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arXiv 2202.04793cs.ITmath.IT
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Low Ambiguity Zone:综合传感和通信系统中的理论界和多普勒弹性序列设计

Low Ambiguity Zone: Theoretical Bounds and Doppler-Resilient Sequence Design in Integrated Sensing and Communication Systems

Zhifan Ye, Zhengchun Zhou, Pingzhi Fan, Zilong Liu, Xianfu Lei, Xiaohu Tang

摘要:

在雷达传感和通信中,设计具有低模糊函数的多普勒弹性序列(DRSs)是一项非常困难的任务,该序列在整个信号持续时间上具有延迟并且在整个信号带宽上具有多普勒频移。然而,实际上,多普勒频率范围通常比发射信号的带宽小得多,并且对于远小于整个信号持续时间的延迟,相对容易获得准同步。受此观察的启发,我们提出了一个新的概念,称为低模糊区(LAZ),这是一个小的区域,相应的模糊函数的利益定义的一定的多普勒频率和延迟。如果感兴趣的最大模糊度值为零,则这种LAZ将减小到零模糊度区域(ZAZ)。在本文中,我们推导出了一组理论界的周期LAZ/ZAZ的单模DRS的频谱约束和没有,其中包括现有的界的周期全球模糊度函数作为特殊情况。这些界可以作为理论设计准则,以衡量对多普勒效应的序列的最优性。然后,我们介绍了四个最佳的构造DRS的推导模糊度下界的基础上的一些代数工具,如有限域上的字符和循环差集。

英文摘要:

In radar sensing and communications, designing Doppler resilient sequences (DRSs) with low ambiguity function for delay over the entire signal duration and Doppler shift over the entire signal bandwidth is an extremely difficult task. However, in practice, the Doppler frequency range is normally much smaller than the bandwidth of the transmitted signal, and it is relatively easy to attain quasi-synchronization for delays far less than the entire signal duration. Motivated by this observation, we propose a new concept called low ambiguity zone (LAZ) which is a small area of the corresponding ambiguity function of interest defined by the certain Doppler frequency and delay. Such an LAZ will reduce to a zero ambiguity zone (ZAZ) if the maximum ambiguity values of interest are zero. In this paper, we derive a set of theoretical bounds on periodic LAZ/ZAZ of unimodular DRSs with and without spectral constraints, which include the existing bounds on periodic global ambiguity function as special cases. These bounds may be used as theoretical design guidelines to measure the optimality of sequences against Doppler effect. We then introduce four optimal constructions of DRSs with respect to the derived ambiguity lower bounds based on some algebraic tools such as characters over finite field and cyclic difference sets.

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