Computing the Performance of Unitary Space-Time Group Constellations from their Character Table

Multiple antennas can greatly increase the data rate and reliability of a wireless communica-tion link in a fading environment. It is well-known that unitary matrices can be used to designdi erentially modulated space-time constellations. These constellations have a particularly e -cient description if they form a nite group under matrix multiplication. In this paper we willshow how to compute parameters of such groups crucial for their use as space-time constellations,using only the character table of the group. Since character tables for many groups are known andtabulated, this method could be used to quickly test, for a given group, which of its irreduciblerepresentations can be used to design good unitary space-time constellations. We demonstrateour method by computing the eigenvalues of all the irreducible representations of the speciallinear group SL2(Fq ) over a nite prime eld Fq of odd characteristic, and study in detail theperformance of a particular 8-dimensional representation of SL2(F17 ).