Extended GFDM Framework: OTFS and GFDM Comparison

Orthogonal time frequency space modulation (OTFS) has been recently proposed to achieve time and frequency diversity, especially in linear time-variant (LTV) channels with large Doppler frequencies. The idea is based on the precoding of the data symbols using symplectic finite Fourier transform (SFFT) then transmitting them by mean of orthogonal frequency division multiplexing (OFDM) waveform. Consequently, the demodulator and channel equalization can be coupled in one processing step. As a distinguished feature, the demodulated data symbols have roughly equal gain independent of the channel selectivity. On the other hand, generalized frequency division multiplexing (GFDM) modulation also employs the spreading over the time and frequency domains using circular filtering. Accordingly, the data symbols are implicitly precoded in a similar way as applying SFFT in OTFS. In this paper, we present an extended representation of GFDM which shows that OTFS can be processed as a GFDM signal with simple permutation. Nevertheless, this permutation is the key factor behind the outstanding performance of OTFS in LTV channels, as demonstrated in this work. Furthermore, the representation of OTFS in the GFDM framework provides an efficient implementation, that has been intensively investigated for GFDM, and facilitates the understanding of the OTFS distinct features.Comment: Accepted in IEEE Global Communications Conference 9-13 December 2018 Abu Dhabi, UA

MULTICARRIER TRANSMISSION TECHNIQUES

In this thesis, multicarrier transmission techniques envisioned for the fifth-generation wireless networks are studied. First, three basic techniques, namely orthogonal frequency-division multiplexing (OFDM), filter-bank multicarrier offset quadrature amplitude modulation (FBMC-OQAM), and generalized frequency-division multiplexing (GFDM) are reviewed in detail. In particular, the block-based structure and cyclic prefixing of OFDM are discussed and its bit error rate (BER) performance is analyzed. Then it is demonstrated that with offset QAM the orthogonality between subcarriers in FBMC-OQAM is preserved. Next, the roles of tail biting technique and circular convolution in GFDM are explained. An efficient implementation of GFDM is also described. Second, circular filterbank multicarrier offset QAM (CFBMC-OQAM), a technique which combines the block-based structure of GFDM and offset QAM of FBMC-OQAM, is presented. Then a precoded scheme is proposed, in which the Walsh-Hadamard (WH) transform is applied to CFBMC-OQAM system, resulting in a precoded scheme called WH-CFBMC-OQAM. The proposed system has a block-based structure and can be implemented efficiently using fast Fourier transform (FTT) and inverse FFT (IFFT). In addition, a cyclic prefix can be inserted to facilitate simple equalization at the receiver. WH-CFBMC-OQAM exploits the frequency diversity by averaging the signal-to-noise ratios (SNRs) over all subcarriers. A theoretical approximation for the bit error rate performance of WH-CFBMC-OQAM over a frequency-selective channel is derived. Under the same system configuration, simulation results demonstrate the excellent performance of the proposed scheme when compared to the performance of other techniques. Simulation also verifies that the theoretical results match perfectly with simulation results for any SNR value

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

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

Real-Time Waveform Prototyping

Mobile Netzwerke der fünften Generation zeichen sich aus durch vielfältigen Anforderungen und Einsatzszenarien. Drei unterschiedliche Anwendungsfälle sind hierbei besonders relevant: 1) Industrie-Applikationen fordern Echtzeitfunkübertragungen mit besonders niedrigen Ausfallraten. 2) Internet-of-things-Anwendungen erfordern die Anbindung einer Vielzahl von verteilten Sensoren. 3) Die Datenraten für Anwendung wie z.B. der Übermittlung von Videoinhalten sind massiv gestiegen. Diese zum Teil gegensätzlichen Erwartungen veranlassen Forscher und Ingenieure dazu, neue Konzepte und Technologien für zukünftige drahtlose Kommunikationssysteme in Betracht zu ziehen. Ziel ist es, aus einer Vielzahl neuer Ideen vielversprechende Kandidatentechnologien zu identifizieren und zu entscheiden, welche für die Umsetzung in zukünftige Produkte geeignet sind. Die Herausforderungen, diese Anforderungen zu erreichen, liegen jedoch jenseits der Möglichkeiten, die eine einzelne Verarbeitungsschicht in einem drahtlosen Netzwerk bieten kann. Daher müssen mehrere Forschungsbereiche Forschungsideen gemeinsam nutzen. Diese Arbeit beschreibt daher eine Plattform als Basis für zukünftige experimentelle Erforschung von drahtlosen Netzwerken unter reellen Bedingungen. Es werden folgende drei Aspekte näher vorgestellt: Zunächst erfolgt ein Überblick über moderne Prototypen und Testbed-Lösungen, die auf großes Interesse, Nachfrage, aber auch Förderungsmöglichkeiten stoßen. Allerdings ist der Entwicklungsaufwand nicht unerheblich und richtet sich stark nach den gewählten Eigenschaften der Plattform. Der Auswahlprozess ist jedoch aufgrund der Menge der verfügbaren Optionen und ihrer jeweiligen (versteckten) Implikationen komplex. Daher wird ein Leitfaden anhand verschiedener Beispiele vorgestellt, mit dem Ziel Erwartungen im Vergleich zu den für den Prototyp erforderlichen Aufwänden zu bewerten. Zweitens wird ein flexibler, aber echtzeitfähiger Signalprozessor eingeführt, der auf einer software-programmierbaren Funkplattform läuft. Der Prozessor ermöglicht die Rekonfiguration wichtiger Parameter der physikalischen Schicht während der Laufzeit, um eine Vielzahl moderner Wellenformen zu erzeugen. Es werden vier Parametereinstellungen 'LLC', 'WiFi', 'eMBB' und 'IoT' vorgestellt, um die Anforderungen der verschiedenen drahtlosen Anwendungen widerzuspiegeln. Diese werden dann zur Evaluierung der die in dieser Arbeit vorgestellte Implementierung herangezogen. Drittens wird durch die Einführung einer generischen Testinfrastruktur die Einbeziehung externer Partner aus der Ferne ermöglicht. Das Testfeld kann hier für verschiedenste Experimente flexibel auf die Anforderungen drahtloser Technologien zugeschnitten werden. Mit Hilfe der Testinfrastruktur wird die Leistung des vorgestellten Transceivers hinsichtlich Latenz, erreichbarem Durchsatz und Paketfehlerraten bewertet. Die öffentliche Demonstration eines taktilen Internet-Prototypen, unter Verwendung von Roboterarmen in einer Mehrbenutzerumgebung, konnte erfolgreich durchgeführt und bei mehreren Gelegenheiten präsentiert werden.:List of figures List of tables Abbreviations Notations 1 Introduction 1.1 Wireless applications 1.2 Motivation 1.3 Software-Defined Radio 1.4 State of the art 1.5 Testbed 1.6 Summary 2 Background 2.1 System Model 2.2 PHY Layer Structure 2.3 Generalized Frequency Division Multiplexing 2.4 Wireless Standards 2.4.1 IEEE 802.15.4 2.4.2 802.11 WLAN 2.4.3 LTE 2.4.4 Low Latency Industrial Wireless Communications 2.4.5 Summary 3 Wireless Prototyping 3.1 Testbed Examples 3.1.1 PHY - focused Testbeds 3.1.2 MAC - focused Testbeds 3.1.3 Network - focused testbeds 3.1.4 Generic testbeds 3.2 Considerations 3.3 Use cases and Scenarios 3.4 Requirements 3.5 Methodology 3.6 Hardware Platform 3.6.1 Host 3.6.2 FPGA 3.6.3 Hybrid 3.6.4 ASIC 3.7 Software Platform 3.7.1 Testbed Management Frameworks 3.7.2 Development Frameworks 3.7.3 Software Implementations 3.8 Deployment 3.9 Discussion 3.10 Conclusion 4 Flexible Transceiver 4.1 Signal Processing Modules 4.1.1 MAC interface 4.1.2 Encoding and Mapping 4.1.3 Modem 4.1.4 Post modem processing 4.1.5 Synchronization 4.1.6 Channel Estimation and Equalization 4.1.7 Demapping 4.1.8 Flexible Configuration 4.2 Analysis 4.2.1 Numerical Precision 4.2.2 Spectral analysis 4.2.3 Latency 4.2.4 Resource Consumption 4.3 Discussion 4.3.1 Extension to MIMO 4.4 Summary 5 Testbed 5.1 Infrastructure 5.2 Automation 5.3 Software Defined Radio Platform 5.4 Radio Frequency Front-end 5.4.1 Sub 6 GHz front-end 5.4.2 26 GHz mmWave front-end 5.5 Performance evaluation 5.6 Summary 6 Experiments 6.1 Single Link 6.1.1 Infrastructure 6.1.2 Single Link Experiments 6.1.3 End-to-End 6.2 Multi-User 6.3 26 GHz mmWave experimentation 6.4 Summary 7 Key lessons 7.1 Limitations Experienced During Development 7.2 Prototyping Future 7.3 Open points 7.4 Workflow 7.5 Summary 8 Conclusions 8.1 Future Work 8.1.1 Prototyping Workflow 8.1.2 Flexible Transceiver Core 8.1.3 Experimental Data-sets 8.1.4 Evolved Access Point Prototype For Industrial Networks 8.1.5 Testbed Standardization A Additional Resources A.1 Fourier Transform Blocks A.2 Resource Consumption A.3 Channel Sounding using Chirp sequences A.3.1 SNR Estimation A.3.2 Channel Estimation A.4 Hardware part listThe demand to achieve higher data rates for the Enhanced Mobile Broadband scenario and novel fifth generation use cases like Ultra-Reliable Low-Latency and Massive Machine-type Communications drive researchers and engineers to consider new concepts and technologies for future wireless communication systems. The goal is to identify promising candidate technologies among a vast number of new ideas and to decide, which are suitable for implementation in future products. However, the challenges to achieve those demands are beyond the capabilities a single processing layer in a wireless network can offer. Therefore, several research domains have to collaboratively exploit research ideas. This thesis presents a platform to provide a base for future applied research on wireless networks. Firstly, by giving an overview of state-of-the-art prototypes and testbed solutions. Secondly by introducing a flexible, yet real-time physical layer signal processor running on a software defined radio platform. The processor enables reconfiguring important parameters of the physical layer during run-time in order to create a multitude of modern waveforms. Thirdly, by introducing a generic test infrastructure, which can be tailored to prototype diverse wireless technology and which is remotely accessible in order to invite new ideas by third parties. Using the test infrastructure, the performance of the flexible transceiver is evaluated regarding latency, achievable throughput and packet error rates.:List of figures List of tables Abbreviations Notations 1 Introduction 1.1 Wireless applications 1.2 Motivation 1.3 Software-Defined Radio 1.4 State of the art 1.5 Testbed 1.6 Summary 2 Background 2.1 System Model 2.2 PHY Layer Structure 2.3 Generalized Frequency Division Multiplexing 2.4 Wireless Standards 2.4.1 IEEE 802.15.4 2.4.2 802.11 WLAN 2.4.3 LTE 2.4.4 Low Latency Industrial Wireless Communications 2.4.5 Summary 3 Wireless Prototyping 3.1 Testbed Examples 3.1.1 PHY - focused Testbeds 3.1.2 MAC - focused Testbeds 3.1.3 Network - focused testbeds 3.1.4 Generic testbeds 3.2 Considerations 3.3 Use cases and Scenarios 3.4 Requirements 3.5 Methodology 3.6 Hardware Platform 3.6.1 Host 3.6.2 FPGA 3.6.3 Hybrid 3.6.4 ASIC 3.7 Software Platform 3.7.1 Testbed Management Frameworks 3.7.2 Development Frameworks 3.7.3 Software Implementations 3.8 Deployment 3.9 Discussion 3.10 Conclusion 4 Flexible Transceiver 4.1 Signal Processing Modules 4.1.1 MAC interface 4.1.2 Encoding and Mapping 4.1.3 Modem 4.1.4 Post modem processing 4.1.5 Synchronization 4.1.6 Channel Estimation and Equalization 4.1.7 Demapping 4.1.8 Flexible Configuration 4.2 Analysis 4.2.1 Numerical Precision 4.2.2 Spectral analysis 4.2.3 Latency 4.2.4 Resource Consumption 4.3 Discussion 4.3.1 Extension to MIMO 4.4 Summary 5 Testbed 5.1 Infrastructure 5.2 Automation 5.3 Software Defined Radio Platform 5.4 Radio Frequency Front-end 5.4.1 Sub 6 GHz front-end 5.4.2 26 GHz mmWave front-end 5.5 Performance evaluation 5.6 Summary 6 Experiments 6.1 Single Link 6.1.1 Infrastructure 6.1.2 Single Link Experiments 6.1.3 End-to-End 6.2 Multi-User 6.3 26 GHz mmWave experimentation 6.4 Summary 7 Key lessons 7.1 Limitations Experienced During Development 7.2 Prototyping Future 7.3 Open points 7.4 Workflow 7.5 Summary 8 Conclusions 8.1 Future Work 8.1.1 Prototyping Workflow 8.1.2 Flexible Transceiver Core 8.1.3 Experimental Data-sets 8.1.4 Evolved Access Point Prototype For Industrial Networks 8.1.5 Testbed Standardization A Additional Resources A.1 Fourier Transform Blocks A.2 Resource Consumption A.3 Channel Sounding using Chirp sequences A.3.1 SNR Estimation A.3.2 Channel Estimation A.4 Hardware part lis

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