A new approach to wireless channel modeling using finite mixture models

This research presents a new approach to modeling a wireless channel using finite mixture models (FMM). Instead of the conventional approach of using non mixtures (single) probability distribution functions, FMMs are used here to model the channel impulse response amplitude statistics. To demonstrate this, a FMM based model of Ultrawideband (UWB) channels amplitude statistics is developed. The hypothesis of this research is that finite mixture models provide better statistical description of channel impulse response amplitudes than non mixtures models.;Though the FMM based model may be extended to narrowband channels, UWB channel is of specific interest. Due to their extremely large bandwidths, the phenomena that justifies the assumption of Rayleigh distribution in narrowband channels are not applicable to UWB channel amplitude statistics. Existing literature suggests the use of Nakagami, Lognormal, Weibull, Rice, and Rayleigh distributions for UWB amplitude statistics. In this research, finite mixture models composed of combinations of constituent PDFs such as Rayleigh, Lognormal, Weibull, Rice and Nakagami are used for modeling the channel amplitude statistics. The use of FMMs is relevant because of their ability to characterize the multimodality in the data. Two sets of Ultrawideband channel data collected by the National Institute of Standards and Technology (NIST) and Schuster et al. at the Swiss Institute of Technology. The measurements were made with line of sight between transmitter (Tx) and receiver (Rx) in an indoor industrial (NIST) and university campus (Schuster et al.) environment in the 2 -- 8 GHz range. The aim of this effort is identify the best statistical model for each significant impulse in the channel impulse response.;The stochastic expectation maximization (SEM) technique is used to estimate the parameters of the FMMs. The resultant FMMs are then compared to one another and to non mixture models using model selection techniques such as Akaike's Information Criteria (AIC). Results indicate that models composed of a mixture of Rayleigh and Lognormal distributions consistently provide good fits for most of the impulses of the UWB channel. Other model selection techniques such as Minimum Description Length (MDL) and Accumulative Predictive Error (APE) also confirmed this finding. This selection of FMM based on Rayleigh and Lognormal distributions is true for both the industrial as well as the university environment channel data. The mixing coefficients indicate that Rayleigh distribution contributes more to the FMM for higher amplitude impulses (impulses occurring at small excess delays) while lognormal distribution contributes the FMM for low amplitude impulses (impulses occurring at large excess delays).