An improved method for calculating the diffraction loss of natural and man made obstacles

A Bayesian Approach to Device-Free Localization: Modeling and Experimental Assessment

“…For target standing at with any azimuth , the term represents the electric field loss due to the target obstruction, computed as the ratio between the field received over the obstructed link and the field measured in free space (i.e., in absence of target). The energy loss due to the diffraction is computed using the Fresnel-Kirchhoff method [19], [20] here extended to the 2D case taking into account the object profile for varying target orientation. Based on the Huygen's principle, the exponential phase term of the electric field is integrated over the two vertical and lateral dimensions [21] as (5) where denote the axes of the 2D plane orthogonal to the LOS path at location .…”

“…Based on (17), the overall field loss , for an object located at same distance from the transmitter and covering now all the positions , can be written as (18) where we used the substitutions and , while measures the lateral section of the obstruction (acting as a knife-edge object) for random orientation . Using the approximation valid for , and since the field loss can be simplified as (19) Using an asymptotic expansion [30] for the integrals in the form valid for large enough , the energy loss (19) scales as (20) The target-induced average attenuation is approximated as (21) being from Jensen inequality. The average term can be simplified by considering the lateral section of the obstruction only 10 as far as the target is confined within the first Fresnel volume.…”

Wireless Sensor Network Modeling and Deployment Challenges in Oil and Gas Refinery Plants

“…Shapes that are more typical in refinery sites (tubes, structural pipe racks, etc.) have been approximated by matching a number of rectangles in the false(x,yfalse) plane to get the same shape of the obstructed areas; this is also illustrated in [20]. For the i th object, the clearance zone ℱi in the false(x,yfalse) plane denotes the region corresponding to the Fresnel volume cross-section that is free from any obstacle.…”

Wireless channel characterization and modeling in oil and gas refinery plants

“…To simplify the reasoning, we assume that the obstacles surrounding the transmitter and the receiver antennas lie in the far-field region, in addition the shape of the obstacles obstructing the Fresnel zones is square or rectangular. Shapes that are more typical in refinery sites (tubes, structural pipe-racks etc...) have been approximated as discussed in [11] (extension not covered here due to space limits). For the i-th object, the zone clearance F i in the (x,y) plane denotes the region of the Fresnel volume circular section that is free from obstacles.…”