Trace-Orthogonal Space-Time Coding

In this paper, we prove that, in MIMO systems affected by flat fading, when the channel is unknown at the transmitter and known at the receiver side, a space-time code does not induce any information loss, regardless of the channel realization, if and only if it is a trace-orthogonal design (TOD). Then, in the effort to find a good tradeoff between performance and receiver complexity, we show that, when symbols are carved from a QPSK constellation, the suboptimal detector composed of a linear MMSE estimator followed by hard decision, achieves the minimum bit error rate (BER), if and only if the encoding matrices are, up to a multiplicative constant, full rank partial isometries. Such matrices constitute what we term a Unitary Trace-Orthogonal Design (UTOD). Finally, we propose a procedure for the synthesis of TODs which, moreover, can guarantee full diversity when information symbols are carved from constellations composed of algebraic numbers, i.e., for (practically) any conceivable complex constellation.