This paper presents an efficient ray-launching method for 2D indoor propagation problem, by including crucial multiple reflection effect inside wall. We here focus on the derivation of the reflected and transmitted ray solutions at/through wall when a magnetic source is located in the indoor environment. An efficient approximation, which is called collective ray approximation, is carried out to bundle or collect the internal multiple reflected rays into the primary one. It is resultantly confirmed from the detailed numerical experiments that the derived collective ray solutions can be confidently effective when the internal reflections strongly contribute to the propagation characteristic in the propagation environment, regardless of angle of the incidence.

This paper presents a numerical approach to the time-domain analysis of N-branch-line couplers. The approach is based on the modified central difference (MCD) method combined with internal boundary treatments, which consist of the time-domain scattering matrix for the three-port junction discontinuity. The behavior of the signal propagation including multiple reflections on the N-branch-line coupler with and without line loss is analyzed and demonstrated in the time domain. Additionally, the S-parameters obtained from Gaussian pulse responses of the N-branch-line directional couplers are shown. The simulated results are in good agreement with those of the commercial simulator.

This paper presents an easy and efficient modification of simplified 2D ray-launching method, by approximately including multiple reflection effect inside walls for indoor environment. In order to precisely carry out the ray-launching procedure inside lossy wall, a simple modification using a true real refraction angle is first introduced, instead of complex one. Furthermore, an efficient approximation is carried out to collect the internal multiple reflected rays into the primary one. We here call it collective ray approach. Consequently, it is confirmed from the detailed considerations that the present ray representations obtained by introducing the real refraction angle are well suitable for indoor propagation analysis, and in particular the collective ray solution can be utilized confidently even when the internal reflections strongly contribute to the propagation feature of the considered indoor environment.

Recently, dielectric lens antennas are paid attentions in ITS applications. Many lens shape designing methods were already developed. And electrical performances were estimated through a ray tracing method. Here, arbitral lens shapes were expressed by a system of power series. In the case of ray tracing, time-consuming three-coordinate root-finder programs were needed to find intersection points of rays on the lens surfaces. In order to calculate complicated structures such as zoned lenses and complicated rays such as multiple reflections between lens surfaces, simple ray tracing methods are requested. In this paper, a simple ray tracing method that utilizes directly designed discrete points of lens surfaces is developed. In this method, a refracted ray is automatically determined for a given incident ray. As for an intersecting point of a lens surface for an outgoing ray, the nearest point to the refracted vector is found out by employing a simple searching procedure. This method is time-saving compared to the previous three-coordinate root-finding program. Through calculated results of focal points and radiation patterns in wide angle beam steering, effectiveness of a developed method is ensured. Application of the developed ray tracing method of complicated multiple reflections are studied. Reflecting points are found out speedily by the same searching procedure. A calculated example of doubly reflected rays is obtained. Through comparing calculated and measured results of wide angle radiation patterns, effectiveness of a developed method is ensured.

Networks in this paper consist of non-commensurate transmission lines with branches and branching resistors at junctions. When signals on a transmission line are divided multiple ways at the junctions of branched lines, multiple reflection waves occur by the impedance mismatching. For the analysis of multiple reflections and network design, lattice diagrams have been used so far. However, the expansions of network transfer functions provide an easier way for the same purpose as in the case of lattice diagram. The output transient responses can be directly calculated from the expansions of network transfer functions or can be numerically calculated by software such as the fast Laplace transform. Therefore, once the network transfer functions are given, calculation of transient responses can be carried out quite easily. In this paper, the expansions of network transfer functions have been derived with respect to delay elements ξi=exp(-sτi) by formularizing the propagation of multiple reflection waves, and then the multi-variable rational network transfer functions have been obtained from the expansions. As an example, a 3-port transmission line network with normalized characteristic impedances 1, 1, 6 and normalized branching resistors 1/23, 1/23, 126/23 has been taken up. As the terminal resistances at output ports can be determined from the relation of the first arriving wave to the steady state, the design of 3-port transmission line networks which will furnish output waveforms similar to the waveform of the input within given tolerances has been considered. The output waveforms have been calculated for pure terminal resistances and for the pure terminal resistances plus parasitic parallel capacitances.