmitted signal Fx is subject to an average energy constraint. The columns of the matrix HF can be viewed as the basis vectors that span a lattice, and we are interested in the precoder F that maximizes the minimum distance of this lattice. This particular problem remains open within the theory of lattices and the communication theory. This paper provides the complete solution for any non-singular M x 2 channel matrix H. For real-valued matrices and vectors, the solution is that HF spans the hexagonal lattice. For complex-valued matrices and vectors, the solution is that HF, when viewed in four-dimensional real-valued space, spans the Schlafli lattice D-4. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Two-dimensional lattices, precoding, linear channel
in
IEEE Transactions on Wireless Communications
volume
12
issue
5
pages
2104 - 2113
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • wos:000321199800013
  • scopus:84878691587
ISSN
1536-1276
DOI
10.1109/TWC.2013.050313.120452
language
English
LU publication?
yes
id
f874165e-34ca-4aba-92a1-c7e366a07b3b (old id 3979244)
date added to LUP
2013-09-06 15:24:15
date last changed
2019-05-14 02:17:09
@article{f874165e-34ca-4aba-92a1-c7e366a07b3b,
  abstract     = {Consider the communication system model y = HFx+n, where H and F are the channel and precoder matrices, x is a vector of data symbols drawn from some lattice-type constellation, such as M-QAM, n is an additive white Gaussian noise vector and y is the received vector. It is assumed that both the transmitter and the receiver have perfect knowledge of the channel matrix H and that the transmitted signal Fx is subject to an average energy constraint. The columns of the matrix HF can be viewed as the basis vectors that span a lattice, and we are interested in the precoder F that maximizes the minimum distance of this lattice. This particular problem remains open within the theory of lattices and the communication theory. This paper provides the complete solution for any non-singular M x 2 channel matrix H. For real-valued matrices and vectors, the solution is that HF spans the hexagonal lattice. For complex-valued matrices and vectors, the solution is that HF, when viewed in four-dimensional real-valued space, spans the Schlafli lattice D-4.},
  author       = {Kapetanovic, Dzevdan and Cheng, Hei Victor and Mow, Wai Ho and Rusek, Fredrik},
  issn         = {1536-1276},
  keyword      = {Two-dimensional lattices,precoding,linear channel},
  language     = {eng},
  number       = {5},
  pages        = {2104--2113},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Wireless Communications},
  title        = {Optimal Two-Dimensional Lattices for Precoding of Linear Channels},
  url          = {http://dx.doi.org/10.1109/TWC.2013.050313.120452},
  volume       = {12},
  year         = {2013},
}