SR-ANM: A Square-Root Atomic Norm Minimization Estimator for Noise-Robust Direction-of-Arrival Estimation

This paper proposes a Square-root Atomic Norm Minimization (SR-ANM) estimator for direction-of-arrival (DoA) estimation in the single measurement vector (SMV) setting. This new framework, inspired by the Square-root Least Absolute Shrinkage and Selection Operator (Square-root LASSO), relies on a residual term based on the $L_2$-norm rather than the usual squared $L_2$-norm so as to obtain an estimator whereby the hyperparameter of the atomic norm in the unconstrained convex optimization problem exhibits robustness to the noise level compared to classical ANM. Experimental verification across a wide signal-to-noise ratio (SNR) range from 0 dB to 40 dB using the the probability of detection and the angular root-mean-squared error (RMSE) confirms the increased noise robustness of the proposed framework compared to ANM.