Download Large-scale Wireless Networks: Stochastic Geometry and Ordering

School of Electrical, Computer and Energy Engineering
PhD Final Oral Defense
Large-scale Wireless Networks: Stochastic Geometry and Ordering
by
Junghoon Lee
March 19, 2014
9:30 AM
GWC 409
Committee:
Dr. Cihan Tepedelenlioglu (chair)
Dr. Andreas Spanias
Dr. Martin Reisslein
Dr. Oliver Kosut
Abstract
Wireless networks are fundamentally limited by the intensity of interference. Since both
the received signal and interference depend on the spatial location of the nodes,
mathematical techniques have been developed in the last decade to provide
communication theoretic results accounting for the network's geometrical configuration.
Often, the location of the nodes in the network can be modeled as random, following a
point process. In this dissertation, various scenarios of wireless communications in largescale networks modeled as point processes are considered.
The first part of the dissertation considers signal reception and detection problems with
symmetric alpha stable noise which is from a large-scale interfering network modeled as
a Poisson point process. For the signal reception problem, the performance of space-time
coding over fading channels with alpha stable noise. We derive pairwise error probability
(PEP) of orthogonal space-time block codes (STBC) with a benchmark genie-aided
receiver (GAR), or the minimum distance receiver (MDR) which is optimal in the
Gaussian case. For general space-time codes we propose a maximum-likelihood (ML)
receiver, and its approximation at high signal-to-noise ratio (SNR). The resulting
asymptotically optimal receiver (AOR) does not depend on noise parameters and is
computationally simple. Then, signal detection in coexisting wireless sensor networks
(WSNs) is considered. We characterize the aggregated signal and interference from a
Poisson random field of nodes and define a binary hypothesis testing problem to detect a
signal in the presence of interference. For the testing problem, we introduce the
maximum likelihood (ML) detector and simpler alternatives. The proposed mixedfractional lower order moment (FLOM) detector is computationally simple and close to
the ML performance, and robust to errors in system parameters. We also derive
asymptotic theoretical performances for the proposed simple detectors.
The second part of the dissertation introduces stochastic ordering of interference
distributions in large-scale networks modeled as point processes. Stochastic orders are
binary relations defined on probability distributions which capture intuitive notions like
being larger or being more variable. Interference is a major performance-limiting factor
in most wireless networks, thus it is important to characterize its statistics. Since closedform results for the distribution of interference for such networks are only available in
limited cases, it is of interest to compare network interference using stochastic orders, for
two different point processes with different fading or path-loss scenarios between the
interferers and the receiver. In this dissertation, conditions on the fading distribution and
path-loss model are given to establish stochastic ordering between interferences.
Moreover, Laplace functional (LF) ordering is defined between point processes and
applied for comparing interference. Then, the LF ordering is extended to a general class
of point processes which have been used for modeling wireless networks in the literature.
It is also shown that the LF ordering of point processes is preserved with respect to
independent operations such as marking, thinning, clustering, superposition, and random
translation. The LF ordering of point processes is a useful tool for comparing spatial
deployments of wireless networks and can be used to establish comparisons of several
performance metrics such as coverage probability, achievable rate, and resource
allocation even when closed form expressions of such metrics are unavailable.
Applications in several network scenarios are also provided.