71 research outputs found

    Sub-Nyquist Sampling: Bridging Theory and Practice

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    Sampling theory encompasses all aspects related to the conversion of continuous-time signals to discrete streams of numbers. The famous Shannon-Nyquist theorem has become a landmark in the development of digital signal processing. In modern applications, an increasingly number of functions is being pushed forward to sophisticated software algorithms, leaving only those delicate finely-tuned tasks for the circuit level. In this paper, we review sampling strategies which target reduction of the ADC rate below Nyquist. Our survey covers classic works from the early 50's of the previous century through recent publications from the past several years. The prime focus is bridging theory and practice, that is to pinpoint the potential of sub-Nyquist strategies to emerge from the math to the hardware. In that spirit, we integrate contemporary theoretical viewpoints, which study signal modeling in a union of subspaces, together with a taste of practical aspects, namely how the avant-garde modalities boil down to concrete signal processing systems. Our hope is that this presentation style will attract the interest of both researchers and engineers in the hope of promoting the sub-Nyquist premise into practical applications, and encouraging further research into this exciting new frontier.Comment: 48 pages, 18 figures, to appear in IEEE Signal Processing Magazin

    Compressed sensing for enhanced through-the-wall radar imaging

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    Through-the-wall radar imaging (TWRI) is an emerging technology that aims to capture scenes behind walls and other visually opaque materials. The abilities to sense through walls are highly desirable for both military and civil applications, such as search and rescue missions, surveillance, and reconnaissance. TWRI systems, however, face with several challenges including prolonged data acquisition, large objects, strong wall clutter, and shadowing effects, which limit the radar imaging performances and hinder target detection and localization

    Compressive Sensing in Communication Systems

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    Mathematical modelling ano optimization strategies for acoustic source localization in reverberant environments

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    La presente Tesis se centra en el uso de técnicas modernas de optimización y de procesamiento de audio para la localización precisa y robusta de personas dentro de un entorno reverberante dotado con agrupaciones (arrays) de micrófonos. En esta tesis se han estudiado diversos aspectos de la localización sonora, incluyendo el modelado, la algoritmia, así como el calibrado previo que permite usar los algoritmos de localización incluso cuando la geometría de los sensores (micrófonos) es desconocida a priori. Las técnicas existentes hasta ahora requerían de un número elevado de micrófonos para obtener una alta precisión en la localización. Sin embargo, durante esta tesis se ha desarrollado un nuevo método que permite una mejora de más del 30\% en la precisión de la localización con un número reducido de micrófonos. La reducción en el número de micrófonos es importante ya que se traduce directamente en una disminución drástica del coste y en un aumento de la versatilidad del sistema final. Adicionalmente, se ha realizado un estudio exhaustivo de los fenómenos que afectan al sistema de adquisición y procesado de la señal, con el objetivo de mejorar el modelo propuesto anteriormente. Dicho estudio profundiza en el conocimiento y modelado del filtrado PHAT (ampliamente utilizado en localización acústica) y de los aspectos que lo hacen especialmente adecuado para localización. Fruto del anterior estudio, y en colaboración con investigadores del instituto IDIAP (Suiza), se ha desarrollado un sistema de auto-calibración de las posiciones de los micrófonos a partir del ruido difuso presente en una sala en silencio. Esta aportación relacionada con los métodos previos basados en la coherencia. Sin embargo es capaz de reducir el ruido atendiendo a parámetros físicos previamente conocidos (distancia máxima entre los micrófonos). Gracias a ello se consigue una mejor precisión utilizando un menor tiempo de cómputo. El conocimiento de los efectos del filtro PHAT ha permitido crear un nuevo modelo que permite la representación 'sparse' del típico escenario de localización. Este tipo de representación se ha demostrado ser muy conveniente para localización, permitiendo un enfoque sencillo del caso en el que existen múltiples fuentes simultáneas. La última aportación de esta tesis, es el de la caracterización de las Matrices TDOA (Time difference of arrival -Diferencia de tiempos de llegada, en castellano-). Este tipo de matrices son especialmente útiles en audio pero no están limitadas a él. Además, este estudio transciende a la localización con sonido ya que propone métodos de reducción de ruido de las medias TDOA basados en una representación matricial 'low-rank', siendo útil, además de en localización, en técnicas tales como el beamforming o el autocalibrado

    White Noise Reduction for Wideband Sensor Array Signal Processing

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    The performance of wideband array signal processing algorithms is dependant on the noise level in the system. In this thesis, a method is proposed for reducing the level of white noise in wideband arrays via a judiciously designed spatial transformation followed by a bank of high-pass filters. The method is initially introduced for uniform linear arrays (ULAs) and analysed in detail. The spectrum of the signal and noise after being processed by the proposed noise reduction method is analysed, and the correlation matrix of the processed noise is derived. The reduced noise level leads to a higher signal-to-noise ratio (SNR) for the system, which can have a significant effect on the performance improvement of various beamforming methods and other array signal processing applications such as direction of arrival (DOA) estimation. The performance of two well-known beamformers, the reference signal based (RSB) beamformer and the linearly constrained minimum variance (LCMV) beamformer is reviewed. Then, the theoretical effect of applying the proposed noise reduction method as a pre-processing step on the performance enhancement of RSB and LCMV beamformers is studied. The theoretical results are then confirmed by simulation. As a representative example of wideband DOA estimation application, a compressive sensing-based DOA estimation method is employed to demonstrate the improved estimation by applying the pre-processing noise reduction method, which is confirmed by simulation. Next, the idea is extended to wideband non-uniform linear arrays (NLAs). Since, NLA does not have a uniform spacing, the beam response of the row vectors of the transformation is distorted. Therefore, the transformation is re-designed using the least squares method to satisfy the band-pass requirements of the transformation. Simulation results show a satisfactory improvement in the the performance of RSB and LCMV beamformers for the NLA structure. The idea is further extended to uniform rectangular arrays (URAs) and uniform circular arrays (UCAs), as two major types of the planar arrays. Two methods are proposed for reducing the effect of white noise in wideband URAs and for each one, a different transformation is designed. The first one is based on a two-dimensional (2D) transformation and the second one is an adaptation of the method developed for the ULA case. The developed method for the UCA structure is based on a one-dimensional (1D) transformation, with modified modulation for the transformation to satisfy the required band-pass characteristics of the transformation. Same as linear array structures, the RSB and LCMV beamformers are used to demonstrate the performance enhancement of the method for planar arrays

    Structured Compressed Sensing: From Theory to Applications

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    Compressed sensing (CS) is an emerging field that has attracted considerable research interest over the past few years. Previous review articles in CS limit their scope to standard discrete-to-discrete measurement architectures using matrices of randomized nature and signal models based on standard sparsity. In recent years, CS has worked its way into several new application areas. This, in turn, necessitates a fresh look on many of the basics of CS. The random matrix measurement operator must be replaced by more structured sensing architectures that correspond to the characteristics of feasible acquisition hardware. The standard sparsity prior has to be extended to include a much richer class of signals and to encode broader data models, including continuous-time signals. In our overview, the theme is exploiting signal and measurement structure in compressive sensing. The prime focus is bridging theory and practice; that is, to pinpoint the potential of structured CS strategies to emerge from the math to the hardware. Our summary highlights new directions as well as relations to more traditional CS, with the hope of serving both as a review to practitioners wanting to join this emerging field, and as a reference for researchers that attempts to put some of the existing ideas in perspective of practical applications.Comment: To appear as an overview paper in IEEE Transactions on Signal Processin
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