Orthogonal time frequency space (OTFS) modulation can effectively convert a doubly dispersive channel into an almost non-fading channel in the delay-Doppler domain. However, one critical issue for OTFS is the very high complexity of equalizers. In this letter, we first reveal the doubly block circulant feature of OTFS channel represented in the delay-Doppler domain. By exploiting this unique feature, we further propose zero-forcing (ZF) and minimum mean squared error (MMSE) equalizers that can be efficiently implemented with the two-dimensional fast Fourier transform. The complexity of our proposed equalizers is gracefully reduced from $\mathcal{O}\left(\left(NM\right)^{3}\right)$ to $\mathcal{O}\left(NM\mathrm{log_{2}}\left(NM\right)\right)$, where $N$ and $M$ are the number of OTFS symbols and subcarriers, respectively. Analysis and simulation results show that compared with other existing linear equalizers for OTFS, our proposed linear equalizers enjoy a much lower computational complexity without any performance loss.
In this work, we derive a equivalent delay-Doppler channel matrix of the Orthogonal Time Frequency Space (OTFS) modulation that has not been studied in previous literature. It has the similar structure as the banded channel matrix of OFDM systems over rapidly time-varying channels. However, the band in the equivalent channel matrix will no longer spread with the increase of the Doppler spread once the length of maximum channel delay spread and the OTFS frame duration are deter- mined. Furthermore, the equivalent channel matrix can simplify the OTFS modulation in the transmitter side. Incorpora…
Recently, a new precoding technique called orthogonal time-frequency signaling (OTFS) has been proposed for time- and frequency-selective communication channels. OTFS precodes a data frame with a complete set of spreading sequences and transmits the results via orthogonal frequency division multiplexing (OFDM). OTFS uses two dimensional (2D) linear spreading sequences in time and frequency which are the basis functions of a symplectic Fourier transform. OTFS allows the utilization of time- and frequency-diversity but requires maximum likelihood decoding to achieve full diversity. In this paper…
This paper presents an analysis of the Orthogonal Time Frequency Space (OTFS) modulation scheme when applied to realistic vehicular channel situations. OTFS modulates symbols in delay-Doppler domain, hoping to exploit diversity in both. The penalty for doing this is the requirement of complex interference cancellation equalizers, as this domain incurs a strong amount of intercarrier and intersymbol interference. We conduct this analysis using measured millimeter wave vehicular channels, and we assume typical physical layer settings for a performance analysis. Our results show that there is a c…
In orthogonal time frequency space (OTFS) modulation, information-carrying symbols reside in the delay-Doppler (DD) domain. By operating in the DD domain, an appealing property for communication arises: time-frequency (TF) dispersive channels encountered in high mobility environments become time-invariant. The time-invariance of the channel in the DD domain enables efficient equalizers for time-frequency dispersive channels. In this paper, we propose an OTFS system based on the discrete Zak transform. The presented formulation not only allows an efficient implementation of OTFS but also simpli…
This paper considers a challenging communication scenario, in which users have heterogenous mobility profiles, e.g., some users are moving at high speeds and some users are static. A new non-orthogonal multiple-access (NOMA) transmission protocol that incorporates orthogonal time frequency space (OTFS) modulation is proposed. Thereby, users with different mobility profiles are grouped together for the implementation of NOMA. The proposed OTFS-NOMA protocol is shown to be applicable to both uplink and downlink transmission, where sophisticated transmit and receive strategies are developed to re…
This paper presents a linear complexity iterative rake detector for the recently proposed orthogonal time frequency space (OTFS) modulation scheme. The basic idea is to extract and combine the received multipath components of the transmitted symbols in the delay-Doppler grid using linear diversity combining schemes like maximal ratio combining (MRC), equal gain combining and selection combining to improve the SNR of the combined signal. We reformulate the OTFS input-output relation in the vector form by placing some null symbols in the delay-Doppler grid thereby exploiting the block circulant …
This paper introduces a new two-dimensional modulation technique called Orthogonal Time Frequency Space (OTFS) modulation. OTFS has the novel and important feature of being designed in the delay-Doppler domain. When coupled with a suitable equalizer, OTFS modulation is able to exploit the full channel diversity over both time and frequency. Moreover, it converts the fading, time-varying wireless channel experienced by modulated signals such as OFDM into a time-independent channel with a complex channel gain that is essentially constant for all symbols. This design obviates the need for transmi…
Advanced Channel Decomposition Techniques in OTFS: A GSVD Approach for Multi-User Downlink
Instituto de Telecomunicações（电信研究所）；Universidade Nova de Lisboa（里斯本新大学）；University of Tokyo（东京大学）；Sup’Com, University of Carthage（迦太基大学高等通信学院）；ISCTE-Instituto Universitário de Lisboa（里斯本大学学院）；Nokia（诺基亚）
Orthogonal time-frequency space (OTFS) scheme, which transforms a time and frequency selective channel into an almost non-selective channel in the delay-Doppler domain, establishes reliable wireless communication for high-speed moving devices. This work designs and analyzes low-complexity zero-forcing (LZ) and minimum mean square error (LM) receivers for multiple-input multiple-output (MIMO)-OTFS systems with perfect and imperfect receive channel state information (CSI). The proposed receivers provide exactly the same solution as that of the conventional counterparts, and reduce the complexity…
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 recent emergence of orthogonal time frequency space (OTFS) modulation as a novel PHY-layer mechanism is more suitable in high-mobility wireless communication scenarios than traditional orthogonal frequency division multiplexing (OFDM). Although multiple studies have analyzed OTFS performance using theoretical and ideal baseband pulseshapes, a challenging and open problem is the development of effective receivers for practical OTFS systems that must rely on non-ideal pulseshapes for transmission. This work focuses on the design of practical receivers for OTFS. We consider a fractionally spa…
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）
In this paper, we propose a general framework that transforms the problems of designing sparse finite-impulseresponse linear equalizers and non-linear decision-feedback equalizers, for multiple antenna systems, into the problem of sparsestapproximation of a vector in different dictionaries. In addition, we investigate several choices of the sparsifying dictionaries under this framework. Furthermore, the worst-case coherences of these dictionaries, which determine their sparsifying effectiveness, are analytically and/or numerically evaluated. Moreover, we show how to reduce the computational co…
Wireless communications over fast fading channels are challenging, requiring either frequent channel tracking or complicated signaling schemes such as orthogonal time frequency space (OTFS) modulation. In this paper, we propose low-complexity frequency domain equalizations to combat fast fading, based on novel discrete delay-time and frequency-Doppler channel models. Exploiting the circular stripe diagonal nature of the frequency-Doppler channel matrix, we introduce low-complexity frequency domain minimum mean square error (MMSE) equalization for OTFS systems with fully resolvable Doppler spre…
Towards Standardizing OTFS: A Candidate Waveform for Next-Generation Wireless Networks
University of Sydney（悉尼大学）；Queen’s University Belfast（贝尔法斯特女王大学）；Technische Universität Berlin（柏林工业大学）；Trinity College Dublin（都柏林三一学院）；Massive Beams GmbH（Massive Beams有限公司）
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…
