Remarks on the Criteria of Constructing MIMO-MAC DMT Optimal Codes

TL;DR

This paper critiques existing criteria for constructing MIMO-MAC DMT optimal codes, providing counterexamples, clarifying conditions for code optimality, and establishing bounds on code parameters.

Contribution

It offers a counterexample to previous DMT results, clarifies the criteria for code optimality in symmetric MIMO-MAC channels, and derives bounds on code parameters for feasible code construction.

Findings

Counterexample shows previous DMT result is incorrect for frequency-selective channels.

In symmetric MIMO-MAC flat fading channels, criteria align with Tse et al.'s results.

Optimal code existence is limited to small multiplexing gains under the proposed criteria.

Abstract

In this paper we investigate the criteria proposed by Coronel et al. for constructing MIMO MAC-DMT optimal codes over several classes of fading channels. We first give a counterexample showing their DMT result is not correct when the channel is frequency-selective. For the case of symmetric MIMO-MAC flat fading channels, their DMT result reduces to exactly the same as that derived by Tse et al., and we therefore focus on their criteria for constructing MAC-DMT optimal codes, especially when the number of receive antennas is sufficiently large. In such case, we show their criterion is equivalent to requiring the codes of any subset of users to satisfy a joint non-vanishing determinant criterion when the system operates in the antenna pooling regime. Finally an upper bound on the product of minimum eigenvalues of the difference matrices is provided, and is used to show any MIMO-MAC codes satisfying their criterion can possibly exist only when the target multiplexing gain is small.