Block- and Rank-Sparse Recovery for Direction Finding in Partly Calibrated Arrays

A sparse recovery approach for direction finding in partly calibrated arrays composed of subarrays with unknown displacements is introduced. The proposed method is based on mixed nuclear norm and l(1) norm minimization and exploits block-sparsity and low-rank structure in the signal model. For efficient implementation a compact equivalent problem reformulation is presented. The new technique is applicable to subarrays of arbitrary topologies and grid-based sampling of the subarray manifolds. In the special case of subarrays with a common baseline our new technique admits extension to a gridless implementation. As shown by simulations, our new block-and rank-sparse direction finding technique for partly calibrated arrays outperforms the state of the art method RARE in difficult scenarios of low sample numbers, low signal-to-noise ratio, or correlated signals.