Cordeiro & Ferrari (1991) use the asymptotic expansion of Harris (1985) for the moment generating function of the score statistic to produce a generalization of Bartlett adjustment for application to the score statistic. It is shown here that Harris's expansion is not invariant under reparameterization and an invariant expansion is derived using a method based on the expected likelihood yoke. A necessary and sufficient condition for the existence of a generalized Bartlett adjustment for an arbitrary statistic is given in terms of its moment generating function. Generalized Bartlett adjustments to the likelihood ratio and score test statistics are derived in the case where the interest parameter is one-dimensional under the assumption of a mis-specified model, where the true distribution is not assumed to be that under the null hypothesis.

This thesis takes as its objective quantifying, comparing, and optimizing multiple-antenna (MIMO) physical layer techniques in dense ad hoc wireless networks. A framework is developed from the spatial shot noise interference model for packet radio network analysis. The framework captures the behavior of a wide variety of signal and interference distributions, which permit inspection of a number of signal processing methods including representatives from most of the major MIMO techniques. Multi-antenna systems for point-to-point are becoming mature and being developed and deployed in many wireless communication systems due to their potential to combat fading, increase spectral efficiency, and overcome interference. The framework permits an algorithm or system designer to view the network from the perspective of a typical user, to optimize performance in the midst of a given environment, or to view the network as a whole, to determine behavior that maximizes network performance. In particular, it enables questions to be answered quantitatively, such as which MIMO techniques perform best in a given environment? Or what rate and power settings should be used across the available spatial modes? Or what is the maximum benefit of channel state information? Or what gain should an individual device, or the network as a whole expect to see given a particular physical layer strategy? The dissertation begins by developing the framework for a generic set of assumptions on network behavior and signal and interference distributions. It then presents a progression of applications to representative MIMO techniques. Broad and intuitive scaling laws are developed as well as detailed exact results for careful comparison. Capacity scaling with the number of antennas is given for systems employing beamforming, selection combining, space-time block coding, and spatial multiplexing. These applications are used as the basis for developing simple distributed algorithms for optimizing MIMO settings with QoS constraints and in heterogeneous networks. Lastly, the framework is expanded to permit comparison and optimization of MIMO performance under alternative medium access strategies. In general it is found that significant performance gains can be reaped with multi-antenna physical layers, provided the proper techniques are employed. It is also shown that the availability of multiple spatial channels impacts the inherent tradeoff between per-link throughput and spatial reuse. / text

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The ever-increasing demand for better mobile experiences is propelling the research communities to look ahead at how future networks can be geared up to meet such demands. It is likely that the next-generation of wireless communications will be revolutionary, outpacing the current systems capabilities in terms connectivity, reliability and intelligence. These trends and predictions will cause a revolutionary change in the wireless communications. In this context, the concept of Ultra-Dense Network (UDN) is poised to be the cornerstone of the development of fifth generation(5G) systems, whereby a massive number of base stations (BSs) are deployed for enhancing the network performance metrics. Though such densification might be economically viable in urban areas, it is mostly unfavorable in rural ones due to the sheer complexity and the various factors involved the planning and installation processes; all of which trigger the need for cost-effective, flexible and easily-implementable solutions. As a result, unmanned aerial vehicles (UAVs) emerge as a promising alternative solution for enhancing wireless coverage. Due to their mobility capabilities, UAVs are of particular importance in events of (i) terrestrial-based cellular systems dilapidation, (ii) infrastructure absence in remote and suburban areas, or (iii) limited-duration events or activities wherein there is a short-term need for supplementary network resources to handle the overload. While a growing body literature works towards characterizing and providing insights into the performance of UAVs-only networks (serving the first two purposes), understanding the performance of such networks when coupled with existing terrestrial BSs remains a challenging, yet interesting, open research venue. Towards this direction, this thesis provides a rigorous analysis of the downlink coverage probability of hybrid aerial-terrestrial networks using tools from Stochastic Geometry. The thesis presents a mathematical model that characterizes the coverage probability metric under different network environments. The proposed model is validated against intensive simulations so as to substantiate the analytical results. The developed work is essential to understanding the premises of one possible solution to the UDNs of tomorrow, capture its key performance metrics and, most importantly, to uncover key design insights and reveal new directions for the wireless communication industry.

Doctor of Philosophy / Department of Electrical and Computer Engineering / Balasubramaniam Natarajan / The number of wireless devices is predicted to skyrocket from about 5 billion in 2015 to 25 billion by 2020. Therefore, traffic volume demand is envisioned to explode in the very near future. The proposed fifth generation (5G) of mobile networks is expected to be a mixture of network components with different sizes, transmit powers, back-haul connections and radio access technologies. While there are many interesting problems within the 5G framework, we address the challenges of energy-related management in a heterogeneous 5G networks. Based on the 5G architecture, in this dissertation, we present some fundamental methodologies to analyze and improve the energy efficiency of 5G network components using mathematical tools from optimization, control theory and stochastic geometry. Specifically, the main contributions of this research include: • We design power-saving modes in small cells to maximize energy efficiency. We first derive performance metrics for heterogeneous cellular networks with sleep modes based on stochastic geometry. Then we quantify the energy efficiency and maximize it with quality-of-service constraint based on an analytical model. We also develop a simple sleep strategy to further improve the energy efficiency according to traffic conditions. • We conduct a techno-economic analysis of heterogeneous cellular networks powered by both on-grid electricity and renewable energy. We propose a scheme to minimize the electricity cost based on a real-time pricing model. • We provide a framework to uncover desirable system design parameters that offer the best gains in terms of ergodic capacity and average achievable throughput for device-to-device underlay cellular networks. We also suggest a two-phase scheme to optimize the ergodic capacity while minimizing the total power consumption. • We investigate the modeling and analysis of simultaneous information and energy transfer in Internet of things and evaluate both transmission outage probability and power outage probability. Then we try to balance the trade-off between the outage performances by careful design of the power splitting ratio. This research provides valuable insights related to the trade-offs between energy-conservation and system performance in 5G networks. Theoretical and simulation results help verify the performance of the proposed algorithms.

In the cellular networks, to support the increasing data rate requirements, many base stations (BSs) with low transmit power and small coverage area are deployed in addition to classical macro cell BSs. Low power nodes, such as micro, pico, and femto nodes (indoor and outdoor), which complement the conventional macro networks, are placed primarily to increase capacity in hotspots (such as shopping malls and conference centers) and to enhance coverage of macro cells near the cell boundary. Combining macro and small cells results in heterogeneous networks (HetNets). An accurate node (BS or user equipment (UE)) model is important in the research, design, evaluation, and deployment of 5G HetNets. The distance between transmitter (TX), receiver (RX), and interferer determines the received signal power and interference signal power. Therefore, the spatial placement of BSs and UEs greatly impacts the performance of cellular networks. However, the investigation on the spatial distribution of UE is limited, though there is ample research on the topic of the spatial distribution of BS. In HetNets, UEs tend to cluster around BSs or social attractors (SAs). The spatial distribution of these UEs is non-uniform. Therefore, the analysis of the impact of non-uniformity of UE distribution on HetNets is essential for designing efficient HetNets. This thesis presents a non-uniform user distribution model based on the existing K-tier BS distribution. Our proposed non-uniform user distribution model is such that a Poisson cluster process with the cluster centers located at SAs in which SAs have a base station offset with their BSs. There are two parameters (cluster radius and base station offset) the combination of which can cover many possible non-uniformity. The heterogeneity analysis of the proposed nonuniform user distribution model is also given. The downlink performance analysis of the designed non-uniform user model is investigated. The numerical results show that our theoretical results closely match the simulation results. Moreover, the effect of BS parameters of small cells such as BS density, BS cell extension bias factor, and BS transmit power is included. At the same time, the uplink coverage probability by the theoretical derivation is also analyzed based on some simplifying assumptions as a result of the added complexity of the uplink analysis due to the UEs’ mobile position and the uplink power control. However, the numerical results show a small gap between the theoretical results and the simulation results, suggesting that our simplifying assumptions are acceptable if the system requirement is not very strict. In addition to the effect of BS density, BS cell extension bias factor, and BS transmit power, the effect of fractional power control factor in the uplink is also introduced. The comparison between the downlink and the uplink is discussed and summarized at the end. The main goal of this thesis is to develop a comprehensive framework of the non-uniform user distribution in order to produce a tractable analysis of HetNets in the downlink and the uplink using the tools of stochastic geometry

Empirical observations have established connections between river network geometry and various hydrophysical quantities of interest. Since rivers can be decomposed into basic components known as links, one would like to understand the physical processes at work in link formation and maintenance. The author develops a natural stochastic geometric model for this problem, for the particular type of link known as exterior links. In the model, the distribution of distance from a uniformly distributed point to a fixed graph is computed. This model yields an approximate expression for the distribution of length of exterior links that incorporates junction angles and drainage density, and compares favorably with observed length distributions. The author goes on to investigate related mathematical questions of independent interest, such as the case where the previously mentioned graph is itself a realization of a random process, and in so doing derives a formula for the first contact distribution of a general random Voronoi tesselation (also associated with the names of Dirichlet and Thiessen). Since this random tesselation is a natural starting point for modelling spatial processes in a wide variety of fields, these results should find immediate applications. It is also shown how these results can be interpreted as a generalization of a classical problem considered by Buffon. / Graduation date: 1991

Modern cellular systems feature increasingly dense base station deployments, augmented by multiple tiers of access points, in an effort to provide higher network capacity as user traffic, especially data traffic, increases. The primary limitation of these dense networks is co-channel interference. The primary source of interference is inter-cell and cross-tier interference, which is especially limiting for users near the boundary of the cells. Inter-cell interference coordination (ICIC) is a broad umbrella term for strategies to improve the performance of the network by having each cell allocate its resources such that the interference experienced in the network is minimized, while maximizing spatial reuse. Fractional frequency reuse (FFR) has been proposed as an ICIC technique in modern wireless networks. The basic idea of FFR is to partition the cell’s bandwidth so that (i) cell-edge users of adjacent cells do not interfere with each other and (ii) interference received by (and created by) cell-interior users is reduced, while (iii) improving spectral reuse compared to conventional frequency reuse. It is attractive for its intuitive implementation and relatively low network coordination requirements compared to other ICIC strategies including interference cancellation, network MIMO, and opportunistic scheduling. There are two common FFR deployment modes: Strict FFR and Soft Frequency Reuse (SFR). This dissertation identifies and addresses key technical challenges associated with fractional frequency reuse in modern cellular networks by utilizing an accurate yet tractable model of both the downlink (base station to mobile) and uplink (mobile to base station) based on the Poisson point process for modeling base station locations. The resulting expressions allow for the development of system design guidelines as a function of FFR parameters and show their impact on important metrics of coverage, rate, power control, and spectral efficiency. This new complete analytical framework addresses system design and performance differences in the uplink and downlink. Also, this model can be applied to cellular networks with multiple tiers of access points, often called heterogeneous cellular networks. The model allows for analysis as a function of system design parameters for users under Strict FFR and SFR with closed and open access between tiers. / text

In this thesis, spectrum sensing techniques are investigated for cognitive radio (CR) networks in order to improve the sensing and transmission performance of secondary networks. Specifically, the detailed exploration comprises of three areas, including single-node spectrum sensing based on eigenvalue-based detection, cooperative spectrum sensing under random secondary networks and full-duplex (FD) spectrum sensing and sharing techniques. In the first technical chapter of this thesis, eigenvalue-based spectrum sensing techniques, including maximum eigenvalue detection (MED), maximum minimum eigenvalue (MME) detection, energy with minimum eigenvalue (EME) detection and the generalized likelihood ratio test (GLRT) eigenvalue detector, are investigated in terms of total error rates and achievable throughput. Firstly, in order to consider the benefits of primary users (PUs) and secondary users (SUs) simultaneously, the optimal decision thresholds are investigated to minimize the total error rate, i.e. the summation of missed detection and false alarm rate. Secondly, the sensing-throughput trade-off is studied based on the GLRT detector and the optimal sensing time is obtained for maximizing the achievable throughput of secondary communications when the target probability of detection is achieved. In the second technical chapter, the centralized GLRT-based cooperative sensing technique is evaluated by utilizing a homogeneous Poisson point process (PPP). Firstly, since collaborating all the available SUs does not always achieve the best sensing performance under a random secondary network, the optimal number of cooperating SUs is investigated to minimize the total error rate of the final decision. Secondly, the achievable ergodic capacity and throughput of SUs are studied and the technique of determining an appropriate number of cooperating SUs is proposed to optimize the secondary transmission performance based on a target total error rate requirement. In the last technical chapter, FD spectrum sensing (FDSS) and sensing-based spectrum sharing (FD-SBSS) are investigated. There exists a threshold pair, not a single threshold, due to the self-interference caused by the simultaneous sensing and transmission. Firstly, by utilizing the derived expressions of false alarm and detection rates, the optimal decision threshold pair is obtained to minimize total error rate for the FDSS scheme. Secondly, in order to further improve the secondary transmission performance, the FD-SBSS scheme is proposed and the collision and spectrum waste probabilities are studied. Furthermore, different antenna partitioning methods are proposed to maximize the achievable throughput of SUs under both FDSS and FD-SBSS schemes.

Doctor of Philosophy / Department of Electrical and Computer Engineering / Balasubramaniam Natarajan / The number of wireless devices is predicted to skyrocket from about 5 billion in 2015 to 25 billion by 2020. Therefore, traffic volume demand is envisioned to explode in the very near future. The proposed fifth generation (5G) of mobile networks is expected to be a mixture of network components with different sizes, transmit powers, back-haul connections and radio access technologies. While there are many interesting problems within the 5G framework, we address the challenges of energy-related management in a heterogeneous 5G networks. Based on the 5G architecture, in this dissertation, we present some fundamental methodologies to analyze and improve the energy efficiency of 5G network components using mathematical tools from optimization, control theory and stochastic geometry. Specifically, the main contributions of this research include: • We design power-saving modes in small cells to maximize energy efficiency. We first derive performance metrics for heterogeneous cellular networks with sleep modes based on stochastic geometry. Then we quantify the energy efficiency and maximize it with quality-of-service constraint based on an analytical model. We also develop a simple sleep strategy to further improve the energy efficiency according to traffic conditions. • We conduct a techno-economic analysis of heterogeneous cellular networks powered by both on-grid electricity and renewable energy. We propose a scheme to minimize the electricity cost based on a real-time pricing model. • We provide a framework to uncover desirable system design parameters that offer the best gains in terms of ergodic capacity and average achievable throughput for device-to-device underlay cellular networks. We also suggest a two-phase scheme to optimize the ergodic capacity while minimizing the total power consumption. • We investigate the modeling and analysis of simultaneous information and energy transfer in Internet of things and evaluate both transmission outage probability and power outage probability. Then we try to balance the trade-off between the outage performances by careful design of the power splitting ratio. This research provides valuable insights related to the trade-offs between energy-conservation and system performance in 5G networks. Theoretical and simulation results help verify the performance of the proposed algorithms.