  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.
