In radar sensing, the self-ambiguity function of the probing waveform plays a crucial role in the resolvability and detection of multiple targets. In the recent Zak-OTFS based radar literature, Gaussian pulse shaping filter has been considered, and it has been shown to offer better range/velocity estimation performance compared to the traditional chirp waveform in scenes with multiple targets. While the self-ambiguity function with Gaussian filter has very low side lobes, its main lobe is wide which compromises resolvability and performance. Motivated by this, we seek filters with better ambiguity characteristics. Specifically, we explore two other known filters, namely, sinc and Gaussian-sinc (GS) filters, and demonstrate that these filters offer better performance compared to Gaussian filter under different scenarios and receiver processing. Towards demonstrating this, we derive closed-form expressions for the self-ambiguity functions of Zak-OTFS waveform with sinc and GS filters. The ambiguity functions of sinc and GS filtered waveforms have narrow main lobes, resulting in better resolvability in scenes with densely populated targets for the basic peak-detection based receiver. The ambiguity function of Gaussian filtered waveform has very low sidelobes, resulting in better performance in sparsely populated scenes. When a receiver with inter-target interference mitigation is used, the sinc and GS filters perform better in both dense and sparsely populated scenes compared to Gaussian filter.

翻译：在雷达感知中，探测波形的自模糊函数对多目标的分辨能力与检测性能至关重要。近期基于Zak-OTFS的雷达文献中，高斯脉冲成形滤波器被广泛采用，研究结果表明，在多目标场景下，相较于传统啁啾波形，该滤波器能提供更优的距离/速度估计性能。尽管采用高斯滤波器的自模糊函数具有极低的旁瓣，但其主瓣宽度较大，从而影响了分辨能力与系统性能。受此启发，我们旨在寻找具有更优模糊特性的滤波器。具体而言，我们探究了两种已知滤波器——sinc滤波器与高斯-sinc（GS）滤波器，并证明在不同场景与接收机处理条件下，这两种滤波器相较于高斯滤波器具有更优性能。为验证这一结论，我们推导了采用sinc与GS滤波器的Zak-OTFS波形自模糊函数的闭式表达式。经sinc与GS滤波后的波形自模糊函数主瓣更窄，从而在对基于基本峰值检测的接收机中，能更好地分辨密集目标场景。而高斯滤波波形的模糊函数旁瓣极低，在稀疏目标场景中表现更优。当采用带有目标间干扰抑制的接收机时，sinc与GS滤波器在密集与稀疏两种场景下均展现出优于高斯滤波器的性能。