Mellin Transform Based Performance Analysis of Fast Frequency Hopping Using Product Combining

Abstract—In this contribution, we analyze the bit error rate (BER) performance of fast frequency hopping (FFH) assisted M-ary frequency shift keying (MFSK) using product combining. Product combining constitutes an efficient yet low-complexity scheme that may be employed in FFH-MFSK receiver to combat the detrimental effects of interference or jamming. We propose a novel approach to the analysis of this receiver system, which is based on the Mellin transform. Using this approach, the probability density function (PDF) of the product combiner output is expressed in a closed form. Based on the resultant PDF, the BER of the FFH-MFSK product combining receiver operating in Rayleigh fading channel is evaluated analytically. It is shown that the Mellin transform simplifies the analysis of the product combining receiver

Multicarrier Frequency Hopping Spread Spectrum Techniques With Quasi-Cyclic Low Density Parity Check Codes Channel Coding

This work presents a new proposed Multicarrier Frequency Hopping Spread Spectrum (MCFH-SS) system employing Quasi-Cyclic Low Density Parity Check (QC-LDPC) codes instead of the conventional LDPC codes. A new technique for constructing the QC-LDPC codes based on row division method is proposed. The new codes offer more flexibility in terms of high girth, multiple code rates and block length. Moreover, a new scheme for channel prediction in MCFH-SS system is proposed. The technique adaptively estimates the channel conditions and eliminates the need for the system to transmit a request message prior to transmitting the packet data. The ready-to-use channel will be occupied with a Pseudonoise (PN) code and use for transmission or else, it will be banned

Digital watermark technology in security applications

With the rising emphasis on security and the number of fraud related crimes around the world, authorities are looking for new technologies to tighten security of identity. Among many modern electronic technologies, digital watermarking has unique advantages to enhance the document authenticity. At the current status of the development, digital watermarking technologies are not as matured as other competing technologies to support identity authentication systems. This work presents improvements in performance of two classes of digital watermarking techniques and investigates the issue of watermark synchronisation. Optimal performance can be obtained if the spreading sequences are designed to be orthogonal to the cover vector. In this thesis, two classes of orthogonalisation methods that generate binary sequences quasi-orthogonal to the cover vector are presented. One method, namely "Sorting and Cancelling" generates sequences that have a high level of orthogonality to the cover vector. The Hadamard Matrix based orthogonalisation method, namely "Hadamard Matrix Search" is able to realise overlapped embedding, thus the watermarking capacity and image fidelity can be improved compared to using short watermark sequences. The results are compared with traditional pseudo-randomly generated binary sequences. The advantages of both classes of orthogonalisation inethods are significant. Another watermarking method that is introduced in the thesis is based on writing-on-dirty-paper theory. The method is presented with biorthogonal codes that have the best robustness. The advantage and trade-offs of using biorthogonal codes with this watermark coding methods are analysed comprehensively. The comparisons between orthogonal and non-orthogonal codes that are used in this watermarking method are also made. It is found that fidelity and robustness are contradictory and it is not possible to optimise them simultaneously. Comparisons are also made between all proposed methods. The comparisons are focused on three major performance criteria, fidelity, capacity and robustness. aom two different viewpoints, conclusions are not the same. For fidelity-centric viewpoint, the dirty-paper coding methods using biorthogonal codes has very strong advantage to preserve image fidelity and the advantage of capacity performance is also significant. However, from the power ratio point of view, the orthogonalisation methods demonstrate significant advantage on capacity and robustness. The conclusions are contradictory but together, they summarise the performance generated by different design considerations. The synchronisation of watermark is firstly provided by high contrast frames around the watermarked image. The edge detection filters are used to detect the high contrast borders of the captured image. By scanning the pixels from the border to the centre, the locations of detected edges are stored. The optimal linear regression algorithm is used to estimate the watermarked image frames. Estimation of the regression function provides rotation angle as the slope of the rotated frames. The scaling is corrected by re-sampling the upright image to the original size. A theoretically studied method that is able to synchronise captured image to sub-pixel level accuracy is also presented. By using invariant transforms and the "symmetric phase only matched filter" the captured image can be corrected accurately to original geometric size. The method uses repeating watermarks to form an array in the spatial domain of the watermarked image and the the array that the locations of its elements can reveal information of rotation, translation and scaling with two filtering processes

Electronic correlations in inhomogeneous model systems: numerical simulation of spectra and transmission

Many fascinating features in condensed matter systems emerge due to the interaction between electrons. Magnetism is such a paramount consequence, which is explained in terms of the exchange interaction of electrons. Another prime example is the metal-to-Mott-insulator transition, where the energy cost of Coulomb repulsion competes against the kinetic energy, the latter favoring delocalization. While systems of correlated electrons are exciting and show remarkable and technologically promising physical properties, they are difficult to treat theoretically. A single-particle description is insufficient; the quantum many-body problem of interacting electrons has to be solved. In the present thesis, we study physical properties of half-metallic ferromagnets which are used in spintronic devices. Half-metals exhibit a metallic spin channel, while the other spin channel is insulating; they are characterized by a high spin polarization. This thesis contributes to the development of numerical methods and applies them to models of half-metallic ferromagnets. Throughout this work, the single-band Hubbard Hamiltonian is considered, and electronic correlations are treated within dynamical mean-field theory. Instead of directly solving the lattice model, the dynamical mean-field theory amounts to solving a local, effective impurity problem that is determined self-consistently. At finite temperatures, this impurity problem is solved employing continuous-time quantum Monte Carlo algorithms formulated in the action formalism. As these algorithms are formulated in imaginary time, an analytic continuation is required to obtain spectral functions. We formulate a version of the N-point Padé algorithm that calculates the location of the poles in a least-squares sense. To directly obtain spectra for real frequencies, we employ Hamiltonian-based tensor network methods at zero temperature. We also summarize the ideas of the density matrix renormalization group algorithm, and of the time evolution using the time-dependent variational principle, employing a diagrammatic notation. Real materials never display perfect translational symmetry. Thus, realistic models require the inclusion of disorder effects. In this work, we discuss these within a single-site approximation, the coherent potential approximation, and combine it with the dynamical mean-field theory, allowing to treat interacting electrons in multicomponent alloys on a local level. We extend this combined scheme to off-diagonal disorder, that is, disorder in the hopping amplitudes, by employing the Blackman–Esterling–Berk formalism. For this purpose, we illustrate the ideas of this formalism using tensor diagrams and provide an efficient implementation. The structure of the effective medium is discussed, and a concentration scaling is proposed that resolves some of its peculiarities. The limit of vanishing hopping between different components is discussed and solved analytically for the Bethe lattice with a general coordination number. We exemplify the combined algorithm for a Bethe lattice, showing results that exhibit alloy-band-insulator to correlated-metal to Mott-insulator transitions. We study models of half-metallic ferromagnets to elucidate the effects of local electronic correlations on the spectral function. To model half-metallicity, a static spin splitting is used to produce the half-metallic density of states. Applying the Padé analytic continuation to the self-energy instead of the Green’s function produces reliable spectral functions agreeing with the zero-temperature results obtained for real frequencies. To address transport properties, we investigate the interface of a half-metallic layer and a metallic, band insulating, or Mott insulating layer. We observe charge reconstruction which induces metallicity at the interface; quasiparticle states are present in the Mott insulating layer even for a large Hubbard interaction. The transmission through a barrier made of such a single interacting half-metallic layer sandwiched by metallic leads is studied employing the Meir–Wingreen formalism. This allows for a transparent calculation of the transmission in the presence of the Hubbard interaction. For a strong coupling of the central layer to the leads, we identify high intensity bound states which do not contribute to the transmission. For small coupling, on the other hand, we find resonant states which enhance the transmission. In particular, we demonstrate that even for a single half-metallic layer, highly polarized transmissions are achievable

Moments of parton distribution functions for the pion and rho meson from Nf = 2+1 lattice QCD

We compute the second Mellin moments of parton distribution functions for the pion and rho meson from $N_f = 2 + 1$ lattice QCD using improved Wilson fermions. Our results are presented in terms of singlet and non-singlet flavor combinations and, for the first time, take disconnected contributions fully into account. Besides condensing the common knowledge about spin-1 structure functions and parton distribution functions, we provide a detailed description of the software stack implemented by our group, in order to compute quark-line connected three-point functions using stochastic estimators. The main application is based on the factorization of the entire correlation function into two parts which are evaluated with open spin- (and to some extent flavor-) indices. This allows us to estimate the two contributions of the factorization simultaneously for many different initial and final states and momenta, with little computational overhead. Our numerical analysis yields moments of the structure function $F_1$ (pion and rho) and of the structure function $b_1$, providing additional contributions in the case of spin-1 particles. To this end we use 26 gauge ensembles, mainly generated by the CLS effort, with pion masses ranging from 214 MeV up to 420 MeV and with five different lattice spacings in the range of 0.05 fm to 0.1 fm in our numerical analysis. This choice of gauge configurations enables us to resolve the quark mass dependencies reliably, as well as to extrapolate to the continuum limit. However, due to the resonance character of the rho meson, our final results are possibly contaminated by additional two-pion states, which we also discuss. We present our results in the $\overline{\text{MS}}$ scheme at $\mu = 2$ GeV We find $$v_2^{(u+d+s)} = 0.220 (207), v_2^{(u+d-2s)} = 0.344 (28), a_2^{(u+d+s)} = 0.285 (295), a_2^{(u+d-2s)} = 0.384 (52), d_2^{(u+d+s)} = 0.226 (124), d_2^{(u+d-2s)} = 0.163 (39),$$ for the second moment $v_2$ of the pion structure function $F_1$, the second moment $a_2$ of the rho structure function $F_1$, and the second moment $d_2$ of the rho structure function $b_1$ respectively. Based on these values we finally conclude, that the valence quarks in the pion carry about 35% of the total momentum, in the rho the valence quarks carry about 40% of the total momentum, and the non-vanishing values for $d_2$ suggest that the quarks in the rho meson carry a substantial amount of orbital angular momentum

Air Force Institute of Technology Research Report 2006

This report summarizes the research activities of the Air Force Institute of Technology’s Graduate School of Engineering and Management. It describes research interests and faculty expertise; lists student theses/dissertations; identifies research sponsors and contributions; and outlines the procedures for contacting the school. Included in the report are: faculty publications, conference presentations, consultations, and funded research projects. Research was conducted in the areas of Aeronautical and Astronautical Engineering, Electrical Engineering and Electro-Optics, Computer Engineering and Computer Science, Systems and Engineering Management, Operational Sciences, Mathematics, Statistics and Engineering Physics

Field theoretic formulation and empirical tracking of spatial processes

Spatial processes are attacked on two fronts. On the one hand, tools from theoretical and statistical physics can be used to understand behaviour in complex, spatially-extended multi-body systems. On the other hand, computer vision and statistical analysis can be used to study 4D microscopy data to observe and understand real spatial processes in vivo. On the rst of these fronts, analytical models are developed for abstract processes, which can be simulated on graphs and lattices before considering real-world applications in elds such as biology, epidemiology or ecology. In the eld theoretic formulation of spatial processes, techniques originating in quantum eld theory such as canonical quantisation and the renormalization group are applied to reaction-di usion processes by analogy. These techniques are combined in the study of critical phenomena or critical dynamics. At this level, one is often interested in the scaling behaviour; how the correlation functions scale for di erent dimensions in geometric space. This can lead to a better understanding of how macroscopic patterns relate to microscopic interactions. In this vein, the trace of a branching random walk on various graphs is studied. In the thesis, a distinctly abstract approach is emphasised in order to support an algorithmic approach to parts of the formalism. A model of self-organised criticality, the Abelian sandpile model, is also considered. By exploiting a bijection between recurrent con gurations and spanning trees, an e cient Monte Carlo algorithm is developed to simulate sandpile processes on large lattices. On the second front, two case studies are considered; migratory patterns of leukaemia cells and mitotic events in Arabidopsis roots. In the rst case, tools from statistical physics are used to study the spatial dynamics of di erent leukaemia cell lineages before and after a treatment. One key result is that we can discriminate between migratory patterns in response to treatment, classifying cell motility in terms of sup/super/di usive regimes. For the second case study, a novel algorithm is developed to processes a 4D light-sheet microscopy dataset. The combination of transient uorescent markers and a poorly localised specimen in the eld of view leads to a challenging tracking problem. A fuzzy registration-tracking algorithm is developed to track mitotic events so as to understand their spatiotemporal dynamics under normal conditions and after tissue damage.Open Acces

Hierarchical dynamics of individual RNA helix base pair formation and disruption

This thesis explores the RNA folding problem using single-molecule field effect transistors (smFETs) to measure the lifetimes of individual RNA base-pairing rearrangements. In the course of this research, considerable computational, chemical, and engineering contributions were developed so that the single-molecule measurements could be conducted and quantified. These advancements have allowed, on the basis of the smFET data collected herein, the quantification of a kinetic model for RNA stem-loop structures which has been generalized to quantitatively explore the phenomenological observation that an RNA found in the bacillus subtilis strain acts as a metabolite-sensing switch, allowing RNA polymerase to transcribe the messenger RNA when the metabolite is present and preventing transcription when the metabolite is absent. Together, the data presented quantify a simple model for the base pairing rearrangements that underlie RNA folding