Separation of chirp scattered returns from a mixture of sinusoidal tones in noise

We consider the problem of source separation of a signal whose elements consist of chirp scattered returns and sinusoidal tones overlapping in time and frequency. Due to the application, both signals are assumed to be highly non-stationary with their parameters rapidly changing. Such a mixture may occur when a device with a single antenna is spectrally constrained while simultaneously communicating information and sensing the environment. Another application is to mitigate interference between two devices which must share the spectrum. We consider a formulation where the chirp scattered returns are modeled as a convolution and the sinusoidal tones are modeled as sparse in the overcomplete inverse discrete Fourier domain. The objective function which is a combination of basis pursuit denoising and deconvolution is formulated with a/i-norm regularizer for each signal. A fast transform based iterative algorithm to obtain the solution is presented and the major steps for deriving the solution are outlined. Simulation results are provided where the non-linear separation algorithm yields a significant improvement in signal reconstruction relative to the standard matched-filter.