Information lossless full-rate full-diversity trace-orthogonal space-time codes

Trace-orthogonality is an important property of linear space-time codes that has emerged relatively recently. In this work we propose a quite general procedure for the generation of such codes for any number of transmit antennas and uses of the channel. Simulations suggest that the use of rectangular encoding matrices, in place of square ones, could be beneficial to the coding gain. Moreover we are able to guarantee full-diversity of the proposed codes when information symbols are carved from the quadratic field ℚ(j). Since the components of any complex number can be approximated with arbitrary precision by rational numbers, our scheme could be used to guarantee full-diversity for any conceivable complex constellation.