Author:  Hu, Jinzhen 
Title:  Probability density of the magnitude of indoor fading 
Degree:  M.Sc. 
Year:  2011 
Subject:  Hong Kong Polytechnic University  Dissertations Radio  Transmitters and transmission  Fading 
Department:  Faculty of Engineering 
Pages:  viii, 82 leaves : ill. (chiefly col.) ; 30 cm. 
InnoPac Record:  http://library.polyu.edu.hk/record=b2415801 
URI:  http://theses.lib.polyu.edu.hk/handle/200/5987 
Abstract:  A transmitted impulse δ(t), after propagating through a multipathchannel, would arrive at a receiver as r(t) = IΣi=1ciδ(t+τi), where τi denotes the ith timedelayed multipath's propagationdelay, Ci denotes the ith timedelayed multipath's complexvalued fading amplitude. Coherent summation of these multipaths would produce an overall fading factor of C = √IΣi=1ci2 . The value of this fading factor depends on the fading channel. For indoor wireless propagation, C would be affected by 1. The indoor floor plan, the position / materials / surfaceroughness / size of walls / furniture / decor. 2. The transmitting / receiving antennas' polarizations, antennatype, horizontal position in the floor plan, vertical positions from the ceiling and floor. 3. The presence / absence of humans and other animals. This C is affected by macroscopic fading, shadowing, and microscopic fading. The last could vary very significantly within fractions of a wavelength (approximately a foot at 1 GHz). This microscopic variation in C could be modeled as a random variable. This dissertation aims to characterize this random variable's probability density. The CINDOOR raytracing software will be used to simulate an indoor environment. To simulate microscopic fading, the faded signal is sampled over a 16 x 16 x 6 grid, spanning over a volume of a wavelength times a wavelength times a wavelength. Implicitly assumed here is that macroscopic fading and shadowing effects remain constant in this volume. The above 1536 spatial samples are then gathered into a histogram. Normalization of the area of this histogram to unity that would give an estimate of the probability density of C, under that one particular propagation environment. This probabilitydensity estimate is then leastsquares fit to various probability densities, to identify the bestfitting density as a mathematical model of the density of C. This bestfitting density turns out to be Weibull. Then, one factor is changed in the propagation environment (e.g. the receiveantenna's polarization) to test how the bestfitting density's parameters may change as a consequence. 
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