Harmonic Retrieval for Non-Circular Coherent Signals via Double Decoupled Atomic Norm Minimization

This paper studies super-resolution harmonic retrieval for strictly non-circular coherent signals. We develop gridless sparse representations of both their covariance and pseudo-covariance matrices over a common matrix-form atom set. This enables the decoupled atomic norm minimization (D-ANM) technique to exploit the sparsity of the covariance and pseudo-covariance matrices jointly. Further, by effectively utilizing the inherent mutual coupling characteristics between the covariance and pseudo-covariance matrices, additional constraints are properly imposed to reflect and enforce desired structure information represented by such matrices and their augmented matrix. It leads to a novel structure-based sparse optimization method, called double decoupled atomic norm minimization (DD-ANM). In addition, performance analysis is provided for the proposed DD-ANM method in practical settings. Simulation results reveal that the proposed DD-ANM outperforms the benchmark methods in terms of lower estimation errors.