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

This paper proposes a novel design of multi-symbol unitary constellation 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 is detected by exhaustive search, whose complexity is sufficiently low in short packet transmission scenarios. To detect the PSK vector, we use the posterior probability as a reliability criterion in the sorted decision-feedback differential detection (sort-DFDD), which results in near-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 called improved-PR-sort-DFDD to detect a more generalized PSK structure, i.e., PSK symbols with unequal modulation orders. This detector also approaches the optimal error performance with polynomial complexity. Simulation results show the merits of our proposed multi-symbol unitary constellation when compared to competing low-complexity unitary constellations.