A class of unitary constellations for differential space-time modulation

We present a new approach to design unitary constellations for differential space-time modulation. By exploiting the rotational invariance of unitary matrices and the property of M-ary PSK symbols, the proposed constellations of size L are derivable from a smaller set of D=L/M unitary matrices (via rotations defined by M-ary PSK symbols) which, in turn, are parameterized by two unitary matrices U₁ and U₂. The proposed constellations share some good properties of group constellations thereby considerably simplifying the optimization of U₁ and U₂. They also possess many other good properties which, when exploited, allow for simplified maximum likelihood decoding. Extensive numerical examples are provided to demonstrate that the proposed constellations in general have larger diversity products than other constellations.