Multiple-Input Multiple-Output Detection Algorithms for Generalized Frequency Division Multiplexing

Since its invention, cellular communication has dramatically transformed personal lifes and the evolution of mobile networks is still ongoing. Evergrowing demand for higher data rates has driven development of 3G and 4G systems, but foreseen 5G requirements also address diverse characteristics such as low latency or massive connectivity. It is speculated that the 4G plain cyclic prefix (CP)-orthogonal frequency division multiplexing (OFDM) cannot sufficiently fulfill all requirements and hence alternative waveforms have been in-vestigated, where generalized frequency division multiplexing (GFDM) is one popular option. An important aspect for any modern wireless communication system is the application of multi-antenna, i.e. MIMO techiques, as MIMO can deliver gains in terms of capacity, reliability and connectivity. Due to its channel-independent orthogonality, CP-OFDM straightforwardly supports broadband MIMO techniques, as the resulting inter-antenna interference (IAI) can readily be resolved. In this regard, CP-OFDM is unique among multicarrier waveforms. Other waveforms suffer from additional inter-carrier interference (ICI), inter-symbol interference (ISI) or both. This possibly 3-dimensional interference renders an optimal MIMO detection much more complex. In this thesis, weinvestigate how GFDM can support an efficient multiple-input multiple-output (MIMO) operation given its 3-dimensional interference structure. To this end, we first connect the mathematical theory of time-frequency analysis (TFA) with multicarrier waveforms in general, leading to theoretical insights into GFDM. Second, we show that the detection problem can be seen as a detection problem on a large, banded linear model under Gaussian noise. Basing on this observation, we propose methods for applying both space-time code (STC) and spatial multiplexing techniques to GFDM. Subsequently, we propose methods to decode the transmitted signals and numerically and theoretically analyze their performance in terms of complexiy and achieved frame error rate (FER). After showing that GFDM modulation and linear demodulation is a direct application of Gabor expansion and transform, we apply results from TFA to explain singularities of the modulation matrix and derive low-complexity expressions for receiver filters. We derive two linear detection algorithms for STC encoded GFDM signals and we show that their performance is equal to OFDM. In the case of spatial multiplexing, we derive both non-iterative and iterative detection algorithms which base on successive interference cancellation (SIC) and minimum mean squared error (MMSE)-parallel interference cancellation (PIC) detection, respectively. By analyzing the error propagation of the SIC algorithm, we explain its significantly inferior performance compared to OFDM. Using feedback information from the channel decoder, we can eventually show that near-optimal GFDM detection can outperform an optimal OFDM detector by up to 3dB for high SNR regions. We conclude that GFDM, given the obtained results, is not a general-purpose replacement for CP-OFDM, due to higher complexity and varying performance. Instead, we can propose GFDM for scenarios with strong frequency-selectivity and stringent spectral and FER requirements

Iterative Demodulation and Decoding for LDPC Coded Generalized Frequency Division Multiplexing

Currently, there is a standardization process underway to design the fifth generation of wireless systems or 5G wireless systems. The ambitious targets set forth for 5G wireless systems call for novel approaches in all layers of the network. At the physical layer (PHY), Orthogonal Frequency Division Multiplexing (OFDM) has become a de facto standard for wireless systems such as 4G cellular and IEEE 802.11 (Wi-Fi) systems. However, the large peak to average power ratio of OFDM signals makes OFDM an unattractive candidate for some services envisioned in 5G systems, particularly in the uplink. Recently, Generalized Frequency Division Multiplexing (GFDM), which is a member of the non-orthogonal multiple access technologies has been proposed as the modulation scheme for 5G wireless systems. GFDM has some advantages over OFDM, such as looser requirements on synchronization, a lower PAPR requirement,as well as a lower out-of-band spectral leakage. However, in GFDM the sub-channels are not orthogonal which results in inter-carrier interference and, hence, an increased uncoded bit error rate. While iterative receivers have been proposed for improving the bit error rate performance of uncoded GFDM, there are very few works that have studied the performance of coded GFDM systems. In this thesis, we investigate the performance of coded systems with GFDM. Using earlier results on soft interference cancellation based turbo equalization and turbo multi-user detection, we design an iterative receiver for GFDM with low density parity check codes. We show that the receiver is able to successfully combat the non-orthogonality of sub-channels in GFDM and provide performance similar to that of coded OFDM systems at an increased receiver complexity

Advanced Channel Estimation Techniques for Multiple-Input Multiple-Output Multi-Carrier Systems in Doubly-Dispersive Channels

Flexible numerology of the physical layer has been introduced in the latest release of 5G new radio (NR) and the baseline waveform generation is chosen to be cyclic-prefix based orthogonal frequency division multiplexing (CP-OFDM). Thanks to the narrow subcarrier spacing and low complexity one tap equalization (EQ) of OFDM, it suits well to time-dispersive channels. For the upcoming 5G and beyond use-case scenarios, it is foreseen that the users might experience high mobility conditions. While the frame structure of the 5G NR is designed for long coherence times, the synchronization and channel estimation (CE) procedures are not fully and reliably covered for diverse applications. The research on alternative multi-carrier waveforms has brought up valuable results in terms of spectral efficiency, applications coexistence and flexibility. Nevertheless, the receiver design becomes more challenging for multiple-input multiple-output (MIMO) non-orthogonal multi-carriers because the receiver must deal with multiple dimensions of interference. This thesis aims to deliver accurate pilot-aided estimations of the wireless channel for coherent detection. Considering a MIMO non-orthogonal multi-carrier, e.g. generalized frequency division multiplexing (GFDM), we initially derive the classical and Bayesian estimators for rich multi-path fading channels, where we theoretically assess the choice of pilot design. Moreover, the well time- and frequency-localization of the pilots in non-orthogonal multi-carriers allows to reuse their energy from cyclic-prefix (CP). Taking advantage of this feature, we derive an iterative approach for joint CE and EQ of MIMO systems. Furthermore, exploiting the block-circularity of GFDM, we comprehensively analyze the complexity aspects, and propose a solution for low complexity implementation. Assuming very high mobility use-cases where the channel varies within the symbol duration, further considerations, particularly the channel coherence time must be taken into account. A promising candidate that is fully independent of the multi-carrier choice is unique word (UW) transmission, where the CP of random nature is replaced by a deterministic sequence. This feature, allows per-block synchronization and channel estimation for robust transmission over extremely doubly-dispersive channels. In this thesis, we propose a novel approach to extend the UW-based physical layer design to MIMO systems and we provide an in-depth study of their out-of-band emission, synchronization, CE and EQ procedures. Via theoretical derivations and simulation results, and comparisons with respect to the state-of-the-art CP-OFDM systems, we show that the proposed UW-based frame design facilitates robust transmission over extremely doubly-dispersive channels.:1 Introduction 1 1.1 Multi-Carrier Waveforms 1 1.2 MIMO Systems 3 1.3 Contributions and Thesis Structure 4 1.4 Notations 6 2 State-of-the-art and Fundamentals 9 2.1 Linear Systems and Problem Statement 9 2.2 GFDM Modulation 11 2.3 MIMO Wireless Channel 12 2.4 Classical and Bayesian Channel Estimation in MIMO OFDM Systems 15 2.5 UW-Based Transmission in SISO Systems 17 2.6 Summary 19 3 Channel Estimation for MIMO Non-Orthogonal Waveforms 21 3.1 Classical and Bayesian Channel Estimation in MIMO GFDM Systems 22 3.1.1 MIMO LS Channel Estimation 23 3.1.2 MIMO LMMSE Channel Estimation 24 3.1.3 Simulation Results 25 3.2 Basic Pilot Designs for GFDM Channel Estimation 29 3.2.1 LS/HM Channel Estimation 31 3.2.2 LMMSE Channel Estimation for GFDM 32 3.2.3 Error Characterization 33 3.2.4 Simulation Results 36 3.3 Interference-Free Pilot Insertion for MIMO GFDM Channel Estimation 39 3.3.1 Interference-Free Pilot Insertion 39 3.3.2 Pilot Observation 40 3.3.3 Complexity 41 3.3.4 Simulation Results 41 3.4 Bayesian Pilot- and CP-aided Channel Estimation in MIMO NonOrthogonal Multi-Carriers 45 3.4.1 Review on System Model 46 3.4.2 Single-Input-Single-Output Systems 47 3.4.3 Extension to MIMO 50 3.4.4 Application to GFDM 51 3.4.5 Joint Channel Estimation and Equalization via LMMSE Parallel Interference Cancellation 57 3.4.6 Complexity Analysis 61 3.4.7 Simulation Results 61 3.5 Pilot- and CP-aided Channel Estimation in Time-Varying Scenarios 67 3.5.1 Adaptive Filtering based on Wiener-Hopf Approac 68 3.5.2 Simulation Results 69 3.6 Summary 72 4 Design of UW-Based Transmission for MIMO Multi-Carriers 73 4.1 Frame Design, Efficiency and Overhead Analysis 74 4.1.1 Illustrative Scenario 74 4.1.2 CP vs. UW Efficiency Analysis 76 4.1.3 Numerical Results 77 4.2 Sequences for UW and OOB Radiation 78 4.2.1 Orthogonal Polyphase Sequences 79 4.2.2 Waveform Engineering for UW Sequences combined with GFDM 79 4.2.3 Simulation Results for OOB Emission of UW-GFDM 81 4.3 Synchronization 82 4.3.1 Transmission over a Centralized MIMO Wireless Channel 82 4.3.2 Coarse Time Acquisition 83 4.3.3 CFO Estimation and Removal 85 4.3.4 Fine Time Acquisition 86 4.3.5 Simulation Results 88 4.4 Channel Estimation 92 4.4.1 MIMO UW-based LMMSE CE 92 4.4.2 Adaptive Filtering 93 4.4.3 Circular UW Transmission 94 4.4.4 Simulation Results 95 4.5 Equalization with Imperfect Channel Knowledge 96 4.5.1 UW-Free Equalization 97 4.5.2 Simulation Results 99 4.6 Summary 102 5 Conclusions and Perspectives 103 5.1 Main Outcomes in Short 103 5.2 Open Challenges 105 A Complementary Materials 107 A.1 Linear Algebra Identities 107 A.2 Proof of lower triangular Toeplitz channel matrix being defective 108 A.3 Calculation of noise-plus-interference covariance matrix for Pilot- and CPaided CE 108 A.4 Bock diagonalization of the effective channel for GFDM 109 A.5 Detailed complexity analysis of Sec. 3.4 109 A.6 CRLB derivations for the pdf (4.24) 113 A.7 Proof that (4.45) emulates a circular CIR at the receiver 11

Performance Analysis of a 5G Transceiver Implementation for Remote Areas Scenarios

The fifth generation of mobile communication networks will support a large set of new services and applications. One important use case is the remote area coverage for broadband Internet access. This use case ha significant social and economic impact, since a considerable percentage of the global population living in low populated area does not have Internet access and the communication infrastructure in rural areas can be used to improve agribusiness productivity. The aim of this paper is to analyze the performance of a 5G for Remote Areas transceiver, implemented on field programmable gate array based hardware for real-time processing. This transceiver employs the latest digital communication techniques, such as generalized frequency division multiplexing waveform combined with 2 by 2 multiple-input multiple-output diversity scheme and polar channel coding. The performance of the prototype is evaluated regarding its out-of-band emissions and bit error rate under AWGN channel.Comment: Presented in 2018 European Conference on Networks and Communications (EuCNC),18-21 June, 2018, Ljubljana, Sloveni

Unified Framework for Multicarrier and Multiple Access based on Generalized Frequency Division Multiplexing

The advancements in wireless communications are the key-enablers of new applications with stringent requirements in low-latency, ultra-reliability, high data rate, high mobility, and massive connectivity. Diverse types of devices, ranging from tiny sensors to vehicles, with different capabilities need to be connected under various channel conditions. Thus, modern connectivity and network techniques at all layers are essential to overcome these challenges. In particular, the physical layer (PHY) transmission is required to achieve certain link reliability, data rate, and latency. In modern digital communications systems, the transmission is performed by means of a digital signal processing module that derives analog hardware. The performance of the analog part is influenced by the quality of the hardware and the baseband signal denoted as waveform. In most of the modern systems such as fifth generation (5G) and WiFi, orthogonal frequency division multiplexing (OFDM) is adopted as a favorite waveform due to its low-complexity advantages in terms of signal processing. However, OFDM requires strict requirements on hardware quality. Many devices are equipped with simplified analog hardware to reduce the cost. In this case, OFDM does not work properly as a result of its high peak-to-average power ratio (PAPR) and sensitivity to synchronization errors. To tackle these problems, many waveforms design have been recently proposed in the literature. Some of these designs are modified versions of OFDM or based on conventional single subcarrier. Moreover, multicarrier frameworks, such as generalized frequency division multiplexing (GFDM), have been proposed to realize varieties of conventional waveforms. Furthermore, recent studies show the potential of using non-conventional waveforms for increasing the link reliability with affordable complexity. Based on that, flexible waveforms and transmission techniques are necessary to adapt the system for different hardware and channel constraints in order to fulfill the applications requirements while optimizing the resources. The objective of this thesis is to provide a holistic view of waveforms and the related multiple access (MA) techniques to enable efficient study and evaluation of different approaches. First, the wireless communications system is reviewed with specific focus on the impact of hardware impairments and the wireless channel on the waveform design. Then, generalized model of waveforms and MA are presented highlighting various special cases. Finally, this work introduces low-complexity architectures for hardware implementation of flexible waveforms. Integrating such designs with software-defined radio (SDR) contributes to the development of practical real-time flexible PHY.:1 Introduction 1.1 Baseband transmission model 1.2 History of multicarrier systems 1.3 The state-of-the-art waveforms 1.4 Prior works related to GFDM 1.5 Objective and contributions 2 Fundamentals of Wireless Communications 2.1 Wireless communications system 2.2 RF transceiver 2.2.1 Digital-analogue conversion 2.2.2 QAM modulation 2.2.3 Effective channel 2.2.4 Hardware impairments 2.3 Waveform aspects 2.3.1 Single-carrier waveform 2.3.2 Multicarrier waveform 2.3.3 MIMO-Waveforms 2.3.4 Waveform performance metrics 2.4 Wireless Channel 2.4.1 Line-of-sight propagation 2.4.2 Multi path and fading process 2.4.3 General baseband statistical channel model 2.4.4 MIMO channel 2.5 Summary 3 Generic Block-based Waveforms 3.1 Block-based waveform formulation 3.1.1 Variable-rate multicarrier 3.1.2 General block-based multicarrier model 3.2 Waveform processing techniques 3.2.1 Linear and circular filtering 3.2.2 Windowing 3.3 Structured representation 3.3.1 Modulator 3.3.2 Demodulator 3.3.3 MIMO Waveform processing 3.4 Detection 3.4.1 Maximum-likelihood detection 3.4.2 Linear detection 3.4.3 Iterative Detection 3.4.4 Numerical example and insights 3.5 Summary 4 Generic Multiple Access Schemes 57 4.1 Basic multiple access and multiplexing schemes 4.1.1 Infrastructure network system model 4.1.2 Duplex schemes 4.1.3 Common multiplexing and multiple access schemes 4.2 General multicarrier-based multiple access 4.2.1 Design with fixed set of pulses 4.2.2 Computational model 4.2.3 Asynchronous multiple access 4.3 Summary 5 Time-Frequency Analyses of Multicarrier 5.1 General time-frequency representation 5.1.1 Block representation 5.1.2 Relation to Zak transform 5.2 Time-frequency spreading 5.3 Time-frequency block in LTV channel 5.3.1 Subcarrier and subsymbol numerology 5.3.2 Processing based on the time-domain signal 5.3.3 Processing based on the frequency-domain signal 5.3.4 Unified signal model 5.4 summary 6 Generalized waveforms based on time-frequency shifts 6.1 General time-frequency shift 6.1.1 Time-frequency shift design 6.1.2 Relation between the shifted pulses 6.2 Time-frequency shift in Gabor frame 6.2.1 Conventional GFDM 6.3 GFDM modulation 6.3.1 Filter bank representation 6.3.2 Block representation 6.3.3 GFDM matrix structure 6.3.4 GFDM demodulator 6.3.5 Alternative interpretation of GFDM 6.3.6 Orthogonal modulation and GFDM spreading 6.4 Summary 7 Modulation Framework: Architectures and Applications 7.1 Modem architectures 7.1.1 General modulation matrix structure 7.1.2 Run-time flexibility 7.1.3 Generic GFDM-based architecture 7.1.4 Flexible parallel multiplications architecture 7.1.5 MIMO waveform architecture 7.2 Extended GFDM framework 7.2.1 Architectures complexity and flexibility analysis 7.2.2 Number of multiplications 7.2.3 Hardware analysis 7.3 Applications of the extended GFDM framework 7.3.1 Generalized FDMA 7.3.2 Enchantment of OFDM system 7.4 Summary 7 Conclusions and Future work

Design and Analysis of GFDM-Based Wireless Communication Systems

Le multiplexage généralisé par répartition en fréquence (GFDM), une méthode de traitement par blocs de modulation multiporteuses non orthogonales, est une candidate prometteuse pour les technologies de forme d'onde pour les systèmes sans fil au-delà de la cinquième génération (5G). La capacité du GFDM à ajuster de manière flexible la taille du bloc et le type de filtres de mise en forme des impulsions en fait une méthode appropriée pour répondre à plusieurs exigences importantes, comme une faible latence, un faible rayonnement hors bande (OOB) et des débits de données élevés. En appliquant aux systèmes GFDM la technique des systèmes à entrées multiples et sorties multiples (MIMO), la technique de MIMO massif ou des codes de contrôle de parité à faible densité (LDPC), il est possible d'améliorer leurs performances. Par conséquent, l'étude de ces systèmes combinés sont d'une grande importance théorique et pratique. Dans cette thèse, nous étudions les systèmes de communication sans fil basés sur le GFDM en considérant trois aspects. Tout d'abord, nous dérivons une borne d'union sur le taux d'erreur sur les bits (BER) pour les systèmes MIMO-GFDM, technique qui est basée sur des probabilités d'erreur par paires exactes (PEP). La PEP exacte est calculée en utilisant la fonction génératrice de moments(MGF) pour les détecteurs à maximum de vraisemblance (ML). La corrélation spatiale entre les antennes et les erreurs d'estimation de canal sont prises en compte dans l'environnement de canal étudié. Deuxièmement, les estimateurs et les précodeurs de canal de faible complexité basés sur une expansion polynomiale sont proposés pour les systèmes MIMO-GFDM massifs. Des pilotes sans interférence sont utilisés pour l'estimation du canal basée sur l'erreur quadratique moyenne minimale(MMSE) pour lutter contre l'influence de la non-orthogonalité entre les sous-porteuses dans le GFDM. La complexité de calcul cubique peut être réduite à une complexité d'ordre au carré en utilisant la technique d'expansion polynomiale pour approximer les inverses de matrices dans l'estimation MMSE conventionnelle et le précodage. De plus, nous calculons les limites de performance en termes d'erreur quadratique moyenne (MSE) pour les estimateurs proposés, ce qui peut être un outil utile pour prédire la performance des estimateurs dans la région de Eₛ/N₀ élevé. Une borne inférieure de Cramér-Rao(CRLB) est dérivée pour notre modèle de système et agit comme une référence pour les estimateurs. La complexité de calcul des estimateurs de canal proposés et des précodeurs et les impacts du degré du polynôme sont également étudiés. Enfin, nous analysons les performances de la probabilité d'erreur des systèmes GFDM combinés aux codes LDPC. Nous dérivons d'abord les expressions du ratio de vraisemblance logarithmique (LLR) initiale qui sont utilisées dans le décodeur de l'algorithme de somme de produits (SPA). Ensuite, basé sur le seuil de décodage, nous estimons le taux d'erreur de trame (FER) dans la région de bas E[indice b]/N₀ en utilisant le BER observé pour modéliser les variations du canal. De plus, une borne inférieure du FER du système est également proposée basée sur des ensembles absorbants. Cette borne inférieure peut agir comme une estimation du FER dans la région de E[indice b]/N₀ élevé si l'ensemble absorbant utilisé est dominant et que sa multiplicité est connue. La quantification a également un impact important sur les performances du FER et du BER. Des codes LDPC basés sur un tableau et construit aléatoirement sont utilisés pour supporter les analyses de performances. Pour ces trois aspects, des simulations et des calculs informatiques sont effectués pour obtenir des résultats numériques connexes, qui vérifient les méthodes proposées.8 372162\u a Generalized frequency division multiplexing (GFDM) is a block-processing based non-orthogonal multi-carrier modulation scheme, which is a promising candidate waveform technology for beyond fifth-generation (5G) wireless systems. The ability of GFDM to flexibly adjust the block size and the type of pulse-shaping filters makes it a suitable scheme to meet several important requirements, such as low latency, low out-of-band (OOB) radiation and high data rates. Applying the multiple-input multiple-output (MIMO) technique, the massive MIMO technique, or low-density parity-check (LDPC) codes to GFDM systems can further improve the systems performance. Therefore, the investigation of such combined systems is of great theoretical and practical importance. This thesis investigates GFDM-based wireless communication systems from the following three aspects. First, we derive a union bound on the bit error rate (BER) for MIMO-GFDM systems, which is based on exact pairwise error probabilities (PEPs). The exact PEP is calculated using the moment-generating function (MGF) for maximum likelihood (ML) detectors. Both the spatial correlation between antennas and the channel estimation errors are considered in the investigated channel environment. Second, polynomial expansion-based low-complexity channel estimators and precoders are proposed for massive MIMO-GFDM systems. Interference-free pilots are used in the minimum mean square error (MMSE) channel estimation to combat the influence of non-orthogonality between subcarriers in GFDM. The cubic computational complexity can be reduced to square order by using the polynomial expansion technique to approximate the matrix inverses in the conventional MMSE estimation and precoding. In addition, we derive performance limits in terms of the mean square error (MSE) for the proposed estimators, which can be a useful tool to predict estimators performance in the high Eₛ/N₀ region. A Cramér-Rao lower bound (CRLB) is derived for our system model and acts as a benchmark for the estimators. The computational complexity of the proposed channel estimators and precoders, and the impacts of the polynomial degree are also investigated. Finally, we analyze the error probability performance of LDPC coded GFDM systems. We first derive the initial log-likelihood ratio (LLR) expressions that are used in the sum-product algorithm (SPA) decoder. Then, based on the decoding threshold, we estimate the frame error rate (FER) in the low E[subscript b]/N₀ region by using the observed BER to model the channel variations. In addition, a lower bound on the FER of the system is also proposed based on absorbing sets. This lower bound can act as an estimate of the FER in the high E[subscript b]/N₀ region if the absorbing set used is dominant and its multiplicity is known. The quantization scheme also has an important impact on the FER and BER performances. Randomly constructed and array-based LDPC codes are used to support the performance analyses. For all these three aspects, software-based simulations and calculations are carried out to obtain related numerical results, which verify our proposed methods

Filter bank multicarrier waveforms for future wireless networks: interference analysis and cancellation

Billions of devices are expected to connect to future wireless networks. Although conventional orthogonal division multiplexing (OFDM) has proven to be an effective physical layer waveform for enhanced mobile broadband (eMBB), it experiences various challenges. For example, OFDM experiences high out-of-band (OOB) emission caused by the use of rectangular filters. This causes interference to adjacent frequency bands and make OFDM highly sensitive to asynchronous transmissions. Filter bank multicarrier (FBMC) systems have emerged as a promising waveform candidate to satisfy the requirements of future wireless networks. They employ prototype filters with faster spectral decay, which results in better OOB emission and spectral efficiency compared to OFDM. Also, FBMC systems support asynchronous transmissions, which can reduce the signaling overhead in future applications. However, in FBMC systems there is no subcarriers orthogonality, resulting in intrinsic interference. The purpose of this thesis is to address the intrinsic interference problem to make FBMC a viable option for practical application in future wireless networks. In this thesis, iterative interference cancellation (IIC) receivers are developed for FBMC systems to improve their performance and applicability in future applications. First, an IIC receiver is studied for uncoded FBMC with quadrature amplitude modulation (FBMC-QAM) systems. To improve the decoding performance, bit-interleaved coded modulation with iterative decoding (BICM-ID) is incorporated into the IIC receiver design and the technique of extrinsic information transfer (EXIT) chart analysis is used to track the convergence of the IIC-based BICM-ID receiver. Furthermore, the energy harvesting capabilities of FBMC is considered. Particularly, FBMC is integrated with a simultaneous wireless information and power transfer (SWIPT) technique. Finally, an interference cancellation receiver is investigated for asynchronous FBMC systems in both single and mixed numerology systems. Analytical expressions are derived for the various schemes and simulations results are shown to verify the performance of the different FBMC systems