In broadband array processing applications, an extension of the eigenvalue decomposition (EVD) to parahermitian Laurent polynomial matrices - named the polynomial matrix EVD (PEVD) - has proven to be a useful tool for the decomposition of space-time covariance matrices and their associated cross-spectral density matrices. Existing PEVD methods typically operate in the time domain and utilise iterative frameworks established by the second-order sequential best rotation (SBR2) or sequential matrix diagonalisation (SMD) algorithms. However, motivated by recent discoveries that establish the existence of an analytic PEVD - which is rarely recovered by SBR2 or SMD - alternative algorithms that better meet analyticity by operating in the discrete Fourier transform (DFT)-domain have received increasing attention. While offering promising results in applications including broadband MIMO and beamforming, the PEVD has seen limited deployment in hardware due to its high computational complexity. If the ...

Matrix factorisations such as the eigen- (EVD) or singular value decomposition (SVD) offer optimality in often various senses to many narrowband signal processing algorithms. For broadband problems, where quantities such as MIMO transfer functions or cross spectral density matrices are conveniently described by polynomial matrices, such narrowband factorisations are suboptimal at best. To extend the utility of EVD and SVD to the broadband case, polynomial matrix factorisations have gained momen- tum over the past decade, and a number of iterative algorithms for particularly the polynomial matrix EVD (PEVD) have emerged. Existing iterative PEVD algorithms produce factorisations that are computationally costly (i) to calculate and (ii) to apply. For the former, iterative algorithms at every step eliminate off-diagonal energy, but this can be a slow process. For the latter, the polynomial order of the resulting factors, directly impacting on the implementa- ...

Since several years, multi-antenna systems are foreseen as a potential solution for increasing the throughput of future wireless communication systems. The aim of this thesis is to study and to improve the transmitter and receiver's techniques of these MIMO (Multiple Input Multiple Output) systems in the context of a multi-carrier transmission. On the one hand, the OFDM (Orthogonal Frequency Division Multiplex) modulation, which transform a frequency selective channel into multiple non frequency selective channels, is particularly well adapted to the conception of MIMO receivers with low complexity. On the other hand, two techniques allowing to improve the exploitation of frequential and/or temporal diversities are associated with OFDM, namely linear precoding (LP-OFDM) and CDMA in a MC-CDMA (Multicarrier Code division Multiplex Access) scheme. We have associated LP-OFDM and MC-CDMA with two MIMO techniques which require no channel state information at the ...

Many scientific and engineering problems require us to process measurements and data in order to extract information. Since we base decisions on information, it is important to design accurate and efficient processing algorithms. This is often done by modeling the signal of interest and the noise in the problem. One type of modeling is Compressed Sensing, where the signal has a sparse or low-rank representation. In this thesis we study different approaches to designing algorithms for sparse and low-rank problems. Greedy methods are fast methods for sparse problems which iteratively detects and estimates the non-zero components. By modeling the detection problem as an array processing problem and a Bayesian filtering problem, we improve the detection accuracy. Bayesian methods approximate the sparsity by probability distributions which are iteratively modified. We show one approach to making the Bayesian method the Relevance Vector ...

In the last decade, cooperation among multiple terminals has been seen as one of the more promising strategies to improve transmission speed in wireless communications networks. Basically, the idea is to mimic an antenna array and apply distributed versions of well-known space-diversity techniques. In this context, the simplest cooperative scheme is the relay channel: all the terminals (relays) that overhear a point-to-point communication between a source and a destination may decide to aid the source by forwarding (relaying) its message. In a mobile system, it is common to assume that the relays do not have any information about the channel between them and the destination. Under this hypothesis, the best solution to exploit the diversity offered by multiple transmitting antennas is to use space-time coding (STC). However, classical STC's are designed for systems with a fixed and usually low number ...

The effectiveness of machine learning (ML) in today's applications largely depends on the goodness of the representation of data used within the ML algorithms. While the massiveness in dimension of modern day data often requires lower-dimensional data representations in many applications for efficient use of available computational resources, the use of uncorrelated features is also known to enhance the performance of ML algorithms. Thus, an efficient representation learning solution should focus on dimension reduction as well as uncorrelated feature extraction. Even though Principal Component Analysis (PCA) and linear autoencoders are fundamental data preprocessing tools that are largely used for dimension reduction, when engineered properly they can also be used to extract uncorrelated features. At the same time, factors like ever-increasing volume of data or inherently distributed data generation impede the use of existing centralized solutions for representation learning that require ...

The theory of statistical signal processing finds a wide variety of applications in the fields of data communications, such as in channel estimation, equalization and symbol detection, and sensor array processing, as in beamforming, and radar systems. Indeed, a large number of these applications can be interpreted in terms of a parametric estimation problem, typically approached by a linear filtering operation acting upon a set of multidimensional observations. Moreover, in many cases, the underlying structure of the observable signals is linear in the parameter to be inferred. This dissertation is devoted to the design and evaluation of statistical signal processing methods under realistic implementation conditions encountered in practice. Traditional statistical signal processing techniques intrinsically provide a good performance under the availability of a particularly high number of observations of fixed dimension. Indeed, the original optimality conditions cannot be theoretically guaranteed ...

This thesis deals with problems of Pattern Recognition in the framework of Machine Learning (ML) and, specifically, Statistical Learning Theory (SLT), using Support Vector Machines (SVMs). The focus of this work is on the geometric interpretation of SVMs, which is accomplished through the notion of Reduced Convex Hulls (RCHs), and its impact on the derivation of new, efficient algorithms for the solution of the general SVM optimization task. The contributions of this work is the extension of the mathematical framework of RCHs, the derivation of novel geometric algorithms for SVMs and, finally, the application of the SVM algorithms to the field of Medical Image Analysis and Diagnosis (Mammography). Geometric SVM Framework's extensions: The geometric interpretation of SVMs is based on the notion of Reduced Convex Hulls. Although the geometric approach to SVMs is very intuitive, its usefulness was restricted by ...

Various real-life data such as time series and multi-sensor recordings can be represented by vectors and matrices, which are one-way and two-way arrays of numerical values, respectively. Valuable information can be extracted from these measured data matrices by means of matrix factorizations in a broad range of applications within signal processing, data mining, and machine learning. While matrix-based methods are powerful and well-known tools for various applications, they are limited to single-mode variations, making them ill-suited to tackle multi-way data without loss of information. Higher-order tensors are a natural extension of vectors (first order) and matrices (second order), enabling us to represent multi-way arrays of numerical values, which have become ubiquitous in signal processing and data mining applications. By leveraging the powerful utitilies offered by tensor decompositions such as compression and uniqueness properties, we can extract more information from multi-way ...

Due to significant advances made over the last few decades in the areas of (wireless) networking, communications and microprocessor fabrication, the use of sensor networks to observe physical phenomena is rapidly becoming commonplace. Over this period, many aspects of sensor networks have been explored, yet a thorough understanding of how to analyse and process the vast amounts of sensor data collected remains an open area of research. This work, therefore, aims to provide theoretical, as well as practical, advances this area. In particular, we consider the problem of inferring certain underlying properties of the monitored phenomena, from our sensor measurements. Within mathematics, this is commonly formulated as an inverse problem; whereas in signal processing, it appears as a (multidimensional) sampling and reconstruction problem. Indeed it is well known that inverse problems are notoriously ill-posed and very demanding to solve; meanwhile ...

Over-complete transforms have recently become the focus of a wide wealth of research in signal processing, machine learning, statistics and related fields. Their great modelling flexibility allows to find sparse representations and approximations of data that in turn prove to be very efficient in a wide range of applications. Sparse models express signals as linear combinations of a few basis functions called atoms taken from a so-called dictionary. Finding the optimal dictionary from a set of training signals of a given class is the objective of dictionary learning and the main focus of this thesis. The experimental evidence presented here focuses on the processing of audio signals, and the role of sparse algorithms in audio applications is accordingly highlighted. The first main contribution of this thesis is the development of a pitch-synchronous transform where the frame-by-frame analysis of audio data ...

This thesis is concerned with the problem of broadband angle of arrival (AoA) estimation for sensor arrays. There is a rich theory of narrowband solutions to the AoA problem, which typically involves the covariance matrix of the received data and matrix factorisations such as the eigenvalue decomposition (EVD) to reach optimality in various senses. For broadband arrays, such as found in sonar, acoustics or other applications where signals do not fulfil the narrowband assumption, working with phase shifts between different signals — as sufficient in the narrowband case — does not suffice and explicit lags need to be taken into account. The required space-time covariance matrix of the data now has a lag dimension, and classical solutions such as those based on the EVD are no longer directly applicable. There are a number of existing broadband AoA techniques, which are ...

In modern devices which provide hands-free speech capturing functionality, such as hands-free communication kits and voice-controlled devices, the received speech signal at the microphones is corrupted by background noise, interfering speech signals, and room reverberation. In many practical situations, the microphones are not necessarily located near the desired source, and hence, the ratio of the desired speech power to the power of the background noise, the interfering speech, and the reverberation at the microphones can be very low, often around or even below 0 dB. In such situations, the comfort of human-to-human communication, as well as the accuracy of automatic speech recognisers for voice-controlled applications can be signi cantly degraded. Therefore, e ffective speech enhancement algorithms are required to process the microphone signals before transmitting them to the far-end side for communication, or before feeding them into a speech recognition ...

Polynomial eigenvalue decomposition (PEVD) is an extension of the eigenvalue decomposition (EVD) for para-Hermitian polynomial matrices, and it has been shown to be a powerful tool for broadband extensions of narrowband signal processing problems. In the context of broadband sensor arrays, the PEVD allows the para-Hermitian matrix that results from the calculation of a space-time covariance matrix of the convolutively mixed signals to be diagonalised. Once the matrix is diagonalised, not only can the correlation between different sensor signals be removed but the signal and noise subspaces can also be identified. This process is referred to as broadband subspace decomposition, and it plays a very important role in many areas that require signal separation techniques for multichannel convolutive mixtures, such as speech recognition, radar clutter suppression, underwater acoustics, etc. The multiple shift second order sequential best rotation (MS-SBR2) algorithm, built ...

The envisioned rapid and exponential increase of wireless data traffic demand in the next years imposes rethinking current wireless cellular networks due to the scarcity of the available spectrum. In this regard, three main drivers are considered to increase the capacity of today's most advanced (4G systems) and future (5G systems and beyond) cellular networks: i) use more bandwidth (more Hz) through spectral aggregation, ii) enhance the spectral efficiency per base station (BS) (more bits/s/Hz/BS) by using multiple antennas at BSs and users (i.e. MIMO systems), and iii) increase the density of BSs (more BSs/km2) through a dense and heterogeneous deployment (known as dense heterogeneous cellular networks). We focus on the last two drivers. First, the use of multi-antenna systems allows exploiting the spatial dimension for several purposes: improving the capacity of a conventional point-to-point wireless link, increasing the number ...