Construction of full diversity $D_n$-lattices for all $n$

TL;DR

This paper constructs families of rotated $D_n$-lattices with full diversity for all dimensions, which are suitable for signal transmission over Gaussian and Rayleigh fading channels, and analyzes their minimum product distances.

Contribution

It introduces new constructions of rotated $D_n$-lattices with full diversity for any dimension and provides bounds for their minimum product distances.

Findings

Constructed rotated $D_n$-lattices with full diversity for all $n$.

Established conditions for ideals used in lattice constructions.

Provided bounds for minimum product distances of these lattices.

Abstract

In this paper we construct some families of rotated $D_n$-lattices with full diversity for any $n$. These lattices can be good for signal transmission over both Gaussian and Rayleigh fading channels. In order to get bounds for their minimum product distances, we show that the $Z$-modules used in \cite{sethoggier} to obtain rotated $\mathbb{Z}^{n}$-lattices with $n$ odd are ideals and find a sufficient condition for such ideals being principal ideals.