Mobile Information Systems

Volume 2015 (2015), Article ID 268989, 8 pages

http://dx.doi.org/10.1155/2015/268989

## A Comparison Study for Investigation of Diffracted Waves between Parallel Edges and Edges with Arbitrary Angle

^{1}Department of Information and Communication Engineering, Fukuoka Institute of Technology (FIT), 3-30-1 Wajiro-Higashi, Higashi-Ku, Fukuoka 811-0295, Japan^{2}Graduate School of Engineering, Fukuoka Institute of Technology (FIT), 3-30-1 Wajiro-Higashi, Higashi-Ku, Fukuoka 811-0295, Japan

Received 4 July 2013; Accepted 1 October 2013

Academic Editor: David Taniar

Copyright © 2015 Jiro Iwashige et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Estimation of the scattering of electromagnetic waves by buildings and other obstacles is very important for wireless communications. In our previous work, we have examined the diffracted fields by two horizontal edges which make an arbitrary angle. In this paper, we compare the diffracted fields between parallel edges and edges with arbitrary angle. The numerical calculation results show that when the angle between two edges increases, relatively strong orthogonal polarized wave components appear, but the principal components are almost the same as the incident wave.

#### 1. Introduction

Electromagnetic waves can be scattered by edges of the buildings in urban areas or edges of the mountain (ridges) for long communication. Thus, the communication quality deteriorates. Therefore, it is important to estimate propagation path from the viewpoint of the effective utilization of the radio wave resources. However, the prediction of the propagation path is not easy.

Until now, there are many research works dealing with estimation of the radio wave propagation path in the urban areas [1, 2]. These papers mainly analyzed and examined the propagation path of radio waves when in the urban area there are many buildings. For the case when the waves exceed building roof, Zhang analyzed propagating radio wave over a large number of buildings [3].

In our previous works, we have examined the diffracted fields by two horizontal edges which make an arbitrary angle [4, 5]. But it is almost impossible to find diffraction points on these edges analytically [6], so we used a method which can find the diffraction points by repetition process [5]. However, it should be noted that edges are not always horizontal. Thus, it is necessary to examine the diffracted field by edges which change in both horizontal and vertical directions [7]. We also discussed the fields diffracted by wedges and showed that wedge shapes, materials, and incident polarization do not have significant effect on diffracted fields except near the wedge surfaces [8].

In this paper, first we survey the double diffraction by two edges which make an arbitrary angle. Then, we refer to coordinate transformation between a total coordinate system and an edge-fixed one and explain the method for finding the diffraction points on two edges with an arbitrary angle which change in both horizontal and vertical directions. For the analysis of diffracted fields, we used GTD (geometrical theory of diffraction) [9, 10]. We make the analysis by including the slope diffraction considering Holm’s method [11, 12]. The numerical calculations are carried out on perfect conductor. The results show that when the angle between two edges increases, relatively strong orthogonal polarized wave components appear, but the principal components are the same as the incident wave.

This paper is organized as follows. In Section 2, we present diffraction by two edges containing coordinate transformation and the method of finding the diffraction points and introduce the diffraction by two edges. In Section 3, we present the numerical examples. Finally, some conclusions are given in Section 4.

#### 2. Diffraction by Two Edges

##### 2.1. Aspect of Double Diffraction

In Figure 1(d), the aspect of double diffraction by edges 1 and 2 is shown. We express edge () by , which makes an arbitrary angle in horizontal and vertical planes. The wave from a source is diffracted twice, at point on and at point on , and it reaches an observation point . We use three coordinate systems , and , and the origins of and are, respectively, at and of coordinate system . The edges and agree with -axsis and -axsis of coordinate systems and . It should be noted that the subscript in means the coordinate system , but the subscript 0 of is omitted. Figure 1(a) shows the front view of two wages. Figures 1(b) and 1(c) show the top view and side view of Figure 1(d). The wedges are supposed to rotated by angle () counterclockwise in a horizontal plane as shown in Figure 1(b) and inclined by angle in a vertical plane in Figure 1(c) (in Figure 1, and are drawn as and ).