[论文解读] OTFS -- Predictability in the Delay-Doppler Domain and its Value to Communication and Radar Sensing

Saif Khan Mohammed, Ronny Hadani+2 more|arXiv (Cornell University)|Feb 17, 2023

PAPR reduction in OFDM参考文献 19被引用 4

一句话总结

该论文证明，在满足晶化条件（即脉冲列周期超过信道扩展）时，延迟-多普勒（DD）域中的OTFS调制可实现可预测的、非衰落的通信与雷达感知。它表明，Zak-OTFS通过直接从导频符号学习输入-输出关系，实现了无需信道模型的运行，其性能优于传统MC-OTFS，尤其在多普勒扩展较大的情况下。

ABSTRACT

In our first paper [2] we explained why the Zak-OTFS input-output (I/O) relation is predictable and non-fading when the delay and Doppler periods are greater than the effective channel delay and Doppler spreads, a condition which we refer to as the crystallization condition. We argued that a communication system should operate within the crystalline regime. It is well known that it is possible to identify a linear time varying (LTV) channel if and only if it is under-spread. The crystallization condition is more restrictive than the under-spread condition, so identification is always possible. In the crystalline regime, we show that Zak-OTFS pilot sequences minimize the complexity of identifying the effective DD domain channel filter. We demonstrate that the filter taps can simply be read off from the response to a single Zak-OTFS pilot. In general, we provide an explicit formula for reconstructing the Zak-OTFS I/O relation from a finite number of received pilot symbols in the delay-Doppler (DD) domain. This reconstruction formula makes it possible to study predictability of the Zak-OTFS I/O relation for a sampled system that operates under finite duration and bandwidth constraints. We analyze reconstruction accuracy for different choices of the delay and Doppler periods, and of the pulse shaping filter. Reconstruction accuracy is high when the crystallization condition is satisfied, implying that it is possible to learn directly the I/O relation without needing to estimate the underlying channel. This opens up the possibility of a model-free mode of operation, which is especially useful when a traditional model-dependent mode of operation (reliant on estimation of the underlying physical channel) is out of reach (for example, when the channel comprises of unresolvable paths, or exhibits a continuous delay-Doppler profile such as in presence of acceleration). Our study clarifies the

研究动机与目标

• 建立OTFS系统在延迟-多普勒域中可预测性的理论基础。
• 识别晶化条件为在双重选择性信道中实现非衰落、可预测系统行为的关键因素。
• 证明Zak-OTFS的输入-输出关系可直接从导频信号学习，而无需估计底层物理信道。
• 将Zak-OTFS与其实多载波近似（MC-OTFS）进行比较，展示在高多普勒扩展下其更高的可预测性与性能。
• 阐明DD域中混叠现象作为不可预测性的根本原因，并提出信道的晶体分解方法。

提出的方法

• 利用有限数量的导频符号，在DD域中推导出Zak-OTFS输入-输出关系的显式重构公式。
• 引入晶体分解概念，将有效DD信道分解为可预测（晶体）与不可预测分量。
• 使用Zak变换将时域信号映射为DD域中的准周期表示，从而实现对脉冲列波形（pulsones）的分析。
• 分析重构精度随延迟与多普勒周期及脉冲成形滤波器设计的变化，证明在晶化条件下具有高精度。
• 通过分析在不完美信道知识下Zak-OTFS与MC-OTFS各自的I/O关系可预测性与误比特率（BER）性能，进行对比。
• 采用信道的规范分解，以隔离因脉冲列与信道扩展不匹配导致的混叠影响。

实验结果

研究问题

• RQ1 在何种条件下，采样后的OTFS系统的输入-输出关系在延迟-多普勒域中是可预测的？
• RQ2 DD域中的混叠如何导致不可预测性？其根本原因是什么？
• RQ3 在不估计底层物理信道的情况下，能在多大程度上直接从导频符号学习输入-输出关系？
• RQ4 Zak-OTFS的可预测性与MC-OTFS相比如何，特别是在高多普勒扩展下？
• RQ5 晶化条件对完美与不完美信道知识场景下的误比特率（BER）性能有何影响？

主要发现

• 晶化条件——即延迟与多普勒周期超过有效信道延迟与多普勒扩展——可确保Zak-OTFS的输入-输出关系可预测且非衰落。
• 当晶化条件满足时，有效DD信道的抽头可直接从单个Zak-OTFS导频信号的响应中读取，从而实现I/O关系的直接学习。
• 在晶化条件满足时，从导频符号重构I/O关系可实现高精度，从而支持免模型运行。
• 在晶化条件满足时，免模型运行下的性能仅略逊于具备完美I/O知识的情况，证明了其鲁棒性。
• 由于混叠减少与更好的信道分辨率，Zak-OTFS在多普勒扩展增大时表现出优于MC-OTFS的可预测性与BER性能。
• 当晶化条件恰好满足时，信道的不可预测分量恰好消失，证实混叠是导致不可预测性的根本原因。