Improved Resolution Estimate for the Two-Dimensional Super-Resolution and a New Algorithm for Direction of Arrival Estimation with Uniform Rectangular Array

In this paper, we develop a new technique to obtain improved estimates for the computational resolution limits in two-dimensional super-resolution problems and present a new idea for developing two-dimensional super-resolution algorithms. To be more specific, our main contributions are fourfold: (1) Our work improves the resolution estimates for number detection and location recovery in two-dimensional super-resolution problems; (2) As a consequence, we derive a stability result for a sparsity-promoting algorithm in two-dimensional super-resolution problems [or direction of arrival Problems (DOA)]. The stability result exhibits the optimal performance of sparsity promoting in solving such problems; (3) Inspired by the new techniques, we propose a new coordinate-combination-based model order detection algorithm for two-dimensional DOA estimation and theoretically demonstrate its optimal performance, and (4) we also propose a new coordinate-combination-based MUSIC algorithm for super-resolving sources in two-dimensional DOA estimation. It has excellent performance and enjoys some advantages compared to the conventional DOA algorithms.

Automated summary

In this paper, a new technique is developed to improve the computational resolution limits in two-dimensional super-resolution problems and a new idea for developing two-dimensional super-resolution algorithms is presented. The main contributions include: (1) Improved resolution estimates for number detection and location recovery in two-dimensional super-resolution problems. (2) Stability result for a sparsity-promoting algorithm in two-dimensional super-resolution problems, indicating its optimal performance. (3) Proposal of a new coordinate-combination-based model order detection algorithm for two-dimensional DOA estimation with demonstrated optimal performance. (4) Proposal of a new coordinate-combination-based MUSIC algorithm for super-resolving sources in two-dimensional DOA estimation with excellent performance and advantages over conventional DOA algorithms.