MPSK modulated constellation design for differential space-time modulation

The constellation design for differential space-time modulation usually requires to construct L (constellation size) unitary matrices making the design complexity increasing rapidly with L. In this correspondence, we propose a new construction technique, which exploits the rotational invariance of unitary matrices and the property of MPSK modulation. The proposed constellations are derivable from a smaller set of D = L/M unitary matrices (via rotations defined by an M-ary PSK symbol) which, in turn, are parameterized by two unitary matrices U₁ and U₂. They share some good property of group constellations thereby considerably simplifying the optimization of U₁ and U₂. They also possess other good properties which allow for simplified maximum likelihood (ML) decoding. Extensive numerical examples are presented to demonstrate that the proposed constellations in general have larger diversity products than other constellations and thus, better error performance.