Estimation of Propagation Characteristics along Random Rough Surface for Sensor Networks

The main focus in the development of wireless communications engineering is providing higher data rates, using lower transmission power, and maintaining quality of services in complicated physical environments, such as an urban area with high-rise buildings, a randomly profiled terrestrial ground and so on. In order to achieve these goals, there has been substantial progress in the development of low-power circuits, digital algorithms for modulation and coding, networking controls, and circuit simulators in recent years [Aryanfar,2007]. However, insufficient improvement has beenmade in wireless channel modelingwhich is one of the most basic and significant engineering problems corresponding to the physical layer of the OSI model. Recently, the sensor network technologies have attracted many researchers’ interest especially in the fields of wireless communications engineering as well as in the fields of sensor engineering. The sensor devices are usually located on the terrestrial surfaces such as dessert, hilly terrain, forest, sea surface and so on, of which profiles are considered to be statistically random. In this context, it is very important to investigate the propagation characteristics of electromagnetic waves traveling along random rough surfaces (RRSs) and construct an efficient as well as reliable sensor network over terrestrial grounds with RRS-like profiles [Uchida,2007], [Uchida,2008], [Uchida,2009], [Honda,2010]. In the early years of our investigations, we applied the finite volume time domain (FVTD) method to estimate the electromagnetic propagation characteristics along one-dimensional (1D) RRSs [Honda,2006], [Uchida,2007]. The FVTDmethod, however, requires too much computer memory and computation time to deal with relatively long RRSs necessary for a sensor network in the realistic situation. To overcome this difficulty, we have introduced the discrete ray tracing method (DRTM) based on the theory of geometrical optics, and we can now deal with considerably long RRSs in comparison with the operating wavelength. The merit of using DRTM is that we can treat very long RRSs compared with the wavelength without much computer memory nor computation time. Thus, the DRTM has become one of the most powerful tools in order to numerically analyze the long-distance propagation characteristics of electromagnetic waves traveling along RRSs [Uchida,2008], [Uchida,2009], [Honda,2010]. In this chapter, we discuss the distance characteristics of electromagnetic waves propagating along homogeneous RRSs which are described statistically in terms of the two parameters, that is, height deviation h and correlation length cl. The distance characteristics of propagation are estimated by introducing an amplitude weighting factor α for field amplitude, an 1