Finding codes for the desired autocorrelation function (ACF) based on phase-coded modulation waveforms has always been a popular research topic, and the relevant literature is abundant. However, the optimized ACF may not be obtained in band-limited hardware due to the extended spectral sidelobes generated by instantaneous phase changes. Polyphase-coded FM (PCFM) waveforms based on continuous phase modulation (CPM), which uses a shape filter to smooth phase jumps, can provide effective spectral containment. However, for PCFM waveforms using the existing optimized phase codes, the original desired property of the ACF, e.g., a low integrated sidelobe level (ISL) or weighted ISL (WISL), will not be obtained because of the smoothness among all phases. Hence, PCFM waveforms based on CPM should be redesigned and optimized. Moreover, designing pulse-agile waveforms with different phase codes to mitigate range ambiguity has also attracted increased attention in recent years. However, different waveforms will yield range sidelobe modulation (RSM) in Doppler processing, which degrades the attendant Doppler coherency, leading to high sidelobes in the Doppler dimension. In this article, optimization algorithms for designing diverse PCFM waveforms and relevant joint mismatched filters (JMMFs) are proposed. A CPM-based cyclic algorithm (CPM-CA) using the method of alternating projection for optimizing the PCFM waveform with a desired ACF is proposed in the first step. The design of multiple diverse PCFM waveforms with similar ACFs and a small RSM effect is also considered. Then, to further optimize the ISL/WISL and reduce the RSM effect, a novel method for designing JMMFs using a cyclic algorithm (JMMF-CA) is proposed. Simulations and an experiment based on a real radar system indicate that the optimized PCFM waveforms and JMMFs using CPM-CA and JMMF-CA can yield a desired ISL/WISL while achieving a small RSM effect with a low loss of signal-to-noise ratio and satisfactory Doppler robustness.

中文翻译：

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优化不同的 PCFM 波形和联合失配滤波器

基于相位编码调制波形寻找所需自相关函数（ACF）的代码一直是一个热门的研究课题，相关文献非常丰富。然而，由于瞬时相位变化产生的扩展频谱旁瓣，在带限硬件中可能无法获得优化的 ACF。基于连续相位调制 (CPM) 的多相编码 FM (PCFM) 波形使用形状滤波器平滑相位跳跃，可以提供有效的频谱抑制。然而，对于使用现有优化相位代码的 PCFM 波形，由于所有相位之间的平滑性，将无法获得 ACF 最初所需的特性，例如低积分旁瓣电平 (ISL) 或加权 ISL (WISL)。因此，应重新设计和优化基于 CPM 的 PCFM 波形。而且，近年来，设计具有不同相位代码的脉冲捷变波形以减轻距离模糊也引起了越来越多的关注。然而，不同的波形会在多普勒处理中产生距离旁瓣调制 (RSM)，这会降低伴随的多普勒相干性，导致多普勒维度中的高旁瓣。在本文中，提出了用于设计不同 PCFM 波形和相关联合失配滤波器 (JMMF) 的优化算法。第一步提出了一种基于 CPM 的循环算法 (CPM-CA)，该算法使用交替投影方法来优化具有所需 ACF 的 PCFM 波形。还考虑了具有相似 ACF 和小 RSM 效应的多种不同 PCFM 波形的设计。然后，为了进一步优化 ISL/WISL 并减少 RSM 效应，提出了一种使用循环算法 (JMMF-CA) 设计 JMMF 的新方法。基于真实雷达系统的仿真和实验表明，使用 CPM-CA 和 JMMF-CA 优化的 PCFM 波形和 JMMF 可以产生所需的 ISL/WISL，同时实现具有低信噪比损失的小 RSM 效应和令人满意的多普勒鲁棒性。