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Differential Unitary Space-Time Constellations From Spherical Codes

We construct a new class of unitary space-time constellations that is suitable for multi-antenna differential signaling. This class of constellations follows a certain structure that is inspired by the so-called biorthogonal spherical codes. As a consequence of this, we show that the proposed class achieves optimal diversity sum in some cases and close-to-optimal diversity sum in the remaining cases. Furthermore, we demonstrate how such constellations are tuned in order to improve the diversity product while maintaining the same diversity sum, thereby yielding constellations with favorable diversity sum and product. Numerical evaluations reveal that the proposed construction achieves close or better performance than the best-known constellations over a wide range of signal-to-noise ratios of typical operation, with the added advantage that it can be generated for any number of transmit antennas.