The generating groups of geometrically uniform spherical signal sets

An [M, n] spherical signal set is a collectionℒ ofM unit-norm vectors in the Euclideann-dimensional space ℛn. Itsconfiguration matrixC is the matrix of the scalar products between pairs of vectors.ℒ isgeometrically uniform if, given any two vectors xi, xjεℒ there exists an isometry that transforms xi to xj while leavingℒ invariant. Agenerating group of ℒ is a group of isometries of ℛn that transform any given vector ofℒ into each of the vectors inℒ while leavingℒ invariant. In this paper we characterize the configuration matrix of a geometrically uniform spherical signal set and we show how its generating groups can be obtained.