Diversity is an essential concept associated with communication reliability in multipath channels since it determines the slope of bit error rate performance in the medium to high signal-to-noise ratio regions. However, most of the existing analytical frameworks were developed for specific modulation schemes while the efficient validation of full multipath diversity for general modulation schemes remains an open problem. To fill this research gap, we propose to utilize random constellation rotation to ease the conditions for full-diversity modulation designs. For linearly precoded cyclic-prefix orthogonal frequency division multiplexing (OFDM) systems, we prove that maximum multipath diversity can be attained as long as the spread matrix does not have zero entries, which is a sufficient but easily satisfied condition. Furthermore, we derive the sufficient and necessary condition for general modulation schemes, whose verification can be divided into validation tasks for each column of the modulation matrix. Based on the proposed conditions, maximum diversity order can be attained with the probability of 1 by enabling a randomly generated rotation pattern for both time and doubly dispersive channels. The theoretical analysis in this paper also demonstrates that the diversity evaluation can be concentrated on the pairwise error probability when the number of error symbols is one, which reduces the complexity of diversity-driven design and performance analysis for novel modulation schemes significantly in both time and doubly dispersive channels. Finally, numerical results for various modulation schemes confirm that the theoretical analysis holds in both time and doubly dispersive channels. Furthermore, when employing practical detectors, the random constellation rotation technique consistently enhance the transmission reliability for both coded and uncoded systems.

翻译：分集是决定多径信道中通信可靠性的核心概念，因为它决定了中高信噪比区域误码率性能曲线的斜率。然而，现有分析框架大多针对特定调制方案构建，而对通用调制方案实现全多径分集的有效验证仍是一个开放性问题。为填补这一研究空白，本文提出利用随机星座旋转来放宽全分集调制设计的条件约束。对于线性预编码循环前缀正交频分复用系统，我们证明只要扩展矩阵不含零元素即可获得最大多径分集——这是一个充分但易于满足的条件。进一步地，我们推导出通用调制方案的充要条件，其验证可分解为对调制矩阵各列的独立检验任务。基于所提条件，通过在时变信道和双弥散信道中启用随机生成的旋转模式，能以概率1达到最大分集阶数。本文的理论分析还表明，分集评估可集中于单符号错误时的成对错误概率，这显著降低了新型调制方案在时变与双弥散信道中分集驱动设计与性能分析的复杂度。最后，多种调制方案的数值结果验证了理论分析在时变与双弥散信道中的普适性。此外，当采用实际检测器时，随机星座旋转技术能持续提升编码与非编码系统的传输可靠性。