In this paper, we propose a novel multi-symbol unitary constellation structure for non-coherent single-input multiple-output (SIMO) communications over block Rayleigh fading channels. To facilitate the design and the detection of large unitary constellations at reduced complexity, the proposed constellations are constructed as the Cartesian product of independent amplitude and phase-shift-keying (PSK) vectors, and hence, can be iteratively detected. The amplitude vector can be detected by exhaustive search, whose complexity is still sufficiently low in short packet transmissions. For detection of the PSK vector, we adopt a maximum-A-posteriori (MAP) criterion to improve the reliability of the sorted decision-feedback differential detection (sort-DFDD), which results in near-optimal error performance in the case of the same modulation order of the transmit PSK symbols at different time slots. This detector is called MAP-based-reliability-sort-DFDD (MAP-R-sort-DFDD) and has polynomial complexity. For the case of different modulation orders at different time slots, we observe that undetected symbols with lower modulation orders have a significant impact on the detection of PSK symbols with higher modulation orders. We exploit this observation and propose an improved detector called improved-MAP-R-sort-DFDD, which approaches the optimal error performance with polynomial time complexity. Simulation results show the merits of our proposed multi-symbol unitary constellation when compared to competing low-complexity unitary constellations.

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