Weak-Fluctuation-Induced Clutter Covariance and Subspace Structure in Single-Snapshot FDA-MIMO GPR

Weak constitutive fluctuations in dispersive subsurface media can induce distributed clutter that reshapes the observation structure of ground-penetrating radar (GPR). This paper analyzes this effect for single-snapshot frequency-diverse array multiple-input multiple-output GPR. Focusing on medium-induced clutter, rather than on general target--clutter joint modeling, it establishes a statistical propagation chain from Cole--Cole parameter perturbations to electromagnetic contrast, first-order Born channel snapshots, clutter covariance, and subspace descriptors. A medium-aware snapshot model and a covariance propagation framework are then derived to characterize how constitutive uncertainty alters observation-domain spectral structure under a local weak-fluctuation regime. Numerical experiments verify the consistency of the proposed propagation relation under the adopted first-order Born and constitutive-linearization approximations. Within the tested setting, medium-induced clutter reshapes the eigenspectrum and changes target--clutter overlap metrics. Spatial correlation length and background-scene variation act as consistently strong structural drivers, while the FDA frequency increment also produces measurable changes in the normalized covariance geometry.