Some Designs and Normalized Diversity Product of n×n Lattice-Based Diagonal Space-Time Codes in Z[ζm

Abstract

Space-time code designs have attracted considerable attentions. There have been several kinds of space-time block code designs, lattics based diagonal space-time block code designs using algebraic number theory. On the basis of the number theory, we construct several kinds of space-time codes about lattices by using the method of [14]. We give a class $2 \times 2$ lattice space-time code with a large normalized diversity product. The diagonal algebraic space-time code was more extensive than reported in reference. We also mainly design diagonal space-time block codes from the algebraic extension approach for three and four transmit antennas by using some of the best known high order algebraic extensions on Z[i] or Z[ζ 6 ], and some determinants of the corresponding generating matrix of the complex lattice have smaller values.