In this paper we propose a new design criterion and a new class of unitarysignal constellations for differential space-time modulation formultiple-antenna systems over Rayleigh flat-fading channels with unknown fadingcoefficients. Extensive simulations show that the new codes have significantlybetter performance than existing codes. We have compared the performance of ourcodes with differential detection schemes using orthogonal design, Cayleydifferential codes, fixed-point-free group codes and product of groups and forthe same bit error rate, our codes allow smaller signal to noise ratio by asmuch as 10 dB. The design of the new codes is accomplished in a systematic waythrough the optimization of a performance index that closely describes the biterror rate as a function of the signal to noise ratio. The new performanceindex is computationally simple and we have derived analytical expressions forits gradient with respect to constellation parameters. Decoding of the proposedconstellations is reduced to a set of one-dimensional closest point problemsthat we solve using parallel sphere decoder algorithms. This decoding strategycan also improve efficiency of existing codes.
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