Mutual Coupling Array Calibration Utilizing Decomposition of Modeled Scattering Matrix

Modern phased-array antenna calibration is essential for advanced radar systems to achieve precise beamforming, sidelobe control, and coherent processing. While mutual coupling-based calibration provides a valuable internal alternative to external far-field references by exploiting near-field element interactions, the problem is fundamentally ill-posed. Measured responses depend simultaneously on transmit coefficients, receive coefficients, and the coupling matrix, making it difficult to isolate true channel errors from array-model mismatch without additional structure.

This thesis presents a Bayesian Maximum A Posteriori (MAP) calibration framework that resolves this ambiguity by embedding physically motivated prior information into the estimation problem. The nominal coupling matrix is decomposed into Infinite, Symmetric, and Reciprocal components, which define low-dimensional parameterizations and prior covariance models. A Maximum Likelihood (ML) stage first generates a data-consistent transceiver initialization, followed by a MAP estimator that refines the solution by jointly addressing structured coupling deviations and measurement uncertainty.

Evaluations using Computational Electromagnetic (CEM) models and measured WaDES array data reveal that the physical array contains more higher-order structural content than the nominal CEM model. Across Monte Carlo trials, highly structured MAP estimators generally achieve lower aggregate error than unconstrained ML and Log Least Squares (LLS) methods. The overlapping-subspace M family offers an optimal balance of structural flexibility, zero-centered phase and magnitude behavior, and tuning robustness. Additionally, parametric sweeps highlight that prior covariance scaling is a critical design parameter: tight reciprocal priors prevent spurious structural absorption, whereas overly loose priors allow model mismatch to contaminate transceiver estimates.

Ultimately, this work demonstrates that internal mutual coupling calibration can achieve autonomy and robustness against model mismatch by parameterizing the nominal coupling matrix into structured components and integrating them as Bayesian priors.