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High-Dimensional MVDR Beamforming: Optimized Solutions Based on Spiked Random Matrix Models

Author

Listed:
  • Liusha Yang

    (UniVersity, Nano Science and Technology Program, Department of Chemistry, The Hong Kong UniVersity of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, - HKUST - Hong Kong University of Science and Technology)

  • Matthew R. Mckay

    (ECE - Electronic and Computer Engineering Department [Hong Kong] - HKUST - Hong Kong University of Science and Technology)

  • Romain Couillet

    (L2S - Laboratoire des signaux et systèmes - UP11 - Université Paris-Sud - Paris 11 - CentraleSupélec - CNRS - Centre National de la Recherche Scientifique)

Abstract

Minimum variance distortionless response (MVDR) beamforming (or Capon beamforming) is among the most popular adaptive array processing strategies due to its ability to provide noise resilience while nulling out interferers. A practical challenge with this beamformer is that it involves the inverse covariance matrix of the received signals, which must be estimated from data. Under modern high-dimensional applications, it is well known that classical estimators can be severely affected by sampling noise, which compromises beamformer performance. Here, we propose a new approach to MVDR beamforming, which is suited to high-dimensional settings. In particular, by drawing an analogy with the MVDR problem and the so-called "spiked models" in random matrix theory, we propose robust beamforming solutions that are shown to outperform classical approaches (e.g., matched filters and sample matrix inversion techniques), as well as more robust solutions, such as methods based on diagonal loading. The key to our method is the design of an optimized inverse covariance estimator, which applies eigenvalue clipping and shrinkage functions that are tailored to the MVDR application. Our proposed MVDR solution is simple, in closed form, and easy to implement.

Suggested Citation

  • Liusha Yang & Matthew R. Mckay & Romain Couillet, 2018. "High-Dimensional MVDR Beamforming: Optimized Solutions Based on Spiked Random Matrix Models," Post-Print hal-01957672, HAL.
  • Handle: RePEc:hal:journl:hal-01957672
    DOI: 10.1109/tsp.2018.2799183
    Note: View the original document on HAL open archive server: https://hal.science/hal-01957672
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    References listed on IDEAS

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    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Johnstone, Iain M. & Lu, Arthur Yu, 2009. "On Consistency and Sparsity for Principal Components Analysis in High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 682-693.
    3. Couillet, Romain & McKay, Matthew, 2014. "Large dimensional analysis and optimization of robust shrinkage covariance matrix estimators," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 99-120.
    4. Ledoit, Olivier & Wolf, Michael, 2015. "Spectrum estimation: A unified framework for covariance matrix estimation and PCA in large dimensions," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 360-384.
    5. Liusha Yang & Romain Couillet & Matthew R. McKay, 2015. "A Robust Statistics Approach to Minimum Variance Portfolio Optimization," Papers 1503.08013, arXiv.org.
    6. Pafka, Szilárd & Kondor, Imre, 2003. "Noisy covariance matrices and portfolio optimization II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 487-494.
    7. Gabor Papp & Szilard Pafka & Maciej A. Nowak & Imre Kondor, 2005. "Random Matrix Filtering in Portfolio Optimization," Papers physics/0509235, arXiv.org.
    8. Michael J. Daniels & Robert E. Kass, 2001. "Shrinkage Estimators for Covariance Matrices," Biometrics, The International Biometric Society, vol. 57(4), pages 1173-1184, December.
    9. Baik, Jinho & Silverstein, Jack W., 2006. "Eigenvalues of large sample covariance matrices of spiked population models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1382-1408, July.
    10. Couillet, Romain, 2015. "Robust spiked random matrices and a robust G-MUSIC estimator," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 139-161.
    11. Damien Passemier & Zhaoyuan Li & Jianfeng Yao, 2017. "On estimation of the noise variance in high dimensional probabilistic principal component analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 51-67, January.
    12. Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
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    Cited by:

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    2. Taras Bodnar & Solomiia Dmytriv & Yarema Okhrin & Nestor Parolya & Wolfgang Schmid, 2020. "Statistical inference for the EU portfolio in high dimensions," Papers 2005.04761, arXiv.org.
    3. Nguyen, An Pham Ngoc & Mai, Tai Tan & Bezbradica, Marija & Crane, Martin, 2023. "Volatility and returns connectedness in cryptocurrency markets: Insights from graph-based methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).

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