Generalized ℓ₂−ℓ_p minimization based DOA estimation for sources with known waveforms in impulsive noise

The direction of arrival (DOA) estimation problem for sources with known waveforms in the presence of impulsive noise is studied. To solve the problem, the impulsive noise is decomposed into Gaussian and sparse parts, and a generalized ℓ₂−ℓ_p minimization based cost function is developed by setting generalized Gaussian distribution (GGD) as the prior distribution of sparse part. Then, to solve this nonconvex problem, the generalized ℓ₂−ℓ_p problem is decoupled into multiple independent and dimension reduced simple ℓ₂−ℓ_p optimization problems with respect to the sparse part, and solved under the accelerated proximal gradient framework. Finally, DOAs and complex amplitudes are estimated from the cleaned data. As demonstrated by simulation results, the proposed method has a better performance than existing ones in the presence of Gaussian mixture model (GMM) and GGD noise, while it is comparable for symmetric α stable (SαS) noise.