Conjugate Augmented Covariance Fitting-Based Parameter Estimation for Sparse Polarimetric Array

Parameter estimation using sparse polarimetric arrays offers functional advantages, such as the capability of joint direction-of-arrival and polarization estimation, compared to state-of-the-art approaches using sparse scalar arrays. However, most existing research on parameter estimation using sparse polarimetric arrays only considers statistical information in the covariance domain. In reality, the statistical information in the conjugate augmented covariance (CAC) domain plays an important role in enhancing degrees-of-freedom (DoFs) and estimation accuracy, especially in the presence of widely encountered uncorrelated noncircular impinging sources. To fully leverage the CAC, a unified framework encompassing sparse polarimetric array design, CAC fitting (CACF) in the joint spatial and polarimetric domain, and closed-form multi-parameter estimation is presented with low computational complexity via eliminating the need for multi-dimensional spectral searching procedures. The proposed sparse polarimetric array achieves increased DoFs provided by leveraging both <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sum</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">difference</i> co-arrays, compared to its counterpart that utilizes only the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">difference</i> co-array. It features both <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sum</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">difference</i> hole-free co-arrays, distinguishing it from most existing designs and enabling effective support for practical parameter estimation scenarios involving a mixture of circular and noncircular signals. It is also easy to implement and requires less electromagnetic isolation. The CACF and its associated closed-form multi-parameter estimation approaches require no iterative, pair matching, or spectral searching procedures, implying great potential in reducing computational complexity. Numerical simulation examples are provided to verify the advantages of the proposed framework, including less mutual coupling effects, enhanced DoFs, effectiveness for different signal cases, and improved estimation performance.