Explicit, Minimum-Delay Space-Time Codes Achieving The Diversity-Multiplexing Gain Tradeoff

In the recent landmark paper of Zheng and Tse it is shown that there exists a fundamental tradeoff between diversity gain and multiplexing gain, referred to as the DiversityMultiplexing gain(D-MG) tradeoff. The present paper presents the first explicit construction of space-time (ST) codes for arbitrary number of transmit antennas that achieve the D-MG tradeoff. It is shown here that ST codes with non-vanishing determinant (NVD) constructed from cyclicdivision-algebras (CDA), are optimal under the D-MG tradeoff for any number nt, nr of transmit and receive antennas and with minimum delay T = nt. The full result shows optimality of a wider class of constructions. CDA-based ST codes with NVD have previously been constructed for restricted values of nt. A unified construction of D-MG optimal CDA-based ST codes with NVD is given here, for any number nt of transmit antennas. The results also establish that for any nt, nr , the D-MG tradeoff at T = nt is the same as that for T ≥ nt + nr − 1. In addition, we also show that the CDA based ST constructions achieve the optimal D-MG tradeoff of a wider class of channels.