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<p>Accurate direction of arrival (DOA) estimation is critical for effective source localization in radar, sonar, and wireless communication systems. However, conventional Minimum Variance Distortionless Response (MVDR) beamformers suffer significant performance degradation due to steering vector mismatches arising from DOA errors, noise uncertainty, and dynamic interference. To address these limitations, this study proposes a Robust Optimum Diagonal Loading (ODL) beamformer in which the diagonal loading factor is analytically derived from steering vector mismatch and noise variance, enabling adaptive robustness without empirical tuning. This research introduces and evaluates a Robust Optimum Diagonal Loading (ODL) beamformer to mitigate these challenges, employing a Uniform Linear Array (ULA) for a detailed comparative analysis with MVDR. The investigation encompasses a wide range of operational conditions, including array sizes from 5 to 30 elements, azimuth angle variations, noise power levels from 0.001 to 8, and DOA mismatch errors up to ± 2°. Simulation results reveal that ODL consistently surpasses MVDR by preserving high-fidelity main lobe alignment, restricting output power fluctuations to ≤ 1.8 dB, and maintaining robust Signal-to-Interference-plus-Noise Ratio (SINR) across diverse elevation, azimuth, and array scaling scenarios. Notably, ODL achieves SINR enhancements of 20–40 dB under mismatch conditions and demonstrates stability in low-noise environments where MVDR performance deteriorates. Overall, the proposed ODL beamformer provides a robust and computationally efficient framework for DOA estimation and adaptive beamforming under non-ideal operating conditions. These results establish ODL as a promising candidate for practical array signal processing applications requiring resilience to steering errors, interference, and noise uncertainty. Future research will explore the extension of ODL to wideband beamforming and the integration of data-driven techniques for real-time optimization.</p> Graphical abstract <p></p>

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Robust ODL beamformer for enhanced DOA estimation and performance comparison with MVDR

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月4日

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  • Md. Kamrul Hasan,
  • Sonia Siddiki,
  • Mohammad Ruhul Amin Bhuiyan,
  • Jubaer Ahamed Bhuiyan,
  • Hayati Mamur,
  • K. M. Fysal Kabir

摘要

Accurate direction of arrival (DOA) estimation is critical for effective source localization in radar, sonar, and wireless communication systems. However, conventional Minimum Variance Distortionless Response (MVDR) beamformers suffer significant performance degradation due to steering vector mismatches arising from DOA errors, noise uncertainty, and dynamic interference. To address these limitations, this study proposes a Robust Optimum Diagonal Loading (ODL) beamformer in which the diagonal loading factor is analytically derived from steering vector mismatch and noise variance, enabling adaptive robustness without empirical tuning. This research introduces and evaluates a Robust Optimum Diagonal Loading (ODL) beamformer to mitigate these challenges, employing a Uniform Linear Array (ULA) for a detailed comparative analysis with MVDR. The investigation encompasses a wide range of operational conditions, including array sizes from 5 to 30 elements, azimuth angle variations, noise power levels from 0.001 to 8, and DOA mismatch errors up to ± 2°. Simulation results reveal that ODL consistently surpasses MVDR by preserving high-fidelity main lobe alignment, restricting output power fluctuations to ≤ 1.8 dB, and maintaining robust Signal-to-Interference-plus-Noise Ratio (SINR) across diverse elevation, azimuth, and array scaling scenarios. Notably, ODL achieves SINR enhancements of 20–40 dB under mismatch conditions and demonstrates stability in low-noise environments where MVDR performance deteriorates. Overall, the proposed ODL beamformer provides a robust and computationally efficient framework for DOA estimation and adaptive beamforming under non-ideal operating conditions. These results establish ODL as a promising candidate for practical array signal processing applications requiring resilience to steering errors, interference, and noise uncertainty. Future research will explore the extension of ODL to wideband beamforming and the integration of data-driven techniques for real-time optimization.

Graphical abstract