Shrinkage estimators of large covariance matrices with Toeplitz targets in array signal processing

Area of Science:

• Statistics
• Statistical Signal Processing

Background:

• Estimating large covariance matrices is crucial in many statistical fields.
• Existing methods may struggle with high-dimensional data and specific matrix structures.

Purpose of the Study:

• To develop new, robust covariance matrix estimators using shrinkage regularization.
• To address the challenge of estimating large covariance matrices with Toeplitz structures.

Main Methods:

• Developed shrinkage regularization techniques for covariance matrix estimation.
• Derived optimal tuning parameters under the mean squared error criterion for complex Gaussian distributions.
• Utilized properties of the complex Wishart distribution to simplify parameters.

Main Results:

• Proposed two novel shrinkage estimators for large-dimensional covariance matrices.
• Derived closed-form optimal tuning parameters by analyzing Toeplitz-structured target matrices.
• Demonstrated the effectiveness of the proposed estimators through simulations and array signal processing applications.

Conclusions:

• The new shrinkage estimators provide a valuable tool for large-dimensional covariance matrix estimation.
• The derived optimal tuning parameters enhance the accuracy and efficiency of the estimation process.
• The proposed methods show competitive performance compared to existing techniques in relevant applications.