A Cyclic-Reconstruction-Based Single-Channel Source Separation with the Coexistence of Strong and Weak Signals

In complex electromagnetic environments, the aliasing of various types of signals such as radar, communication, navigation and jamming is increasing, requiring effective source separation method to deal with it. However, the signal-to-noise ratio (SNR) of each signal differs significantly, which brings severe challenges to source separation. In this paper, a cyclic-reconstruction-based single-channel source separation (CRSS) method is proposed. First, a sparse observation model for aliasing signals is established based on Fourier decomposition of the instantaneous amplitude (IA) terms. Considering the coexistence of both strong and weak signals, the reconstruction of each sub-signal is carried out in order of the SNR value, strong component first, then weak ones. For each component, the reconstruction is conducted based on joint estimation of IA and instantaneous frequency (IF). For the estimation of IA, the generalized approximate message passing (GAMP) is applied. For the estimation of IF, an optimization model for IF is established and an analytic solution to the optimization problem is obtained. After each reconstructed signal component is obtained, it is removed from the aliasing signal until the loop ends. Both simulated and experimental results show that the proposed method can effectively separate time-frequency-aliased signals, and still has a good performance especially in scenarios where strong and weak signals coexist.