Robust Iterative Sparse ML-Based Approaches for CES Data Model: Application to DOA Estimation

SCM is widely used in the design of array signal processing algorithms that perform well for CCG distributed samples. However, SCM-based DOA estimation algorithms are inaccurate for CES data models. This article aims to extend the conventional SCM-based iterative sparse SMLA for DOA estimation to encompass more general circular CES distributed observations. These extended RSMLA use robust CES-based ML-estimators of the CM instead of SCM, or more generally M-estimators. Joint and interleaved computation of M-estimators and the RSMLA are also proposed [denoted as IRSMLA algorithms] when the size of the observed CES vector, $M$, is of the same order as the samples size, $N$, or when $N < M$. To improve DOA estimation accuracy and eliminate grid mismatch, refined approaches (referred to as RSMLA-RML) that combines the power-based RSMLA and robust ML (RML) methods are also proposed, in which an alternative RML cost function is minimized over a scalar DOA parameter. Performance comparisons are made between the developed approaches and existing DOA estimation algorithms as well as CRB in terms of sample size, SNR, DOA separation, signal source correlation parameters, and computational cost, demonstrating superior performance over existing schemes for heavy-tailed CES distributed observations. Moreover, it is experimentally demonstrated that the proposed algorithms perform effectively even when the encountered source signals are coherent, despite being derived under the assumption of uncorrelated sources.