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Study of Robust Direction Finding Based on Joint Sparse Representation

Y. Li, W. Xiao, L. Zhao, Z. Huang, Q. Li, L. Li, R. C. de Lamare

TL;DR

This work tackles robust direction-of-arrival estimation in the presence of impulsive noise by modeling disturbances as Gaussian noise plus sparse outliers and formulating a sparse recovery problem. It introduces the Minimax Logarithmic Concave (MLC) sparsity prior and an on-grid/off-grid framework solved with ADMM, enabling simultaneous handling of outliers and grid mismatch. The method demonstrates improved RMSE over several robust baselines across varying SNRs, snapshot counts, and outlier probabilities, including coherent-source cases. The approach offers practical robustness for radar and wireless applications where impulsive disturbances and model mismatch are common, by delivering accurate DOA estimates alongside a refined off-grid correction.

Abstract

Standard Direction of Arrival (DOA) estimation methods are typically derived based on the Gaussian noise assumption, making them highly sensitive to outliers. Therefore, in the presence of impulsive noise, the performance of these methods may significantly deteriorate. In this paper, we model impulsive noise as Gaussian noise mixed with sparse outliers. By exploiting their statistical differences, we propose a novel DOA estimation method based on sparse signal recovery (SSR). Furthermore, to address the issue of grid mismatch, we utilize an alternating optimization approach that relies on the estimated outlier matrix and the on-grid DOA estimates to obtain the off-grid DOA estimates. Simulation results demonstrate that the proposed method exhibits robustness against large outliers.

Study of Robust Direction Finding Based on Joint Sparse Representation

TL;DR

This work tackles robust direction-of-arrival estimation in the presence of impulsive noise by modeling disturbances as Gaussian noise plus sparse outliers and formulating a sparse recovery problem. It introduces the Minimax Logarithmic Concave (MLC) sparsity prior and an on-grid/off-grid framework solved with ADMM, enabling simultaneous handling of outliers and grid mismatch. The method demonstrates improved RMSE over several robust baselines across varying SNRs, snapshot counts, and outlier probabilities, including coherent-source cases. The approach offers practical robustness for radar and wireless applications where impulsive disturbances and model mismatch are common, by delivering accurate DOA estimates alongside a refined off-grid correction.

Abstract

Standard Direction of Arrival (DOA) estimation methods are typically derived based on the Gaussian noise assumption, making them highly sensitive to outliers. Therefore, in the presence of impulsive noise, the performance of these methods may significantly deteriorate. In this paper, we model impulsive noise as Gaussian noise mixed with sparse outliers. By exploiting their statistical differences, we propose a novel DOA estimation method based on sparse signal recovery (SSR). Furthermore, to address the issue of grid mismatch, we utilize an alternating optimization approach that relies on the estimated outlier matrix and the on-grid DOA estimates to obtain the off-grid DOA estimates. Simulation results demonstrate that the proposed method exhibits robustness against large outliers.
Paper Structure (8 sections, 2 theorems, 26 equations, 4 figures, 2 algorithms)

This paper contains 8 sections, 2 theorems, 26 equations, 4 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Signal Model
  3. Proposed DOA Estimation Algorithm
  4. Minimax Logarithmic Concave Function
  5. On-Grid Model
  6. Off-Grid Gap Estimation
  7. Simulation Results
  8. Conclusions

Key Result

Lemma 1

For $\lambda>0$, $\gamma>0$, $\eta>0$, the function $\phi(\textit{x}):\mathbb{C} \rightarrow \mathbb{R}^{+}$ is equivalent to the optimal solution of the following optimization problem: where

Figures (4)

  • Figure 1: Sparsity-inducing functions. Here $\lambda=1$, $\gamma=2$, $\eta=0.4$ for MLC; $\lambda=1$, $\gamma=2$ for MC.
  • Figure 2: RMSE of uncorrelated DOA estimates for (left) different SNR and for (right) different number of snapshots, with $M=10$ and $p=0.1$.
  • Figure 3: RMSE of uncorrelated DOA estimates for (left) different outlier probability ($p$) and (right) for different angular separation, with SNR = 10dB and $T$ = 30.
  • Figure 4: RMSE of coherent DOA estimates for different SNR.

Theorems & Definitions (2)

  • Lemma 1
  • Lemma 2