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 ...

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- ...

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 ...

The concept of polynomial matrices is introduced and the potential application of polynomial matrix decompositions is discussed within the general context of multi-channel digital signal processing. A recently developed technique, known as the second order sequential rotation algorithm (SBR2), for performing the eigenvalue decomposition of a para-Hermitian polynomial matrix (PEVD) is presented. The potential benefit of using the SBR2 algorithm to impose strong decorrelation on the signals received by a broadband sensor array is demonstrated by means of a suitable numerical simulation. This demonstrates how the polynomial matrices produced as a result of the PEVD can be of unnecessarily high order. This is undesirable for many practical applications and slows down the iterative computational procedure. An effective truncation technique for controlling the growth in order of these polynomial matrices is proposed. Depending on the choice of truncation parameters, it provides ...

There are an increasing number of problems that can be solved using paraunitary filter banks. The design of optimal orthonormal filter banks for the efficient coding of signals has received considerable interest over the years. In contrast, very little attention has been given to the problem of constructing paraunitary matrices for the purpose of broadband signal subspace estimation. This thesis begins by relating these two areas of research. A frequency-domain method of diagonalising parahermitian polynomial matrices is proposed and shown to have fundamental limitations. Then the thesis focuses on the development of a novel time-domain technique that extends the eigenvalue decomposition to polynomial matrices, referred to as the second order sequential best rotation (SBR2) algorithm. This technique imposes strong decorrelation on its input signals by applying a sequence of elementary paraunitary matrices which constitutes a generalisation of the classical Jacobi ...

This thesis addresses the formulation of and solution to broadband minimum variance distortionless response (MVDR) beamforming. Two approaches to this problem are considered, namely, generalised sidelobe canceller (GSC) and Capon beamformers. These are examined based on a novel technique which relies on polynomial matrix formulations. The new scheme is based on the second order statistics of the array sensor measurements in order to estimate a space-time covariance matrix. The beamforming problem can be formulated based on this space-time covariance matrix. Akin to the narrowband problem, where an optimum solution can be derived from the eigenvalue decomposition (EVD) of a constant covariance matrix, this utility is here extended to the broadband case. The decoupling of the space-time covariance matrix in this case is provided by means of a polynomial matrix EVD. The proposed approach is initially exploited to design a GSC ...

This thesis proposes different methods to reduce the computational complexity as well as increasing the adaptation rate of adaptive broadband beamformers. This is performed exemplarily for the generalised sidelobe canceller (GSC) structure. The GSC is an alternative implementation of the linearly constrained minimum variance beamformer, which can utilise well-known adaptive filtering algorithms, such as the least mean square (LMS) or the recursive least squares (RLS) to perform unconstrained adaptive optimisation. A direct DFT implementation, by which broadband signals are decomposed into frequency bins and processed by independent narrowband beamforming algorithms, is thought to be computationally optimum. However, this setup fail to converge to the time domain minimum mean square error (MMSE) if signal components are not aligned to frequency bins, resulting in a large worst case error. To mitigate this problem of the so-called independent frequency bin (IFB) processor, overlap-save ...

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 ...

The majority of communication systems need the previous knowledge of the channel, which is usually estimated by means of a training sequence. However, the transmission of pilot symbols provokes a reduction in bandwidth efficiency, which precludes the system from reaching the limits predicted by the Information Theory. This problem has motivated the development of a large number of blind channel estimation and equalization techniques, which are able to obtain the channel or the source without the need of transmitting a training signal. Usually, these techniques are based on the previous knowledge of certain properties of the signal, such as its belonging to a finite alphabet, or its higher-order statistics. However, in the case of multiple-input multipleoutput (MIMO) systems, it has been proven that the second-order statistics of the observations provide the sufficient information for solving the blind problem. The aim ...

The widespread use of mobile internet and smart applications has led to an explosive growth in mobile data traffic. With the rise of smart homes, smart buildings, and smart cities, this demand is ever growing since future communication systems will require the integration of multiple networks serving diverse sectors, domains and applications, such as multimedia, virtual or augmented reality, machine-to-machine (M2M) communication / the Internet of things (IoT), automotive applications, and many more. Therefore, in the future, the communication systems will not only be required to provide Gbps wireless connectivity but also fulfill other requirements such as low latency and massive machine type connectivity while ensuring the quality of service. Without significant technological advances to increase the system capacity, the existing telecommunications infrastructure will be unable to support these multi-dimensional requirements. This poses an important demand for suitable waveforms with ...

The interest in the field of speech enhancement emerges from the increased usage of digital speech processing applications like mobile telephony, digital hearing aids and human-machine communication systems in our daily life. The trend to make these applications mobile increases the variety of potential sources for quality degradation. Speech enhancement methods can be used to increase the quality of these speech processing devices and make them more robust under noisy conditions. The name "speech enhancement" refers to a large group of methods that are all meant to improve certain quality aspects of these devices. Examples of speech enhancement algorithms are echo control, bandwidth extension, packet loss concealment and noise reduction. In this thesis we focus on single-microphone additive noise reduction and aim at methods that work in the discrete Fourier transform (DFT) domain. The main objective of the presented research ...

Chapter 2 contains a short introduction to the fundamentals of compressed sensing theory, which is the larger context of this thesis. We start with introducing the key concepts of sparsity and sparse representations of signals. We discuss the central problem of compressed sensing, i.e. how to adequately recover sparse signals from a small number of measurements, as well as the multiple formulations of the reconstruction problem. A large part of the chapter is devoted to some of the most important conditions necessary and/or sufficient to guarantee accurate recovery. The aim is to introduce the reader to the basic results, without the burden of detailed proofs. In addition, we also present a few of the popular reconstruction and optimization algorithms that we use throughout the thesis. Chapter 3 presents an alternative sparsity model known as analysis sparsity, that offers similar recovery ...

Multi-input multi-output (MIMO) wireless networks and distributed MIMO relaying wireless networks have attracted significant attention in current generation of wireless communication networks, and will play a key role in the next generation of wireless net- works. The improvement of network capacity, data rate and reliability can be achieved at the cost of increasing computational complexity of employing space-time coding (STC) and distributed STC (DSTC) in MIMO and distributed MIMO relaying networks, respectively. Efficient designs and algorithms to achieve high diversity and coding gains with low computational complexity in encoding and decoding of STC and DSTC schemes are essential. In this thesis, DSTC designs with high diversity and coding gains and efficient detection and code matrices optimization algorithms in cooperative MIMO networks are proposed. Firstly, adaptive power allocation (PA) algorithms with different criteria for a coop- erative MIMO network equipped with ...

Matrices, as natural representation of linear mappings in finite dimension, play a crucial role in signal processing and machine learning. Multiplying a vector by a full rank matrix a priori costs of the order of the number of non-zero entries in the matrix, in terms of arithmetic operations. However, matrices exist that can be applied much faster, this property being crucial to the success of certain linear transformations, such as the Fourier transform or the wavelet transform. What is the property that allows these matrices to be applied rapidly ? Is it easy to verify ? Can weapproximate matrices with ones having this property ? Can we estimate matrices having this property ? This thesis investigates these questions, exploring applications such as learning dictionaries with efficient implementations, accelerating the resolution of inverse problems or Fast Fourier Transform on graphs.

The topic of this thesis is speech enhancement with a focus on models of voiced speech. Speech is divided into two subcategories dependent on the characteristics of the signal. One part is the voiced speech, the other is the unvoiced. In this thesis, we primarily focus on the voiced speech parts and utilise the structure of the signal in relation to speech enhancement. The basis for the models is the harmonic model which is a very often used model for voiced speech because it describes periodic signals perfectly. First, we consider the problem of non-stationarity in the speech signal. The speech signal changes its characteristics continuously over time whereas most speech analysis and enhancement methods assume stationarity within 20-30 ms. We propose to change the model to allow the fundamental frequency to vary linearly over time by introducing a chirp ...