Gridless Parameter Estimation in Partly Calibrated Rectangular Arrays

TL;DR

This paper introduces a gridless sparse approach for direction-of-arrival estimation in partly calibrated rectangular arrays, outperforming traditional subspace methods especially with correlated sources and sensor failures.

Contribution

It develops a novel gridless sparse formulation leveraging shift invariances, with algorithms based on ADMM and convex approximation, enhancing robustness and accuracy in challenging scenarios.

Findings

Superior error performance in highly correlated scenarios

Robustness to source correlation and sensor failures

Applicable to both partly and fully calibrated arrays

Abstract

Spatial frequency estimation from a mixture of noisy sinusoids finds applications in various fields. While subspace-based methods offer cost-effective super-resolution parameter estimation, they demand precise array calibration, posing challenges for large antennas. In contrast, sparsity-based approaches outperform subspace methods, especially in scenarios with limited snapshots or correlated sources. This study focuses on direction-of-arrival (DOA) estimation using a partly calibrated rectangular array with fully calibrated subarrays. A gridless sparse formulation leveraging shift invariances in the array is developed, yielding two competitive algorithms under the alternating direction method of multipliers (ADMM) and successive convex approximation frameworks, respectively. Numerical simulations show the superior error performance of our proposed method, particularly in highly correlated scenarios, compared to the conventional subspace-based methods. It is demonstrated that the proposed formulation can also be adopted in the fully calibrated case to improve the robustness of the subspace-based methods to the source correlation. Furthermore, we provide a generalization of the proposed method to a more challenging case where a part of the sensors is unobservable due to failures.