in this method) is drawn in the same figure in a constant way with the number of buildings. It can be clearly observed that the error of Bertoni's solution sharply increases when the number of considered knife edges is progressively smaller.Finally, the attenuation at the reference point for different values of h w , considering h tx ϭ 10 m, h ke ϭ 20 m, f ϭ 900 MHz, w ϭ 50, n ϭ 100, ␥ ϭ 90Њ, soft polarization, terrain parameters ϭ 0.012 S/m, r ϭ 15, and ϭ 0.23 m, and d 1 ϭ 100 m and d 2 ϭ 200 m, is presented in Figure 5, that is, assuming spherical-wave incidence over the buildings and demonstrating, once again, the versatility of the proposed formulation. It can be noted that, at first, when the height of the wedge grows, the total attenuation decreases, since although the diffraction losses caused by the wedge increase, the ones that occur due to the multiplebuilding diffraction are reduced to a greater extent due to the larger angle of incidence that impinges over the array of knife edges. However, as can be observed, from one specific value of h w on, the growth in the losses produced by the wedge exceeds the decrease in the ones caused by the buildings (due to the larger angle of incidence), since the abovementioned decrease stops at a certain large angle, as the multiple diffraction losses produced by the building rooftops are no longer relevant when the angle of incidence over these latter is very large.
CONCLUSIONSA formulation expressed in terms of UTD coefficients for the analysis of multiple diffraction in urban areas where a bare wedgeshaped hill causes shadowing of the transmitter from the receiver (NLOS) has been presented. The solution, which has a good computational efficiency due to the recursive technique that utilizes, has been validated through the comparison with the method given by Bertoni [4] with good agreement. Furthermore, the numerical results for the cases of small number of buildings considered as well as spherical-wave incidence over these latter have been shown, demonstrating in this way the greater versatility of the propounded solution compared to the existing formulation.
ACKNOWLEDGMENTThe authors thank the Ministerio de Educación y Ciencia, Spain, for funding this work (TEC2004-04866-C04-04). been demonstrated in the "twilight zone" between static and microwave frequencies. The "twilight zone" is a difficult regime for numerical simulation, because this is the zone where circuit theory meets full-wave electromagnetic theory [1]. In circuit theory involving capacitors and inductors, the electric field (representing the world of the capacitors) and the magnetic field (representing the world of the inductors) are weakly coupled, and the current decomposes itself into curl-free (irrotational) and divergence free (solenoidal) components. This decomposition is known as Helmholtz decomposition. Any numerical code that fails to capture the aforementioned physics correctly will break down.The surface integral-equation (SIE) method has proven to be a powerful tool in electrodynamic an...
