<p> EEG is a noninvasive technique useful for the human brain mapping and for the estimation of neural electrical activities in human brain. A goal of processing EEG signals of a subject is the localization of neural current sources in human brain known as dipoles. Although this location estimation problem can be modeled as a particular kind of parameter estimation problem as in array signal processing, the nonlinear structure of an EEG electrode array, which is much more complicated than a traditional sensor array, makes the problem more difficult. </p> <p> In this thesis, we formulate the inverse problem of the forward model on computing the scalp EEG at a finite set of sensors from multiple dipole sources. It is observed that the geometric structure of the EEG array plays a crucial role in ensuring a unique solution for this problem. We first present a necessary and sufficient condition in the model of a single rotating dipole, that guarantees its location to be uniquely determined, when the second-order statistic of the EEG observation is available. In addition, for a single rotating dipole, a closed-form solution to uniquely determine its position is obtained by exploiting the geometrical structure of the EEG array. </p> <p> In the case of multiple dipoles, we suggest the use of the Maximum Likelihood (ML) estimator, which is often considered optimum in parameter estimation. We propose an efficient localization algorithm based on QR decomposition. Depending on whether or not the probability density functions of the dipole amplitude and the noise are available, we utilize the non-coherent ML or the LS as the criterion to develop a unified successive localization algorithm, so that solving the original multi-dipole optimization problem can be approximated by successively solving a series of single-dipole optimization problems. Numerical simulations show that our methods have much smaller estimation errors than the existing RAP-MUSIC method under non-ideal situations such as low SNR with small number of EEG sensors. </p> / Thesis / Master of Applied Science (MASc)

Digital satellite communication systems are equipped with nonlinear amplifiers such as travelling wave tube (TWT) amplifiers at or near saturation for better efficiency. The TWT exhibits nonlinear distortion in both amplitude and phase (AM/AM and AM/PM) conversion, respectively. That is, in the digital satellite communication the transmission is disturbed not only by the non-linearity of transmitter amplifier, but also by the inter-symbol interference (ISI) with additive white Gaussian noise. To compensate the non-linearity of the transmitter amplifier and ISI, in this thesis, a new nonlinear compensation scheme consists of the predistorter and adaptive third-order Volterra-based equalizer, with the inverse QRD-RLS (IQRD-RLS) algorithm, which are located before and after the nonlinear channel, is proposed respectively. The third-order Volterra filter (TVF) equalizer based on the IQRD-RLS algorithm achieve superior performance, in terms of convergence rate, steady-state mean-squared error (MSE), and numerically stable. They are highly amenable to parallel implementation using array architectures, such as systolic arrays. The computer simulation results using the M-ary PSK modulation scheme are carried out the signal¡¦s constellation diagrams, the learning curve of the MSE and the bit error rate (BER) are compared with conventional least mean square (LMS), gradient adaptive lattice (GAL) and adaptive LMS with lattice pre-filter algorithms.

The object of the thesis research is to realize a complex-valued QR decomposition (QRD) algorithm on FPGAs for MIMO communication systems. The challenge is to implement a QRD processor that efficiently utilizes hardware resources to meet throughput requirements in MIMO systems. By studying the basic QRD algorithm using Givens rotations and the CORDIC algorithm, the thesis develops a master-slave structure to more efficiently implement CORDIC-based Givens rotations compared to traditional methods. Based on the master-slave structure, an processing-element array architecture is proposed to further improve result precision and to achieve near-theoretical latency with parallelized normalization and rotations. The proposed architecture also demonstrates flexible scalability through implementations for different sizes of QRDs. The QRD implementations can process 7.41, 1.90 and 0.209 million matrices per second for two by two, four by four and eight by eight QRDs respectively. This study has built the foundation to develop QRD processors that can fulfill high throughput requirements for MIMO systems.

To satisfy the growing demands of the mobile and personal broadband communications, recently, many innovative technologies have been devised and extensively used for wireless transmission and reception. In the wireless communication systems, even though the performance would be degraded due to channel characteristics, such as multipath fading and background noise, those impacts can be eliminated dramatically through the utilization of diversity and combining. However, some different kinds of interfering sources, including the significant structure interference due to their operation as multiple access in the cellular communication systems, referred to as the multiple access interference (MAI), and inevitable jammers appeared in the overlapped frequency band for common utility, are still existing and now become the main difficulties to collapse the reception performance and system capacity. To suppress the interferences, some advanced signal processing methods, e.g., smart antenna (SA), multiuser detection, interference cancellation, adaptive optimization, and frequency/ frame synchronization, have been suggested to not only alleviate the effects fundamentally but also enhance the signal quality. Orthogonal frequency division multiplexing (OFDM) is a significant multicarrier (MC) technology, and has been widely employed in some commercial communications, such as digital broadcasting and wireless local area network (WLAN). It is considered to be the one of the most promising techniques to combat multipath fading and MAI for the downlinks transmission of the broadband systems. Moreover, spatial processing exploits the diversity provided by SA or intelligent antenna arrays, in which the adaptive beamformer is utilized, and it is an alternative approach to increase the efficiency of wireless system capacity and performance without allocating additional frequency spectrum. It allows the system to make full use of spatial diversity due to multiple antennas. In this dissertation, the wireless communications based on the OFDM technique and the applications of SA are considered. Also, an adaptive linearly constrained (LC) approach via inverse QR-decomposition (IQRD) recursive least-squares (RLS) algorithm is emphasized. The proposed LC-IQRD-RLS algorithm has the merits, such as numerical stability, fast convergence rate, and implementation efficiency, over the conventional adaptive algorithms. Furthermore, by incorporating with derivative constraint, the narrowband array could improve the robustness against to the wideband and coherent jammers. Here, the iterative quadratic maximum likelihood (IQML) algorithm with norm constraint set is utilized to estimate the jammer subspace. Computer simulations verify that the use of narrowband beamformer with an appropriate algorithm, e.g., LC-IQRD-RLS or IQML, could achieve the desired performance for jammer suppression. Next, their applications to the MC-CDMA system with frequency combining process will be fully addressed. In fact, the frequency diversity is achieved through the optimization approach, based on constrained minimum output energy (CMOE) criterion. Unfortunately, it is very sensitive to the signal mismatch due to channel estimation error. To deal with the mismatch problem, the invariant-property provided by constant modulus (CM) criterion along with the LC-IQRD-RLS algorithm is developed. Simulation results show that the frequency combiner with the robust LCCM IQRD-RLS algorithm could be used to recover the transmitted signal without channel mismatch or distortion, and mitigate the MAI efficiently even in the significant near-far effect environment. To further enhance the detection performance and increase system capacity, the space-time MC-CDMA receiver is proposed by combining the advantages of SA and multicarrier transmission technique. This direct fully space-time MC-CDMA receiver can be implemented via a mathematical operator, i.e., kronecker product. For further investigation, a theoretical analysis could be evaluated under certain assumptions to obtain a closed-form expression of bit error rate (BER). This will help us look more inside the impacts due to the numbers of subcarriers and array sensors. In the last chapter, the familiar problem of carrier frequency offset (CFO) is investigated following the standard of IEEE 802.11 a/g OFDM-based WLAN. The overall frequency synchronization scheme consists of three parts, viz., the coarse and fine automatic frequency control (AFC) circuits, and phase locked loop (PLL). With the proposed frequency synchronization scheme, it reserves 2dB power consumption compared with the current specification even some timing issues presented.

The hierarchical (<i>H-</i>) matrix format allows storing a variety of dense matrices from certain applications in a special data-sparse way with linear-polylogarithmic complexity. Many operations from linear algebra like matrix-matrix and matrix-vector products, matrix inversion and LU decomposition can be implemented efficiently using the <i>H</i>-matrix format. Due to its importance in solving many problems in numerical linear algebra like least-squares problems, it is also desirable to have an efficient QR decomposition of <i>H</i>-matrices. In the past, two different approaches for this task have been suggested. We will review the resulting methods and suggest a new algorithm to compute the QR decomposition of an <i>H</i>-matrix. Like other <i>H</i>-arithmetic operations the <i>H</i>QR decomposition is of linear-polylogarithmic complexity. We will compare our new algorithm with the older ones by using two series of test examples and discuss benefits and drawbacks of the new approach.

abstract: This thesis report aims at introducing the background of QR decomposition and its application. QR decomposition using Givens rotations is a efficient method to prevent directly matrix inverse in solving least square minimization problem, which is a typical approach for weight calculation in adaptive beamforming. Furthermore, this thesis introduces Givens rotations algorithm and two general VLSI (very large scale integrated circuit) architectures namely triangular systolic array and linear systolic array for numerically QR decomposition. To fulfill the goal, a 4 input channels triangular systolic array with 16 bits fixed-point format and a 5 input channels linear systolic array are implemented on FPGA (Field programmable gate array). The final result shows that the estimated clock frequencies of 65 MHz and 135 MHz on post-place and route static timing report could be achieved using Xilinx Virtex 6 xc6vlx240t chip. Meanwhile, this report proposes a new method to test the dynamic range of QR-D. The dynamic range of the both architectures can be achieved around 110dB. / Dissertation/Thesis / M.S. Electrical Engineering 2014

Orientadores: Carlile Campos Lavor, Jose Mario Martinez / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-11T21:12:00Z (GMT). No. of bitstreams: 1 Goncalves_MarcosRobertodaSilva_M.pdf: 1220561 bytes, checksum: e3b9dadf0b151f53d8a3e0e572b4c7ab (MD5) Previous issue date: 2008 / Resumo: Neste trabalho, abordamos o problema da determinação de pontos de intersecção de n esferas no Rn. Este problema, além de ser importante matematicamente, é um problema com muitas aplicações, que vão desde a localização de pontos no globo, pelo sistema GPS, até a posicionamento de átomos em estruturas moleculares. O problema de encontrar a intersecção de n esferas no Rn é, em geral, formulado como um conjunto de n equações não-lineares, onde se deseja determinar a sua solução através de um método eficiente e confiável. Mostramos que, com exceção de alguns casos, o problema é geralmente resolvido de forma eficaz, empregando técnicas de álgebra linear. Reformulamos o problema de forma a convertê-lo em um problema linear e apresentamos dois métodos baseados na decomposição de matrizes. Testamos os métodos para casos particulares de baixa dimensão, analisando o custo computacional e possíveis dificuldades que podem surgir devido a erros de medição. / Abstract: We consider the problem of determining the points of intersection of n spheres in R n. This problem has many applications, such as the location of points on the globe by the GPS system and problems related to molecular geometry optimization. The problem of finding the intersection of n spheres in R n is generally expressed as a set of nonlinear equations, where we want to establish an efficient and reliable method to find their solution. We show that, in general, the problem can be solved effectively employing techniques of linear algebra. We reformulate the problem in order to transform it into a linear problem and present two methods based on the decomposition of matrices. We also test the methods in small instances and analyze the computational cost and possible difficulties that may arise due to errors of measurement. / Mestrado / Mestre em Matemática

The emphasis on higher data rates, spectral efficiency and cost reduction has driven the field towards linear modulation techniques such as quadrature phase shift keying (QPSK), quadrature amplitude modulation (QAM), wideband code division multiple access (WCDMA), and orthogonal frequency division multiplexing (OFDM). The result is a complex signal with a non-constant envelope and a high peak-to-average power ratio. This characteristic makes these signals particularly sensitive to the intrinsic nonlinearity of the RF power amplifier (PA) in the transmitter. The nonlinearity will generate intermodulation (IMD) components, also referred to as out-of-band emission or spectral re-growth, which interfere with adjacent channels. Such distortion, or so called Adjacent Channel Interference (ACI), is strictly limited by FCC and ETSI regulations. Meanwhile, the nonlinearity also causes in-band distortion which degrades the bit error rate performance. Typically, the required linearity can be achieved either by reducing power efficiency or by using linearization techniques. For a Class-A PA, simply “backing off” the input power level can improve linearity; however, for high peak to average power ration (PAPR) signals, this normally reduces the power efficiency down to 10% while increasing heat dissipation up to 90%.When considering the vast number of base stations that wireless operators need to account for, increasing power consumption, or in other words, power back-off is not a viable tradeoff. Therefore, amplifier linearization has become an important technology and a desirable alternative to backing-off an amplifier in modern communications systems. In this work, a novel adaptive algorithm is presented for predistorter linearization of power amplifiers. This algorithm uses Pade-Chebyshev polynomials and a QR decomposition followed by back substitution to find the pre-distorter coefficients.This algorithm is implemented on a Field Programmable Gate Array (Stratix 1S80).The implementation provides improved linearization and also runs the algorithm fast enough so that the adaptive part can be done quickly. Yet another challenge was the integration of a transmitter, receiver and this adaptive algorithm into a single FPGA chip and its communication with a base station. The work thus presents a novel pre-distortion implementation technique using an FPGA and a soft processor (Nios 2) which provides significant intermodulation distortion suppression.

The hierarchical (<i>H-</i>) matrix format allows storing a variety of dense matrices from certain applications in a special data-sparse way with linear-polylogarithmic complexity. Many operations from linear algebra like matrix-matrix and matrix-vector products, matrix inversion and LU decomposition can be implemented efficiently using the <i>H</i>-matrix format. Due to its importance in solving many problems in numerical linear algebra like least-squares problems, it is also desirable to have an efficient QR decomposition of <i>H</i>-matrices. In the past, two different approaches for this task have been suggested. We will review the resulting methods and suggest a new algorithm to compute the QR decomposition of an <i>H</i>-matrix. Like other <i>H</i>-arithmetic operations the <i>H</i>QR decomposition is of linear-polylogarithmic complexity. We will compare our new algorithm with the older ones by using two series of test examples and discuss benefits and drawbacks of the new approach.

[EN] Model-based computed tomography (CT) image reconstruction is dominated by iterative algorithms. Although long reconstruction times remain as a barrier in practical applications, techniques to speed up its convergence are object of investigation, obtaining impressive results. In this thesis, a direct algorithm is proposed for model-based image reconstruction. The model-based approximation relies on the construction of a model matrix that poses a linear system which solution is the reconstructed image. The proposed algorithm consists in the QR decomposition of this matrix and the resolution of the system by a backward substitution process. The cost of this image reconstruction technique is a matrix vector multiplication and a backward substitution process, since the model construction and the QR decomposition are performed only once, because of each image reconstruction corresponds to the resolution of the same CT system for a different right hand side. Several problems regarding the implementation of this algorithm arise, such as the exact calculation of a volume intersection, definition of fill-in reduction strategies optimized for CT model matrices, or CT symmetry exploit to reduce the size of the system. These problems have been detailed and solutions to overcome them have been proposed, and as a result, a proof of concept implementation has been obtained. Reconstructed images have been analyzed and compared against the filtered backprojection (FBP) and maximum likelihood expectation maximization (MLEM) reconstruction algorithms, and results show several benefits of the proposed algorithm. Although high resolutions could not have been achieved yet, obtained results also demonstrate the prospective of this algorithm, as great performance and scalability improvements would be achieved with the success in the development of better fill-in strategies or additional symmetries in CT geometry. / [ES] En la reconstrucción de imagen de tomografía axial computerizada (TAC), en su modalidad model-based, prevalecen los algoritmos iterativos. Aunque los altos tiempos de reconstrucción aún son una barrera para aplicaciones prácticas, diferentes técnicas para la aceleración de su convergencia están siendo objeto de investigación, obteniendo resultados impresionantes. En esta tesis, se propone un algoritmo directo para la reconstrucción de imagen model-based. La aproximación model-based se basa en la construcción de una matriz modelo que plantea un sistema lineal cuya solución es la imagen reconstruida. El algoritmo propuesto consiste en la descomposición QR de esta matriz y la resolución del sistema por un proceso de sustitución regresiva. El coste de esta técnica de reconstrucción de imagen es un producto matriz vector y una sustitución regresiva, ya que la construcción del modelo y la descomposición QR se realizan una sola vez, debido a que cada reconstrucción de imagen supone la resolución del mismo sistema TAC para un término independiente diferente. Durante la implementación de este algoritmo aparecen varios problemas, tales como el cálculo exacto del volumen de intersección, la definición de estrategias de reducción del relleno optimizadas para matrices de modelo de TAC, o el aprovechamiento de simetrías del TAC que reduzcan el tama\~no del sistema. Estos problemas han sido detallados y se han propuesto soluciones para superarlos, y como resultado, se ha obtenido una implementación de prueba de concepto. Las imágenes reconstruidas han sido analizadas y comparadas frente a los algoritmos de reconstrucción filtered backprojection (FBP) y maximum likelihood expectation maximization (MLEM), y los resultados muestran varias ventajas del algoritmo propuesto. Aunque no se han podido obtener resoluciones altas aún, los resultados obtenidos también demuestran el futuro de este algoritmo, ya que se podrían obtener mejoras importantes en el rendimiento y la escalabilidad con el éxito en el desarrollo de mejores estrategias de reducción de relleno o simetrías en la geometría TAC. / [CA] En la reconstrucció de imatge tomografia axial computerizada (TAC) en la seua modalitat model-based prevaleixen els algorismes iteratius. Tot i que els alts temps de reconstrucció encara són un obstacle per a aplicacions pràctiques, diferents tècniques per a l'acceleració de la seua convergència estàn siguent objecte de investigació, obtenint resultats impressionants. En aquesta tesi, es proposa un algorisme direct per a la recconstrucció de image model-based. L'aproximació model-based es basa en la construcció d'una matriu model que planteja un sistema lineal quina sol·lució es la imatge reconstruida. L'algorisme propost consisteix en la descomposició QR d'aquesta matriu i la resolució del sistema per un procés de substitució regresiva. El cost d'aquesta tècnica de reconstrucció de imatge es un producte matriu vector i una substitució regresiva, ja que la construcció del model i la descomposició QR es realitzen una sola vegada, degut a que cada reconstrucció de imatge suposa la resolució del mateix sistema TAC per a un tèrme independent diferent. Durant la implementació d'aquest algorisme sorgixen diferents problemes, tals com el càlcul exacte del volum de intersecció, la definició d'estratègies de reducció de farcit optimitzades per a matrius de model de TAC, o el aprofitament de simetries del TAC que redueixquen el tamany del sistema. Aquestos problemes han sigut detallats y s'han proposat solucions per a superar-los, i com a resultat, s'ha obtingut una implementació de prova de concepte. Les imatges reconstruides han sigut analitzades i comparades front als algorismes de reconstrucció filtered backprojection (FBP) i maximum likelihood expectation maximization (MLEM), i els resultats mostren varies ventajes del algorisme propost. Encara que no s'han pogut obtindre resolucions altes ara per ara, els resultats obtinguts també demostren el futur d'aquest algorisme, ja que es prodrien obtindre millores importants en el rendiment i la escalabilitat amb l'éxit en el desemvolupament de millors estratègies de reducció de farcit o simetries en la geometria TAC. / Iborra Carreres, A. (2015). Development of a New 3D Reconstruction Algorithm for Computed Tomography (CT) [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/59421