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This paper presents an efficient optimization technique for gridless {2-D}line spectrum estimation, named decoupled atomic norm minimization (D-ANM). Theframework of atomic norm minimization (ANM) is considered, which has beensuccessfully applied in 1-D problems to allow super-resolution frequencyestimation for correlated sources even when the number of snapshots is highlylimited. The state-of-the-art 2-D ANM approach vectorizes the 2-D measurementsto their 1-D equivalence, which incurs huge computational cost and may becometoo costly for practical applications. We develop a novel decoupled approach of2-D ANM via semi-definite programming (SDP), which introduces a new matrix-formatom set to naturally decouple the joint observations in both dimensionswithout loss of optimality. Accordingly, the original large-scale 2-D problemis equivalently reformulated via two decoupled one-level Toeplitz matrices,which can be solved by simple 1-D frequency estimation with pairing. Comparedwith the conventional vectorized approach, the proposed D-ANM technique reducesthe computational complexity by several orders of magnitude with respect to theproblem size. It also retains the benefits of ANM in terms of precise signalrecovery, small number of required measurements, and robustness to sourcecorrelation. The complexity benefits are particularly attractive forlarge-scale antenna systems such as massive MIMO, radar signal processing andradio astronomy.

Efficient Two-Dimensional Line Spectrum Estimation Based on Decoupled Atomic Norm Minimization