A number theory based dual transmit antennas space-time code

We construct a full data rate space-time block code over M=2 transmit-antennas and T=2 symbol periods, and we prove it achieves a transmit diversity of 2 over all 4-dimensional constellations carved from the 4-dimensional ring of complex integers Z[i]/sup 4/. Further, we optimize the coding gain of our ST code and then compare it to the Alamouti scheme (see Alamouti, S.M., IEEE Journal Selec. Areas on Communications, vol.16, p.1451-8, 1998). For N>1, we prove that our code has a better performance than the Alamouti code. The performance improvement is further enhanced when N or the size of the constellation increases. We relate the problem of ST diversity gain to algebraic number theory, and the ST coding gain optimization to the theory of simultaneous Diophantine approximation in the geometry of numbers.