On space-time code design

It is shown that the separation between space-time code matrices can be described in terms of a metric of Euclidean type, which is defined via the singular values of difference code matrices, and arises naturally from a minimization of the pairwise error probability. Essentially, the distance between complex space-time code matrices is the Euclidean distance between the respective - demultiplexed and concatenated - transmit antenna streams, expressed in terms of the structure inherent to the multiple antenna arrangement. It is further shown that the determinant criterion can be strengthened, in a manner that not only suggests an optimum space-time code matrix structure, but also outlines the central role played by the Euclidean distance in quasi-static fading. Theorem 5 - which claims that in order to optimize the product distance one must optimize the Euclidean distance -establishes a close interdependence between product and Euclidean distances; it thereby links the performance determining factors in quasi-static and independent fading, and rigorously establishes the relevance of combining space-time coding and modulation in fading environments. A multidimensional space-time constellation for two transmit antennas, and its coset partitioning-based on traces of differences between constellation matrices-are described. Example codes constitute the first reporting of a space-time coded modulation scheme for fading channels, whereby a space-time constellation is partitioned in cosets.