## Advanced Algorithms for Polynomial Matrix Eigenvalue Decomposition (2017)

Polynomial Matrix Eigenvalue Decomposition Techniques for Multichannel Signal Processing

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 ...

Wang, Zeliang — Cardiff University

Algorithms and Techniques for Polynomial Matrix Decompositions

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 ...

Foster, Joanne — Cardiff University

Broadband angle of arrival estimation using polynomial matrix decompositions

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 ...

Alrmah, Mohamed Abubaker — University of Strathclyde

Polynomial Matrix Decompositions and Paraunitary Filter Banks

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 ...

Redif, Soydan — University of Southampton

Subspace-based exponential data fitting using linear and multilinear algebra

The exponentially damped sinusoidal (EDS) model arises in numerous signal processing applications. It is therefore of great interest to have methods able to estimate the parameters of such a model in the single-channel as well as in the multi-channel case. Because such a model naturally lends itself to subspace representation, powerful matrix approaches like HTLS in the single-channel case, HTLSstack in the multi-channel case and HTLSDstack in the decimative case have been developed to estimate the parameters of the underlying EDS model. They basically consist in stacking the signal in Hankel (single-channel) or block Hankel (multi- channel) data matrices. Then, the signal subspace is estimated by means of the singular value decomposition (SVD). The parameters of the model, namely the amplitudes, the phases, the damping factors, and the frequencies, are estimated from this subspace. Note that the sample covariance matrix ...

Papy, Jean-Michel — Katholieke Universiteit Leuven

Precoding and Equalisation for Broadband MIMO Systems

Joint precoding and equalisation can help to effectively exploit the advantages of multi-input multi-output (MIMO) wireless communications systems. For broadband MIMO channels with channel state information (CSI) such techniques to date rely on block transmission where guard intervals are applied to mitigate inter-block (IBI) and inter-symbol interference (ISI) but reduce spectral efficiency. Therefore, this thesis investigates novel MIMO transceiver designs to improve the transmission rate and error performance. Firstly, a broadband MIMO precoding and equalisation design is proposed which combines a recently proposed broadband singular value decomposition (BSVD) algorithm for MIMO decoupling with conventional block transmission techniques to address the remaining broadband SISO subchannels. It is demonstrated that the BSVD helps not only to remove co-channel interference within a MIMO channel, but also reduces ISI at a very small loss in channel energy, leading to an improved error performance and ...

Ta, Chi Hieu — University of Strathclyde

Broadband adaptive beamforming with low complexity and frequency invariant response

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 ...

Koh, Choo Leng — University of Southampton

Multi-microphone noise reduction and dereverberation techniques for speech applications

In typical speech communication applications, such as hands-free mobile telephony, voice-controlled systems and hearing aids, the recorded microphone signals are corrupted by background noise, room reverberation and far-end echo signals. This signal degradation can lead to total unintelligibility of the speech signal and decreases the performance of automatic speech recognition systems. In this thesis several multi-microphone noise reduction and dereverberation techniques are developed. In Part I we present a Generalised Singular Value Decomposition (GSVD) based optimal filtering technique for enhancing multi-microphone speech signals which are degraded by additive coloured noise. Several techniques are presented for reducing the computational complexity and we show that the GSVD-based optimal filtering technique can be integrated into a `Generalised Sidelobe Canceller' type structure. Simulations show that the GSVD-based optimal filtering technique achieves a larger signal-to-noise ratio improvement than standard fixed and adaptive beamforming techniques and ...

Doclo, Simon — Katholieke Universiteit Leuven

Contributions to signal analysis and processing using compressed sensing techniques

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 ...

Cleju, Nicolae — "Gheorghe Asachi" Technical University of Iasi

Transmission over Time- and Frequency-Selective Mobile Wireless Channels

The wireless communication industry has experienced rapid growth in recent years, and digital cellular systems are currently designed to provide high data rates at high terminal speeds. High data rates give rise to intersymbol interference (ISI) due to so-called multipath fading. Such an ISI channel is called frequency selective. On the other hand, due to terminal mobility and/or receiver frequency offset the received signal is subject to frequency shifts (Doppler shifts). Doppler shift induces time-selectivity characteristics. The Doppler effect in conjunction with ISI gives rise to a so-called doubly selective channel (frequency- and time-selective). In addition to the channel effects, the analog front-end may suffer from an imbalance between the I and Q branch amplitudes and phases as well as from carrier frequency offset. These analog front-end imperfections then result in an additional and significant degradation in system performance, especially ...

Barhumi, Imad — Katholieke Universiteit Leuven

Bayesian methods for sparse and low-rank matrix problems

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 ...

Sundin, Martin — Department of Signal Processing, Royal Institute of Technology KTH

Cooperative Techniques for Interference Management in Wireless Networks

In the last few years, wireless devices have evolved to unimaginable heights. Current forecasts suggest that, in the near future, every device that may take advantage of a wireless connection will have one. In addition, there is a gradual migration to smart devices and high-speed connections, and, as a consequence, the overall mobile traffic is expected to experience a tremendous growth in the next years. The multiuser interference will hence become the main limiting factor and the most critical point to address. As instrumental to efficiently manage interference between different systems, this thesis provides a thorough study on cooperative techniques. That is, users share information and exploit it to improve the overall performance. Since multiuser cooperation represents a very broad term, we will focus on algorithm design and transceiver optimization for three cooperative scenarios that capture some of the main ...

Lameiro, Christian — University of Cantabria

Antenna Arrays for Multipath and Interference Mitigation in GNSS Receivers

This thesis deals with the synchronization of one or several replicas of a known signal received in a scenario with multipath propagation and directional interference. A connecting theme along this work is the systematic application of the maximum likelihood (ML) principle together with a signal model in which the spatial signatures are unstructured and the noise term is Gaussian- distributed with an unknown correlation matrix. This last assumption is key in obtaining estimators that are capable of mitigating the disturbing signals that exhibit a certain structure, and this is achieved without resorting to the estimation of the parameters of those signals. On the other hand, the assumption of unstructured spatial signatures is interesting from a practical standpoint and facilitates the estimation problem since the estimates of these signatures can be obtained in closed form. This constitutes a first step towards ...

Seco-Granados, Gonzalo — Universitat Politecnica de Catalunya

Precoding and Relaying Algorithms for Multiuser MIMO Downlink Channels

In the last years, research has focused on multiple-input multiple-output (MIMO) wireless technology due to the capacity and performance improvement it provides, offering a higher spectral efficiency. In addition, when multiple users take part in the network, the scenario becomes much more complex, since resources like bandwidth, time or transmission power must be shared. Furthermore, the performance of the system is degraded as a consequence of the noise and multiuser interference (MUI). When the transmission is conducted from a base station (BS) to multiple users, a pre-equalization stage called precoding is applied. By means of this, each user will be able to interpret the signal independently, without the knowledge of the channel. Precoding techniques are classified into linear and non-linear. In fact, the non-linear Tomlinson-Harashima precoding (THP) and vector precoding (VP) techniques have been shown to achieve very good results ...

Jimenez, Idoia — University of Mondragon

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.

Le Magoarou, Luc — INRIA, Technicolor

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