This article presents an adaptive waveform design method using multitone sinusoidal frequency modulation (MTSFM). The MTSFM waveform's modulation function is represented as a finite Fourier series expansion. The Fourier coefficients are utilized as a discrete set of design parameters. These design parameters can be modified to shape the spectrum, auto-correlation function (ACF), and ambiguity function (AF) shapes of the waveform. The MTSFM waveform model naturally possesses the constant envelope and spectral compactness properties that make it well suited for transmission on practical radar/sonar transmitters which utilize high power amplifiers. The MTSFM has an exact mathematical definition for its time-series using generalized Bessel functions which allow for deriving closed-form analytical expressions for its spectrum, AF, and ACF. These expressions allow for establishing well-defined optimization problems that finely tune the MTSFM's properties. This adaptive waveform design model is demonstrated by optimizing MTSFM waveforms that initially possess a “thumbtack-like” AF shape. The resulting optimized designs possess substantially improved sidelobe levels over specified regions in the range-Doppler plane without increasing their time-bandwidth product. Simulations additionally demonstrate that the optimized thumbtacklike MTSFM waveforms are competitive with thumbtacklike phase-coded waveforms derived from design algorithms available in the published literature.

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使用多音正弦频率调制的自适应发射波形设计

本文提出了一种使用多音正弦频率调制（MTSFM）的自适应波形设计方法。MTSFM波形的调制功能表示为有限傅立叶级数展开。傅立叶系数被用作设计参数的离散集。可以修改这些设计参数，以对波形进行频谱成形，自相关函数（ACF）和模糊函数（AF）形状。MTSFM波形模型自然具有恒定的包络和频谱紧凑性，因此非常适合在使用高功率放大器的实际雷达/声纳发射机上进行传输。MTSFM使用广义的Bessel函数对其时间序列进行了精确的数学定义，从而可以为其光谱，AF和ACF得出闭合形式的分析表达式。这些表达式允许建立定义明确的优化问题，以优化MTSFM的属性。通过优化最初具有“ thumbtack-like” AF形状的MTSFM波形，可以演示这种自适应波形设计模型。所得的优化设计在距离多普勒平面的指定区域上具有显着改善的旁瓣电平，而没有增加其时间带宽积。仿真还表明，优化的图钉状MTSFM波形与从已出版文献中提供的设计算法得出的图钉状相位编码波形具有竞争力。通过优化最初具有“ thumbtack-like” AF形状的MTSFM波形，可以演示这种自适应波形设计模型。所得的优化设计在距离多普勒平面的指定区域上具有显着改善的旁瓣电平，而没有增加其时间带宽积。仿真还表明，优化的图钉状MTSFM波形与从已出版文献中提供的设计算法得出的图钉状相位编码波形具有竞争力。通过优化最初具有“ thumbtack-like” AF形状的MTSFM波形，可以演示这种自适应波形设计模型。所得的优化设计在距离多普勒平面的指定区域上具有显着改善的旁瓣电平，而没有增加它们的时间带宽积。仿真还表明，优化的图钉状MTSFM波形与从已出版文献中提供的设计算法得出的图钉状相位编码波形具有竞争力。