While a number of signal structures have been proposed for radar, frequency modulation (FM) remains the most common in practice because it is well-suited to high-power transmitters, which tend to introduce significant distortion to other waveform classes. That said, various forms of coding provide useful parameterizations for which a variety of optimization methods can be readily applied to accomplish different operational goals. To that end, the polyphase-coded FM (PCFM) implementation was previously devised as a means to bridge this gap between optimizable parameters and physically realizable waveforms. However, the original method employed to optimize PCFM waveforms involved a piecewise greedy search that, while relatively effective, was rather slow and cumbersome. Here, the continuous nature of this framework is leveraged to formulate a gradient-based optimization approach that updates all parameters simultaneously and can be efficiently performed using fast Fourier transforms, thus facilitating a general design methodology for practical waveforms that is directly extensible to myriad waveform-diverse arrangements. Results include a large number of optimization assessments to discern performance trends in aggregate and detailed analysis of specific cases, as well as both loopback and free-space experimental measurements to demonstrate practical efficacy.

中文翻译：

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基于梯度的PCFM雷达波形优化

尽管已经提出了许多用于雷达的信号结构，但实际上频率调制（FM）仍然是最常见的，因为它非常适合于高功率发射器，后者会给其他波形类别带来明显的失真。就是说，各种形式的编码提供了有用的参数化，可以很容易地将各种优化方法应用于这些参数化，以实现不同的操作目标。为此，先前已设计了多相编码FM（PCFM）实施方案，以弥合可优化参数与物理可实现波形之间的这种差距。但是，用于优化PCFM波形的原始方法涉及分段贪婪搜索，该搜索虽然相对有效，但却相当缓慢且麻烦。这里，利用该框架的连续性来制定基于梯度的优化方法，该方法可以同时更新所有参数，并且可以使用快速傅立叶变换有效地执行此操作，从而为可直接扩展到无数种波形多样安排的实际波形提供了通用的设计方法。结果包括大量优化评估，以识别特定案例的汇总和详细分析中的性能趋势，以及环回和自由空间实验测量值，以证明实际效果。因此，为实际的波形提供了一种通用的设计方法，该方法可以直接扩展到多种多样的波形。结果包括大量优化评估，以识别特定案例的汇总和详细分析中的性能趋势，以及环回和自由空间实验测量值，以证明实际效果。因此，为实际波形提供了一种通用的设计方法，该方法可以直接扩展到无数种波形多样的布置。结果包括大量优化评估，以识别特定案例的汇总和详细分析中的性能趋势，以及环回和自由空间实验测量值，以证明实际效果。