Investigation of two high-rate algebraic space-time codes

The algebraic properties of two new space-time block codes over M transmitter antennas and T symbol periods are examined. The first code transmits at a rate of 2 symbols per channel use and has a transmit diversity of 2 over all 4-dimensional constellations carved from Z[i]/sup 4/ for M=T=2. From this code, we construct a space-time block code for M=T=3 which transmits at a rate of 4/3 symbols per channel use and has a transmit diversity of 3. We give upper and lower bounds to the achieved coding gains and prove that irrational numbers that are poorly approximated by rational numbers are particularly useful to enhance the coding gains of our schemes.