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

TL;DR

This paper analyzes how random dispersive media induce cross-frequency clutter in single-snapshot FDA-MIMO-GPR, introducing a metric to quantify coupling strength and demonstrating its stability and impact on signal processing tasks.

Contribution

It develops a theoretical framework for characterizing cross-frequency clutter structure in dispersive media and proposes a metric to measure coupling strength, validated through numerical experiments.

Findings

The proposed metric distinguishes coupled and uncoupled structures.

The analysis remains consistent under various modeling assumptions in weakly dispersive scenes.

Cross-frequency structure influences whitening and principal-subspace extraction.

Abstract

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.