On regularization parameter for L0-sparse covariance fitting based DOA estimation

In sparse DOA estimation methods, the regularization parameter λ is generally empirically tuned. In this paper, we provide a statistical method allowing to estimate an admissible interval where λ must be chosen. This work is conducted in the case of an Uniform Circular Array, well known for its θ invariant performances, and vectorized covariance matrix observation. In the recent work [1], it is shown that the equivalence between the L0-constrained problem and the corresponding regularized one is obtained for λ belonging to a given interval. This interval is conditional to an observation. The purpose of this work is to generalize this result for stochastic observations, providing so an interval I of λ valid in all scenarios for an UCA. This interval is not data dependent. Simulation results validate the proposed approach.