Real-domain decoder for full-rate full-diversity STBC with multidimensional constellations

In this letter, we present a new maximum likelihood (ML) decoding algorithm for space time block codes (STBCs) that employ multidimensional constellations. We start with a lattice representation for STBCs which transforms complex channel models into real matrix equations. Based on the lattice representation, we propose a new decoding algorithm for quasiorthogonal STBCs (QO-STBC) which allows simpleML decoding with performance identical to the conventional ML decoder. Multidimensional rotated constellations are constructed for the QO-STBCs to achieve full diversity. As a consequence, for quasi-orthogonal designs with an arbitrary number of transmit antennas N (N ≤ 4), the proposed decoding scheme achieves full rate and full diversity while reducing the decoding complexity from 𝒪(M
_c
^N/2
) to 𝒪(M
_c
^N/4
) in a M
_c
-QAM constellation.