  In this paper we propose a new design criterion and a new class of unitary
signal constellations for differential space-time modulation for
multiple-antenna systems over Rayleigh flat-fading channels with unknown fading
coefficients. Extensive simulations show that the new codes have significantly
better performance than existing codes. We have compared the performance of our
codes with differential detection schemes using orthogonal design, Cayley
differential codes, fixed-point-free group codes and product of groups and for
the same bit error rate, our codes allow smaller signal to noise ratio by as
much as 10 dB. The design of the new codes is accomplished in a systematic way
through the optimization of a performance index that closely describes the bit
error rate as a function of the signal to noise ratio. The new performance
index is computationally simple and we have derived analytical expressions for
its gradient with respect to constellation parameters. Decoding of the proposed
constellations is reduced to a set of one-dimensional closest point problems
that we solve using parallel sphere decoder algorithms. This decoding strategy
can also improve efficiency of existing codes.
