Optimal TwoDimensional Lattices for Precoding of Linear Channels
(2013) In IEEE Transactions on Wireless Communications 12(5). p.21042113 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 latticetype constellation, such as MQAM, 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 latticetype constellation, such as MQAM, 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 nonsingular M x 2 channel matrix H. For realvalued matrices and vectors, the solution is that HF spans the hexagonal lattice. For complexvalued matrices and vectors, the solution is that HF, when viewed in fourdimensional realvalued space, spans the Schlafli lattice D4. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/3979244
 author
 Kapetanovic, Dzevdan; Cheng, Hei Victor; Mow, Wai Ho and Rusek, Fredrik ^{LU}
 organization
 publishing date
 2013
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Twodimensional lattices, precoding, linear channel
 in
 IEEE Transactions on Wireless Communications
 volume
 12
 issue
 5
 pages
 2104  2113
 publisher
 IEEEInstitute of Electrical and Electronics Engineers Inc.
 external identifiers

 wos:000321199800013
 scopus:84878691587
 ISSN
 15361276
 DOI
 10.1109/TWC.2013.050313.120452
 language
 English
 LU publication?
 yes
 id
 f874165e34ca4aba92a1c7e366a07b3b (old id 3979244)
 date added to LUP
 20130906 15:24:15
 date last changed
 20190514 02:17:09
@article{f874165e34ca4aba92a1c7e366a07b3b, 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 latticetype constellation, such as MQAM, 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 nonsingular M x 2 channel matrix H. For realvalued matrices and vectors, the solution is that HF spans the hexagonal lattice. For complexvalued matrices and vectors, the solution is that HF, when viewed in fourdimensional realvalued space, spans the Schlafli lattice D4.}, author = {Kapetanovic, Dzevdan and Cheng, Hei Victor and Mow, Wai Ho and Rusek, Fredrik}, issn = {15361276}, keyword = {Twodimensional lattices,precoding,linear channel}, language = {eng}, number = {5}, pages = {21042113}, publisher = {IEEEInstitute of Electrical and Electronics Engineers Inc.}, series = {IEEE Transactions on Wireless Communications}, title = {Optimal TwoDimensional Lattices for Precoding of Linear Channels}, url = {http://dx.doi.org/10.1109/TWC.2013.050313.120452}, volume = {12}, year = {2013}, }