# Lattice coding for Rician fading channels from Hadamard rotations

## TL;DR

This paper investigates lattice coding for Rician fading channels, demonstrating that Hadamard rotations optimize packing density and outperform other rotations in simulations for millimeter-wave wireless communications.

## Contribution

It proves Hadamard rotations maximize diamond-packing density for lattice codes and shows their superior performance in Rician channels through simulations.

## Key findings

- Hadamard rotations maximize diamond-packing density.
- Hadamard rotations outperform algebraic rotations.
- Simulations confirm improved performance in Rician channels.

## Abstract

In this paper, we study lattice coding for Rician fading wireless channels. This is motivated in particular by preliminary studies suggesting the Rician fading model for millimeter-wavelength wireless communications. We restrict to lattice codes arising from rotations of $\mathbb{Z}^n$, and to a single-input single-output (SISO) channel. We observe that several lattice design criteria suggest the optimality of Hadamard rotations. For instance, we prove that Hadamard rotations maximize the diamond-packing density among all rotated $\mathbb{Z}^n$ lattices. Finally, we provide simulations to show that Hadamard rotations outperform optimal algebraic rotations and cross-packing lattices in the Rician channel.