Multi-Dimensional and Non-Uniform Constellation Optimization via the Special Orthogonal Group

TL;DR

This paper develops a method to optimize multi-dimensional constellations for Rayleigh fading channels using special orthogonal group rotations, enhancing capacity without relying on specific assumptions.

Contribution

It introduces a universal construction of rotation matrices for dimensions that are powers of two, improving CM capacity for various constellations and SNR levels.

Findings

Optimized rotation matrices increase CM capacity across dimensions.

Joint non-uniform and rotated constellations further improve capacity.

Simulation results confirm the effectiveness of the proposed method.

Abstract

With the goal of optimizing the CM capacity of a finite constellation over a Rayleigh fading channel, we construct for all dimensions which are a power of 2 families of rotation matrices which optimize a certain objective function controlling the CM capacity. Our construction does not depend on any assumptions about the constellation, dimension, or signal-to-noise ratio. We confirm the benefits of our construction for uniform and non-uniform constellations at a large range of SNR values through numerous simulations. We show that in two and four dimensions one can obtain a further potential increase in CM capacity by jointly considering non-uniform and rotated constellations.