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<p> The rapid increasing bandwidth requirement of communication systems demands powerful numerical simulation tools for optics fiber. The computational efficient, memory saving and stable are of the most important characteristics for any simulation tools used for long-haul and broadband optics fiber. An optimized split-step digital filtering method is developed in this paper. The concept of Fourier integral and Fourier series are used in extracting a FIR filter which is used to fit the original transfer function. A further optimization process which employs windowing technique to improve computation efficiency had also been done. Compared with split-step frequency method, our method improves the computation efficiency. Only simple shifts and multiplications are needed in our method. This optimized digital filtering method differs from the former digital filtering method in a sense that the filter length of the FIR filter we extracted is reduced to a very small number. The computation time can be saved as much as 96% than before. This method can also be used to solve coupled nonlinear Schrodinger equation which governs polarization mode dispersion effect in fibers. A new simulation scheme for PMD is proposed to save computation time. The propagation results shows good accordance to those already published results. </p> / Thesis / Master of Applied Science (MASc)

Yes / In this communication, nine years of local radiosonde meteorological data, from 1997 to 2005, have been used to calculate the vertical refractivity gradient, ΔN, in the lowest atmospheric layer above the ground surface. The values obtained are used to estimate the parameter β0, which represents the probability of non-standard propagation. Hourly, monthly and yearly distributions of ΔN in the first 100 meters above the ground are given. Monthly and yearly variations of the mean of ΔN and β0 are provided and the β0 values are compared with the ITU maps.

Due to the enormous performance gains associated with the use of antenna arrays in wireless networks, it is inevitable that these technologies will become an integral part of future systems. This report focuses on signal propagation modeling for antenna array systems and on its relationship to the performance of these systems. Accurate simulation and analytical models are prerequisite to the characterization of antenna array system performance. Finally, an understanding of the performance of these systems in various environments is needed for effective overall network design. This report begins with an overview of the fundamentals of antenna array systems. A survey of vector channel models is presented. Angle of arrival and time of arrival statistics for the circular and elliptical (Liberti's Model) models are derived. A generalized optimum output SINR analysis is derived for space-time processing structures in frequency selective fading channels. The hardware and software of the MPRG Antenna Array Testbed (MAAT) is described. A literature review of previous antenna array propagation measurements is given. Antenna array measurement results obtained with the MAAT are used to compare the properties of the received signal vector in the various environmental conditions. The influence of channel parameters on the ability of antenna arrays to separate the signals of two users on the reverse link is studied using simulation. Finally, forward link beamforming techniques are reviewed. / Ph. D.

The Earth's ionosphere is a dynamic environment strongly coupled to the neutral atmosphere, magnetosphere and solar activity. In the context of this research, we restrict our interest to the mid-latitude (a.k.a., sub-auroral) ionosphere during quiet geomagnetic conditions. The Super Dual Auroral Radar Network (SuperDARN) is composed of more than 30 low-power High Frequency (HF, from 8-18 MHz) Doppler radars covering the sub-auroral, auroral and polar ionosphere in both hemispheres. SuperDARN radars rely on the dispersive properties of the ionosphere at HF to monitor dynamic features of the ionosphere. Though originally designed to follow auroral expansion during active periods, mid-latitude SuperDARN radars have observed ground and ionospheric scatter revealing several interesting features of the mid-latitude ionosphere during periods of moderate to low geomagnetic activity. The past 7 years' expansion of SuperDARN to mid-latitudes, combined with the recent extended solar minimum, provides large-scale continuous views of the sub-auroral ionosphere for the first time. We have leveraged these circumstances to study prominent and recurring features of the mid-latitude ionosphere under quiet geomagnetic conditions. First, we seek to establish a better model of HF propagation effects on SuperDARN observations. To do so, we developed a ray-tracing model coupled with the International Reference Ionosphere (IRI). This model is tested against another well established ray-tracing model, then optimized to be compared to SuperDARN observations (Chapter 2). The first prominent ionospheric feature studied is an anomaly in the standard ionospheric model of photo-ionization and recombination. This type of event provides an ideal candidate for testing the ray-tracing model and analyzing propagation effects in SuperDARN observations. The anomaly was first observed in ground backscatter occurring around sunset for the Blackstone, VA SuperDARN radar. We established that it is related to an unexpected enhancement in electron densities that leads to increased refraction of the HF signals. Using the ray-tracing, IRI model, and measurements from the Millstone Hill Incoherent Scatter Radar (ISR), we showed that this enhancement is part of a global phenomenon in the Northern Hemisphere, and is possibly related to the Southern Hemisphere's Weddell Sea Anomaly. We also tested a potential mechanism involving thermospheric winds and geomagnetic field configuration which showed promising results and will require further modeling to confirm (Chapter 3). The second ionospheric feature was a type of decameter-scale irregularity associated with very low drift velocities. Previous work had established that these irregularities occur throughout the year, during nighttime, and equatorward of both the auroral regions and the plasmapause boundary. An initial analysis suggested that the Temperature Gradient Instability (TGI) was responsible for the growth of such irregularities. We first used our ray-tracing model to distinguish between HF propagation effects and irregularity occurrence in SuperDARN observations. This revealed the irregularities to be widespread within the mid-latitude ionosphere and located in the bottom-side F-region (Chapter 4). A second study using measurements from the Millstone Hill ISR revealed that TGI driven growth was possible but only in the top-side F-region ionosphere. We found that initial growth may occur primarily at larger wavelengths, with subsequent cascade to decameter-scale with coupling throughout the F-region (Chapter 5). In summary, the research conducted during this PhD program has established a robust method to analyze quiet-time SuperDARN observations. It also furthered our physical understanding of some prominent features of the mid-latitude ionosphere. It leaves behind a flexible ray-tracing model, multiple online tools to browse SuperDARN data, and a thorough and growing Space Science API providing access to multiple datasets, models and visualization tools. / Ph. D.

This dissertation outlines work accomplished in the pursuit of this degree. This report is also designed to be a general introduction to the concepts and techniques of small-scale radio channel modeling. At the present time, there does not exist a comprehensive introduction and overview of basic concepts in this field. Furthermore, as the wireless industry continues to mature and develop technology, the need is now greater than ever for more sophisticated channel modeling research. Each chapter of this preliminary report is, in itself, a stand-alone topic in channel modeling theory. Culled from original reports and journal papers, each chapter makes a unique contribution to the field of channel modeling. Original contributions in this report include: 1. joint characterization of time-varying, space-varying, and frequency-varying channels under the rubric of duality 2. rules and definitions for constructing channel models that solve Maxwell's equations 3. overview of probability density functions that describe random small-scale fading 4. techniques for modeling a small-scale radio channel using an angle spectrum 5. overview of techniques for describing fading statistics in wireless channels 6. results from a wideband spatio-temporal measurement campaign Together, the chapters provide a cohesive overview of basic principles. The discussion of the wideband spatio-temporal measurement campaign at 1920 MHz makes an excellent case study in applied channel modeling and ties together much of the theory developed in this dissertation. / Ph. D.

Position location has become one of the more important tasks for improving communication and networking performance for future commercial wireless systems. It is also the enabling technology for many control and sensing applications envisioned by the wireless sensor networks (WSN). Despite its meaningfulness and many algorithms being developed in the past several years, position location in harsh propagation environments remains to be a challenging issue, due mainly to the lack of sufficient infrastructure support and the prominent phenomenon of non-line-of-sight (NLOS) signal propagation. Recently, adopting the concept of collaborative position location has attracted much research interest due to its potential in overcoming the abovementioned two difficulties. In this work, we approach collaborative position location from two different angles. Specifically, we investigate the optimal performance of collaborative position location, which serves as a theoretical performance benchmark. In addition, we developed a computationally efficient algorithm for collaborative position location and incorporated an effective NLOS mitigation method to improve its performance in NLOS-dense environments. Overall, our work provides insight into both theoretical and practical aspects of collaborative position location. / Ph. D.

Ring-opening metathesis polymerization (ROMP) has gained attention over the last few decades for its versatility and robustness. Through the use of highly active metal catalysts, such as Grubbs' first-generation catalyst [G1, (PCy3)2(Cl)2RuCHPh] and Grubbs' third-generation catalyst [G3, (H2IMes)(Cl)2(pyr)2RuCHPh], ROMP can exhibit living characteristics for some monomer classes, most commonly substituted norbornenes. The high livingness of ROMP makes it well-suited for the synthesis of complex polymer architectures (e.g., bottlebrush polymers, star polymers, and (multi)block copolymers, among others). However, compared to other living polymerizations, quantitative studies on the kinetic factors affecting living characteristics in ROMP are lacking. This work describes the effects of several reaction factors on the livingness in Ru-mediated ROMP of norbornene-based monomers. We performed thorough studies on the effects of the anchor group, the series of atoms directly attached to the norbornene, in the synthesis of both linear and bottlebrush polymers. Using small molecule norbornene monomers, we studied monomer HOMO energy, rate of propagation (kp), catalyst decomposition [a proxy for the termination rate constant (kt)], and livingness in ROMP as measured by the kp/kt ratio. HOMO energies were used to predict the reactivity of various monomers based on the hypothesis that high HOMO energy would lead to high monomer reactivity and high kp values. We observed a positive correlation between the HOMO energy and kp with both G1 and G3 catalysts, but we observed a plateau in kp for monomers with the highest HOMO energy when polymerized with G3 catalyst. These results suggested that above a certain level, HOMO energy no longer influenced the rate-determining step. Additionally, the anchor group had no apparent effect on catalyst decomposition with either catalyst. Therefore, when examining the livingness in ROMP of linear polymers, differences in the kp/kt ratios were primarily controlled by the kp value. When studying the synthesis of bottlebrush polymers, we found a similar positive correlation between HOMO energy and kp for five macromonomer (MM) species. To evaluate livingness of MMs, we targeted various backbone degrees of polymerization (Nbb), 100–2000, and found that MMs with high kp,obs values reached higher conversion with lower dispersities (Đ) at high target Nbb values than MMs with low kp,obs values. Finally, we investigated the synthesis of bottlebrush pseudo-pentablock copolymers using MMs with the highest and lowest kp anchor groups. This study revealed higher MM conversion and lower Đ values for each block for the MM with the highest kp anchor group, compared to the lowest kp MM. Furthering the anchor group study, we synthesized a small molecule monomer and two macromonomers containing a norbornene–benzoladderene structure. We found this anchor group had a higher HOMO energy than all other (macro)monomers previously studied. However, kp was not higher for the small molecule monomer compared to the other monomers studied, supporting the plateau in rate observed for monomers above a certain HOMO energy. The higher HOMO energy for MMs did increase kp for one of the MM compared to other MMs previously studied, however the MM with side-chains in the ortho position on the anchor group had a lower kp than expected. This low kp was attributed to the side-chains being in closer proximity to the reactive chain end, compared to the MM with side-chains in the meta position, hindering addition of new MM units. Altogether, these experiments revealed how the anchor group impacts kp and livingness in ROMP, two factors that are essential for the synthesis of precise bottlebrush (co)polymers. The final chapter of this dissertation evaluates the effect of reaction atmosphere on livingness in Ru-mediated ROMP. Here we envisioned that changing the atmosphere, from under air to on a Schlenk line under N2 to in an N2-filled glovebox, would reduce the rate of chain termination and improve livingness in ROMP of small molecule and macromonomers. We synthesized linear or bottlebrush pseudo-pentablock copolymers to evaluate the livingness of foud (macro)monomer structures in three different atmospheres. We found better agreement between Mn,expected and Mn,obs as well as lower overall and apparent Đ values for the bottlebrush polymers polymerized in N2 atmospheres. Interestingly, the effect was more prominent for low kp (macro)monomers; in other words, ROMP reactions of (macro)monomers with high kp values were successful under air, but for those with low kp values, a glovebox was required to observe good control. / Doctor of Philosophy / Ring-opening metathesis polymerization (ROMP) is a powerful chemical method used to make a wide variety of polymers. With use of ruthenium-based catalysts, ROMP can exhibit living characteristics for some monomer classes, making it well-suited for the synthesis of precise linear and bottlebrush polymers. However, compared to other living polymerizations, quantitative studies on the kinetic factors affecting living characteristics in ROMP are lacking. This work describes the effects of several reaction factors on the livingness in ROMP of norbornene-based monomers. We thoroughly studied the effects of the anchor group, the series of atoms directly attached to the norbornene, in the synthesis of both linear and bottlebrush polymers. Using small molecule norbornene monomers, we studied the monomer HOMO energy, rate of propagation (kp), catalyst decomposition, and the livingness in ROMP. We used HOMO energy to predict the reactivity of various monomers and found that high HOMO energy led to high kp values. Additionally, the anchor group had no apparent effect on catalyst decomposition; however, the large variations in kp meant that the anchor group influenced livingness in ROMP. When studying the synthesis of bottlebrush polymers, we found a similar positive correlation between HOMO energy and kp for five macromonomer (MM) species. Attaching a polymer side-chain to the norbornene decreases kp significantly, therefore our goal was to evaluate the livingness in ROMP under conditions that experience lower kp than linear polymers. We targeted large bottlebrush polymers, backbone degree of polymerization (Nbb) up to 2000, The final portion of this dissertation evaluates the effect of reaction atmosphere on the livingness in Ru-mediated ROMP. A large factor of livingness is kt, which in ROMP is typically decomposition of the catalyst chain end evidenced by low molecular weight tails in size exclusion chromatography traces. Here we envisioned changing the atmosphere, from air to inert, would prevent chain termination and improve the livingness in ROMP. We again used the synthesis of linear and bottlebrush pentablock copolymers to evaluate the livingness of six (macro)monomer structures in three different reaction atmospheres, air, N2, and in a glove box. Polymerizations under N2 or in the glove box produced more well-defined polymers than polymerizations in air by a marginal degree. Therefore, the livingness in ROMP improves when air is removed.

A phase-space asymptotic approach to wave propagation in homogeneous dispersive and dissipative media is discussed which has several advantages by comparison to conventional techniques, such as the stationary phase method, ordinary ray tracing, etc. This approach, which is based on the wave-kinetic theory [1,2], is used to examine in detail three types of one-dimensional canonic dispersive and dissipative media: cubic dispersive and quadratic dissipative, cubic dispersive and quartic dissipative, quintic dispersive and quartic dissipative. Purely dissipative media are also investigated. The analysis is also carried out using standard Fourier techniques for comparison purposes. For an arbitrary medium, exact solutions are impossible. Approximations must be made which give rise to new basic functions defined in integral form. The method of steepest descents [3], the WKB method [4], the method of dominant balance [4] and the FORMAC73 language [5] are utilized to find asymptotic series for these functions. / M.S.