Design of Unitary Space-Time Codes from Representations of SU (2)

We explicitly construct an irreducible four-dimensional unitary representation of the Lie group SU (2) and use it for the construction of high-rate unitary space-time codes for four transmit antennas. The tools we use are invariant integration on the group to unitarize the representation, and dense spherical codes on the three-dimensional sphere. Our construction calls for the design of such spherical codes in which the angle between any two points is well separated from 120 degrees. We give a partial solution to this restricted design problem and use numerical optimization techniques to optimize our solution.