IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 9, 2010 895 Analysis and Simulation of the Propagation Channel Complexity on Signal Fading Victor G. Kononov and Constantine A. Balanis, Life Fellow, IEEE Abstract—Radio propagation environment with scatterers restricted to the far-zone is analyzed to demonstrate how signal fading is affected by the complexity of the environment. To simulate signal fading, an approximate model based on infinite perfectly conducting (PEC) cylindrical scatterers is used and simulated. Depending on the scattering environment, the simu- lated data match the classical models of Extreme value, Gamma, Rayleigh, and Generalized Gamma. Index Terms—Extreme value, fading, Gamma, Generalized Gamma, multipath, propagation channel, Rayleigh. I. INTRODUCTION I N WIRELESS communications, as the signal propagates through a communication channel, it is being delayed, scattered, reflected, and diffracted by multiple obstacles such as buildings, mountains, rough terrain, vehicles, etc. Thus, the received signal is usually degraded due to the interference be- tween direct, delayed, and scattered components and so on. The cumulative effect of the communication channel on the signal propagation is referred to as signal fading. In complex practical propagation channels, signal fading is usually treated stochas- tically. Depending on the radio propagation environment, there are different classical statistical models that describe signal fading [1], [2]. Among the plethora of communication channels, in this letter we focus our attention on channels with the following properties. • The receiver is stationary and the scatterers are moving. • All scatterers are in the far-zone of the receiver. • The motion of the scatterers is random. Stationary scatterers and those moving along predefined paths are avoided because they imply a particular scattering scenario and therefore reduce the generality of the system. For the same reason, moving receivers are not considered as well. Our objective is to analyze the impact the scattering envi- ronment complexity has on the choice of the statistical fading model. By complexity, we refer to the number and/or size of the scatterers. The fading models considered here are the following: • Extreme value [3]; • Gamma [3]; Manuscript received July 08, 2010; revised August 20, 2010; accepted Au- gust 27, 2010. Date of publication September 02, 2010; date of current version September 27, 2010. The authors are with the School of Electrical, Computer, and Energy Engi- neering, Arizona State University, Tempe, AZ 85287-5706 USA (e-mail: Victor. Kononov@asu.edu; BALANIS@asu.edu). Digital Object Identifier 10.1109/LAWP.2010.2072951 • Rayleigh [3]; • Generalized Gamma [4], [5]. These models were found to be more representative in de- scribing signal fading in our simulations. Radio propagation environments with physical scatterers, such as buildings and vehicles, are usually very difficult to model and simulate. Therefore, in our analysis and simulations, we utilize an approximate model for the propagation channel, which consists of infinitely long cylindrical scatterers. Such an approximate model is considered acceptable because the fading models under consideration do not depend on the shape of the scatterers. II. MODELING OF THE DYNAMIC ENVIRONMENT As indicated in Section I, the dynamic environment under consideration consists of a stationary receiver and multiple ran- domly moving scatterers. Numerically, such an environment is simulated by a series of static geometrical arrangements. Each configuration is solved for the parameter of interest. The number of such configurations depends on the desired sample size, i.e., the number of observations. The critical step is the solution of the electromagnetic prop- agation problem with multiple scatterers. The advantage of the considered approximate propagation channel (see Section I) is that it allows us to treat signal propagation deterministically. In other words, we can compute the exact amplitude of the signal at any point in the region of interest by solving the Helmholtz equation analytically. The solution to such a multiscattering problem is obtained by applying the so-called orders-of-scat- tering approach [6]–[10]. Fig. 1 depicts our typical model for the dynamic scattering en- vironment; it consists of a finite region of radius . Within this region, there are infinitely long perfectly conducting (PEC) cylinders placed in random motion. The observation point, the receiving antenna, is at the center of the region. The signal trans- mitted by the base station is assumed to be a plane wave incident from . The motion of the cylinders is simulated by a series of static configurations, where for each configuration the position of the cylinders is computed as follows: (1) (2) where the subscript refers to the cylinder number, subscript is the configuration number, is the radius of the th cylinder, and and are the random numbers generated by the FORTRAN random number generator RANDOM_NUMBER. This generator produces real pseudorandom numbers with a uniform 1536-1225/$26.00 © 2010 IEEE