Fundamental Limits of Infinite Constellations in MIMO Fading Channels

TL;DR

This paper explores the fundamental limits of infinite constellations in MIMO fading channels, establishing bounds on diversity order and demonstrating how lattice-based ICs can achieve optimal diversity-multiplexing tradeoff.

Contribution

It introduces an upper bound on IC diversity order and shows that lattice-based ICs can attain the optimal diversity-multiplexing tradeoff in MIMO channels.

Findings

Derived an upper bound on IC diversity order for any antenna configuration.

Proved that lattice-based ICs can achieve the optimal diversity-multiplexing tradeoff.

Provided a framework for lattice design in multiple-antenna channels.

Abstract

The fundamental and natural connection between the infinite constellation (IC) dimension and the best diversity order it can achieve is investigated in this paper. In the first part of this work we develop an upper bound on the diversity order of IC's for any dimension and any number of transmit and receive antennas. By choosing the right dimensions, we prove in the second part of this work that IC's in general and lattices in particular can achieve the optimal diversity-multiplexing tradeoff of finite constellations. This work gives a framework for designing lattices for multiple-antenna channels using lattice decoding.