Direction-of-arrival (DOA) estimation under low signal-to-noise ratio (SNR), limited snapshots, and strong interference remains a fundamental challenge in array signal processing. This paper proposes a multi-constraint covariance matrix reconstruction framework that simultaneously exploits three complementary structural properties of uniform linear array covariance matrices: Hermitian Toeplitz structure, low-rank signal subspace, and sparse interference patterns. An adaptive alternating direction method of multipliers algorithm with provable O(1/k) convergence rate is developed, incorporating robust Toeplitz projection via Huber M-estimation and position-adaptive sparse weights. Comprehensive Monte Carlo simulations (500 trials) demonstrate statistically significant improvements over nine baseline methods: 38% root-mean-square error reduction versus MUSIC at <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$-10$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <mn>10</mn> </mrow> </math></EquationSource> </InlineEquation> dB SNR (Cohen’s <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$d = 1.6$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>=</mo> <mn>1.6</mn> </mrow> </math></EquationSource> </InlineEquation>), 72% resolution probability at <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$5^\circ $</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>5</mn> <mo>∘</mo> </msup> </math></EquationSource> </InlineEquation> sub-Rayleigh separation, and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$O(M^3)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo stretchy="false">(</mo> <msup> <mi>M</mi> <mn>3</mn> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> per-iteration complexity with 187 ms average runtime. Ablation analysis confirms synergistic constraint contributions (Toeplitz: 48%, low-rank: 33%, sparse: 19%), validating non-redundant operation on orthogonal problem aspects. The proposed framework advances covariance-based DOA estimation through rigorous theoretical foundations and comprehensive empirical validation.

High-Resolution DOA Estimation for Multi-constrained Covariance Matrix Reconstruction

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发表日期：

2026年3月26日

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Xiaohong Huang,
Jiayu Cao,
Zhao Zhang

摘要

Direction-of-arrival (DOA) estimation under low signal-to-noise ratio (SNR), limited snapshots, and strong interference remains a fundamental challenge in array signal processing. This paper proposes a multi-constraint covariance matrix reconstruction framework that simultaneously exploits three complementary structural properties of uniform linear array covariance matrices: Hermitian Toeplitz structure, low-rank signal subspace, and sparse interference patterns. An adaptive alternating direction method of multipliers algorithm with provable O(1/k) convergence rate is developed, incorporating robust Toeplitz projection via Huber M-estimation and position-adaptive sparse weights. Comprehensive Monte Carlo simulations (500 trials) demonstrate statistically significant improvements over nine baseline methods: 38% root-mean-square error reduction versus MUSIC at $-10$ $- 10$ dB SNR (Cohen’s $d = 1.6$ $d = 1.6$ ), 72% resolution probability at $5^\circ $ $5^{\circ}$ sub-Rayleigh separation, and $O(M^3)$ $O (M^{3})$ per-iteration complexity with 187 ms average runtime. Ablation analysis confirms synergistic constraint contributions (Toeplitz: 48%, low-rank: 33%, sparse: 19%), validating non-redundant operation on orthogonal problem aspects. The proposed framework advances covariance-based DOA estimation through rigorous theoretical foundations and comprehensive empirical validation.