A unified approach to sparse signal processing

A unified view of the area of sparse signal processing is presented in tutorial form by bringing together various fields in which the property of sparsity has been successfully exploited. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common potential benefits of significant reduction in sampling rate and processing manipulations through sparse signal processing are revealed. The key application domains of sparse signal processing are sampling, coding, spectral estimation, array processing, compo-nent analysis, and multipath channel estimation. In terms of the sampling process and reconstruction algorithms, linkages are made with random sampling, compressed sensing and rate of innovation. The redundancy introduced by channel coding i

Review of Recent Trends

This work was partially supported by the European Regional Development Fund (FEDER), through the Regional Operational Programme of Centre (CENTRO 2020) of the Portugal 2020 framework, through projects SOCA (CENTRO-01-0145-FEDER-000010) and ORCIP (CENTRO-01-0145-FEDER-022141). Fernando P. Guiomar acknowledges a fellowship from “la Caixa” Foundation (ID100010434), code LCF/BQ/PR20/11770015. Houda Harkat acknowledges the financial support of the Programmatic Financing of the CTS R&D Unit (UIDP/00066/2020).MIMO-OFDM is a key technology and a strong candidate for 5G telecommunication systems. In the literature, there is no convenient survey study that rounds up all the necessary points to be investigated concerning such systems. The current deeper review paper inspects and interprets the state of the art and addresses several research axes related to MIMO-OFDM systems. Two topics have received special attention: MIMO waveforms and MIMO-OFDM channel estimation. The existing MIMO hardware and software innovations, in addition to the MIMO-OFDM equalization techniques, are discussed concisely. In the literature, only a few authors have discussed the MIMO channel estimation and modeling problems for a variety of MIMO systems. However, to the best of our knowledge, there has been until now no review paper specifically discussing the recent works concerning channel estimation and the equalization process for MIMO-OFDM systems. Hence, the current work focuses on analyzing the recently used algorithms in the field, which could be a rich reference for researchers. Moreover, some research perspectives are identified.publishersversionpublishe

MIMO signal processing in offset-QAM based filter bank multicarrier systems

Next-generation communication systems have to comply with very strict requirements for increased flexibility in heterogeneous environments, high spectral efficiency, and agility of carrier aggregation. This fact motivates research in advanced multicarrier modulation (MCM) schemes, such as filter bank-based multicarrier (FBMC) modulation. This paper focuses on the offset quadrature amplitude modulation (OQAM)-based FBMC variant, known as FBMC/OQAM, which presents outstanding spectral efficiency and confinement in a number of channels and applications. Its special nature, however, generates a number of new signal processing challenges that are not present in other MCM schemes, notably, in orthogonal-frequency-division multiplexing (OFDM). In multiple-input multiple-output (MIMO) architectures, which are expected to play a primary role in future communication systems, these challenges are intensified, creating new interesting research problems and calling for new ideas and methods that are adapted to the particularities of the MIMO-FBMC/OQAM system. The goal of this paper is to focus on these signal processing problems and provide a concise yet comprehensive overview of the recent advances in this area. Open problems and associated directions for future research are also discussed.Peer ReviewedPostprint (author's final draft

Preamble-Based Channel Estimation for CP-OFDM and OFDM/OQAM Systems: A Comparative Study

In this paper, preamble-based least squares (LS) channel estimation in OFDM systems of the QAM and offset QAM (OQAM) types is considered, in both the frequency and the time domains. The construction of optimal (in the mean squared error (MSE) sense) preambles is investigated, for both the cases of full (all tones carrying pilot symbols) and sparse (a subset of pilot tones, surrounded by nulls or data) preambles. The two OFDM systems are compared for the same transmit power, which, for cyclic prefix (CP) based OFDM/QAM, also includes the power spent for CP transmission. OFDM/OQAM, with a sparse preamble consisting of equipowered and equispaced pilots embedded in zeros, turns out to perform at least as well as CP-OFDM. Simulations results are presented that verify the analysis

Advanced tensor based signal processing techniques for wireless communication systems and biomedical signal processing

Many observed signals in signal processing applications including wireless communications, biomedical signal processing, image processing, and machine learning are multi-dimensional. Tensors preserve the multi-dimensional structure and provide a natural representation of these signals/data. Moreover, tensors provide often an improved identifiability. Therefore, we benefit from using tensor algebra in the above mentioned applications and many more. In this thesis, we present the benefits of utilizing tensor algebra in two signal processing areas. These include signal processing for MIMO (Multiple-Input Multiple-Output) wireless communication systems and biomedical signal processing. Moreover, we contribute to the theoretical aspects of tensor algebra by deriving new properties and ways of computing tensor decompositions. Often, we only have an element-wise or a slice-wise description of the signal model. This representation of the signal model does not reveal the explicit tensor structure. Therefore, the derivation of all tensor unfoldings is not always obvious. Consequently, exploiting the multi-dimensional structure of these models is not always straightforward. We propose an alternative representation of the element-wise multiplication or the slice-wise multiplication based on the generalized tensor contraction operator. Later in this thesis, we exploit this novel representation and the properties of the contraction operator such that we derive the final tensor models. There exist a number of different tensor decompositions that describe different signal models such as the HOSVD (Higher Order Singular Value Decomposition), the CP/PARAFAC (Canonical Polyadic / PARallel FACtors) decomposition, the BTD (Block Term Decomposition), the PARATUCK2 (PARAfac and TUCker2) decomposition, and the PARAFAC2 (PARAllel FACtors2) decomposition. Among these decompositions, the CP decomposition is most widely spread and used. Therefore, the development of algorithms for the efficient computation of the CP decomposition is important for many applications. The SECSI (Semi-Algebraic framework for approximate CP decomposition via SImultaneaous matrix diagonalization) framework is an efficient and robust tool for the calculation of the approximate low-rank CP decomposition via simultaneous matrix diagonalizations. In this thesis, we present five extensions of the SECSI framework that reduce the computational complexity of the original framework and/or introduce constraints to the factor matrices. Moreover, the PARAFAC2 decomposition and the PARATUCK2 decomposition are usually described using a slice-wise notation that can be expressed in terms of the generalized tensor contraction as proposed in this thesis. We exploit this novel representation to derive explicit tensor models for the PARAFAC2 decomposition and the PARATUCK2 decomposition. Furthermore, we use the PARAFAC2 model to derive an ALS (Alternating Least-Squares) algorithm for the computation of the PARAFAC2 decomposition. Moreover, we exploit the novel contraction properties for element wise and slice-wise multiplications to model MIMO multi-carrier wireless communication systems. We show that this very general model can be used to derive the tensor model of the received signal for MIMO-OFDM (Multiple-Input Multiple-Output - Orthogonal Frequency Division Multiplexing), Khatri-Rao coded MIMO-OFDM, and randomly coded MIMO-OFDM systems. We propose the transmission techniques Khatri-Rao coding and random coding in order to impose an additional tensor structure of the transmit signal tensor that otherwise does not have a particular structure. Moreover, we show that this model can be extended to other multi-carrier techniques such as GFDM (Generalized Frequency Division Multiplexing). Utilizing these models at the receiver side, we design several types for receivers for these systems that outperform the traditional matrix based solutions in terms of the symbol error rate. In the last part of this thesis, we show the benefits of using tensor algebra in biomedical signal processing by jointly decomposing EEG (ElectroEncephaloGraphy) and MEG (MagnetoEncephaloGraphy) signals. EEG and MEG signals are usually acquired simultaneously, and they capture aspects of the same brain activity. Therefore, EEG and MEG signals can be decomposed using coupled tensor decompositions such as the coupled CP decomposition. We exploit the proposed coupled SECSI framework (one of the proposed extensions of the SECSI framework) for the computation of the coupled CP decomposition to first validate and analyze the photic driving effect. Moreover, we validate the effects of scull defects on the measurement EEG and MEG signals by means of a joint EEG-MEG decomposition using the coupled SECSI framework. Both applications show that we benefit from coupled tensor decompositions and the coupled SECSI framework is a very practical tool for the analysis of biomedical data.Zahlreiche messbare Signale in verschiedenen Bereichen der digitalen Signalverarbeitung, z.B. in der drahtlosen Kommunikation, im Mobilfunk, biomedizinischen Anwendungen, der Bild- oder akustischen Signalverarbeitung und dem maschinellen Lernen sind mehrdimensional. Tensoren erhalten die mehrdimensionale Struktur und stellen eine natürliche Darstellung dieser Signale/Daten dar. Darüber hinaus bieten Tensoren oft eine verbesserte Trennbarkeit von enthaltenen Signalkomponenten. Daher profitieren wir von der Verwendung der Tensor-Algebra in den oben genannten Anwendungen und vielen mehr. In dieser Arbeit stellen wir die Vorteile der Nutzung der Tensor-Algebra in zwei Bereichen der Signalverarbeitung vor: drahtlose MIMO (Multiple-Input Multiple-Output) Kommunikationssysteme und biomedizinische Signalverarbeitung. Darüber hinaus tragen wir zu theoretischen Aspekten der Tensor-Algebra bei, indem wir neue Eigenschaften und Berechnungsmethoden für die Tensor-Zerlegung ableiten. Oftmals verfügen wir lediglich über eine elementweise oder ebenenweise Beschreibung des Signalmodells, welche nicht die explizite Tensorstruktur zeigt. Daher ist die Ableitung aller Tensor-Unfoldings nicht offensichtlich, wodurch die multidimensionale Struktur dieser Modelle nicht trivial nutzbar ist. Wir schlagen eine alternative Darstellung der elementweisen Multiplikation oder der ebenenweisen Multiplikation auf der Grundlage des generalisierten Tensor-Kontraktionsoperators vor. Weiterhin nutzen wir diese neuartige Darstellung und deren Eigenschaften zur Ableitung der letztendlichen Tensor-Modelle. Es existieren eine Vielzahl von Tensor-Zerlegungen, die verschiedene Signalmodelle beschreiben, wie die HOSVD (Higher Order Singular Value Decomposition), CP/PARAFAC (Canonical Polyadic/ PARallel FACtors) Zerlegung, die BTD (Block Term Decomposition), die PARATUCK2-(PARAfac und TUCker2) und die PARAFAC2-Zerlegung (PARAllel FACtors2). Dabei ist die CP-Zerlegung am weitesten verbreitet und wird findet in zahlreichen Gebieten Anwendung. Daher ist die Entwicklung von Algorithmen zur effizienten Berechnung der CP-Zerlegung von besonderer Bedeutung. Das SECSI (Semi-Algebraic Framework for approximate CP decomposition via Simultaneaous matrix diagonalization) Framework ist ein effizientes und robustes Werkzeug zur Berechnung der approximierten Low-Rank CP-Zerlegung durch simultane Matrixdiagonalisierung. In dieser Arbeit stellen wir fünf Erweiterungen des SECSI-Frameworks vor, welche die Rechenkomplexität des ursprünglichen Frameworks reduzieren bzw. Einschränkungen für die Faktormatrizen einführen. Darüber hinaus werden die PARAFAC2- und die PARATUCK2-Zerlegung in der Regel mit einer ebenenweisen Notation beschrieben, die sich in Form der allgemeinen Tensor-Kontraktion, wie sie in dieser Arbeit vorgeschlagen wird, ausdrücken lässt. Wir nutzen diese neuartige Darstellung, um explizite Tensormodelle für diese beiden Zerlegungen abzuleiten. Darüber hinaus verwenden wir das PARAFAC2-Modell, um einen ALS-Algorithmus (Alternating Least-Squares) für die Berechnung der PARAFAC2-Zerlegungen abzuleiten. Weiterhin nutzen wir die neuartigen Kontraktionseigenschaften für elementweise und ebenenweise Multiplikationen, um MIMO Multi-Carrier-Mobilfunksysteme zu modellieren. Wir zeigen, dass dieses sehr allgemeine Modell verwendet werden kann, um das Tensor-Modell des empfangenen Signals für MIMO-OFDM- (Multiple- Input Multiple-Output - Orthogonal Frequency Division Multiplexing), Khatri-Rao codierte MIMO-OFDM- und zufällig codierte MIMO-OFDM-Systeme abzuleiten. Wir schlagen die Übertragungstechniken der Khatri-Rao-Kodierung und zufällige Kodierung vor, um eine zusätzliche Tensor-Struktur des Sendesignal-Tensors einzuführen, welcher gewöhnlich keine bestimmte Struktur aufweist. Darüber hinaus zeigen wir, dass dieses Modell auf andere Multi-Carrier-Techniken wie GFDM (Generalized Frequency Division Multiplexing) erweitert werden kann. Unter Verwendung dieser Modelle auf der Empfängerseite entwerfen wir verschiedene Typen von Empfängern für diese Systeme, die die traditionellen matrixbasierten Lösungen in Bezug auf die Symbolfehlerrate übertreffen. Im letzten Teil dieser Arbeit zeigen wir die Vorteile der Verwendung von Tensor-Algebra in der biomedizinischen Signalverarbeitung durch die gemeinsame Zerlegung von EEG-(ElectroEncephaloGraphy) und MEG- (MagnetoEncephaloGraphy) Signalen. Diese werden in der Regel gleichzeitig erfasst, wobei sie gemeinsame Aspekte derselben Gehirnaktivität beschreiben. Daher können EEG- und MEG-Signale mit gekoppelten Tensor-Zerlegungen wie der gekoppelten CP Zerlegung analysiert werden. Wir nutzen das vorgeschlagene gekoppelte SECSI-Framework (eine der vorgeschlagenen Erweiterungen des SECSI-Frameworks) für die Berechnung der gekoppelten CP Zerlegung, um zunächst den photic driving effect zu validieren und zu analysieren. Darüber hinaus validieren wir die Auswirkungen von Schädeldefekten auf die Messsignale von EEG und MEG durch eine gemeinsame EEG-MEG-Zerlegung mit dem gekoppelten SECSI-Framework. Beide Anwendungen zeigen, dass wir von gekoppelten Tensor-Zerlegungen profitieren, wobei die Methoden des gekoppelten SECSI-Frameworks erfolgreich zur Analyse biomedizinischer Daten genutzt werden können

High mobility in OFDM based wireless communication systems

Orthogonal Frequency Division Multiplexing (OFDM) has been adopted as the transmission scheme in most of the wireless systems we use on a daily basis. It brings with it several inherent advantages that make it an ideal waveform candidate in the physical layer. However, OFDM based wireless systems are severely affected in High Mobility scenarios. In this thesis, we investigate the effects of mobility on OFDM based wireless systems and develop novel techniques to estimate the channel and compensate its effects at the receiver. Compressed Sensing (CS) based channel estimation techniques like the Rake Matching Pursuit (RMP) and the Gradient Rake Matching Pursuit (GRMP) are developed to estimate the channel in a precise, robust and computationally efficient manner. In addition to this, a Cognitive Framework that can detect the mobility in the channel and configure an optimal estimation scheme is also developed and tested. The Cognitive Framework ensures a computationally optimal channel estimation scheme in all channel conditions. We also demonstrate that the proposed schemes can be adapted to other wireless standards easily. Accordingly, evaluation is done for three current broadcast, broadband and cellular standards. The results show the clear benefit of the proposed schemes in enabling high mobility in OFDM based wireless communication systems.Orthogonal Frequency Division Multiplexing (OFDM) wurde als Übertragungsschema in die meisten drahtlosen Systemen, die wir täglich verwenden, übernommen. Es bringt mehrere inhärente Vorteile mit sich, die es zu einem idealen Waveform-Kandidaten in der Bitübertragungsschicht (Physical Layer) machen. Allerdings sind OFDM-basierte drahtlose Systeme in Szenarien mit hoher Mobilität stark beeinträchtigt. In dieser Arbeit untersuchen wir die Auswirkungen der Mobilität auf OFDM-basierte drahtlose Systeme und entwickeln neuartige Techniken, um das Verhalten des Kanals abzuschätzen und seine Auswirkungen am Empfänger zu kompensieren. Auf Compressed Sensing (CS) basierende Kanalschätzverfahren wie das Rake Matching Pursuit (RMP) und das Gradient Rake Matching Pursuit (GRMP) werden entwickelt, um den Kanal präzise, robust und rechnerisch effizient abzuschätzen. Darüber hinaus wird ein Cognitive Framework entwickelt und getestet, das die Mobilität im Kanal erkennt und ein optimales Schätzungsschema konfiguriert. Das Cognitive Framework gewährleistet ein rechnerisch optimales Kanalschätzungsschema für alle möglichen Kanalbedingungen. Wir zeigen außerdem, dass die vorgeschlagenen Schemata auch leicht an andere Funkstandards angepasst werden können. Dementsprechend wird eine Evaluierung für drei aktuelle Rundfunk-, Breitband- und Mobilfunkstandards durchgeführt. Die Ergebnisse zeigen den klaren Vorteil der vorgeschlagenen Schemata bei der Ermöglichung hoher Mobilität in OFDM-basierten drahtlosen Kommunikationssystemen