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 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 ...

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 ...

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- ...

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 ...

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 ...

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 ...

Filter bank based multicarrier is an evolution with many advantages over the widespread OFDM multicarrier scheme. The author of the thesis stands behind this statement and proposes various solutions for practical physical layer problems based on filter bank processing of wireless communications signals. Filter banks are an evolved form of subband processing, harnessing the key advantages of original efficient subband processing based on the fast Fourier transforms and addressing some of its shortcomings, at the price of a somewhat increased implementation complexity. The main asset of the filter banks is the possibility to design very frequency selective subband filters to compartmentalize the overall spectrum into well isolated subbands, while still making very efficient use of the assigned bandwidth. This thesis first exploits this main feature of the filter banks in the subband system configuration, in which the analysis filter bank ...

The thriving development of wireless communications calls for innovative and advanced signal processing techniques targeting at an enhanced performance in terms of reliability, throughput, robustness, efficiency, flexibility, etc.. This thesis addresses such a compelling demand and presents new and intriguing progress towards fulfilling it. We mainly concentrate on two advanced multi-dimensional signal processing challenges for wireless systems that have attracted tremendous research attention in recent years, multi-carrier Multiple-Input Multiple-Output (MIMO) systems and multi-dimensional harmonic retrieval. As the key technologies of wireless communications, the numerous benefits of MIMO and multi-carrier modulation, e.g., boosting the data rate and improving the link reliability, have long been identified and have ignited great research interest. In particular, the Orthogonal Frequency Division Multiplexing (OFDM)-based multi-user MIMO downlink with Space-Division Multiple Access (SDMA) combines the twofold advantages of MIMO and multi-carrier modulation. It is the essential element ...

For a number of applications like acoustic echo cancellation, adaptive filters are required to identify very long impulse responses. To reduce the computational cost in implementations, adaptive filtering in subband is known to be beneficial. Based on a review of popular fullband adaptive filtering algorithms and various subband approaches, this thesis investigates the implementation, design, and limitations of oversampled subband adaptive filter systems based on modulated complex and real valued filter banks. The main aim is to achieve a computationally efficient implementation for adaptive filter systems, for which fast methods of performing both the subband decomposition and the subband processing are researched. Therefore, a highly efficient polyphase implementation of a complex valued modulated generalized DFT (GDFT) lter bank with a judicious selection of properties for non-integer oversampling ratios is introduced. By modification, a real valued single sideband modulated lter bank ...

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 ...

Due to the extensive growth of big data applications, the widespread use of multisensor technologies, and the need for efficient data representations, multidimensional techniques are a primary tool for many signal processing applications. Multidimensional arrays or tensors allow a natural representation of high-dimensional data. Therefore, they are particularly suited for tasks involving multi-modal data sources such as biomedical sensor readings or multiple-input and multiple-output (MIMO) antenna arrays. While tensor-based techniques were still in their infancy several decades ago, nowadays, they have already proven their effectiveness in various applications. There are many different tensor decompositions in the literature, and each finds use in diverse signal processing fields. In this thesis, we focus on two tensor factorization models: the rank-(Lr,Lr,1) Block-Term Decomposition (BTD) and the Multilinear Generalized Singular Value Decomposition (ML-GSVD) that we propose in this thesis. The ML-GSVD is an extension ...

In nowadays communication systems, error correction provides robust data transmission through imperfect (noisy) channels. Error correcting codes are a crucial component in most storage and communication systems – wired or wireless –, e.g. GSM, UMTS, xDSL, CD/DVD. At least as important as the data integrity issue is the recent realization that error correcting codes fundamentally change the trade-offs in system design. High-integrity, low redundancy coding can be applied to increase data rate, or battery life time or by reducing hardware costs, making it possible to enter mass market. When it comes to the design of error correcting codes and their properties, there are two main theories that play an important role in this work. Classical coding theory aims at finding the best code given an available block length. This thesis focuses on the ubiquitous Reed-Solomon codes, one of the major ...

Abstract Future mobile networks are envisioned to provide wireless access to a massive number of devices. The substantial increase in connectivity comes mainly from machine-type communication (MTC), for which a large number of low-rate transmissions take place. Accommodating access for such a large number of user equipment (UEs) can be inefficient if applied to current network architectures, which are mainly based on orthogonal multiple access (OMA) and scheduling-based transmissions. This is due to the resulting control overhead and increased access delay. The framework of non-orthogonal multiple access (NOMA) has attracted attention recently as a promising solution to tackle these issues. It allows multiple UEs to access the network simultaneously over the same resources, and provides naturally, the support for grant-free access, in which no explicit scheduling of the UEs is required. Motivated by the potential benefits of NOMA in enabling ...