Geometrical and Numerical Design of Structured Unitary Space-Time Constellations

There exist two important design criteria for unitary space time codes. In the situation where the signal-to-noise ratio (SNR) is large the diversity product (DP) of a constellation should be as large as possible. It is less known that the diversity sum (DS) is a very important design criterion for codes working in a low SNR environment. So far, no general method to design good-performing constellations with large diversity for any number of transmit antennas and any transmission rate exists. In this correspondence, we propose constellations with suitable structures, which allow one to construct codes with excellent diversity using geometrical symmetry and numerical methods. The presented design methods work for any dimensional constellation and for any transmission rate 3722 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 8, AUGUST 2006 so the bound in (22) applies with = 1 2 logD= log q. Plugging this value of into (22) and manipulating the resulting expression, we obtain the bound of the theorem.