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Analysis of Partially-Calibrated Sparse Subarrays for Direction Finding with Extended Degrees of Freedom

W. S. Leite, R. C. de Lamare

TL;DR

This work extends coarray MUSIC to partially calibrated sparse arrays by introducing GCA-MUSIC, which leverages per-subarray difference coarrays and a subspace-intersection spectrum merging rule to exploit increased degrees of freedom. By combining SS-SCA-based processing with a convex-set projection that aligns the subspaces across subarrays, the method can identify more sources than physical sensors and maintain high-resolution DOA estimation. Comparisons against G-MUSIC and AVCA-MUSIC show substantial RMSE improvements, particularly when the source count exceeds per-subarray sensor counts, with performance benefiting most from geometry choices that maximize DoF. The approach offers a practical pathway to high-resolution DOA estimation in distributed or asynchronous sensing platforms while reducing inter-subarray cross-covariance requirements.

Abstract

This paper investigates the problem of direction-of-arrival (DOA) estimation using multiple partially-calibrated sparse subarrays. In particular, we present the Generalized Coarray Multiple Signal Classification (GCA-MUSIC) DOA estimation algorithm to scenarios with partially-calibrated sparse subarrays. The proposed GCA-MUSIC algorithm exploits the difference coarray for each subarray, followed by a specific pseudo-spectrum merging rule that is based on the intersection of the signal subspaces associated to each subarray. This rule assumes that there is no a priori knowledge about the cross-covariance between subarrays. In that way, only the second-order statistics of each subarray are used to estimate the directions with increased degrees of freedom, i.e., the estimation procedure preserves the coarray Multiple Signal Classification and sparse arrays properties to estimate more sources than the number of physical sensors in each subarray. Numerical simulations show that the proposed GCA-MUSIC has better performance than other similar strategies.

Analysis of Partially-Calibrated Sparse Subarrays for Direction Finding with Extended Degrees of Freedom

TL;DR

This work extends coarray MUSIC to partially calibrated sparse arrays by introducing GCA-MUSIC, which leverages per-subarray difference coarrays and a subspace-intersection spectrum merging rule to exploit increased degrees of freedom. By combining SS-SCA-based processing with a convex-set projection that aligns the subspaces across subarrays, the method can identify more sources than physical sensors and maintain high-resolution DOA estimation. Comparisons against G-MUSIC and AVCA-MUSIC show substantial RMSE improvements, particularly when the source count exceeds per-subarray sensor counts, with performance benefiting most from geometry choices that maximize DoF. The approach offers a practical pathway to high-resolution DOA estimation in distributed or asynchronous sensing platforms while reducing inter-subarray cross-covariance requirements.

Abstract

This paper investigates the problem of direction-of-arrival (DOA) estimation using multiple partially-calibrated sparse subarrays. In particular, we present the Generalized Coarray Multiple Signal Classification (GCA-MUSIC) DOA estimation algorithm to scenarios with partially-calibrated sparse subarrays. The proposed GCA-MUSIC algorithm exploits the difference coarray for each subarray, followed by a specific pseudo-spectrum merging rule that is based on the intersection of the signal subspaces associated to each subarray. This rule assumes that there is no a priori knowledge about the cross-covariance between subarrays. In that way, only the second-order statistics of each subarray are used to estimate the directions with increased degrees of freedom, i.e., the estimation procedure preserves the coarray Multiple Signal Classification and sparse arrays properties to estimate more sources than the number of physical sensors in each subarray. Numerical simulations show that the proposed GCA-MUSIC has better performance than other similar strategies.
Paper Structure (9 sections, 9 equations, 5 figures)

This paper contains 9 sections, 9 equations, 5 figures.

Table of Contents

  1. Introduction
  2. System Model and Problem Statement
  3. Proposed GCA-MUSIC DOA Estimation Method
  4. Type-II Sparse Linear Arrays
  5. Coarray MUSIC with Sparse Subarrays
  6. Simulation
  7. Arrays and subarrays characterization
  8. GCA-MUSIC performance comparison
  9. Conclusion

Figures (5)

  • Figure 1: Weight functions for Type-II arrays with $L=3$ subarrays and $N=7$ sensors each.
  • Figure 2: Weight functions for each SpSub and the associated SCA with $N=7$ sensors.
  • Figure 3: RMSE performance curves against SNR for Type-II NAQ2 array. $\text{T}=100$ snapshots. $D=6$ sources located at $\boldsymbol{\mathbf{\theta}}=[-0.7,-0.5,-0.3,0.3,0.5,0.7]$.
  • Figure 4: RMSE performance curves against SNR for GCA-MUSIC with four geometries: ULA, NAQ2, SNAQ2, and MRA. $\text{T}=100$ snapshots. $D=6$ sources located at $\boldsymbol{\mathbf{\theta}}=[-0.7,-0.5,-0.3,0.3,0.5,0.7]$.
  • Figure 5: RMSE performance curves against SNR for Type-II NAQ2 array. $\text{T}=100$ snapshots. $D=6$ sources located at $\boldsymbol{\mathbf{\theta}}=[-0.7,-0.5,-0.3,0,0.3,0.5,0.7]$.

Theorems & Definitions (3)

  • Definition 1: Sparse Subarray (SpSub)
  • Definition 2: Subcoarray (SCA)
  • Definition 3: Spatially Smoothed Subcoarray (SS-SCA)