Sphere Lower Bound for Rotated Lattice Constellations in Fading Channels

TL;DR

This paper analyzes the error probability of rotated lattice constellations in fading channels, demonstrating that optimal rotations approach the theoretical lower bound and highlighting the importance of diversity in performance.

Contribution

It introduces the sphere lower bound as a benchmark for rotated lattice constellations in fading channels and shows optimal rotations achieve near-bound performance.

Findings

Sphere lower bound has full diversity in fading channels.

Optimal rotations with maximum minimum product distance perform close to the bound.

Random rotations lack diversity and perform poorly compared to optimal rotations.

Abstract

We study the error probability performance of rotated lattice constellations in frequency-flat Nakagami-$m$ block-fading channels. In particular, we use the sphere lower bound on the underlying infinite lattice as a performance benchmark. We show that the sphere lower bound has full diversity. We observe that optimally rotated lattices with largest known minimum product distance perform very close to the lower bound, while the ensemble of random rotations is shown to lack diversity and perform far from it.