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案。为降低大规模酉星座设计与检测的复杂度，所提星座被构造为独立幅度向量与相移键控（PSK）向量的笛卡尔积，因此可实现迭代检测。幅度向量采用穷举搜索检测，在短分组传输场景中其复杂度足够低。对于PSK向量的检测，本文在排序判决反馈差分检测（sort-DFDD）中采用后验概率作为可靠性准则，从而在调制阶数相等的PSK符号下获得接近最优的误码性能。该检测器称为基于后验概率可靠性的排序DFDD（PR-sort-DFDD），其复杂度为多项式级。针对调制阶数不等的广义PSK结构，本文进一步提出改进型检测器improved-PR-sort-DFDD，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，与现有低复杂度酉星座相比，所提多符号酉星座具有显著优势。