Multi-component LFM Signals Detection and Separation using Fourier-Bessel Series Expansion

The Fourier-Bessel (FB) series expansion with a variable window length is introduced to determine the number of multi-component linear frequency modulated (LFM) signals, and to separate the signal components. This method is mainly tackled into two stages, with the first being a coarse component number detection, which is determined as the number of pinnacles obtained by the fractional Fourier transform (FrFT). Secondly, a fine number determination of close-frequency components is obtained by adopting a large window length in FB series expansion, and the individual components are separated and reconstructed by several corresponding FB coefficients. Simulation results indicate that the proposed method outperforms the Radon transform with the time-frequency (TF) analysis methods in component number determination correctness, individual component separation accuracy, and robustness in low SNR.