I. Introduction
The analysis of propagation loss on radio signals is an essential step in the planning and design of mobile communication systems and other radio networks located in urban areas. In this way, many formulations have been presented assuming that buildings are illuminated directly by a transmitting source placed at a certain distance, based either on the uniform theory of diffraction (UTD) or on physical optics (PO) [1]–[3]. Nevertheless, for both area coverage and interference predictions, the study of cases where a terrain elevation obstructs the propagation path between the transmitter and the buildings can turn out interesting when the city is surrounded by mountainous or hilly areas, as depicted in Fig. 1. A solution for this scenario is proposed by Bertoni [4], where the total attenuation existing at the indicated reference point is obtained by firstly analyzing only the diffraction loss of the radio signal over the hill (reaching the receiver assuming an absence of buildings) and then adding to this result the multiple diffraction loss caused by the latter, which is approximated as a factor assuming a plane-wave incidence over the city (a large distance between the hill and the urban area), as well as an elevated number of mentioned buildings [5]. Therefore, the total attenuation is obtained by the summation of (which includes the free-space loss) and , as can be observed in Fig. 2. In [6], the authors proposed a new solution, expressed in terms of UTD coefficients, for the analysis of the multiple diffraction existing in the scenario under study, considering the hill modeled as a wedge, which solves the limitations of the method given in [4], since neither a plane-wave incidence over the city nor an elevated number of buildings have to be assumed, thus allowing for the study of the above-mentioned environment when the urban area consists of a small number of buildings, as well as when a spherical-wave incidence over the latter is considered. However, when considering that the terrain elevation obstructing the propagation path between the transmitter and buildings has a rounded shape, a cylindrical structure modeling the hill could be more appropriate, in order to accurately predict radio signal path loss. In this way, several works have been published, in which propagation and diffraction over rounded surfaces is analyzed [7]–[9]. Furthermore, Piazzi and Bertoni [10] present an analysis of the effect on the path loss of a cylindrical hill with buildings located all along its surface shadowing the receiver in urban environments; the same scenario is also studied by García et al. [11].
Scheme of the considered propagation environment when the hill is modeled as a wedge.
Scheme of the two contributions to path loss, as considered by Bertoni for the scenario in Fig. 1.