Research Article A Temporal Millimeter Wave Propagation Model for Tunnels Using Ray Frustum Techniques and FFT Choonghyen Kwon, 1 Hayeon Kim, 1 Haengseon Lee, 1 Hyo Hyun Choi, 2 Woo-jin Byun, 3 and Kwangseon Kim 3 1 Department of Electronic Engineering, Sogang University, 1 Sinsu-dong, Mapo-gu, Seoul 121-742, Republic of Korea 2 Department of Computer Science, Inha Technical College, 100 Inha-ro, Nam-gu, Incheon 402-752, Republic of Korea 3 Radio Technology Group, Electronics and Telecommunications Research Institute, 218 Gajeong-ro, Yuseong-gu, Daejeon 305-700, Republic of Korea Correspondence should be addressed to Haengseon Lee; leehs95@sogang.ac.kr Received 14 November 2013; Revised 20 February 2014; Accepted 7 March 2014; Published 7 April 2014 Academic Editor: Felipe C´ atedra Copyright © 2014 Choonghyen Kwon et al. Tis 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. A temporal millimeter wave propagation model for tunnels is presented using ray frustum techniques and fast Fourier transform (FFT). To directly estimate or simulate efects of millimeter wave channel properties on the performance of communication services, time domain impulse responses of demodulated signals should be obtained, which needs rather large computation time. To mitigate the computational burden, ray frustum techniques are used to obtain frequency domain transfer function of millimeter wave propagation environment and FFT of equivalent low pass signals are used to retrieve demodulated waveforms. Tis approach is numerically efcient and helps to directly estimate impact of tunnel structures and surfaces roughness on the performance of millimeter wave communication services. 1. Introduction With the advent of widespread use of mobile communication services, the need for accurate wireless channel models for environments has increased [1] to ensure the quality of services for both persons and objects such as vehicles manned and unmanned. In particular, the demand for rail- way communication systems has increased that necessitate the use of millimeter wave band with by far large band- widths to accommodate passenger’s wireless data demand [2]. Te properties of millimeter wave channels have been investigated using ray optical approaches combined with the uniform theory of difraction [3]. Unlike other full wave analysis techniques, the ray optical or ray tracing approaches limit the interactions among scatterers to those dictated by Snell’s law or law of difractions [4, 5]. Although the number of interactions is kept minimized, the amount of computa- tion needed to determine whether unobstructed ray paths between interacting faces of objects exist grows enormously. To increase computational efciency further, various space division techniques and path fnding algorithms have been invented and utilized [6–13]. Among those, ray frustum techniques use frustums to form regions in which refected, transmitted, or difracted waves can be received [13]. Te frustums help to determine whether the scattered waves reach a receiver’s position and to fnd scattering points satisfying geometrical optics principles using virtual source positions. Tose techniques have been used to predict path loss, delay spread, distribution of feld strength, and so on as a function of frequency. In this paper, more direct, practical, and numerically efcient approach to characterize millimeter wave propa- gation channels of tunnels is proposed which gives time domain impulse responses of the demodulated baseband signals. Time domain propagation models have been given interest in the feld of ultrawide band application, where impulse responses are obtained by inverse Fourier transform or convolution of time domain responses with very wide bandwidths [14]. Due to the large bandwidths, time needed to the inversion becomes very large. Te impulse responses Hindawi Publishing Corporation International Journal of Antennas and Propagation Volume 2014, Article ID 172924, 9 pages http://dx.doi.org/10.1155/2014/172924