Remarks on the criteria of constructing MIMO-MAC DMT optimal codes

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 show by a counterexample that their DMT result might not be correct when the channel has selective fading. For the case of symmetric MIMO-MAC flat fading channels, we study their criteria for constructing MAC-DMT optimal codes when the number of receive antennas is sufficiently large. We show their criterion is equivalent to requiring the codes of any subset of users to satisfy a joint non-vanishing determinant criterion when operating 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 MIMO-MAC lattice codes satisfying their criterion exist only when the target multiplexing gain is small.