DMT-optimal, low ML-complexity STBC-schemes for asymmetric MIMO systems

For an n_t transmit, n_r receive antenna (n_t × n_r) MIMO system with quasi-static Rayleigh fading, it was shown by Elia et al. that space-time block code-schemes (STBC-schemes) which have the non-vanishing determinant (NVD) property and are based on minimal-delay STBCs (STBC block length equals n_t) with a symbol rate of n_t complex symbols per channel use (rate-n_t STBC) are diversity-multiplexing gain tradeoff (DMT)-optimal for arbitrary values of n_r. Further, explicit linear STBC-schemes (LSTBC-schemes) with the NVD property were also constructed. However, for asymmetric MIMO systems (where n_r <; n_t), with the exception of the Alamouti code-scheme for the 2×1 system and rate-1, diagonal STBC-schemes with NVD for an n_t ×1 system, no known minimal-delay, rate-n_r LSTBC-scheme has been shown to be DMT-optimal. In this paper, we first obtain an enhanced sufficient criterion for an STBC-scheme to be DMT optimal and using this result, we show that for certain asymmetric MIMO systems, many well-known LSTBC-schemes which have low ML-decoding complexity are DMT-optimal, a fact that was unknown hitherto.