An Enhanced DMT-Optimality Criterion for STBC Schemes for Asymmetric MIMO Systems

For any nt transmit, nr receive antenna ( nt×nr) multiple-input multiple-output (MIMO) system in a quasi-static Rayleigh fading environment, it was shown by Elia that linear space-time block code schemes (LSTBC schemes) that have the nonvanishing determinant (NVD) property are diversity-multiplexing gain tradeoff (DMT)-optimal for arbitrary values of nr if they have a code rate of nt complex dimensions per channel use. However, for asymmetric MIMO systems (where ), with the exception of a few LSTBC schemes, it is unknown whether general LSTBC schemes with NVD and a code rate of nr 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{nt,nr} 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.