Atom-Constrained Maximum Likelihood Gridless DOA with Wirtinger Gradients

A log-likelihood gridless sparse direction-of-arrival (DOA) estimation is presented. The likelihood fit is optimized using the sample covariance matrix and a reconstructed covariance matrix constrained to a few atoms. This approach enables using Wirtinger gradients for DOA. The sensitivity to local minima is mitigated by initializing with the best DOAs from a gridded DOA method. In simulations, the method achieves the Cramer-Rao bound and offers superior resolution compared to conventional gridless DOA methods.