A Numerical Approach for Designing Unitary Space Time Codes with Large Diversity Product and Diversity Sum∗

Unitary space-time modulation using multiple antennas promises reliable communication at high transmission rates. The basic principles are well understood and certain criteria for designing good unitary constellations have been presented. However so far no general method to design good-performing constellation with large diversity product and diversity sum for any number of transmit antennas and for any transmission rate exists. In this paper, we define a diversity function and analyze its limiting behavior. This results in two important design criteria: the diversity product and the diversity sum. Numerical methods are derived which allows one to construct codes with excellent diversity function and excellent diversity product and sum. The numerical approach is very flexible and it allows one to construct constellations of any dimension with an arbitrary given size. This flexibility is very useful when excellent constellations with certain parameters are required for some applications.