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.

翻译：本文针对块瑞利衰落信道下的非相干单输入多输出（SIMO）通信，提出了一种新颖的多符号酉星座设计方法。为降低大型酉星座设计与检测的复杂度，所提星座通过独立幅度向量和相移键控（PSK）向量的笛卡尔积构造，从而实现迭代检测。幅度向量采用穷举搜索检测，在短包传输场景中复杂度足够低。针对PSK向量的检测，我们采用后验概率作为排序判决反馈差分检测（sort-DFDD）的可靠性准则，该方案对等调制阶数的PSK符号可达到近似最优的误码性能。将该检测器称为基于后验概率可靠性排序的DFDD（PR-sort-DFDD），其复杂度为多项式级。进一步提出改进型检测器improved-PR-sort-DFDD，适用于更广义的PSK结构——即具有非等调制阶数的PSK符号，该检测器同样以多项式复杂度逼近最优误码性能。仿真结果表明，与低复杂度酉星座竞品相比，所提多符号酉星座具有显著优势。