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The recently developed theory of geometrically uniform trellis codes is applied to the case of multidimensional PSK constellations. The symmetry group of an L X MPSK constellation is completely characterized. Conditions for rotational invariance of geometrically uniform partitions of a signal constellation are given. Through suitable algorithms, geometrically uniform partitions of L X MPSK ( M = 4,8,16 and L = 1 , 2 , 3 , 4 ) constellations are found, which present good characteristics in termsdoi:10.1109/18.265490 fatcat:zc3qp2g6wja63bjpv2w3zojim4