Structured Compressed Sensing: From Theory to Applications

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

A study of high density bit transition requirements versus the effects on BCH error correcting codes

The use of PN sequence generators to create a minimum number of transitions in an NRZ bit stream is described. The CSG encoder/decoder design was constructed and demonstrated

Non-linear Recovery of Sparse Signal Representations with Applications to Temporal and Spatial Localization

Foundations of signal processing are heavily based on Shannon's sampling theorem for acquisition, representation and reconstruction. This theorem states that signals should not contain frequency components higher than the Nyquist rate, which is half of the sampling rate. Then, the signal can be perfectly reconstructed from its samples. Increasing evidence shows that the requirements imposed by Shannon's sampling theorem are too conservative for many naturally-occurring signals, which can be accurately characterized by sparse representations that require lower sampling rates closer to the signal's intrinsic information rates. Finite rate of innovation (FRI) is a new theory that allows to extract underlying sparse signal representations while operating at a reduced sampling rate. The goal of this PhD work is to advance reconstruction techniques for sparse signal representations from both theoretical and practical points of view. Specifically, the FRI framework is extended to deal with applications that involve temporal and spatial localization of events, including inverse source problems from radiating fields. We propose a novel reconstruction method using a model-fitting approach that is based on minimizing the fitting error subject to an underlying annihilation system given by the Prony's method. First, we showed that this is related to the problem known as structured low-rank matrix approximation as in structured total least squares problem. Then, we proposed to solve our problem under three different constraints using the iterative quadratic maximum likelihood algorithm. Our analysis and simulation results indicate that the proposed algorithms improve the robustness of the results with respect to common FRI reconstruction schemes. We have further developed the model-fitting approach to analyze spontaneous brain activity as measured by functional magnetic resonance imaging (fMRI). For this, we considered the noisy fMRI time course for every voxel as a convolution between an underlying activity inducing signal (i.e., a stream of Diracs) and the hemodynamic response function (HRF). We then validated this method using experimental fMRI data acquired during an event-related study. The results showed for the first time evidence for the practical usage of FRI for fMRI data analysis. We also addressed the problem of retrieving a sparse source distribution from the boundary measurements of a radiating field. First, based on Green's theorem, we proposed a sensing principle that allows to relate the boundary measurements to the source distribution. We focused on characterizing these sensing functions with particular attention for those that can be derived from holomorphic functions as they allow to control spatial decay of the sensing functions. With this selection, we developed an FRI-inspired non-iterative reconstruction algorithm. Finally, we developed an extension to the sensing principle (termed eigensensing) where we choose the spatial eigenfunctions of the Laplace operator as the sensing functions. With this extension, we showed that eigensensing principle allows to extract partial Fourier measurements of the source functions from boundary measurements. We considered photoacoustic tomography as a potential application of these theoretical developments

Space time transceiver design over multipath fading channels

Imperial Users onl

Low Latency Audio Processing

PhDLatency in the live audio processing chain has become a concern for audio engineers and system designers because significant delays can be perceived and may affect synchronisation of signals, limit interactivity, degrade sound quality and cause acoustic feedback. In recent years, latency problems have become more severe since audio processing has become digitised, high-resolution ADCs and DACs are used, complex processing is performed, and data communication networks are used for audio signal transmission in conjunction with other traffic types. In many live audio applications, latency thresholds are bounded by human perceptions. The applications such as music ensembles and live monitoring require low delay and predictable latency. Current digital audio systems either have difficulties to achieve or have to trade-off latency with other important audio processing functionalities. This thesis investigated the fundamental causes of the latency in a modern digital audio processing system: group delay, buffering delay, and physical propagation delay and their associated system components. By studying the time-critical path of a general audio system, we focus on three main functional blocks that have the significant impact on overall latency; the high-resolution digital filters in sigma-delta based ADC/DAC, the operating system to process low latency audio streams, and the audio networking to transmit audio with flexibility and convergence. In this work, we formed new theory and methods to reduce latency and accurately predict latency for group delay. We proposed new scheduling algorithms for the operating system that is suitable for low latency audio processing. We designed a new system architecture and new protocols to produce deterministic networking components that can contribute the overall timing assurance and predictability of live audio processing. The results are validated by simulations and experimental tests. Also, this bottom-up approach is aligned with the methodology that could solve the timing problem of general cyber-physical systems that require the integration of communication, software and human interactions

Modem design for digital satellite communications

The thesis is concerned with the design of a phase-shift keying system for a digital modem, operating over a satellite link. Computer simulation tests and theoretical analyses are used to assess the proposed design. The optimum design of both transmitter and receiver filters for the system to be used in the modem are discussed. Sinusoidal roll-off spectrum with different roll-off factor and optimum truncation lengths of the sample impulse response are designed for the proposed scheme to approximate to the theoretical ideal. It has used an EF bandpass filter to band limit the modulated signal, which forms part of the satellite channel modelling. The high power amplifier (HPA) at the earth station has been used in the satellite channel modelling due to its effect in introducing nonlinear AMAM and AM-PM conversion effects and distortion on the transmitted signal from the earth station. The satellite transponder is assumed to be operating in a linear mode. Different phase-shift keying signals such as differentially encoded quaternary phase-shift keying (DEQPSK), offset quaternary phase-shift keying (OQPSK) and convolutionally encoded 8PSK (CE8PSK) signals are analysed and discussed in the thesis, when the high power amplifier (HPA) at the earth station is operating in a nonlinear mode. Convolutional encoding is discussed when applied to the system used in the modem, and a Viterbi -algorithm decoder at the receiver has been used, for CE8PSK signals for a nonlinear satellite channel. A method of feed-forward synchronisation scheme is designed for carrier recovery in CE8PSK receiver. The thesis describes a method of baseband linearizing the baseband signal in order to reduce the nonlinear effects caused by the HPA at the earth station. The scheme which compensates for the nonlinear effects of the HPA by predistorting the baseband signal prior to modulation as opposed to correcting the distortion after modulation, thus reducing the effects of nonlinear distortion introduced by the HPA. The results of the improvement are presented. The advanced technology of digital signal processors (DSPs) has been used in the implementation of the demodulation and digital filtering parts of the modem replacing large parts of conventional circuits. The Viterbi-algorithm decoder for CE8PSK signals has been implemented using a digital signal processor chip, giving excellent performance and is a cost effective and easy way for future developments and any modifications, The results showed that, by using the various studied techniques, as well as the implementation of digital signal processor chip in parts of the modem, a potentially more cost effective modem can be obtained

D11.2 Consolidated results on the performance limits of wireless communications

Deliverable D11.2 del projecte europeu NEWCOM#The report presents the Intermediate Results of N# JRAs on Performance Limits of Wireless Communications and highlights the fundamental issues that have been investigated by the WP1.1. The report illustrates the Joint Research Activities (JRAs) already identified during the first year of the project which are currently ongoing. For each activity there is a description, an illustration of the adherence and relevance with the identified fundamental open issues, a short presentation of the preliminary results, and a roadmap for the joint research work in the next year. Appendices for each JRA give technical details on the scientific activity in each JRA.Peer ReviewedPreprin