Full Polarimetric Scattering Matrix Estimation with Single-Channel Echoes via Time-Varying Polarization Modulation

Polarimetric information is essential for scattering interpretation and target characterization in synthetic aperture radar (SAR) remote sensing, yet many resource-constrained platforms (e.g., small satellites and unmanned aerial vehicles (UAVs)) operate with limited polarization modes or even a single radio frequency (RF) chain, which limits full polarimetric scattering acquisition. To address this limitation, this paper proposes a single-channel framework for estimating the full polarization scattering matrix (PSM) enabled by time-varying polarization modulation. The transmit/receive polarization states are steered along predefined trajectories on the Poincaré sphere to generate time-varying polarization tags that are encoded into the received echoes through the target’s polarization-varying response. A compact observation model is then derived to relate the single-channel echoes, the known polarization tags, and the unknown PSM; based on this, the PSM is then estimated via a least squares formulation with a low-rank approximation. Simulation results demonstrate the robust reconstruction of the full polarimetric scattering matrix under diverse modulation trajectories. For arbitrarily chosen random point targets, when the signal-to-noise ratio (SNR) exceeds −20 dB, the polarimetric similarity coefficient approaches 1, and the estimation errors of Pauli power components converge toward zero. Furthermore, the method’s reliability is validated on distributed vegetation clutter. Quantitative metrics demonstrate near-perfect statistical consistency, with polarimetric entropy and alpha angle errors within 0.14%. Overall, the proposed approach provides a practical pathway to enhance the availability of full polarimetric scattering information under limited-observation conditions, confirming its feasibility for downstream analysis in complex natural scenes while maintaining a single radio frequency (RF) chain architecture augmented by a polarization modulator.