New Acceleration of Nearly Optimal Univariate Polynomial Root-findERS

Univariate polynomial root-finding has been studied for four millennia and is still the subject of intensive research. Hundreds of efficient algorithms for this task have been proposed. Two of them are nearly optimal. The first one, proposed in 1995, relies on recursive factorization of a polynomial, is quite involved, and has never been implemented. The second one, proposed in 2016, relies on subdivision iterations, was implemented in 2018, and promises to be practically competitive, although user's current choice for univariate polynomial root-finding is the package MPSolve, proposed in 2000, revised in 2014, and based on Ehrlich's functional iterations. By proposing and incorporating some novel techniques we significantly accelerate both subdivision and Ehrlich's iterations. Moreover our acceleration of the known subdivision root-finders is dramatic in the case of sparse input polynomials. Our techniques can be of some independent interest for the design and analysis of polynomial root-finders.Comment: 89 pages, 5 figures, 2 table

Wireless Localization in the Absence of GPS

In this thesis, wireless localization is investigated based on multiple noisy estimates of the time-difference of arrival (TDOA) at each pair of the n \u3e= 4 sensors with different but known locations using WiFi opportunistic signals. Our work is comprehensive and includes channel estimation, symbol detection, TDOA estimation, and location estimation. To mitigate the multipath issue induced by wideband signals, such as WiFi, frequency-division is employed to decompose the wideband RF signal into multiple non-overlapping narrowband signals. To minimize the adverse effects of the clock drift, time-division is proposed to divide the signal into multiple non-overlapping signals in the time domain. In addition, Kalman filtering is proposed, assuming the wide-sense stationary and uncorrelated scattering (WSSUS) channel and the first order auto-regressive (AR) model are used. Because of the multiple TDOA estimates at each pair of the WiFi receiver sensors, an efficient algorithm is developed to estimate the target location. The localization technique developed in this thesis can also be extended to other radio frequency (RF) signals, as shown in our simulation study for out-door localization. The simulation results in our thesis show the effectiveness of the wireless localization, although further work is needed to resolve the nonlinear estimation problem involved in localization based on TDOA estimates

Blockwise Transform Image Coding Enhancement and Edge Detection

The goal of this thesis is high quality image coding, enhancement and edge detection. A unified approach using novel fast transforms is developed to achieve all three objectives. Requirements are low bit rate, low complexity of implementation and parallel processing. The last requirement is achieved by processing the image in small blocks such that all blocks can be processed simultaneously. This is similar to biological vision. A major issue is to minimize the resulting block effects. This is done by using proper transforms and possibly an overlap-save technique. The bit rate in image coding is minimized by developing new results in optimal adaptive multistage transform coding. Newly developed fast trigonometric transforms are also utilized and compared for transform coding, image enhancement and edge detection. Both image enhancement and edge detection involve generalised bandpass filtering wit fast transforms. The algorithms have been developed with special attention to the properties of biological vision systems

Study and implementation of a low complexity receiver using TCH codes

The use of coding in telecommunications systems reveals to be a technique with an essential contribution to the improvement of the recovery of transmitted signals. Depending on the circumstances to which a signal is subjected at transmission, by recurring to coding, it is possible to attenuate the unfavorable effects that result from this process, obtaining a signal with superior quality in comparison with a scenario where the presence of coding is absent. This study aims to test the feasibility of a high-rate wireless communications system using TCH codes being applied to an OFDM signal, subjected to noise components introduced by a wireless AWGN channel, considering a free path propagation model. Due to their correlation properties, the use of TCH codes reveals to be adequate since they allow the same codewords to be used to realize both error correction and channel estimation, mitigating the channels effects, leading to the realization of a receiver with lower complexity. With the intent of performing a qualitative analysis to this system, a simple simulation is executed in MATLAB where an OFDM signal is generated, being therefore applied various TCH codes and, through channel estimation, obtain the BER for their respective code lengths and, consequently, coding gains. The results were obtained for the modulation indexes of 16, 64 and 256-QAM. These demonstrate that the implementation of TCH codes is a viable option to reduce the rate of recovered errors, enabling the reception of a signal with better reliability, especially for higher code lengths and modulation indexes.O uso de codificação em sistemas de telecomunicações revela-se uma técnica com um contributo essencial na melhoria da recuperação de sinais transmitidos. Dependendo das circunstâncias às quais um sinal é submetido aquando a sua transmissão, com recurso à codificação, é possível atenuar os efeitos adversos resultantes deste processo, obtendo uma qualidade no sinal recebido superior face a um cenário com ausência da mesma. Este estudo tem como objetivo testar a exequibilidade de um sistema de comunicações sem fios para alto débito usando códigos TCH e aplicando-os a um sinal OFDM, sujeito a componentes de ruído introduzidos por um canal sem fios AWGN, considerando um modelo de propagação em espaço livre. Devido às propriedades de correlação destes códigos, a sua utilização revela-se adequada pois permite que as mesmas palavras de código sejam utilizadas para efetuar correção de erros, minimizando os efeitos do canal, possibilitando o desenvolvimento de um recetor com menor complexidade. Visando efetuar uma análise qualitativa do sistema, é realizada uma simulação simples em MATLAB onde é gerado um sinal OFDM ao qual são aplicados diversos códigos TCH, realizando estimação de canal com a finalidade de obter o BER para os diferentes comprimentos dos códigos e, consequentemente, ganhos de codificação relativos aos mesmos. Os resultados obtidos foram realizados para os índices de modulação 16, 64 e 256-QAM. Estes demonstram que o uso destes códigos é uma opção viável para reduzir os erros detetados, permitindo recuperar o sinal com maior fiabilidade, especialmente para comprimentos de código e índices de modulação elevados

A spectral scheme for Kohn-Sham density functional theory of clusters

Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems -- the plane-wave method -- is a spectral method based on eigenfunction expansion, we formulate a spectral method designed towards solving the Kohn-Sham equations for clusters. This allows for efficient calculation of the electronic structure of clusters (and molecules) with high accuracy and systematic convergence properties without the need for any artificial periodicity. The basis functions in this method form a complete orthonormal set and are expressible in terms of spherical harmonics and spherical Bessel functions. Computation of the occupied eigenstates of the discretized Kohn-Sham Hamiltonian is carried out using a combination of preconditioned block eigensolvers and Chebyshev polynomial filter accelerated subspace iterations. Several algorithmic and computational aspects of the method, including computation of the electrostatics terms and parallelization are discussed. We have implemented these methods and algorithms into an efficient and reliable package called ClusterES (Cluster Electronic Structure). A variety of benchmark calculations employing local and non-local pseudopotentials are carried out using our package and the results are compared to the literature. Convergence properties of the basis set are discussed through numerical examples. Computations involving large systems that contain thousands of electrons are demonstrated to highlight the efficacy of our methodology. The use of our method to study clusters with arbitrary point group symmetries is briefly discussed.Comment: Manuscript submitted (with revisions) to Journal of Computational Physic

Optical Orthogonal Frequency Division Multiplexed communication systems: analysis, design and optimization

En este trabajo se realiza una intensiva labor teórica de descripción de sistemas de comunicaciones ópticas que utilizan la técnica de multiplexación por división de frecuencias ortogonales (OFDM en inglés), más concretamente en sistemas con modulación directa de la intensidad de un láser y detección directa. Se parte pues de un modelo analítico que estudia con detalle todos aquellos fenómenos que afectan a la señal de información detectada en el receptor. Tales fenómenos son: la nolinealidad del láser, las modulaciones de intensidad y de fase ópticas, la propagación a través de la fibra óptica teniendo en cuenta la dispersión cromática de primer orden, y la detección de intensidad óptica final mediante un detector de ley cuadrática. El modelo analítico es validado mediante comparaciones con resultados obtenidos a través de simulaciones con software comercial. Dada la característica singularidad de las señales OFDM debidas a su naturaleza multi-portadora, la amplitud de la señal generada es aleatoria, y el modelo analítico es complementado con un estudio que contempla el recorte o "clipping" en el transmisor. Además, se tiene en cuenta los efectos de filtrado de la señal a lo largo de sistema de comunicaciones. Con el trabajo analítico realizado se está en disposición de realizar una descripción bastante completa de los principales fenómenos y realizar estudios para evaluar el funcionamiento final ante diferentes valores de los parámetros del sistema. Es bien sabido que los sistemas de comunicaciones ópticas con modulación y detección directa se ven perjudicados por la distorsión no lineal, que para señales multi-portadora como OFDM se traduce en la mezcla de los símbolos de información que transportan las diferentes subportadoras. Para mitigar la distorsión no lineal y así mejorar el funcionamiento del sistema, se propone el uso de una técnica de pre-distorsión que se basa en el modelo analítico previamente propuesto. Esta técnica mejora la eficiencia de modulación, haciendo posible incrementar el término de la señal de información sin que se vea incrementada la distorsión no lineal en el receptor. La técnica aquí propuesta se compara también con otra ya publicada con el objetivo de evaluar su funcionamiento. Otra técnica para la mejora de sistemas con modulación y detección directas es la realizada mediante filtrado óptico. Aunque se conoce de forma más o menos intuitiva su funcionamiento para formatos de modulación ópticos tradicionales, es preciso disponer de una formulación matemática para señales ópticas OFDM para entender de forma exacta su principio de operación, las mejoras obtenidas, así como su potencial. En esta estapa se realiza esta formulación matemática ampliando el análisis teórico previamente propuesto, y se aplica para evaluar el funcionamiento obtenido con diversas estructuras de filtrado óptico. Finalmente, puesto que un potencial escenario de funcionamiento para señales ópticas OFDM son las redes de acceso donde operan más de un usuario, se propone y se estudia la técnica "interleaving division multiple access" (IDMA) en combinación con OFDM.Sánchez Costa, C. (2014). Optical Orthogonal Frequency Division Multiplexed communication systems: analysis, design and optimization [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/39375TESI

Automatic modulation classification of communication signals

The automatic modulation recognition (AMR) plays an important role in various civilian and military applications. Most of the existing AMR algorithms assume that the input signal is only of analog modulation or is only of digital modulation. In blind environments, however, it is impossible to know in advance if the received communication signal is analogue modulated or digitally modulated. Furthermore, it is noted that the applications of the currently existing AMR algorithms designed for handling both analog and digital communication signals are rather restricted in practice. Motivated by this, an AMR algorithm that is able to discriminate between analog communication signals and digital communication signals is developed in this dissertation. The proposed algorithm is able to recognize the concrete modulation type if the input is an analog communication signal and to estimate the number of modulation levels and the frequency deviation if the input is an exponentially modulated digital communication signal. For linearly modulated digital communication signals, the proposed classifier will classify them into one of several nonoverlapping sets of modulation types. In addition, in M-ary FSK (MFSK) signal classification, two classifiers have also been developed. These two classifiers are also capable of providing good estimate of the frequency deviation of a received MFSK signal. For further classification of linearly modulated digital communication signals, it is often necessary to blindly equalize the received signal before performing modulation recognition. This doing generally requires knowing the carrier frequency and symbol rate of the input signal. For this purpose, a blind carrier frequency estimation algorithm and a blind symbol rate estimation algorithm have been developed. The carrier frequency estimator is based on the phases of the autocorrelation functions of the received signal. Unlike the cyclic correlation based estimators, it does not require the transmitted symbols being non-circularly distributed. The symbol rate estimator is based on digital communication signals\u27 cyclostationarity related to the symbol rate. In order to adapt to the unknown symbol rate as well as the unknown excess bandwidth, the received signal is first filtered by using a bank of filters. Symbol rate candidates and their associated confident measurements are extracted from the fourth order cyclic moments of the filtered outputs, and the final estimate of symbol rate is made based on weighted majority voting. A thorough evaluation of some well-known feature based AMR algorithms is also presented in this dissertation