This letter presents a high resolution method which separates close components of a multi-component linear frequency modulated (LFM) signal and eliminates their Cross-Terms (CTs). We first investigate the energy distribution of the Auto-Terms (ATs) and CTs in ambiguity plane. This reveals that the energy of the CTs of parallel close components is significant around the origin. We propose to mask the samples in which the CTs may have interferences with the ATs. This mask is signal-dependent and its directions are determined using the relationship between the radial slices of ambiguity function (AF) and the fractional Fourier transform (FrFT). Exploiting sparsity in time-frequency (TF) domain and by solving an $\ell _1$-norm minimization problem, the localized time-frequency distribution (TFD) is extracted from the acquired samples of the AF. Simulation results reveal significant improvements in the efficiency compared to previous works.

中文翻译：

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多分量 LFM 信号的稀疏局部时频能量分布

这封信提出了一种高分辨率方法，它分离多分量线性调频 (LFM) 信号的接近分量并消除它们的交叉项 (CT)。我们首先研究了模糊平面中自动术语 (AT) 和 CT 的能量分布。这表明平行接近分量的 CT 能量在原点附近是显着的。我们建议屏蔽 CT 可能与 AT 干扰的样本。该掩码依赖于信号，其方向是使用模糊函数 (AF) 的径向切片和分数傅立叶变换 (FrFT) 之间的关系确定的。利用时频 (TF) 域中的稀疏性并通过求解 $\ell_1$-范数最小化问题，从获取的 AF 样本中提取局部时频分布 (TFD)。