Sparsely Localized Time-Frequency Energy Distributions for Multi-Component LFM Signals

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.