Near-Ground Channel Modeling for Distributed Cooperative Communications

Analysis of Propagation for Wireless Sensor Networks in Outdoors

“…Thus, by substituting Eqs. (9) and (12) in Eq. (11), the expression of received power for free space conditions using isotropic antennas results:…”

“…For example, a well-known approach is based on the principle of the first Fresnel ellipse clearance, for which the breakpoint distance corresponds to the point where the ground reaches the first Fresnel zone † , as depicted in Fig. 9, and results as [12]: Although it can be found in the open literature some expressions to calculate this distance (see Table 1 for instance), it has been pointed out by some authors that a single distance is sometimes difficult to be determined, and a "transition region" between the two slopes can be identified instead. In this situation, a double regression analysis is carried out from experimental data.…”

“…Thus, the closer the antenna is to the surface, the shorter the node range is, which is attributed to the obstruction of ground to the transmission path. Recently, modeling based on diffraction theory for near-ground channel in WSNs has been published [12], with good results compared to independent measurement campaigns. Basically, Torabi and Zekavat define three propagation regions derived from a geometry where antennas are at relatively low height as can be found in some applications of WSNs [12]:…”

“…4, and Δϕ represents its phase difference as explained in Section 6. The term ρ ef is defined in [12] as an effective reflection coefficient, which, as the authors claim, stands for the "surface" waves (see Section 9 below), incident polarization and surface correlation length, whose analysis is valid for low-grazing incident angles as the case at hand. See [12] and references therein for details on the derivation of ρ ef .…”

“…Based on the above, the physical and mathematical explanations for the two-slope model are exposed in Section 7 including some comments on its use in WSNs. The diffraction phenomenon for wireless sensor networks is revised in Section 8, where some details of the recent approach taken in [12] are highlighted. The relative closeness of nodes to the ground also motivates us to address some particularities of the surface waves as explained in Section 9, where definitions provided in the investigation on the topic and approaches proving the absence of surface waves are included.…”