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A discretization-free sparse and parametric approach for linear array signal processing (1312.7695v2)

Published 30 Dec 2013 in cs.IT and math.IT

Abstract: Direction of arrival (DOA) estimation in array processing using uniform/sparse linear arrays is concerned in this paper. While sparse methods via approximate parameter discretization have been popular in the past decade, the discretization may cause problems, e.g., modeling error and increased computations due to dense sampling. In this paper, an exact discretization-free method, named as sparse and parametric approach (SPA), is proposed for uniform and sparse linear arrays. SPA carries out parameter estimation in the continuous range based on well-established covariance fitting criteria and convex optimization. It guarantees to produce a sparse parameter estimate without discretization required by existing sparse methods. Theoretical analysis shows that the SPA parameter estimator is a large-snapshot realization of the maximum likelihood estimator and is statistically consistent (in the number of snapshots) under uncorrelated sources. Other merits of SPA include improved resolution, applicability to arbitrary number of snapshots, robustness to correlation of the sources and no requirement of user-parameters. Numerical simulations are carried out to verify our analysis and demonstrate advantages of SPA compared to existing methods.

Citations (169)

Summary

  • The paper introduces a discretization-free Sparse and Parametric Approach (SPA) for direction of arrival (DOA) estimation in linear arrays, eliminating limitations of grid-based methods.
  • SPA uses covariance fitting and convex optimization to operate in a continuous parameter space, demonstrating superior resolution and statistical properties compared to existing methods in simulations.
  • This robust method handles source correlation and low SNR, offering potential for improved DOA estimation in applications like radar, sonar, and wireless communications without requiring user-defined parameters.

Discretization-Free Sparse and Parametric Approach for Linear Array Signal Processing

The paper presents an innovative method for direction of arrival (DOA) estimation in array signal processing, addressing the limitations associated with discretization-based sparse methods. The authors introduce a discretization-free method known as the Sparse and Parametric Approach (SPA) for both uniform linear arrays (ULAs) and sparse linear arrays (SLAs). SPA uses covariance fitting criteria and convex optimization to operate in a continuous parameter space, significantly improving accuracy without the constraints associated with traditional grid-based methods.

Key Contributions and Methodology

The core of SPA is its discretization-free nature, which eliminates modeling errors and computational overhead caused by dense grid sampling. SPA operates by estimating parameters in a continuous range using established covariance fitting criteria, circumventing the need for a discretization grid. This is accomplished through convex optimization, enabling a sparse parameter estimate that avoids the approximation errors typical in previous sparse methods relying on parameter discretization.

The SPA method differentiates itself by ensuring that the parameter estimates are sparse and statistically consistent in the scenario of uncorrelated source signals. Theoretical analysis confirms that the SPA estimator aligns with the maximum likelihood estimator in large-snapshot scenarios and maintains consistency across varying numbers of snapshots. Additionally, its robustness to source correlation and independence from user-defined parameters enhance both practicality and applicability.

The proposed method is proven advantageous through numerical simulations as compared to existing methodologies, such as SPICE, IAA, MUSIC, and OGSBI-SVD. The simulations demonstrate SPA's superior resolution capabilities and statistical properties, particularly in scenarios involving low signal-to-noise ratios (SNRs) and coherent signals.

Practical and Theoretical Implications

The implications of SPA extend to various fields requiring precise DOA estimation, offering a reliable tool for applications in radar, sonar, and wireless communications. SPA’s robust performance in low SNR and its ability to handle coherent sources suggest its potential in environments with significant noise interference. The absence of requirement for user parameters simplifies deployment in real-world scenarios, reducing the need for expert calibration.

Future Directions

The paper suggests several avenues for future research, including the exploration of SPA extensions to general array geometries and the development of model order selection techniques within SPA to estimate source numbers automatically. Furthermore, the paper notes the potential benefits of gridless methods in spectral analysis and proposes examining connections between SPA and atomic norm-based methods.

In summary, the discretization-free SPA offers significant advances in linear array signal processing by addressing key limitations of existing methods, enhancing both resolution and consistency, and paving the way for richer analyses and applications.