Compressive Sensing Based Separation of Nonstationary and Stationary Signals Overlapping in Time-Frequency

A compressive sensing (CS) approach for nonstationary signal separation is proposed. This approach is motivated by challenges in radar signal processing, including separations of micro-Doppler and main body signatures. We consider the case where the signal of interest assumes sparse representation over a given basis. Other signals present in the data overlap with the desired signal in the time and frequency domains, disallowing conventional windowing or filtering operations to be used for desired signal recovery. The proposed approach uses linear time-frequency representations to reveal the data local behavior. Using the L-statistics, only the time-frequency (TF) points that belong to the desired signal are retained, whereas the common points and others pertaining only to the undesired signals are deemed inappropriate and cast as missing samples. These samples amount to reduced frequency observations in the TF domain. The linear relationship between the measurement and sparse domains permits the application of CS techniques to recover the desired signal without significant distortion. We focus on sinusoidal desired signals with sparse frequency-domain representation but show that the analysis can be straightforwardly generalized to nonsinusoidal signals with known structures. Several examples are provided to demonstrate the effectiveness of the proposed approach.