A novel demixing algorithm for joint target detection and impulsive noise suppression

This work considers a collocated radar scenario where a probing signal is emitted toward the targets of interest and records the received echoes. Estimating the relative delayDoppler shifts of the targets allows determining their relative locations and velocities. However, the received radar measurements are often affected by impulsive non-Gaussian noise which makes a few measurements partially corrupted. While demixing radar signal and impulsive noise is challenging in general by traditional subspace-based methods, atomic norm minimization (ANM) has been recently developed to perform this task in a much more efficient manner. Nonetheless, the ANM cannot identify close delay-Doppler pairs and also requires many measurements. Here, we propose a smoothed ℓ0 atomic optimization problem encouraging both the sparse features of the targets and the impulsive noise. We design a majorization-minimization algorithm that converges to the solution of the proposed nonconvex problem using alternating direction method of multipliers (ADMM). Simulations results verify the superior accuracy of our proposed algorithm even for very close delay-Doppler pairs in comparison to ANM with around 40 dB improvement.