Guest Speaker Series: Statistical Applications of Spherically-Invariant Random Processes to Modeling of Wireless Fading Channels

Guest Speaker: Distinguished Professor Kung Yao, Electrical Engineering Department, UCLA

Thursday, April 19, 2012
10:00 AM - 12:00 PM

Abstract

Fading phenomena can significantly degrade the performance of many wireless communication systems.  Extensive field measurements over many years have yielded fading envelope statistics modeled by Rayleigh, Rician, Weibull, Nakagami-m, K_v, lognormal, etc. pdfs.  Our recent unified spherically-invariant random process (SIRP) model for the fading channel requires the non-negative valued fading envelope rv X = V · R, where R is either the Rayleigh rv (in the NLOS case) or the Rician rv (in the LOS case), V is a non-negative scalar rv independent of R, and · is the multiplication of the two rvs.  For various known f_X(.) fading envelope pdfs (as given above),  corresponding f_V(.) pdfs having been found with some efforts using Mellin transforms and Fox H-function methods.  The associated f_V(.) pdfs can be used for BER evaluations simpler - to much simpler than directly using the f_X(.) pdfs.  While the SIRP model may justify various known fading envelope pdfs from the statistical point of view, can these pdfs be justified from the physical RF propagation point of view?  The Rayleigh fading envelope pdf follows from the effects of CLT on the sum of large number of small iid rvs associated with uniformly distributed phase.  The Rician fading effect results from one large dominant term in the sum of the large number of small iid rvs.   Nakagami, over thirty years of analytical and experimental work in fading radio channel research (1940-1960), has found various complicated fading envelope pdfs with non-uniform phases, based on physical modeling of the random phasors in the fading channels.   However, from the work of A. Ichimaru (private communications) in optical and RF propagations through random media, it appears these fading phenomena with non-uniform phase distributions are associated with transmission intensity normalized variance D values near or greater than unity, which are due to complex wave-random media turbulence interactions.  Turbulence effects are known to exhibit non-linear dynamical (chaotic) properties.   In the SIRP fading model, we have obtained a “half-Cauchy-like” fat-tailed f_X(.) pdf, that does not have a finite mean nor finite second moment (and no finite variance) with an explicit associated f_V(.) pdf.   Asymptotic analysis shows such a pdf can have an arbitrarily large value of D as predicted by the Ichimaru conjecture.   Infinite variance pdfs (such as the half-Cauchy pdf ) can be used as the Frobenius-Perron (FP) invariant pdf in non-linear dynamical theory to generate chaotic waveforms (K. Umeno, 98).  Recent result of T. Akimoto (DDAP, Sept. 08)) shows our “half-Cauchy-like” pdf can also be used as the invariant pdf in the FP method to generate chaotic waveforms. Yet, using the f_V(.) pdf associated with the “half-Cauchy-like” f_X(.) applied to a BPSK system, its BERs have well behaved values not very different from those of Rayleigh fading statistic.  Thus, the unified SIRP fading model encompasses not only the known fading envelope pdfs but may predict envelope pdfs associated with strong wave-random media interactions associated with chaotic properties.

About the Speaker

Kung Yao received the B.S.E. (Highest Honors), M.A. and Ph.D. degrees in electrical engineering all from Princeton University, Princeton, N.J.  Then he was a NAS-NRC Postdoctoral Fellow at UC Berkeley.  Presently, he is a Distinguished Professor in the EE Department at UCLA.  In 1985-1988, he served as an Assistant Dean of the School of Engineering and Applied Science at UCLA.  His research and professional interests include sensor networks, communication theory and system, and signal/array processing.  Dr. Yao received the 1993 IEEE Signal Processing Society Senior Award in VLSI Signal Processing and the 2008 Joint IEEE Communication Theory Society – IEEE Information Theory Society Paper Award.  He is the co-editor of a two volume series of an IEEE Reprint Book on "High Performance VLSI Signal Processing," IEEE Press, 1997.  He is the co-author of the book “Detection and Estimation for Communication and Radar Systems,” to be published by Cambridge Press, 2012.  Dr. Yao is an IEEE Life Fellow.  He has served as associate editors of various sensor networking and communication journals and also organized various sessions in these topics.  He has been the PI and Co-PI of various government and industrial sensor networking and communication research grants in recent years.  He is a research faculty in the National Science Foundation funded Center on Embedded Networked Sensing (CENS) at UCLA and the co-PI of the Public Safety Network Systems Laboratory.