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 ...

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 ...

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 develops new mathematical theory and presents novel recovery algorithms for discrete linear dynamical systems (LDS) with sparsity constraints on either control inputs or initial state. The recovery problems in this framework manifest as the problem of reconstructing one or more sparse signals from a set of noisy underdetermined linear measurements. The goal of our work is to design algorithms for sparse signal recovery which can exploit the underlying structure in the measurement matrix and the unknown sparse vectors, and to analyze the impact of these structures on the efficacy of the recovery. We answer three fundamental and interconnected questions on sparse signal recovery problems that arise in the context of LDS. First, what are necessary and sufficient conditions for the existence of a sparse solution? Second, given that a sparse solution exists, what are good low-complexity algorithms that ...

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 ...

This thesis investigates filter bank based multicarrier modulation using offset quadrature amplitude modulation (FBMC/OQAM), which is characterised by a critically sampled FBMC system that achieves full spectral efficiency in the sense of being free of redundancy. As a starting point, a performance comparison between FBMC/OQAM and oversampled (OS) FBMC systems is made in terms of per-subband fractionally spaced equalisation in order to compensate for the transmission distortions caused by dispersive channels. Simulation results show the reduced performance in equalising FBMC/OQAM compared to OS-FBMC, where the advantage for the latter stems from the use of guard bands. Alternatively, the inferior performance of FBMC/OQAM can be assigned to the inability of a per-subband equaliser to address the problem of potential intercarrier interference (ICI) in this system. The FBMC/OQAM system is analysed by representing the equivalent transmultiplexed channel including the filter banks as ...

Since the late 1990s, massive multiple-input multiple-output (MIMO) has been suggested to improve the achievable data rate in wireless communication systems. To overcome the high path losses in the high frequency bands, the use of massive MIMO will be a must rather than an option in future wireless communication systems. At the same time, due to the high cost and high energy consumption of the traditional fully digital beamforming architecture, a new beamforming architecture is required. Among the proposed solutions, the hybrid analog digital (HAD) beamforming architecture has received considerable attention. The promising massive MIMO gains heavily rely on the availability of accurate channel state information (CSI). This thesis considers a wideband massive MIMO orthogonal frequency division multiplexing (OFDM) system. We propose a channel estimation method called sequential alternating least squares approximation (SALSA) by exploiting a hidden tensor structure in ...

Never before has speech been captured as often by electronic devices equipped with one or multiple microphones, serving a variety of applications. It is the key aspect in digital telephony, hearing devices, and voice-driven human-to-machine interaction. When speech is recorded, the microphones also capture a variety of further, undesired sound components due to adverse acoustic conditions. Interfering speech, background noise and reverberation, i.e. the persistence of sound in a room after excitation caused by a multitude of reflections on the room enclosure, are detrimental to the quality and intelligibility of target speech as well as the performance of automatic speech recognition. Hence, speech enhancement aiming at estimating the early target-speech component, which contains the direct component and early reflections, is crucial to nearly all speech-related applications presently available. In this thesis, we compare, propose and evaluate existing and novel approaches ...

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 ...

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 ...

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 ...

The fifth-generation (5G) is in its business version, and researchers have started to look at the potential technologies to be employed in the next generation. In this context, intelligent reflecting surface (IRS) is a promising technology for the sixth-generation (6G) of wireless systems by introducing the smart radio environment concept. The promised gains of IRS-assisted communications depend on the accuracy of the channel state information. Using a tensor framework, particularly tensor decomposition, we propose different solutions to solve the channel estimation problem for different scenarios. We firstly address the receiver design for an IRS-assisted multiple-input multiple-output (MIMO) communication system via a tensor modeling approach to solve the channel estimation problem using supervised (pilot-assisted) methods. Considering a structured time-domain pattern of pilots and IRS phase shifts, we present two channel estimation methods that rely on a parallel factors (PARAFAC) tensor modeling ...