A Group-Sparsity-Based Hyperparameter-Free Framework for Wideband DOA Estimation

A group-sparsity-based (GS-based) underdetermined wideband direction-of-arrival (DOA) estimation framework, which is free of hyperparameters, is proposed to resolve more sources than the sensor number. Based on the subband model via frequency decomposition, a direct wideband extension of the narrowband SPICE method is first presented, fusing subband results jointly. Then, in order to tackle the underdetermined DOA estimation problem with a uniform linear array (ULA), a GS-based wideband sparse iterative covariance estimation (GSWSPICE) framework is proposed, where information acquired by subbands of interest are exploited simultaneously. Specifically, considering two a priori information on source spectrum under the proposed framework, the wideband cost function is reformulated to yield two improved objective functions and constraint structures, respectively. It significantly reduces the estimation parameters while fully exploiting the subband model's enhanced degrees of freedoms. Accordingly, two methods, i.e., GS-WSPICE (P_up) and GS-WSPICE (P_uf), are introduced as effective underdetermined solutions, where sparse arrays are not needed. Proposed methods are proved to be convex and can be expressed in semidefinite programming (SDP) form. Then, an efficient Cyclic Solution is developed, while a dynamic-dictionary-based hybrid Cyclic and SDP Solution is proposed to further reduce computational complexity. Numerical and experimental results validate the effectiveness of proposed hyperparameter-free methods, where the time-consuming hyperparameter tuning process is not required any more compared to existing wideband methods.