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Single-Snapshot Gridless 2D-DoA Estimation for UCAs: A Joint Optimization Approach

Salar Nouri

TL;DR

This work addresses single-snapshot gridless 2D-DOA estimation for Uniform Circular Arrays by formulating a unified optimization that jointly designs a data-adaptive transformation $\mathbf{T}$ and estimates azimuth-elevation pairs $(\theta_k,\phi_k)$. An iALM-based solver avoids SDP by reformulating the atomic norm via a Burer–Monteiro factorization and enforcing semi-infinite manifold constraints through a tractable CAD-like structure, solved with block coordinate descent. The method demonstrates superior accuracy and resolution in simulations against 2D-MUSIC and grid-based Lasso, while maintaining practical runtimes, particularly in challenging low-SNR and closely spaced-source scenarios. The JADE approach offers a robust, gridless framework for single-shot array processing, with potential extensions to other geometries and wider bandwidths.

Abstract

This paper tackles the challenging problem of gridless two-dimensional (2D) direction-of-arrival (DOA) estimation for a uniform circular array (UCA) from a single snapshot of data. Conventional gridless methods often fail in this scenario due to prohibitive computational costs or a lack of robustness. We propose a novel framework that overcomes these limitations by jointly estimating a manifold transformation matrix and the source azimuth-elevation pairs within a single, unified optimization problem. This problem is solved efficiently using an inexact Augmented Lagrangian Method (iALM), which completely circumvents the need for semidefinite programming. By unifying the objectives of data fidelity and transformation robustness, our approach is uniquely suited for the demanding single-snapshot case. Simulation results confirm that the proposed iALM framework provides robust and high-resolution, gridless 2D-DOA estimates, establishing its efficacy for challenging array signal processing applications.

Single-Snapshot Gridless 2D-DoA Estimation for UCAs: A Joint Optimization Approach

TL;DR

This work addresses single-snapshot gridless 2D-DOA estimation for Uniform Circular Arrays by formulating a unified optimization that jointly designs a data-adaptive transformation and estimates azimuth-elevation pairs . An iALM-based solver avoids SDP by reformulating the atomic norm via a Burer–Monteiro factorization and enforcing semi-infinite manifold constraints through a tractable CAD-like structure, solved with block coordinate descent. The method demonstrates superior accuracy and resolution in simulations against 2D-MUSIC and grid-based Lasso, while maintaining practical runtimes, particularly in challenging low-SNR and closely spaced-source scenarios. The JADE approach offers a robust, gridless framework for single-shot array processing, with potential extensions to other geometries and wider bandwidths.

Abstract

This paper tackles the challenging problem of gridless two-dimensional (2D) direction-of-arrival (DOA) estimation for a uniform circular array (UCA) from a single snapshot of data. Conventional gridless methods often fail in this scenario due to prohibitive computational costs or a lack of robustness. We propose a novel framework that overcomes these limitations by jointly estimating a manifold transformation matrix and the source azimuth-elevation pairs within a single, unified optimization problem. This problem is solved efficiently using an inexact Augmented Lagrangian Method (iALM), which completely circumvents the need for semidefinite programming. By unifying the objectives of data fidelity and transformation robustness, our approach is uniquely suited for the demanding single-snapshot case. Simulation results confirm that the proposed iALM framework provides robust and high-resolution, gridless 2D-DOA estimates, establishing its efficacy for challenging array signal processing applications.
Paper Structure (18 sections, 9 equations, 1 figure, 1 table, 1 algorithm)

This paper contains 18 sections, 9 equations, 1 figure, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. 2D System and Single-Snapshot Signal Model
  4. Problem Formulation
  5. Preliminaries for Joint Transformation and Estimation
  6. Proposed Methodology: A Unified Framework
  7. The Unified Optimization Problem
  8. Tractable Reformulation for the Solver
  9. Reformulating the Atomic Norm
  10. Final Problem Structure
  11. Primal Subproblem Solution via Block Coordinate Descent
  12. Algorithm Convergence
  13. Computational Complexity Analysis
  14. Numerical Results
  15. Simulation Setup
  16. ...and 3 more sections

Figures (1)

  • Figure 1: Performance evaluation of the proposed JADE- framework. (a) vs. , showing superior accuracy. (b) Scatter plot of estimates for two close sources, demonstrating high resolution. (c) Convergence of the objective and feasibility gap.