Linking Dispersive-Medium Uncertainty to Clutter Analysis in Single-Snapshot FDA-MIMO-GPR

This paper addresses the modeling gap between complex dispersive-medium characterization and clutter statistical analysis in single-snapshot frequency diverse array multiple-input multiple-output ground-penetrating radar (FDA-MIMO-GPR). Existing FDA-MIMO clutter studies have rarely incorporated subsurface dispersion, dissipation, and random inhomogeneity in an explicit statistical framework. To bridge this gap, a continuous relaxation spectrum is adopted to describe complex media, and a statistical propagation chain is established from random relaxation-spectrum perturbations to complex permittivity, complex wavenumber, steering-vector perturbation, medium-induced additional clutter covariance, and total clutter covariance. On this basis, the effects of medium randomness on covariance spectral spreading, effective rank, effective clutter-subspace dimension, and target-clutter separability are further characterized. Numerical results show close agreement between the derived theory and Monte Carlo sample statistics across multiple stages of the propagation chain. The results further indicate that medium uncertainty not only changes clutter-covariance entries, but also reshapes its eigenspectrum and effective subspace, thereby influencing the geometric separation between target and clutter. The study provides an explicit and interpretable theoretical interface for embedding complex-medium uncertainty into FDA-MIMO-GPR clutter statistical analysis.