HIGH PERFORMANCE, LOW COST SUBSPACE DECOMPOSITION AND POLYNOMIAL ROOTING FOR REAL TIME DIRECTION OF ARRIVAL ESTIMATION: ANALYSIS AND IMPLEMENTATION

This thesis develops high performance real-time signal processing modules for direction of arrival (DOA) estimation for localization systems. It proposes highly parallel algorithms for performing subspace decomposition and polynomial rooting, which are otherwise traditionally implemented using sequential algorithms. The proposed algorithms address the emerging need for real-time localization for a wide range of applications. As the antenna array size increases, the complexity of signal processing algorithms increases, making it increasingly difficult to satisfy the real-time constraints. This thesis addresses real-time implementation by proposing parallel algorithms, that maintain considerable improvement over traditional algorithms, especially for systems with larger number of antenna array elements. Singular value decomposition (SVD) and polynomial rooting are two computationally complex steps and act as the bottleneck to achieving real-time performance. The proposed algorithms are suitable for implementation on field programmable gated arrays (FPGAs), single instruction multiple data (SIMD) hardware or application specific integrated chips (ASICs), which offer large number of processing elements that can be exploited for parallel processing. The designs proposed in this thesis are modular, easily expandable and easy to implement. Firstly, this thesis proposes a fast converging SVD algorithm. The proposed method reduces the number of iterations it takes to converge to correct singular values, thus achieving closer to real-time performance. A general algorithm and a modular system design are provided making it easy for designers to replicate and extend the design to larger matrix sizes. Moreover, the method is highly parallel, which can be exploited in various hardware platforms mentioned earlier. A fixed point implementation of proposed SVD algorithm is presented. The FPGA design is pipelined to the maximum extent to increase the maximum achievable frequency of operation. The system was developed with the objective of achieving high throughput. Various modern cores available in FPGAs were used to maximize the performance and details of these modules are presented in detail. Finally, a parallel polynomial rooting technique based on Newton’s method applicable exclusively to root-MUSIC polynomials is proposed. Unique characteristics of root-MUSIC polynomial’s complex dynamics were exploited to derive this polynomial rooting method. The technique exhibits parallelism and converges to the desired root within fixed number of iterations, making this suitable for polynomial rooting of large degree polynomials. We believe this is the first time that complex dynamics of root-MUSIC polynomial were analyzed to propose an algorithm. In all, the thesis addresses two major bottlenecks in a direction of arrival estimation system, by providing simple, high throughput, parallel algorithms

Evaluating techniques for parallelization tuning in MPI, OmpSs and MPI/OmpSs

Parallel programming is used to partition a computational problem among multiple processing units and to define how they interact (communicate and synchronize) in order to guarantee the correct result. The performance that is achieved when executing the parallel program on a parallel architecture is usually far from the optimal: computation unbalance and excessive interaction among processing units often cause lost cycles, reducing the efficiency of parallel computation. In this thesis we propose techniques oriented to better exploit parallelism in parallel applications, with emphasis in techniques that increase asynchronism. Theoretically, this type of parallelization tuning promises multiple benefits. First, it should mitigate communication and synchronization delays, thus increasing the overall performance. Furthermore, parallelization tuning should expose additional parallelism and therefore increase the scalability of execution. Finally, increased asynchronism would provide higher tolerance to slower networks and external noise. In the first part of this thesis, we study the potential for tuning MPI parallelism. More specifically, we explore automatic techniques to overlap communication and computation. We propose a speculative messaging technique that increases the overlap and requires no changes of the original MPI application. Our technique automatically identifies the application’s MPI activity and reinterprets that activity using optimally placed non-blocking MPI requests. We demonstrate that this overlapping technique increases the asynchronism of MPI messages, maximizing the overlap, and consequently leading to execution speedup and higher tolerance to bandwidth reduction. However, in the case of realistic scientific workloads, we show that the overlapping potential is significantly limited by the pattern by which each MPI process locally operates on MPI messages. In the second part of this thesis, we study the potential for tuning hybrid MPI/OmpSs parallelism. We try to gain a better understanding of the parallelism of hybrid MPI/OmpSs applications in order to evaluate how these applications would execute on future machines and to predict the execution bottlenecks that are likely to emerge. We explore how MPI/OmpSs applications could scale on the parallel machine with hundreds of cores per node. Furthermore, we investigate how this high parallelism within each node would reflect on the network constraints. We especially focus on identifying critical code sections in MPI/OmpSs. We devised a technique that quickly evaluates, for a given MPI/OmpSs application and the selected target machine, which code section should be optimized in order to gain the highest performance benefits. Also, this thesis studies techniques to quickly explore the potential OmpSs parallelism inherent in applications. We provide mechanisms to easily evaluate potential parallelism of any task decomposition. Furthermore, we describe an iterative trialand-error approach to search for a task decomposition that will expose sufficient parallelism for a given target machine. Finally, we explore potential of automating the iterative approach by capturing the programmers’ experience into an expert system that can autonomously lead the search process. Also, throughout the work on this thesis, we designed development tools that can be useful to other researchers in the field. The most advanced of these tools is Tareador – a tool to help porting MPI applications to MPI/OmpSs programming model. Tareador provides a simple interface to propose some decomposition of a code into OmpSs tasks. Tareador dynamically calculates data dependencies among the annotated tasks, and automatically estimates the potential OmpSs parallelization. Furthermore, Tareador gives additional hints on how to complete the process of porting the application to OmpSs. Tareador already proved itself useful, by being included in the academic classes on parallel programming at UPC.La programación paralela consiste en dividir un problema de computación entre múltiples unidades de procesamiento y definir como interactúan (comunicación y sincronización) para garantizar un resultado correcto. El rendimiento de un programa paralelo normalmente está muy lejos de ser óptimo: el desequilibrio de la carga computacional y la excesiva interacción entre las unidades de procesamiento a menudo causa ciclos perdidos, reduciendo la eficiencia de la computación paralela. En esta tesis proponemos técnicas orientadas a explotar mejor el paralelismo en aplicaciones paralelas, poniendo énfasis en técnicas que incrementan el asincronismo. En teoría, estas técnicas prometen múltiples beneficios. Primero, tendrían que mitigar el retraso de la comunicación y la sincronización, y por lo tanto incrementar el rendimiento global. Además, la calibración de la paralelización tendría que exponer un paralelismo adicional, incrementando la escalabilidad de la ejecución. Finalmente, un incremente en el asincronismo proveería una tolerancia mayor a redes de comunicación lentas y ruido externo. En la primera parte de la tesis, estudiamos el potencial para la calibración del paralelismo a través de MPI. En concreto, exploramos técnicas automáticas para solapar la comunicación con la computación. Proponemos una técnica de mensajería especulativa que incrementa el solapamiento y no requiere cambios en la aplicación MPI original. Nuestra técnica identifica automáticamente la actividad MPI de la aplicación y la reinterpreta usando solicitudes MPI no bloqueantes situadas óptimamente. Demostramos que esta técnica maximiza el solapamiento y, en consecuencia, acelera la ejecución y permite una mayor tolerancia a las reducciones de ancho de banda. Aún así, en el caso de cargas de trabajo científico realistas, mostramos que el potencial de solapamiento está significativamente limitado por el patrón según el cual cada proceso MPI opera localmente en el paso de mensajes. En la segunda parte de esta tesis, exploramos el potencial para calibrar el paralelismo híbrido MPI/OmpSs. Intentamos obtener una comprensión mejor del paralelismo de aplicaciones híbridas MPI/OmpSs para evaluar de qué manera se ejecutarían en futuras máquinas. Exploramos como las aplicaciones MPI/OmpSs pueden escalar en una máquina paralela con centenares de núcleos por nodo. Además, investigamos cómo este paralelismo de cada nodo se reflejaría en las restricciones de la red de comunicación. En especia, nos concentramos en identificar secciones críticas de código en MPI/OmpSs. Hemos concebido una técnica que rápidamente evalúa, para una aplicación MPI/OmpSs dada y la máquina objetivo seleccionada, qué sección de código tendría que ser optimizada para obtener la mayor ganancia de rendimiento. También estudiamos técnicas para explorar rápidamente el paralelismo potencial de OmpSs inherente en las aplicaciones. Proporcionamos mecanismos para evaluar fácilmente el paralelismo potencial de cualquier descomposición en tareas. Además, describimos una aproximación iterativa para buscar una descomposición en tareas que mostrará el suficiente paralelismo en la máquina objetivo dada. Para finalizar, exploramos el potencial para automatizar la aproximación iterativa. En el trabajo expuesto en esta tesis hemos diseñado herramientas que pueden ser útiles para otros investigadores de este campo. La más avanzada es Tareador, una herramienta para ayudar a migrar aplicaciones al modelo de programación MPI/OmpSs. Tareador proporciona una interfaz simple para proponer una descomposición del código en tareas OmpSs. Tareador también calcula dinámicamente las dependencias de datos entre las tareas anotadas, y automáticamente estima el potencial de paralelización OmpSs. Por último, Tareador da indicaciones adicionales sobre como completar el proceso de migración a OmpSs. Tareador ya se ha mostrado útil al ser incluido en las clases de programación de la UPC

Data-driven discovery of coordinates and governing equations

The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable identification of both the structure and parameters of a nonlinear dynamical system from data. The resulting models have the fewest terms necessary to describe the dynamics, balancing model complexity with descriptive ability, and thus promoting interpretability and generalizability. This provides an algorithmic approach to Occam's razor for model discovery. However, this approach fundamentally relies on an effective coordinate system in which the dynamics have a simple representation. In this work, we design a custom autoencoder to discover a coordinate transformation into a reduced space where the dynamics may be sparsely represented. Thus, we simultaneously learn the governing equations and the associated coordinate system. We demonstrate this approach on several example high-dimensional dynamical systems with low-dimensional behavior. The resulting modeling framework combines the strengths of deep neural networks for flexible representation and sparse identification of nonlinear dynamics (SINDy) for parsimonious models. It is the first method of its kind to place the discovery of coordinates and models on an equal footing.Comment: 25 pages, 6 figures; added acknowledgment

Audio Source Separation Using Sparse Representations

This is the author's final version of the article, first published as A. Nesbit, M. G. Jafari, E. Vincent and M. D. Plumbley. Audio Source Separation Using Sparse Representations. In W. Wang (Ed), Machine Audition: Principles, Algorithms and Systems. Chapter 10, pp. 246-264. IGI Global, 2011. ISBN 978-1-61520-919-4. DOI: 10.4018/978-1-61520-919-4.ch010file: NesbitJafariVincentP11-audio.pdf:n\NesbitJafariVincentP11-audio.pdf:PDF owner: markp timestamp: 2011.02.04file: NesbitJafariVincentP11-audio.pdf:n\NesbitJafariVincentP11-audio.pdf:PDF owner: markp timestamp: 2011.02.04The authors address the problem of audio source separation, namely, the recovery of audio signals from recordings of mixtures of those signals. The sparse component analysis framework is a powerful method for achieving this. Sparse orthogonal transforms, in which only few transform coefficients differ significantly from zero, are developed; once the signal has been transformed, energy is apportioned from each transform coefficient to each estimated source, and, finally, the signal is reconstructed using the inverse transform. The overriding aim of this chapter is to demonstrate how this framework, as exemplified here by two different decomposition methods which adapt to the signal to represent it sparsely, can be used to solve different problems in different mixing scenarios. To address the instantaneous (neither delays nor echoes) and underdetermined (more sources than mixtures) mixing model, a lapped orthogonal transform is adapted to the signal by selecting a basis from a library of predetermined bases. This method is highly related to the windowing methods used in the MPEG audio coding framework. In considering the anechoic (delays but no echoes) and determined (equal number of sources and mixtures) mixing case, a greedy adaptive transform is used based on orthogonal basis functions that are learned from the observed data, instead of being selected from a predetermined library of bases. This is found to encode the signal characteristics, by introducing a feedback system between the bases and the observed data. Experiments on mixtures of speech and music signals demonstrate that these methods give good signal approximations and separation performance, and indicate promising directions for future research

A Reconfigurable Digital Multiplier and 4:2 Compressor Cells Design

With the continually growing use of portable computing devices and increasingly complex software applications, there is a constant push for low power high speed circuitry to support this technology. Because of the high usage and large complex circuitry required to carry out arithmetic operations used in applications such as digital signal processing, there has been a great focus on increasing the efficiency of computer arithmetic circuitry. A key player in the realm of computer arithmetic is the digital multiplier and because of its size and power consumption, it has moved to the forefront of today\u27s research. A digital reconfigurable multiplier architecture will be introduced. Regulated by a 2-bit control signal, the multiplier is capable of double and single precision multiplication, as well as fault tolerant and dual throughput single precision execution. The architecture proposed in this thesis is centered on a recursive multiplication algorithm, where a large multiplication is carried out using recursions of simpler submultiplier modules. Within each sub-multiplier module, instead of carry save adder arrays, 4:2 compressor rows are utilized for partial product reduction, which present greater efficiency, thus result in lower delay and power consumption of the whole multiplier. In addition, a study of various digital logic circuit styles are initially presented, and then three different designs of 4:2 compressor in Domino Logic are presented and simulation results confirm the property of proposed design in terms of delay, power consumption and operation frequenc

Computationally efficient, one-pass algorithm for morphological filters

International audienceMany useful morphological filters are built as long concatenations of erosions and dilations: openings, closings, size distributions, sequential filters, etc. This paper proposes a new algorithm implementing morphological dilation and erosion of functions. It supports rectangular structuring element, runs in linear time w.r.t. the image size and constant time w.r.t. the structuring element size, and has minimal memory usage. It has zero algorithm latency and processes data in stream. These properties are inherited by operators composed by concatenation, and allow their efficient implementation. We show how to compute in one pass an Alternate Sequential Filter (ASF(n)) regardless the number of stages n. This algorithm opens the way to such time-critical applications where the complexity and memory requirements of serial morphological operators represented a bottleneck limiting their usability. (C) 2011 Elsevier Inc. All rights reserved