Closed-form approximations of the peak-to-average power ratio distribution for multi-carrier modulation and their applications

International audienceThe theoretical analysis of the peak-to-average power ratio (PAPR) distribution for an orthogonal frequency division multiplexing (OFDM) system, depends on the particular waveform considered in the modulation system. In this paper, we generalize this analysis by considering the generalized waveforms for multi-carrier (GWMC) modulation system based on any family of modulation functions, and we derive a general approximate expression for the cumulative distribution function (CDF) of its PAPR, for both finite and infinite integration time. These equations allow us to directly find the expressions of the PAPR distribution for any particular functions and characterize the behaviour of the PAPR distribution associated with different transmission and observation scenarios. In addition to that, a new approach to formulating the PAPR reduction problem as an optimization problem, is presented in this study

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

L'optimalité de l'OFDM en termes de performance en PAPR

National audienceLes systèmes multi-porteuses, et en particulier leur structure de modulation, connaissent un intérêt croissant. Suivant la forme d'onde considérée, plusieurs mesures de performance peuvent changer comme le PAPR (Peak-to-Average Power Ratio), l'efficacité spectrale, le taux d'erreur ou la complexité d'implémentation. Dans ce papier, nous montrons que, sous certaines contraintes sur les formes d'ondes, l'OFDM (Orthogonal Frequency Division Multiplexing) est une structure de modulation optimale en termes de PAPR

Single- versus Multi-Carrier Terahertz-Band Communications: A Comparative Study

The prospects of utilizing single-carrier (SC) and multi-carrier (MC) waveforms in future terahertz (THz)-band communication systems remain unresolved. On the one hand, the limited multi-path components at high frequencies result in frequency-flat channels that favor low-complexity wideband SC systems. On the other hand, frequency-dependent molecular absorption and transceiver characteristics and the existence of multi-path components in indoor sub-THz systems can still result in frequency-selective channels, favoring off-the-shelf MC schemes such as orthogonal frequency-division multiplexing (OFDM). Variations of SC/MC designs result in different THz spectrum utilization, but spectral efficiency is not the primary concern with substantial available bandwidths; baseband complexity, power efficiency, and hardware impairment constraints are predominant. This paper presents a comprehensive study of SC/MC modulations for THz communications, utilizing an accurate wideband THz channel model and highlighting the various performance and complexity trade-offs of the candidate schemes. Simulations demonstrate that discrete-Fourier-transform spread orthogonal time-frequency space (DFT-s-OTFS) achieves a lower peak-to-average power ratio (PAPR) than OFDM and OTFS and enhances immunity to THz impairments and Doppler spreads, but at an increased complexity cost. Moreover, DFT-s-OFDM is a promising candidate that increases robustness to THz impairments and phase noise (PHN) at a low PAPR and overall complexity.Comment: 18 pages, 12 figures, journa

L'optimalité de l'OFDM en termes de performance en PAPR

National audienceLes systèmes multi-porteuses, et en particulier leur structure de modulation, connaissent un intérêt croissant. Suivant la forme d'onde considérée, plusieurs mesures de performance peuvent changer comme le PAPR (Peak-to-Average Power Ratio), l'efficacité spectrale, le taux d'erreur ou la complexité d'implémentation. Dans ce papier, nous montrons que, sous certaines contraintes sur les formes d'ondes, l'OFDM (Orthogonal Frequency Division Multiplexing) est une structure de modulation optimale en termes de PAPR

OFDM with hybrid number and Index modulation

A novel transmission scheme is introduced for efficient data transmission by conveying additional information bits through jointly changing the index and number of active subcarriers within each orthogonal frequency division multiplexing (OFDM) subblock. The proposed scheme is different from the conventional OFDM-subcarrier number modulation (OFDM-SNM) and OFDM-index modulation (OFDM-IM), in which data bits are transmitted using either number or index of active subcarriers. The proposed modulation technique offers superior spectral and energy efficiency compared to its counterparts OFDM-SNM and OFDM-IM, especially at low modulation orders such as binary phase shift keying (BPSK) that can provide high reliability and low complexity, thus making it very suitable for meeting the requirements of Internet of things (IoT) applications. Bit error rate (BER) performance analysis is provided for the proposed scheme, and Monte Carlo simulations are presented to prove the consistency of the simulated BER with the analyzed one. More importantly, it is demonstrated that the proposed scheme can offer much superior BER performance compared to that of OFDM-IM and classical OFDM under equivalent power and spectral efficiency values.No sponso