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 simple ML decoding with performance identical to the conventional ML decoder. Multidimensional rotated

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... nstellations 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 N/2 c ) to O(M N/4 c ) in a Mc-QAM constellation. Index Terms-Diversity methods, maximum likelihood decoding (MLD), multidimensional rotated constellations, space-time block codes (STBC).