Finite-Distance Physical-Optics Modeling and Simulation of Radio-Altimeter Echoes in Representative Urban Scenes

Radio altimetry is important for sensing the near-ground altitude of airborne platforms operating at several-kilometre altitudes. In urban environments, multipath propagation and coherent superposition from buildings and ground surfaces can alter echo delay, energy, and waveform, thereby affecting downstream ranging and altitude-estimation decisions. Conventional echo models often cannot retain the geometric propagation delays, material properties, polarization transformations, and coherent phase relationships of individual scattering components in kilometer-scale three-dimensional scenes, limiting their ability to reconstruct physically consistent time-domain echoes. To address this, this study combines radio-altimetry echo simulation with electromagnetic simulation of urban environments and develops a finite-distance spherical-wave physical-optics method for modeling time-domain echoes in large-scale urban scenes. The method maps the scattering responses of urban surface facets to the received time-domain echo. Representative cases verify the accuracy of calculations of scattering amplitude, range attenuation, and two-way propagation delay. The results show that a uniform material assignment predominantly affects echo amplitude and energy while exerting only a limited influence on the delay structure. In contrast, variations in urban geometry alter the spatial locations and orientations of effective scattering facets and the coherence relationships among their complex fields, resulting in distinct main-peak positions, energy-delay distributions, and early- and late-arriving multipath structures.