Vegetation is a very complex propagation medium, and multiple scattering effects play a significant role in the propagation of microwave and millimeter (mm)-wave signals through foliage. At frequencies above 1 GHz,both the coherent and incoherent field components have to be taken into account and vegetation has to be modeled as a random medium of discrete scatterers having a wide variety of sizes and shapes. Multiscattering can be studied effectively by using transport theory. In prior studies, theories have been developed for microwave and mm-wave propagation in vegetation using transport theory for continuous wave and pulsed signals. In this study, the theory has been extended to the more realistic cases of incident fields in the form of pulsed beam waves that are confined within a specified solid angle. Such spherical or diverging incident beam waves are very important in many practical applications since millimeter, optical and acoustic waves are often confined within a small conical angle. For spherical beam waves that propagate in vegetation, the range dependence, the effects of angular spread (beam broadening), and pulse broadening are determined. Pulse broadening is important especially in digital communications, where it may cause intersymbol interference and--depending on the data rate--a significant increase in bit error rate.

The specific problem that is analyzed is that of a periodic sequence of spherical pulses incident from free space (air) onto a forest region (vegetation). The forest is modeled as a half-space of randomly distributed particles, which scatter and absorb electromagnetic energy. The incident pulse train under investigation, as mentioned before, is a characteristic of the radiation produced by a microwave or mm-wave antenna.