A Statistical Channel Model for Stochastic Antenna Inclination Angles

Hindawi International Journal of Antennas and Propagation Volume 2019, Article ID 3487149, 12 pages https://doi.org/10.1155/2019/3487149 Research Article A Statistical Channel Model for Stochastic Antenna Inclination Angles Gang Liu, Ming Zhang, and Yaming Bo College of Electronic and Optical Engineering & College of Microelectronics, Nanjing University of Posts and Telecommunications, Nanjing 210003, China Correspondence should be addressed to Yaming Bo; Received 28 August 2018; Accepted 3 February 2019; Published 28 March 2019 Guest Editor: Raed A. Abd-Alhameed Copyright © 2019 Gang Liu 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. The actions of a person holding a mobile device are not a static state but can be considered as a stochastic process since users can change the way they hold the device very frequently in a short time. The change in antenna inclination angles with the random actions will result in varied received signal intensity. However, very few studies and conventional channel models have been performed to capture the features. In this paper, the relationships between the statistical characteristics of the electric field and the antenna inclination angles are investigated and modeled based on a three-dimensional (3D) fast ray-tracing method considering both the diffraction and reflections, and the radiation patterns of an antenna with arbitrary inclination angles are deducted and included in the method. Two different conditions of the line-of-sight (LOS) and non-line-of-sight (NLOS) in the indoor environment are discussed. Furthermore, based on the statistical analysis, a semiempirical probability density function of antenna inclination angles is presented. Finally, a novel statistical channel model for stochastic antenna inclination angles is proposed, and the ergodic channel capacity is analyzed. 1. Introduction Wireless communication technology has been widely used in communication systems for its mobility, convenience, flexibility, and lower cost compared with wired transmission. However, the signals are significantly affected by the surrounding environment and undergo fading and time variation before arriving at the receiver. In order to achieve a higher rate and more reliable communication, the acquisition of accurate channel state information (CSI) and channel modelling is fundamental and crucial in designing a wireless communication system and has been attracting researchers’ attention. A basic framework of the geometry-based stochastic channel modelling approach (GSCMA) is developed in [1] for three different scenarios with the corresponding channel parameters such as delay spread, angle spread, shadow fading, angle of departure, angle of arrival, and delay power spectrum extracted from a large number of measurements. Additionally, a polarized channel model is also proposed based on crosspolarization discrimination (XPD) when considering the depolarization effect of channels on electromagnetic waves. The WINNER II channel model [2] extends the number of scenarios to more than a dozen but follows the same channel modelling approach. Furthermore, the WINNER II channel model allows propagation between line-of-sight (LOS) and non-line-of-sight (NLOS) conditions for a same scenario. Analogously, a number of channel models are established using GSCMA but assuming that the scatterers are distributed on regular geometries in two or three dimensions such as the one-ring model [3], twin-cluster model [4], and elliptical model [5] considering only the azimuth angle and the double-cylinder model [6], two-sphere model [7], and multiconfocal ellipsoid model [8] considering the influence of the elevation angle. However, these conventional channel models are assumed to be generally stationary, but this is not sufficiently applicable for the channels of the massive multiple-input multiple-output (MIMO) recognized as one of the most important candidate technologies for the fifth-generation (5G) mobile communication systems due to the potential and additional advantages compared with conventional MIMO technologies [9–11]. 2 International Journal of Antennas and Propagation Tx 61m A z 48.5m y E 2.4m 1.05m 2.1m C B x 23.9m 1.05m D 2.1m Figure 1: The three-dimensional layout of the T-shaped corridor. Consequently, several novel models [12–14] are developed to capture the new features observed from the measurements such as the spherical wave front, nonstationary effect on the antenna array axis and the time axis. The above channel models are independent of the antenna configurations and element radiation patterns. Instead, the correlative channel models such as the Kronecker model [15] and the Weichselberger model [16] use the correlation matrices at the mobile station (MS) and base station (BS) without knowing the distribution of scatterers or clusters resulting in a lower complexity. However, few studies of the channel modelling for stochastic antenna inclination angles have been done. It is known that mobile devices are not fixed on walls or people’s desks as routers or computers. Instead, people communicate using a mobile device whenever and wherever possible; for instance, they are lying down, standing, and walking. The way people hold a mobile device is not a static state but a stochastic process since users can change the way they hold the mobile device very frequently even in a few seconds. Consequently, the antenna inclination angles will change with the rotation of the mobile devices leading to the variation of received signals due to the polarization mismatch between the signals and antennas. In this paper, a statistical channel model for stochastic antenna inclination angles in the indoor environment is developed based on a modified three-dimensional (3D) fast ray-tracing method. Two different conditions of LOS and NLOS for a common scenario of the T-shaped corridor for an indoor environment are investigated. Furthermore, in order to capture the stochastic characteristics of people holding a mobile device, a semiempirical probability density function (PDF) of antenna inclination angles is proposed, and closed expressions for the radiation patterns of a half-wave antenna for arbitrary inclination angles are deducted based on the principle of coordinate transformation. Finally, the ergodic capacities under two different conditions are analyzed based on the proposed channel model. This paper is organized as follows. A modified 3D fast ray-tracing method is introduced, and the validity and accuracy of the method in predicting the electromagnetic fields are verified in Section II. In Section III, the statistical channel model for stochastic antenna inclination angles is presented in detail. The numerical results are analyzed in Section IV, and conclusions are drawn in Section V. 2. Sim (...truncated)