# Super-Resolution DOA Estimation for Arbitrary Array Geometries Using a Single Noisy Snapshot

## TL;DR

This paper introduces a gridless super-resolution method for direction-of-arrival estimation from a single noisy snapshot, applicable to arbitrary sensor array geometries, and demonstrates high-resolution results in simulations.

## Contribution

It extends gridless super-resolution DOA estimation to arbitrary array geometries with noisy data, using a dual polynomial approach and polynomial rooting techniques.

## Key findings

- High-resolution DOA estimation achieved in simulations.
- Effective in white and colored noise scenarios.
- Applicable to circular and random planar arrays.

## Abstract

We address the problem of search-free DOA estimation from a single noisy snapshot for sensor arrays of arbitrary geometry, by extending a method of gridless super-resolution beamforming to arbitrary arrays with noisy measurements. The primal atomic norm minimization problem is converted to a dual problem in which the periodic dual function is represented with a trigonometric polynomial using truncated Fourier series. The number of terms required for accurate representation depends linearly on the distance of the farthest sensor from a reference. The dual problem is then expressed as a semidefinite program and solved in polynomial time. DOA estimates are obtained via polynomial rooting followed by a LASSO based approach to remove extraneous roots arising in root finding from noisy data, and then source amplitudes are recovered by least squares. Simulations using circular and random planar arrays show high resolution DOA estimation in white and colored noise scenarios.