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

Abstract

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.

Figures (7)

• Figure 1: Baseline comparisons for the front-end covariance propagation. The theoretical and Monte Carlo results are highly consistent for both the permittivity covariance and the wavenumber covariance, supporting the first part of the statistical propagation chain.
• Figure 2: Baseline comparisons for the local steering covariance at representative patches. The theoretical and Monte Carlo results remain consistent across the selected patches, while the dominant approximation error is associated with the first-order linearization from $\delta k_c(\omega)$ to $\delta\bm a(\theta,r)$.
• Figure 3: Baseline comparisons for the aggregated covariance matrices $\bm R_{\mathrm{med}}$ and $\bm R_c$. The theoretical and Monte Carlo results exhibit the same dominant structure after scene-level aggregation, supporting the covariance construction at the global level.
• Figure 4: Error trends under the perturbation-strength scan. As the perturbation strength increases, the steering linearization error grows rapidly, whereas the covariance-level errors remain comparatively stable. This indicates that the effective validity range of the first-order theory is primarily limited by the exponential steering mapping from $\delta k_c(\omega)$ to $\delta\bm a(\theta,r)$.
• Figure 5: Convergence trends with respect to the Monte Carlo sample size. The covariance-level errors decrease substantially as $n_{\mathrm{mc}}$ increases, indicating that the large discrepancies at low sample counts are primarily caused by finite-sample estimation effects rather than inconsistency of the theoretical propagation chain.