We present Affine Frequency Division Multiplexing (AFDM), a new chirp-based multicarrier transceiver scheme for high mobility communications in next-generation wireless systems. AFDM is based on discrete affine Fourier transform (DAFT), a generalization of discrete Fourier transform characterized with two parameters that can be adapted to better cope with doubly dispersive channels. Based on the derived input-output relation, the DAFT parameters underlying AFDM are set in such a way to avoid that time domain channel paths with distinct delays or Doppler frequency shifts overlap in the DAFT domain. The resulting DAFT domain impulse response thus conveys a full delay-Doppler representation of the channel. We show that AFDM can achieve the full diversity of linear time-varying (LTV) channels. Our analytical results are validated through numerical simulations, which evince that AFDM outperforms state-of-the-art multicarrier schemes in terms of bit error rate (BER) in doubly dispersive channels.
Resolving the Discontinuity of Continuous-Time AFDM Waveforms
State Key Laboratory of IoT for Smart City, University of Macau（澳门大学物联网智能城市国家重点实验室）；Department of Electrical and Computer Engineering, The University of Hong Kong（香港大学电气与计算机工程系）
Affine Frequency Division Multiplexing (AFDM), a new chirp-based multicarrier waveform for high mobility communications, is introduced here. AFDM is based on discrete affine Fourier transform (DAFT), a generalization of discrete Fourier transform, which is characterized by two parameters that can be adapted to better cope with doubly dispersive channels. First, we derive the explicit input-output relation in the DAFT domain showing the effect of AFDM parameters in the input-output relation. Second, we show how the DAFT parameters underlying AFDM have to be set so that the resulting DAFT domain…
Affine Frequency Division Multiplexing (AFDM), which is based on discrete affine Fourier transform (DAFT), has recently been proposed for reliable communication in high-mobility scenarios. Two low complexity detectors for AFDM are introduced here. Approximating the channel matrix as a band matrix via placing null symbols in the AFDM frame in the DAFT domain, a low complexity MMSE detection is proposed by means of the $\rm{LDL}$ factorization. Furthermore, exploiting the sparsity of the channel matrix, we propose a low complexity iterative decision feedback equalizer (DFE) based on weighted max…
Low-Complexity Channel Estimation for Internet of Vehicles AFDM Communications With Sparse Bayesian Learning
Northwestern Polytechnical University（西北工业大学）；Shaanxi University of Science and Technology（陕西科技大学）；Nanyang Technological University（南洋理工大学）；South China University of Technology（华南理工大学）；Xidian University（西安电子科技大学）
Multi-Functional Chirp Signalling for Next-Generation Multi-Carrier Wireless Networks: Communications, Sensing and ISAC Perspectives
University of Essex（埃塞克斯大学）；University of Surrey（萨里大学）；University College London（伦敦大学学院）；Nanyang Technological University（南洋理工大学）；University of Southampton（南安普顿大学）
CP-OFDM Achieves Lower Ranging CRB Than Frequency-Spread Waveforms in the Large-Sample Regime
National Mobile Communications Research Laboratory, Southeast University（东南大学国家移动通信实验室）；Department of Communication Engineering, Beijing University of Posts and Telecommunications（北京邮电大学通信工程系）；Ministry of Education Key Laboratory of Mathematics and Information Networks, School of Mathematical Sciences, Beijing University of Posts and Telecommunications（北京邮电大学数学科学学院数学与信息网络教育部重点实验室）；Frontiers Science Center for Mobile Information Communication and Security, Southeast University（东南大学移动信息通信与安全前沿科学中心）；Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Southeast University（东南大学复杂系统测量与控制教育部重点实验室）；Department of Electrical and Electronic Engineering, University College London（伦敦大学学院电气与电子工程系）
On Discrete Ambiguity Functions of Random Communication Waveforms
Southern University of Science and Technology（南方科技大学）；Southeast University（东南大学）；Beijing University of Posts and Telecommunications（北京邮电大学）；Technical University of Berlin（柏林工业大学）；Beijing Institute of Technology（北京理工大学）；Huawei Technologies Co., Ltd.（华为技术有限公司）；University College London（伦敦大学学院）
Low-complexity Equalization of Zak-OTFS Via Neumann Series
Duke University（杜克大学）；Department of Electrical Engineering, Indian Institute of Technology Delhi（德里印度理工学院电气工程系）；Cohere Technologies Inc.（Cohere科技有限公司）；Department of Mathematics, University of Texas at Austin（德克萨斯大学奥斯汀分校数学系）
Orthogonal time frequency space (OTFS) is a promising technology for high-mobility wireless communications. However, the equalization realization in practical OTFS systems is a great challenge when the non-ideal rectangular waveforms are adopted. In this paper, first of all, we theoretically prove that the effective channel matrix under rectangular waveforms holds the block-circulant property and the special Fourier transform structure with time-domain channel. Then, by exploiting the proved property and structure, we further propose the corresponding low-complexity algorithms for two mainstre…
The Fourth Generation (4G) of mobile communication systems was optimized to offer high data rates with high terminal mobility by ensuring strict synchronism and perfect orthogonality. However, the trend for novel applications, that had not been feasible a few years back, reveals major limits of this strict synchronism and imposes new challenges and severe requirements. But, coarse synchronization can dramatically damage the waveforms orthogonality in the Orthogonal Frequency Division Multiplexing (OFDM) signals, which results in oppressive Inter-Carrier Interference (ICI) and Inter-Symbol Inte…
The (inverse) discrete Fourier transform (DFT/IDFT) is often perceived as essential to orthogonal frequency-division multiplexing (OFDM) systems. In this paper, a deep complex-valued convolutional network (DCCN) is developed to recover bits from time-domain OFDM signals without relying on any explicit DFT/IDFT. The DCCN can exploit the cyclic prefix (CP) of OFDM waveform for increased SNR by replacing DFT with a learned linear transform, and has the advantage of combining CP-exploitation, channel estimation, and intersymbol interference (ISI) mitigation, with a complexity of $\mathcal{O}(N^2)$…
The sixth-generation (6G) wireless networks are envisioned to provide a global coverage for the intelligent digital society of the near future, ranging from traditional terrestrial to non-terrestrial networks, where reliable communications in high-mobility scenarios at high carrier frequencies would play a vital role. In such scenarios, the conventional orthogonal frequency division multiplexing (OFDM) modulation, that has been widely used in both the fourth-generation (4G) and the emerging fifth-generation (5G) cellular systems as well as in WiFi networks, is vulnerable to severe Doppler spre…
We consider the problem of uplink timing synchronization for Orthogonal Time Frequency Space (OTFS) modulation based systems where information is embedded in the delay-Doppler (DD) domain. For this, we propose a novel Random Access (RA) preamble waveform based on OTFS modulation. We also propose a method to estimate the round-trip propagation delay between a user terminal (UT) and the base station (BS) based on the received RA preambles in the DD domain. This estimate (known as the timing advance estimate) is fed back to the respective UTs so that they can advance their uplink timing in order …
Vehicle-to-everything (V2X) is considered as one of the most important applications of future wireless communication networks. However, the Doppler effect caused by the vehicle mobility may seriously deteriorate the performance of the vehicular communication links, especially when the channels exhibit a large number of Doppler frequency offsets (DFOs). Orthogonal time frequency space (OTFS) is a new waveform designed in the delay-Doppler domain, and can effectively convert a doubly dispersive channel into an almost non-fading channel, which makes it very attractive for V2X communications. In t…
The orthogonal time frequency space (OTFS) modulation has emerged as a promising modulation scheme for high mobility wireless communications. To enable efficient OTFS detection in the delay-Doppler (DD) domain, the DD domain channels need to be acquired accurately. To achieve the low latency requirement in future wireless communications, the time duration of the OTFS block should be small, therefore fractional Doppler shifts have to be considered to avoid significant modelling errors due to the assumption of integer Doppler shifts. However, there lack investigations on the estimation of OTFS c…
A new line of research on communications and signals design for Wireless Power Transfer (WPT) has recently emerged in the communication literature. Promising signal strategies to maximize the power transfer efficiency of WPT rely on (energy) beamforming, waveform, modulation and transmit diversity, and a combination thereof. To a great extent, the study of those strategies has so far been limited to theoretical performance analysis. In this paper, we study the real over-the-air performance of all the aforementioned signal strategies for WPT. To that end, we have designed, prototyped and experi…
Zhejiang Provincial Key Laboratory of Multi-Modal Communication Networks and Intelligent Information Processing, College of Information Science and Electronic Engineering, Zhejiang University（浙江省级多模通信网络与智能信息处理重点实验室，信息科学与电子工程学院，浙江大学）；State Key Laboratory of Integrated Services Networks, Xidian University（集成服务网络国家重点实验室，西安电子科技大学）；School of Information Science, Japan Advanced Institute of Science and Technology (JAIST)（信息科学学院，日本科学技术先进研究院（JAIST））
