A fast algorithm for LR-2 factorization of Toeplitz matrices

In this paper a new order recursive algorithm for the efficient −1 factorization of Toeplitz matrices is described. The proposed algorithm can be seen as a fast modified Gram-Schmidt method which recursively computes the orthonormal columns i, i = 1,2, …,p, of , as well as the elements of R−1, of a Toeplitz matrix with dimensions L × p. The factor estimation requires 8Lp MADS (multiplications and divisions). Matrix −1 is subsequently estimated using 3p2 MADS. A faster algorithm, based on a mixed and −1 updating scheme, is also derived. It requires 7Lp + 3.5p2 MADS. The algorithm can be efficiently applied to batch least squares FIR filtering and system identification. When determination of the optimal filter is the desired task it can be utilized to compute the least squares filter in an order recursive way. The algorithm operates directly on the experimental data, overcoming the need for covariance estimates. An orthogonalized version of the proposed −1 algorithm is derived. Matlab code implementing the algorithm is also supplied

Improved approximate QR-LS algorithms for adaptive filtering

This paper studies a class of O(N) approximate QR-based least squares (A-QR-LS) algorithm recently proposed by Liu in 1995. It is shown that the A-QR-LS algorithm is equivalent to a normalized LMS algorithm with time-varying stepsizes and element-wise normalization of the input signal vector. It reduces to the QR-LMS algorithm proposed by Liu et al. in 1998, when all the normalization constants are chosen as the Euclidean norm of the input signal vector. An improved transform-domain approximate QR-LS (TA-QR-LS) algorithm, where the input signal vector is first approximately decorrelated by some unitary transformations before the normalization, is proposed to improve its convergence for highly correlated signals. The mean weight vectors of the algorithms are shown to converge to the optimal Wiener solution if the weighting factor w of the algorithm is chosen between 0 and 1. New Givens rotations-based algorithms for the A-QR-LS, TA-QR-LS, and the QR-LMS algorithms are proposed to reduce their arithmetic complexities. This reduces the arithmetic complexity by a factor of 2, and allows square root-free versions of the algorithms be developed. The performances of the various algorithms are evaluated through computer simulation of a system identification problem and an acoustic echo canceller. © 2004 IEEE.published_or_final_versio

Simulating both parity sectors of the Hubbard Model with Tensor Networks

Tensor networks are a powerful tool to simulate a variety of different physical models, including those that suffer from the sign problem in Monte Carlo simulations. The Hubbard model on the honeycomb lattice with non-zero chemical potential is one such problem. Our method is based on projected entangled pair states (PEPS) using imaginary time evolution. We demonstrate that it provides accurate estimators for the ground state of the model, including cases where Monte Carlo simulations fail miserably. In particular it shows near to optimal, that is linear, scaling in lattice size. We also present a novel approach to directly simulate the subspace with an odd number of fermions. It allows to independently determine the ground state in both sectors. Without a chemical potential this corresponds to half filling and the lowest energy state with one additional electron or hole. We identify several stability issues, such as degenerate ground states and large single particle gaps, and provide possible fixes.Comment: 20 pages, 20 figure

Effi cient algorithms for iterative detection and decoding in Multiple-Input and Multiple-Output Communication Systems

This thesis fits into the Multiple-Input Multiple-Output (MIMO) communication systems. Nowadays, these schemes are the most promising technology in the field of wireless communications. The use of this technology allows to increase the rate and the quality of the transmission through the use of multiple antennas at the transmitter and receiver sides. Furthermore, the MIMO technology can also be used in a multiuser scenario, where a Base Station (BS) equipped with several antennas serves several users that share the spatial dimension causing interference. However, employing precoding algorithms the signal of the multiuser interference can be mitigated. For these reasons, the MIMO technology has become an essential key in many new generation communications standards. On the other hand, Massive MIMO technology or Large MIMO, where the BS is equipped with very large number of antennas (hundreds or thousands) serves many users in the same time-frequency resource. Nevertheless, the advantages provided by the MIMO technology entail a substantial increase in the computational cost. Therefore the design of low-complexity receivers is an important issue which is tackled throughout this thesis. To this end, one of the main contributions of this dissertation is the implementation of efficient soft-output detectors and precoding schemes. First, the problem of efficient soft detection with no iteration at the receiver has been addressed. A detailed overview of the most employed soft detectors is provided. Furthermore, the complexity and performance of these methods are evaluated and compared. Additionally, two low-complexity algorithms have been proposed. The first algorithm is based on the efficient Box Optimization Hard Detector (BOHD) algorithm and provides a low-complexity implementation achieving a suitable performance. The second algorithm tries to reduce the computational cost of the Subspace Marginalization with Interference Suppression (SUMIS) algorithm. Second, soft-input soft-output (SISO) detectors, which are included in an iterative receiver structure, have been investigated. An iterative receiver improves the performance with respect to no iteration, achieving a performance close to the channel capacity. In contrast, its computational cost becomes prohibitive. In this context, three algorithms are presented. Two of them achieve max-log performance reducing the complexity of standard SISO detectors. The last one achieves near max-log performance with low complexity. The precoding problem has been addressed in the third part of this thesis. An analysis of some of the most employed precoding techniques has been carried out. The algorithms have been compared in terms of performance and complexity. In this context, the impact of the channel matrix condition number on the performance of the precoders has been analyzed. This impact has been exploited to propose an hybrid precoding scheme that reduces the complexity of the previously proposed precoders. In addition, in Large MIMO systems, an alternative precoder scheme is proposed. In the last part of the thesis, parallel implementations of the SUMIS algorithm are presented. Several strategies for the parallelization of the algorithm are proposed and evaluated on two different platforms: multicore central processing unit (CPU) and graphics processing unit (GPU). The parallel implementations achieve a significant speedup compared to the CPU version. Therefore, these implementations allow to simulate a scalable quasi optimal soft detector in a Large MIMO system much faster than by conventional simuLa presente tesis se enmarca dentro de los sistemas de comunicaciones de múltiples antenas o sistemas MIMO. Hoy en día, estos sistemas presentan una de las tecnologías más prometedoras dentro de los sistemas comunicaciones inalámbricas. A través del uso de múltiples antenas en ambos lados, transmisor y receptor, la tasa de transmisión y la calidad de la misma es aumentada. Por otro lado, la tecnología MIMO puede ser utilizada en un escenario multiusuario, donde una estación base (BS) la cual está equipada con varias antenas, sirve a varios usuarios al mismo tiempo, estos usuarios comparten dimensión espacial causando interferencias multiusuario. Por todas estas razones, la tecnología MIMO ha sido adoptada en muchos de los estándares de comunicaciones de nueva generación. Por otro lado, la tecnología MIMO Masivo, en la cual la estación base está equipada con un gran número de antenas (cientos o miles) que sirve a muchos usuarios en el mismo recurso de tiempo-frecuencia. Sin embargo, las ventajas proporcionadas por los sistemas MIMO implican un aumento en el coste computacional requerido. Por ello, el diseño de receptores de baja complejidad es una cuestión importante en estos sistemas. Para conseguir esta finalidad, las principales contribuciones de la tesis se basan en la implementación de algoritmos de detección soft y esquemas de precodificación eficientes. En primer lugar, el problema de la detección soft eficiente en un sistema receptor sin iteración es abordado. Una descripción detallada sobre los detectores soft más empleados es presentada. Por otro lado, han sido propuestos dos algoritmos de bajo coste. El primer algoritmo está basado en el algoritmo Box Optimization Hard Detector (BOHD) y proporciona una baja complejidad de implementación logrando un buen rendimiento. El segundo de los algoritmos propuestos intenta reducir el coste computacional del conocido algoritmo Subspace Marginalization with Interference Suppression (SUMIS). En segundo lugar, han sido investidados detectores de entrada y salida soft (SISO, soft-input soft-output) los cuales son ejecutados en estructuras de recepción iterativa. El empleo de un receptor iterativo mejora el rendimiento del sistema con respecto a no realizar realimentación, pudiendo lograr la capacidad óptima. Por el contrario, el coste computacional se vuelve prohibitivo. En este contexto, tres algoritmos han sido presentados. Dos de ellos logran un rendimiento óptimo, reduciendo la complejidad de los detectores SISO óptimos que normalmente son empleados. Por el contrario, el otro algoritmo logra un rendimiento casi óptimo a baja complejidad. En la tercera parte, se ha abordado el problema de la precodificación. Se ha llevado a cabo un análisis de algunas de las técnicas de precodificación más usadas. En este contexto, se ha evaluado el impacto que el número de condición de la matriz de canal tiene en el rendimiento de los precodificadores. Además, se ha aprovechado este impacto para proponer un precodificador hibrido. Por otro lado, en MIMO Masivo, se ha propuesto un esquema precodificador. En la última parte de la tesis, la implementación paralela del algoritmo SUMIS es presentada. Varias estrategias sobre la paralelización del algoritmo han sido propuestas y evaluadas en dos plataformas diferentes: Unidad Central de Procesamiento multicore (multicore CPU) y Unidad de Procesamiento Gráfico (GPU). Las implementaciones paralelas consiguen una mejora de speedup. Estas implementaciones permiten simular para MIMO Masivo y de forma más rápida que por simulación convencional, un algoLa present tesi s'emmarca dins dels sistemes de comunicacions de múltiples antenes o sistemes MIMO. Avui dia, aquestos sistemes presenten una de les tecnologies més prometedora dins dels sistemes de comunicacions inalàmbriques. A través de l'ús de múltiples antenes en tots dos costats, transmissor y receptor, es pot augmentar la taxa de transmissió i la qualitat de la mateixa. D'altra banda, la tecnologia MIMO es pot utilitzar en un escenari multiusuari, on una estació base (BS) la qual està equipada amb diverses antenes serveix a diversos usuaris al mateix temps, aquests usuaris comparteixen dimensió espacial causant interferències multiusuari. Per totes aquestes raons, la tecnologia MIMO ha sigut adoptada en molts dels estàndars de comunicacions de nova generació. D'altra banda, la tecnologia MIMO Massiu, en la qual l'estació base està equipada amb un gran nombre d'antenes (centenars o milers) que serveix a molts usuaris en el mateix recurs de temps-freqüència. No obstant això, els avantatges proporcionats pels sistemes MIMO impliquen un augment en el cost computacional requerit. Per això, el disseny de receptors de baixa complexitat és una qüestió important en aquests sistemes. Per tal d'aconseguir esta finalitat, les principals contribucions de la tesi es basen en la implementació d'algoritmes de detecció soft i esquemes de precodificació eficients. En primer lloc, és abordat el problema de la detecció soft eficient en un sistema receptor sense interacció. Una descripció detallada dels detectors soft més emprats és presentada. D'altra banda, han sigut proposats dos algorismes de baix cost. El primer algorisme està basat en l'algorisme Box Optimization Hard Decoder (BOHD) i proporciona una baixa complexitat d'implementació aconseguint un bon resultat. El segon dels algorismes proposats intenta reduir el cost computacional del conegut algoritme Subspace Marginalization with Interference Suppression (SUMIS). En segon lloc, detectors d'entrada i eixidia soft (SISO, soft-input soft-output) els cuals són executats en estructures de recepció iterativa han sigut investigats. L'ocupació d'un receptor iteratiu millora el rendiment del sistema pel que fa a no realitzar realimentació, podent aconseguir la capacitat òptima. Per contra, el cost computacional es torna prohibitiu. En aquest context, tres algorismes han sigut presentats. Dos d'ells aconsegueixen un rendiment òptim, reduint la complexitat dels detectors SISO òptims que normalment són emprats. Per contra, l'altre algorisme aconsegueix un rendiment quasi òptim a baixa complexitat. En la tercera part, s'ha abordat el problema de la precodificació. S'ha dut a terme una anàlisi d'algunes de les tècniques de precodificació més usades, prestant especial atenció al seu rendiment i a la seua complexitat. Dins d'aquest context, l'impacte que el nombre de condició de la matriu de canal té en el rendiment dels precodificadors ha sigut avaluat. A més, aquest impacte ha sigut aprofitat per a proposar un precodificador híbrid , amb la finalitat de reduir la complexitat d'algorismes prèviament proposats. D'altra banda, en MIMO Massiu, un esquema precodificador ha sigut proposat. En l'última part, la implementació paral·lela de l'algorisme SUMIS és presentada. Diverses estratègies sobre la paral·lelizació de l'algorisme han sigut proposades i avaluades en dues plataformes diferents: multicore CPU i GPU. Les implementacions paral·leles aconsegueixen una millora de speedup quan el nombre d'àntenes o l'ordre de la constel·lació incrementen. D'aquesta manera, aquestes implementacions permeten simular per a MIMO Massiu, i de forma més ràpida que la simulació convencional.Simarro Haro, MDLA. (2017). Effi cient algorithms for iterative detection and decoding in Multiple-Input and Multiple-Output Communication Systems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/86186TESI

Full nonperturbative QCD simulations with 2+1 flavors of improved staggered quarks

Dramatic progress has been made over the last decade in the numerical study of quantum chromodynamics (QCD) through the use of improved formulations of QCD on the lattice (improved actions), the development of new algorithms and the rapid increase in computing power available to lattice gauge theorists. In this article we describe simulations of full QCD using the improved staggered quark formalism, ``asqtad'' fermions. These simulations were carried out with two degenerate flavors of light quarks (up and down) and with one heavier flavor, the strange quark. Several light quark masses, down to about 3 times the physical light quark mass, and six lattice spacings have been used. These enable controlled continuum and chiral extrapolations of many low energy QCD observables. We review the improved staggered formalism, emphasizing both advantages and drawbacks. In particular, we review the procedure for removing unwanted staggered species in the continuum limit. We then describe the asqtad lattice ensembles created by the MILC Collaboration. All MILC lattice ensembles are publicly available, and they have been used extensively by a number of lattice gauge theory groups. We review physics results obtained with them, and discuss the impact of these results on phenomenology. Topics include the heavy quark potential, spectrum of light hadrons, quark masses, decay constant of light and heavy-light pseudoscalar mesons, semileptonic form factors, nucleon structure, scattering lengths and more. We conclude with a brief look at highly promising future prospects.Comment: 157 pages; prepared for Reviews of Modern Physics. v2: some rewriting throughout; references update

Algorithms in Lattice QCD

The enormous computing resources that large-scale simulations in Lattice QCD require will continue to test the limits of even the largest supercomputers into the foreseeable future. The efficiency of such simulations will therefore concern practitioners of lattice QCD for some time to come. I begin with an introduction to those aspects of lattice QCD essential to the remainder of the thesis, and follow with a description of the Wilson fermion matrix M, an object which is central to my theme. The principal bottleneck in Lattice QCD simulations is the solution of linear systems involving M, and this topic is treated in depth. I compare some of the more popular iterative methods, including Minimal Residual, Corij ugate Gradient on the Normal Equation, BI-Conjugate Gradient, QMR., BiCGSTAB and BiCGSTAB2, and then turn to a study of block algorithms, a special class of iterative solvers for systems with multiple right-hand sides. Included in this study are two block algorithms which had not previously been applied to lattice QCD. The next chapters are concerned with a generalised Hybrid Monte Carlo algorithm (OHM C) for QCD simulations involving dynamical quarks. I focus squarely on the efficient and robust implementation of GHMC, and describe some tricks to improve its performance. A limited set of results from HMC simulations at various parameter values is presented. A treatment of the non-hermitian Lanczos method and its application to the eigenvalue problem for M rounds off the theme of large-scale matrix computations

Algorithms and structures for long adaptive echo cancellers

The main theme of this thesis is adaptive echo cancellation. Two novel independent approaches are proposed for the design of long echo cancellers with improved performance. In the first approach, we present a novel structure for bulk delay estimation in long echo cancellers which considerably reduces the amount of excess error. The miscalculation of the delay between the near-end and the far-end sections is one of the main causes of this excess error. Two analyses, based on the Least Mean Squares (LMS) algorithm, are presented where certain shapes for the transitions between the end of the near-end section and the beginning of the far-end one are considered. Transient and steady-state behaviours and convergence conditions for the proposed algorithm are studied. Comparisons between the algorithms developed for each transition are presented, and the simulation results agree well with the theoretical derivations. In the second approach, a generalised performance index is proposed for the design of the echo canceller. The proposed algorithm consists of simultaneously applying the LMS algorithm to the near-end section and the Least Mean Fourth (LMF) algorithm to the far-end section of the echo canceller. This combination results in a substantial improvement of the performance of the proposed scheme over both the LMS and other algorithms proposed for comparison. In this approach, the proposed algorithm will be henceforth called the Least Mean Mixed-Norm (LMMN) algorithm. The advantages of the LMMN algorithm over previously reported ones are two folds: it leads to a faster convergence and results in a smaller misadjustment error. Finally, the convergence properties of the LMMN algorithm are derived and the simulation results confirm the superior performance of this proposed algorithm over other well known algorithms