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.

Medium-Induced Cross-Frequency Clutter Structure in Single-Snapshot FDA-MIMO-GPR With a Weak-Dispersion Criterion

This paper investigates the cross-frequency structure of background clutter induced by random dispersive media in single-snapshot FDA-MIMO-GPR. Representative media are modeled by the Cole--Cole formulation to relate dispersive constitutive behavior to the reference propagation environment and observation-domain statistics. A normalized incremental contrast function is introduced under a reference-medium framework, and a single-snapshot background-response expression with first-order propagation-kernel feedback is derived. Based on this expression, a cross-frequency coupling strength of the leading-order background covariance is defined. Numerical results show that, in weakly dispersive scenes, the proposed analysis remains consistent across constitutive mapping, the zeroth-order propagation skeleton, first-order distorted-Born truncation, propagation-kernel feedback, and single-channel response closure. The proposed metric distinguishes uncoupled and explicitly coupled constructions, remains stable under pure energy scaling, responds clearly to correlation length and relaxation-location parameters, and corresponds directly to the error of the frequency block-diagonal approximation. Additional experiments show that the resulting cross-frequency structure affects whitening and principal-subspace extraction. In scenes with pronounced relaxation, abrupt breakdown under strong perturbations and high-error plateaus indicate that the present theory is mainly applicable within the validity range of first-order feedback.

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.