This paper presents two uniform theories of diffraction–physical optics (UTD-PO) formulations
to undertake analysis of radiowave multiple diffraction resulting from the presence of
both buildings and trees in vegetated urban areas, with the assumption of spherical-wave incidence.
The solutions presented consider buildings modeled as knife-edges and rectangular sections (the
latter being more complex and realistic) and the effect of the tree canopy (the assumption is that
this exceeds the height of the average rooftop) is taken into account by adding proper attenuation
factors/phasors to building diffraction phenomena. The validation of these formulations has been
undertaken by comparing with other methods and measurements performed at 39 GHz on a scaledmodel
of the environment under analysis, consisting of an array of bricks and bonsai trees. The chief
advantage of the solutions put forward is that because of recursion, the calculations only include
single diffractions. This avoids any requirement for higher-order diffraction terms in the diffraction
coefficients, which means less computer time/power is demanded. The results of this work may be
useful when planning future mobile communication systems, including 6G networks and beyond.
