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Study of Noncoherent Sparse Subarrays for Direction Finding Based on Low-Rank and Sparse Recovery

W. Leite, R. C. de Lamare

TL;DR

This work addresses noncoherent direction-of-arrival estimation using sparse subarrays by formulating a MMV problem that leverages low-rank and sparse recovery across multiple snapshots. It extends a convex optimization approach to the MMV setting, solving for a rank-one factor that yields sparse DOA support on a grid, and constructs DOA estimates from the resulting proxy spectra. The paper introduces two array designs, Type-I (split from a predefined sparse geometry) and Type-II (unions of translated subarrays), proving via DoF analysis and simulations that Type-II offers superior DOA performance for noncoherent processing. The approach demonstrates the benefit of multi-record data and sparse-array geometry in improving DOA accuracy, with practical implications for compressive sensing-based sensing arrays and calibrated subarray design.

Abstract

This paper investigates the problem of noncoherent direction-of-arrival (DOA) estimation using different sparse subarrays. In particular, we present a Multiple Measurements Vector (MMV) model for noncoherent DOA estimation based on a low-rank and sparse recovery optimization problem. Moreover, we develop two different practical strategies to obtain sparse arrays and subarrays: i) the subarrays are generated from a main sparse array geometry (Type-I sparse array), and ii) the sparse subarrays that are directly designed and grouped together to generate the whole sparse array (Type-II sparse array). Numerical results demonstrate that the proposed MMV model can benefit from multiple data records and that Type-II sparse noncoherent arrays are superior in performance for DOA estimation

Study of Noncoherent Sparse Subarrays for Direction Finding Based on Low-Rank and Sparse Recovery

TL;DR

This work addresses noncoherent direction-of-arrival estimation using sparse subarrays by formulating a MMV problem that leverages low-rank and sparse recovery across multiple snapshots. It extends a convex optimization approach to the MMV setting, solving for a rank-one factor that yields sparse DOA support on a grid, and constructs DOA estimates from the resulting proxy spectra. The paper introduces two array designs, Type-I (split from a predefined sparse geometry) and Type-II (unions of translated subarrays), proving via DoF analysis and simulations that Type-II offers superior DOA performance for noncoherent processing. The approach demonstrates the benefit of multi-record data and sparse-array geometry in improving DOA accuracy, with practical implications for compressive sensing-based sensing arrays and calibrated subarray design.

Abstract

This paper investigates the problem of noncoherent direction-of-arrival (DOA) estimation using different sparse subarrays. In particular, we present a Multiple Measurements Vector (MMV) model for noncoherent DOA estimation based on a low-rank and sparse recovery optimization problem. Moreover, we develop two different practical strategies to obtain sparse arrays and subarrays: i) the subarrays are generated from a main sparse array geometry (Type-I sparse array), and ii) the sparse subarrays that are directly designed and grouped together to generate the whole sparse array (Type-II sparse array). Numerical results demonstrate that the proposed MMV model can benefit from multiple data records and that Type-II sparse noncoherent arrays are superior in performance for DOA estimation
Paper Structure (10 sections, 1 theorem, 15 equations, 3 figures, 1 algorithm)

This paper contains 10 sections, 1 theorem, 15 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Statement
  3. Proposed DOA Estimation Method
  4. Sparse and low-rank recovery with multiple snapshots
  5. Type-I and Type-II array geometries
  6. Analysis of manifold structure and degrees of freedom
  7. Type-I
  8. Type-II
  9. Simulation
  10. Conclusion

Key Result

Theorem 1

Consider a Type-II array with geometry as defined in Definition def:IISLA with equal-aperture subarrays. If $1\leq \mu \leq \kappa$, then the number of DoF of the array $\mathbb{S}$ is upper-bounded by $L(\text{sDoF}-1)+2(L-1)\mu+1$, where sDoF is the number of DoF for each subarray. If $\mu>\kappa$ The number of DoF is the cardinality of the support of $w(n)$. This support set has always an odd n

Figures (3)

  • Figure 1: Beampattern for Type-I and Type-II arrays.
  • Figure 2: RMSE performance curves against SNR for Type-I and Type-II arrays. $T=10$ snapshots. $D=5$ sources located at $\theta=[0,0.2,0.4,0.6,0.8]$.
  • Figure 3: RMSE performance curves against snapshots for Type-I and Type-II arrays. $\text{SNR}=10$ dB. $D=5$ sources located at $\theta=[0,0.2,0.4,0.6,0.8]$.

Theorems & Definitions (3)

  • Definition 1: Type-I Sparse Linear Array
  • Definition 2: Type-II Sparse Linear Array
  • Theorem 1