Optimal Two-Dimensional Lattices for Precoding of Linear Channels
2013 (English)In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 12, no 5, 2104-2113 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE) , 2013. Vol. 12, no 5, 2104-2113 p.
Two-dimensional lattices, precoding, linear channel
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-95979DOI: 10.1109/TWC.2013.050313.120452ISI: 000321199800013OAI: oai:DiVA.org:liu-95979DiVA: diva2:641628
Funding Agencies|Swedish Foundation for Strategic Research through its Center for High Speed Wireless Communication at Lund University, Sweden||AoE grant from the University Grants Committee of the Hong Kong Special Administration Region, China|E-02/08|2013-08-192013-08-122016-05-31