Abstract
We construct a full data rate space-time (ST) block code over M=2 transmit antennas and T=2 symbol periods, and we prove that it achieves a transmit diversity of 2 over all constellations carved from Z[i]/sup 4/. Further, we optimize coding gain of proposed code and then compare it to Alamouti code. It is shown that new code outperforms Alamouti (see IEEE J Select. Areas Commun., vol.16, p.1451-58, 1998) code at low and high signal-to-noise ratio (SNR) when number of receive antennas N>1. The performance improvement is further enhanced when N or size of constellation increases. We relate problem of ST diversity gain to algebraic number theory, and coding gain optimization to theory of simultaneous Diophantine approximation in geometry of numbers. We find that coding gain optimization is equivalent to finding irrational numbers the furthest, from any simultaneous rational approximations.
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