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Direction-of-Arrival and Noise Covariance Matrix joint estimation for beamforming

Vitor Gelsleichter Probst Curtarelli, Stephan Paul, Anderson Wedderhoff Spengler

TL;DR

This work addresses the joint estimation of the Noise Covariance Matrix (NCM) and the Direction-of-Arrival (DoA) of an interfering source to improve beamforming in reverberant environments. It introduces a broadband cost function and a quasi-linear variance estimation that replace exhaustive searches, enabling DoA estimation across all frequency bins and robust NCM characterization. The method yields accurate DoA estimates and, when integrated into an LCMV beamformer, achieves superior interference suppression and reduced distortion of the desired signal compared to MUSIC-based approaches. Simulations across diverse room conditions and sensor configurations demonstrate robustness and practical gains for real-time signal enhancement and tracking with minimal reliance on voice-activity detectors.

Abstract

We propose a joint estimation method for the Direction-of-Arrival (DoA) and the Noise Covariance Matrix (NCM) tailored for beamforming applications. Building upon an existing NCM framework, our approach simplifies the estimation procedure by deriving an quasi-linear solution, instead of the traditional exhaustive search. Additionally, we introduce a novel DoA estimation technique that operates across all frequency bins, improving robustness in reverberant environments. Simulation results demonstrate that our method outperforms classical techniques, such as MUSIC, in mid- to high-angle scenarios, achieving lower angular errors and superior signal enhancement through beamforming. The proposed framework was also fared against other techniques for signal enhancement, having better noise rejection and interference canceling capabilities. These improvements are validated using both theoretical and empirical performance metrics.

Direction-of-Arrival and Noise Covariance Matrix joint estimation for beamforming

TL;DR

This work addresses the joint estimation of the Noise Covariance Matrix (NCM) and the Direction-of-Arrival (DoA) of an interfering source to improve beamforming in reverberant environments. It introduces a broadband cost function and a quasi-linear variance estimation that replace exhaustive searches, enabling DoA estimation across all frequency bins and robust NCM characterization. The method yields accurate DoA estimates and, when integrated into an LCMV beamformer, achieves superior interference suppression and reduced distortion of the desired signal compared to MUSIC-based approaches. Simulations across diverse room conditions and sensor configurations demonstrate robustness and practical gains for real-time signal enhancement and tracking with minimal reliance on voice-activity detectors.

Abstract

We propose a joint estimation method for the Direction-of-Arrival (DoA) and the Noise Covariance Matrix (NCM) tailored for beamforming applications. Building upon an existing NCM framework, our approach simplifies the estimation procedure by deriving an quasi-linear solution, instead of the traditional exhaustive search. Additionally, we introduce a novel DoA estimation technique that operates across all frequency bins, improving robustness in reverberant environments. Simulation results demonstrate that our method outperforms classical techniques, such as MUSIC, in mid- to high-angle scenarios, achieving lower angular errors and superior signal enhancement through beamforming. The proposed framework was also fared against other techniques for signal enhancement, having better noise rejection and interference canceling capabilities. These improvements are validated using both theoretical and empirical performance metrics.

Paper Structure

This paper contains 33 sections, 2 theorems, 28 equations, 6 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Signal model
  3. Observed signal covariance matrix modeling
  4. DoA and NCM estimation
  5. Variances estimation
  6. Unconstrained solution
  7. Constrained solution
  8. DoA estimation
  9. General approximation
  10. Planar and linear arrays
  11. Minimization scheme
  12. Proposed model's features
  13. Filtering and Beamforming
  14. NCM+DoA exploiting filters
  15. Full-framework outline
  16. ...and 18 more sections

Key Result

theorem 1

If the global minimum isn't in the feasible region, the constrained minimum lies in its boundary.[] We assume that $\boldsymbol{\mathrm{\upsigma}} [n] ^\dagger > \boldsymbol{\mathrm{0}} [n]$, strictly greater; that is, the constrained minimum isn't on the boundary where some entries are $0$. Thr with Note that $A > 0$, indicating that $J(t)$ is a positively-curved quadratic function in $t$. B

Figures (6)

  • Figure 1: Example of room layout, with: desired (green pentagon), interfering (yellow triangle), and correlated (blue diamond) sources; direct-path (opaque, with the color of the respective source) and reverberations (translucent gray arrows); and a sensor array (red rectangle), with sensors represented by small circles.
  • Figure 2: Proposed NCM-DoA estimation technique + filtering scheme flowchart.
  • Figure 3: Angle prediction error statistics (boxplots), for parameters in \ref{['tab:sec5:simulation_parameters']}.
  • Figure 4: Angle prediction error statistics (boxplots), for situations with invalid assumptions.
  • Figure 5: Global angle prediction error statistics, for each considered situation (base case, eccentric array, and transposed voice types), with simplified parameter set.
  • ...and 1 more figures

Theorems & Definitions (2)

  • theorem 1
  • theorem 2