Systematic and optimal cyclotomic lattices and diagonal space-time block code designs

Authors:
Genyuan Wang;Huiyong Liao;Haiquan Wang;Xiang-Gen Xia
Affiliations:
Dept. of Electr. & Comput. Eng., Univ. of Delaware, Newark, DE, USA;-;-;-
Venue:
IEEE Transactions on Information Theory
Year:
2004

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Abstract

In this correspondence, a new and systematic design of cyclotomic lattices with full diversity is proposed by using some algebraic number theory. This design provides infinitely many full diversity cyclotomic lattices for a given lattice size. Based on the packing theory and the concrete form of the design, optimal cyclotomic lattices are presented by minimizing the mean transmission signal power for a given minimum (diversity) product (or equivalently maximizing the minimum product for a given mean transmission signal power). The newly proposed cyclotomic lattices can be applied to both space-time code designs for multi-antenna systems and linear precode design for signal space diversity in single antenna systems over fast Rayleigh fading channels. Although there are some cyclotomic lattices/space-time codes existing in the literature, most of them are not optimal.