论文标题
团体理论宽带雷达波形设计
Group-Theoretic Wideband Radar Waveform Design
论文作者
论文摘要
我们在设计遵循所需宽带歧义函数（WAF）的雷达波形的背景下研究了仿射群的理论。 WAF是通过将信号与其时间删除，多普勒偏移和延迟的复制品相关联获得的。我们将WAF定义视为$ a \ cdot x + b $的统一表示的系数函数。这本质上是应用于雷达波形设计的代数问题。关于该主题的先前工作在很大程度上分析了窄带歧义函数。在这里，我们表明，当感兴趣的潜在宽带信号是脉冲或脉搏列时，可以构建一个紧密的框架来设计该波形。具体而言，我们通过最小化框架的边界常数的比率来设计雷达信号，以便在WAF中获得较低的旁白。通过基于差异集构建代码手册来实现最小化，以实现Welch界限。我们表明，因此获得的紧密框架与定义WAF的小波变换有关。
We investigate the theory of affine groups in the context of designing radar waveforms that obey the desired wideband ambiguity function (WAF). The WAF is obtained by correlating the signal with its time-dilated, Doppler-shifted, and delayed replicas. We consider the WAF definition as a coefficient function of the unitary representation of the group $a\cdot x + b$. This is essentially an algebraic problem applied to the radar waveform design. Prior works on this subject largely analyzed narrow-band ambiguity functions. Here, we show that when the underlying wideband signal of interest is a pulse or pulse train, a tight frame can be built to design that waveform. Specifically, we design the radar signals by minimizing the ratio of bounding constants of the frame in order to obtain lower sidelobes in the WAF. This minimization is performed by building a codebook based on difference sets in order to achieve the Welch bound. We show that the tight frame so obtained is connected with the wavelet transform that defines the WAF.
