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This paper proposes a novel design of multi-symbol unitary constellation fornon-coherent single-input multiple-output (SIMO) communications over blockRayleigh fading channels. To facilitate the design and the detection of largeunitary constellations at reduced complexity, the proposed constellations areconstructed as the Cartesian product of independent amplitude andphase-shift-keying (PSK) vectors, and hence, can be iteratively detected. Theamplitude vector is detected by exhaustive search, whose complexity issufficiently low in short packet transmission scenarios. To detect the PSKvector, we use the posterior probability as a reliability criterion in thesorted decision-feedback differential detection (sort-DFDD), which results innear-optimal error performance for PSK symbols with equal modulation orders.This detector is called posteriori-based-reliability-sort-DFDD (PR-sort-DFDD)and has polynomial complexity. We also propose an improved detector calledimproved-PR-sort-DFDD to detect a more generalized PSK structure, i.e., PSKsymbols with unequal modulation orders. This detector also approaches theoptimal error performance with polynomial complexity. Simulation results showthe merits of our proposed multi-symbol unitary constellation when compared tocompeting low-complexity unitary constellations.

Design and Detection of Unitary Constellations in Non-Coherent SIMO Systems for Short Packet Communications