Abstract:
Multiple antennas can greatly increase the data rate and reliability
of a wireless communication link in a fading environment. It is
well-known that unitary matrices can be used to design differentially
modulated space-time constellations. These constellations have a
particularly efficient description if they form a finite group under
matrix multiplication. In this paper we will show 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 and tabulated, this method
could be used to quickly test, for a given group, which of its
irreducible representations can be used to design good unitary
space-time constellations. We demonstrate our method by computing the
eigenvalues of all the irreducible representations of the special
linear group SL(2,q) over a finite prime field F_q of odd
characteristic, and study in detail the performance of a particular
8-dimensional representation of SL(2,17).
Status:
Bell Labs Technical Memorandum
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