Efficient Super-Resolution Two-Dimensional Harmonic Retrieval Via Enhanced Low-Rank Structured Covariance Reconstruction

Abstract

This paper develops an enhanced low-rank structured covariance reconstruction (LRSCR) method based on the decoupled atomic norm minimization (D-ANM), for super-resolution two-dimensional (2D) harmonic retrieval with multiple measurement vectors. This LRSCR-D-ANM approach exploits a potential structure hidden in the covariance by transferring the basic LRSCR to an efficient D-ANM formulation, which permits a sparse representation over a matrix-form atom set with decoupled 1D frequency components. The new LRSCR-D-ANM method builds upon the existence of a generalized Vandermonde decomposition of its solution, which otherwise cannot be guaranteed by the basic LRSCR unless a very conservative condition holds. Further, a low-complexity solution of the LRSCR-D-ANM is provided for fast implementation with negligible performance loss. Simulation results verify the advantages of the proposed LRSCR-D-ANM over the basic LRSCR, in terms of the wider applicability and the lower complexity.