Gridless super-resolution direction finding for strictly non-circular sources based on atomic norm minimization

The recently developed super-resolution framework by Candes enables direction-of-arrival (DOA) estimation from a sparse spatial power spectrum in the continuous domain with infinite precision in the noise-free case. By means of atomic norm minimization (ANM), the discretization of the spatial domain is no longer required, which overcomes the basis mismatch problem in conventional sparse signal recovery (SSR)-based DOA estimation. In this paper, we incorporate additional signal structure, i.e., the strict second-order non-circularity (NC) of the signals, into the ANM framework for the noisy multiple measurement vector (MMV) model. Due to the NC preprocessing step, the NC ANM problem provides a two-level Hermitian Toeplitz structured solution matrix, which possesses a two-dimensional Vandermonde decomposition such that desired the spatial frequencies can be uniquely extracted via NC Standard/Unitary ESPRIT in closed-form. The presented NC ANM procedure efficiently exploits the NC signal structure, resulting in both a reduced estimation error and an increased source identifiability compared to the conventional ANM approach. Simulation results demonstrate the superior performance of the proposed method.