Joint Constellation Design for Noncoherent MIMO Multiple-Access Channels

TL;DR

This paper introduces new criteria for designing joint constellations in noncoherent MIMO MACs, optimizing error performance without channel knowledge, and demonstrates improved results over existing methods.

Contribution

The paper proposes novel design metrics based on error bounds, geometric interpretation, and simplified high-SNR metrics for joint constellation design in noncoherent MIMO MACs.

Findings

Proposed metrics effectively optimize constellation design.

Numerical results outperform pilot-based schemes.

Partitioning and precoding strategies improve performance.

Abstract

We consider the joint constellation design problem for the noncoherent multiple-input multiple-output multiple-access channel (MAC). By analyzing the noncoherent maximum-likelihood detection error, we propose novel design criteria so as to minimize the error probability. As a baseline approach, we adapt several existing design criteria for the point-to-point channel to the MAC. Furthermore, we propose new design criteria. Our first proposed design metric is the dominating term in nonasymptotic lower and upper bounds on the pairwise error probability exponent. We give a geometric interpretation of the bound using Riemannian distance in the manifold of Hermitian positive definite matrices. From an analysis of this metric at high signal-to-noise ratio, we obtain further simplified metrics. For any given set of constellation sizes, the proposed metrics can be optimized over the set of constellation symbols. Motivated by the simplified metric, we propose a simple constellation construction consisting in partitioning a single-user constellation. We also provide a generalization of our previously proposed construction based on precoding individual constellations of lower dimensions. For a fixed joint constellation, the design metrics can be further optimized over the per-user transmit power, especially when the users transmit at different rates. Considering unitary space-time modulation, we investigate the option of building each individual constellation as a set of truncated unitary matrices scaled by the respective transmit power. Numerical results show that our proposed metrics are meaningful, and can be used as objectives to generate constellations through numerical optimization that perform better, for the same transmission rate and power constraint, than a common pilot-based scheme and the constellations optimized with existing metrics.