An Enhanced DMT-optimality Criterion for STBC-schemes for Asymmetric MIMO Systems

For any $n_t$ transmit, $n_r$ receive antenna ($n_t\times n_r$) MIMO system in a quasi-static Rayleigh fading environment, it was shown by Elia et al. that linear space-time block code-schemes (LSTBC-schemes) which have the non-vanishing determinant (NVD) property are diversity-multiplexing gain tradeoff (DMT)-optimal for arbitrary values of $n_r$ if they have a code-rate of $n_t$ complex dimensions per channel use. However, for asymmetric MIMO systems (where $n_r < n_t$), with the exception of a few LSTBC-schemes, it is unknown whether general LSTBC-schemes with NVD and a code-rate of $n_r$ complex dimensions per channel use are DMT-optimal. In this paper, an enhanced sufficient criterion for any STBC-scheme to be DMT-optimal is obtained, and using this criterion, it is established that any LSTBC-scheme with NVD and a code-rate of $\min\{n_t,n_r\}$ complex dimensions per channel use is DMT-optimal. This result settles the DMT-optimality of several well-known, low-ML-decoding-complexity LSTBC-schemes for certain asymmetric MIMO systems.