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. The filter taps can simply be read off from the response to a single Zak-OTFS point (impulse) pulsone waveform, and the I/O relation can be reconstructed for a sampled system that operates under finite duration and bandwidth constraints. Predictability opens up the possibility of a model-free mode of operation. The time-domain realization of a Zak-OTFS point pulsone is a pulse train modulated by a tone, hence the name, pulsone. The Peak-to-Average Power Ratio (PAPR) of a pulsone is about $15$ dB, and we describe a general method for constructing a spread pulsone for which the time-domain realization has a PAPR of about 6dB. We construct the spread pulsone by applying a type of discrete spreading filter to a Zak-OTFS point pulsone. The self-ambiguity function of the point pulsone is supported on the period lattice ${\Lambda}_{p}$, and by applying a discrete chirp filter, we obtain a spread pulsone with a self-ambiguity function that is supported on a rotated lattice ${\Lambda^*}$. We show that if the channel satisfies the crystallization conditions with respect to ${\Lambda^*}$ then the effective DD domain filter taps can simply be read off from the cross-ambiguity between the channel response to the spread pulsone and the transmitted spread pulsone. If, in addition, the channel satisfies the crystallization conditions with respect to the period lattice ${\Lambda}_{p}$, then in an OTFS frame consisting of a spread pilot pulsone and point data pulsones, after cancelling the received signal corresponding to the spread pulsone, we can recover the channel response to any data pulsone.

翻译：Zak-OTFS的输入/输出关系在时延和多普勒周期大于有效信道时延和多普勒扩展时具有可预测性和非衰落特性，这一条件我们称为结晶条件。滤波器抽头可直接从单个Zak-OTFS点（脉冲）脉冲波的响应中读取，且对于在有限持续时间和带宽约束下运行的采样系统，其输入/输出关系可重构。可预测性为无模型操作模式提供了可能。Zak-OTFS点脉冲波的时域实现是由单音调制的脉冲序列，故得名脉冲波。脉冲波的峰均功率比约为15dB，我们提出了一种通用方法构建扩展脉冲波，使其时域实现的PAPR降至约6dB。通过将一类离散扩展滤波器应用于Zak-OTFS点脉冲波，我们构建了扩展脉冲波。点脉冲波的自模糊函数支撑在周期格点$\Lambda_{p}$上，而通过应用离散啁啾滤波器，我们获得的自模糊函数支撑在旋转格点$\Lambda^{*}$上的扩展脉冲波。结果表明：若信道相对于$\Lambda^{*}$满足结晶条件，则有效DD域滤波器抽头可直接从扩展脉冲波的信道响应与发送扩展脉冲波的互模糊函数中读取；若信道同时相对于周期格点$\Lambda_{p}$满足结晶条件，则在由扩展导频脉冲波和点数据脉冲波组成的OTFS帧中，消除扩展脉冲波对应的接收信号后，可恢复任意数据脉冲波的信道响应。