Aalo, Valentine A.

The statistics of random sum is studied and used to evaluate performance metrics
in wireless networks. Pertinent wireless network performance measures such as call
completion/dropping probabilities and the average number of handovers usually require
the probability distributions of the cell dwell time and call holding time; and are therefore
not easy to evaluate. The proposed performance evaluation technique requires the
moments of the cell dwell time and is given in terms of the Laplace transform function of
the call holding time. Multimedia services that have Weibull and generalized gamma
distributed call holding times are investigated. The proposed approximation method uses
the compound geometric random sum distribution and requires that the geometric
parameter be very small. For applications in which this parameter is not sufficiently
small, a result is derived that improves the accuracy (to order of the geometric parameter)
of the performance measures evaluated.

System modeling has the potential to enhance system design productivity by providing a
platform for system performance evaluations. This model must be designed at an abstract
level, hiding system details. However, it must represent any subsystem or its components
at any level of specification details. In order to model such a system, we will need to
combine various models-of-computation (MOC). MOC provide a framework to model
various algorithms and activities, while accounting for and exploiting concurrency and
synchronization aspects. Along with supporting various MOC, a modeling environment
should also support a well developed library. In this thesis, we have explored various
modeling environments. MLDesigner (MLD) is one such modeling environment that
supports a well developed library and integrates various MOC. We present an overview
and discuss the process of system modeling with MLD. We further present an abstract
model of a Network-on-Chip in MLD and show latency results for various customizable
parameters for this model.

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.

In wireless systems such as cellular systems, frequency reuse is employed to extend the
coverage area but this process introduces undesirable co-channel interference. A tradeoff must be
made between increasing system capacity and transmission quality when planning, designing and
deploying such wireless systems. In order to meet the explosive demand for high data rate
wireless services for a growing population within a given geographical area, future wireless
cellular networks will adopt smaller cells, such as femtocells, that are serviced by low-power
base stations. As the deployment of femto-cellular base stations rapidly increases in the coming
years, interference coordination and management will be the primary challenge in such
heterogeneous networks. In this work, we derive a novel closed form expression for the
cumulative distribution function CDF and coverage probability for a small cell wireless network
operating in a Nakagami fading environment in the presence of Gaussian noise and impulsive
interference modeled as an alpha-stable process. With these results, we can determine the
probabilistic access thresholds that provide the best probable tradeoff between system capacity
and network quality.

Modern cancerous tumor diagnostics is nearly impossible without invasive
methods, such as biopsy, that may require involved surgical procedures. In recent years
some work has been done to develop alternative non-invasive methods of medical
diagnostics. For this purpose, the data obtained from an ultrasound image of the body crosssection,
has been analyzed using statistical models, including Rayleigh, Rice, Nakagami,
and K statistical distributions. The homodyned-K (H-K) distribution has been found to be
a good statistical tool to analyze the envelope and/or the intensity of backscattered signal
in ultrasound tissue characterization. However, its use has usually been limited due to the
fact that its probability density function (PDF) is not available in closed-form. In this work
we present a novel closed-form representation for the H-K distribution. In addition, we propose using the first order approximation of the H-K distribution, the I-K distribution
that has a closed-form, for the ultrasound tissue characterization applications. More
specifically, we show that some tissue conditions that cause the backscattered signal to
have low effective density values, can be successfully modeled by the I-K PDF. We
introduce the concept of using H-K PDF-based and I-K PDF-based entropies as additional
tools for characterization of ultrasonic breast tissue images. The entropy may be used as a
goodness of fit measure that allows to select a better-fitting statistical model for a specific
data set. In addition, the values of the entropies as well as the values of the statistical
distribution parameters, allow for more accurate classification of tumors.

The open nature of the wireless medium makes the wireless communication
susceptible to eavesdropping attacks. In addition, fading and shadowing significantly
degrade the performance of the communication system in the wireless networks. A
versatile approach to circumvent the issues of eavesdropping attacks while exploiting the
physical properties of the wireless channel is the so-called physical layer-security. In this
work, we consider a model in which two legitimate users communicate in the presence of
an eavesdropper. We investigate the performance of the wireless network at the physical
layer that is subject to a variety of fading environments that may be modeled by the
Rayleigh, Nakagami-m, and Generalized-K distributions, to mention a few. We use the
secrecy outage probability (SOP) as the standard performance metrics to study the
performance of the wireless networks. We propose two different approaches to compute
the secrecy outage probability, and derive explicit expressions for the secrecy outage probability that allow us to characterize the performance of the wireless networks.
Specifically, we use a direct integration approach as well as a Taylor series base approach
to evaluate the secrecy outage probability. Finally, we use computer simulations, based
on MATLAB, to confirm the analytical results.

Natural and manmade noise signals tend to exhibit impulsive behaviors. Therefore modeling those signals as α-stable processes is better suited towards the development of a practical spectrum sensing scheme. However, the performances of detectors operating in an α-stable noise environment are difficult to evaluate. This is because an α-stable random variable can usually only be modeled by the characteristic function since closed-form expressions are usually not available except for the special values of the characteristic exponent that correspond to the Cauchy and Gaussian noise distributions. In this thesis, we derive a general closed-form expression for the probability density function (PDF) of symmetric alpha stable processes having rational characteristic exponent (0<α≤2). Consequently, we obtain analytical expressions for the PDF and corresponding complementary cumulative distribution function (CCDF) of the proposed fractional lower order moment (FLOM) detector. Utilizing false alarm and detection probabilities, the performance analysis of the proposed spectrum sensing scheme is conducted with the assumption that the cognitive radio (CR) users are operating in non-fading channels. We validate the analytical results with Monte Carlo simulations. The effect of the distribution parameters on the receiver operating characteristic (ROC) curves is verified.

In this thesis, we study the effect of Rice fading on the performance of Global Positioning System (GPS) receivers. The field-theoretic foundation of pseudo-random-noise (PRN) codes, their implementation, and their use in generating unique navigation messages in the GPS receiver is reviewed. The processing of the spread-spectrum signals within the digital delay locked loop (DDLL) in the receiver is also considered. In particular, we derive numerical expressions that can be easily evaluated for the probability error and the mean-time to lose-lock, for a DDL operating in an additive white gaussian noise (AWGN) channel in the presence of Rice fading. The results obtained generalize results in the literature for the Rayleigh fading environment.

This thesis is concerned with the performance analysis of mobile cellular systems under various distributions of portable users. The performance measure used is the average outage probability. Performance analysis is performed for macrocellular as well as microcellular systems, for different distributions of mobile users such as uniform, ring, and bell distribution. The outage probability is evaluated for systems with hexagonal, triangular, and square grid layouts. The effect of macroscopic diversity on system performance is also considered. Finally, computer simulations are used to verify the evaluated results.

Capture effect has shown considerable improvement on performance of slotted ALOHA systems. Further, improvement is expected by increasing the number of base stations. The performance of such slotted ALOHA systems is analyzed with the aid of Equilibrium point analysis. Packet dropping due to finite number of retransmissions is taken into account. The numerical results indicate that the finite number of retransmission trials mainly contribute to the improvement of the packet dropping probability in the range of light input traffic. The use of multiple base stations improves the overall throughput and the average transmission delay in the range of heavy input traffic.