Fast-Decodable MIDO Codes with Large Coding Gain

In this paper, a new method is proposed to obtain full-diversity, rate-2 (rate of 2 complex symbols per channel use) space-time block codes (STBCs) that are full-rate for multiple input, double output (MIDO) systems. Using this method, rate-2 STBCs for $4\times2$, $6 \times 2$, $8\times2$ and $12 \times 2$ systems are constructed and these STBCs are fast ML-decodable, have large coding gains, and STBC-schemes consisting of these STBCs have a non-vanishing determinant (NVD) so that they are DMT-optimal for their respective MIDO systems. It is also shown that the SR-code [R. Vehkalahti, C. Hollanti, and F. Oggier, "Fast-Decodable Asymmetric Space-Time Codes from Division Algebras," IEEE Trans. Inf. Theory, Apr. 2012] for the $4\times2$ system, which has the lowest ML-decoding complexity among known rate-2 STBCs for the $4\times2$ MIDO system with a large coding gain for 4-/16-QAM, has the same algebraic structure as the STBC constructed in this paper for the $4\times2$ system. This also settles in positive a previous conjecture that the STBC-scheme that is based on the SR-code has the NVD property and hence is DMT-optimal for the $4\times2$ system.