In orthogonal time sequency multiplexing (OTSM) modulation, the information symbols are conveyed in the delay-sequency domain upon exploiting the inverse Walsh Hadamard transform (IWHT). It has been shown that OTSM is capable of attaining a bit error ratio (BER) similar to that of orthogonal time-frequency space (OTFS) modulation at a lower complexity, since the saving of multiplication operations in the IWHT. Hence we provide its BER performance analysis and characterize its detection complexity. We commence by deriving its generalized input-output relationship and its unconditional pairwise error probability (UPEP). Then, its BER upper bound is derived in closed form under both ideal and imperfect channel estimation conditions, which is shown to be tight at moderate to high signal-to-noise ratios (SNRs). Moreover, a novel approximate message passing (AMP) aided OTSM detection framework is proposed. Specifically, to circumvent the high residual BER of the conventional AMP detector, we proposed a vector AMP-based expectation-maximization (VAMP-EM) detector for performing joint data detection and noise variance estimation. The variance auto-tuning algorithm based on the EM algorithm is designed for the VAMP-EM detector to further improve the convergence performance. The simulation results illustrate that the VAMP-EM detector is capable of striking an attractive BER vs. complexity trade-off than the state-of-the-art schemes as well as providing a better convergence. Finally, we propose AMP and VAMP-EM turbo receivers for low-density parity-check (LDPC)-coded OTSM systems. It is demonstrated that our proposed VAMP-EM turbo receiver is capable of providing both BER and convergence performance improvements over the conventional AMP solution.

翻译：在正交时间序列复用（OTSM）调制中，信息符号通过逆沃尔什-哈达玛变换（IWHT）在延迟-序列域中传输。研究表明，由于IWHT中乘法运算的节省，OTSM能够以较低的复杂度实现与正交时频空间（OTFS）调制相近的误比特率（BER）。因此，本文分析了其BER性能并表征了其检测复杂度。我们首先推导了其广义输入-输出关系以及无条件成对错误概率（UPEP）。随后，在理想信道估计与非完美信道估计条件下，推导了其BER上界的闭式表达式，该上界在中高信噪比（SNR）下具有紧致性。此外，提出了一种新型近似消息传递（AMP）辅助的OTSM检测框架。具体而言，为规避传统AMP检测器的高残余BER，我们提出了一种基于向量AMP的期望最大化（VAMP-EM）检测器，用于联合数据检测与噪声方差估计。基于EM算法的方差自动调谐机制被设计用于VAMP-EM检测器，以进一步提升收敛性能。仿真结果表明，VAMP-EM检测器能够比现有方案实现更具吸引力的BER与复杂度权衡，并提供更优的收敛性。最后，我们为低密度奇偶校验（LDPC）编码的OTSM系统提出了AMP与VAMP-EM Turbo接收机。实验证明，与常规AMP方案相比，所提出的VAMP-EM Turbo接收机能够在BER与收敛性能上实现双重提升。