On the Diversity-Multiplexing Tradeoff of Unconstrained Multiple-Access Channels

TL;DR

This paper analyzes the optimal diversity-multiplexing tradeoff in unconstrained multiple-access MIMO channels, revealing conditions under which infinite constellations achieve or fail to achieve the optimal DMT, and providing geometric insights.

Contribution

It characterizes the DMT of unconstrained multiple-access channels, identifying regimes where infinite constellations are optimal or suboptimal, and offers a geometric interpretation of these results.

Findings

Infinite constellations attain the optimal DMT when N ≥ (K+1)M-1.

For N < (K+1)M-1, infinite constellations cannot achieve the optimal DMT.

Shaping region considerations are crucial in heavily loaded networks for optimal DMT.

Abstract

In this work the optimal diversity-multiplexing tradeoff (DMT) is investigated for the multiple-input multiple-output fading multiple-access channels with no power constraints (infinite constellations). For K users (K>1), M transmit antennas for each user, and N receive antennas, infinite constellations in general and lattices in particular are shown to attain the optimal DMT of finite constellations for the case N equals or greater than (K+1)M-1, i.e., user limited regime. On the other hand for N<(K+1)M-1 it is shown that infinite constellations can not attain the optimal DMT. This is in contrast to the point-to-point case in which infinite constellations are DMT optimal for any M and N. In general, this work shows that when the network is heavily loaded, i.e. K>max(1,(N-M+1)/M), taking into account the shaping region in the decoding process plays a crucial role in pursuing the optimal DMT. By investigating the cases where infinite constellations are optimal and suboptimal, this work also gives a geometrical interpretation to the DMT of infinite constellations in multiple-access channels.