Stochastic Modeling of Wireless Communications in a Fading Environment via Fox's H-Function

In wireless communications systems, it is well known that the instantaneous
received signal is a random variable that follows a given distribution. The randomness
mainly stems from e ects such as multipath fading, shadowing, and interference.
The received signal is a relevant metric, such that several distributions have been
used in the literature to characterize it. However, as new radio technologies emerge,
the known distributions are deemed insu cient to t simulated and measure data.
Subsequently, as the wireless industry moves onto the fth generation (5G), newer
distributions are proposed to well represent the received signal for new wireless technologies,
including those operating in the millimeter-wave (mmWave) band. These
are mainly application speci c and may not be adequate to model complex 5G devices
performance. Therefore, there is a need to unify and generalize the received signal
distributions used for performance analysis of wireless systems.
Secondly, an explosion of new radio technologies and devices operating in the
same limited radio spectrum to collect and share data at alarming rates is expected.
Such an explosion coupled with the 5G promise of ubiquitous connectivity and network
densi cation, will thrust interference modeling in dense networks to the fore-front. Thus, interference characterization is essential when analyzing such wireless
networks.
Thirdly, the classical distributions used to model the received signal do not
account for the inherent mobility feature for emerging radio technologies, such as
avionics systems (e.g. drones), which may make the distributions inadequate as mobility
e ects can no longer be ignored.
Consequently, in this dissertation, we propose the use of a unifying distribution,
the Fox's H-function distribution, with subsume ability to represent several
traditional and future distributions, as a statistical tool to evaluate the performance
of wireless communications systems. Additionally, two interference models, one with
a xed number and the other with a random number of interferers, are considered to
derive interference statistics, and further utilize the results to analyze system performance
under the e ect of interference. Finally, we extend the classical distributions
to include the mobility regime for several wireless network topologies, and perform
network analysis. The analytical results are validated using computer Monte Carlo
simulations.