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 spread. In this context, this article aims to introduce a recently proposed two-dimensional modulation scheme referred to as orthogonal time-frequency space (OTFS) modulation, which conveniently accommodates the channel dynamics via modulating information in the delay-Doppler domain. This article provides an easy-reading overview of OTFS, highlighting its underlying motivation and specific features. The critical challenges of OTFS and our preliminary results are presented. We also discuss a range of promising research opportunities and potential applications of OTFS in 6G wireless networks.
Super-resolution is generally referred to as the task of recovering fine details from coarse information. Motivated by applications such as single-molecule imaging, radar imaging, etc., we consider parameter estimation of complex exponentials from their modulations with unknown waveforms, allowing for non-stationary blind super-resolution. This problem, however, is ill-posed since both the parameters associated with the complex exponentials and the modulating waveforms are unknown. To alleviate this, we assume that the unknown waveforms live in a common low-dimensional subspace. Using a liftin…
Joint radar-communication (JRC) waveform can be used for simultaneous radar detection and communication in the same frequency band. However, radar detection processing requires the prior knowledge of the waveform including the embedded information for matched filtering. To remove this requirement, we propose a unimodular JRC waveform based on composite modulation where the internal modulation embeds information by mapping the bit sequence to different orthogonal signals, and the external modulation performs phase modulation on the internal waveform to satisfy the demand of detection. By adjust…
Non-stationary blind super-resolution is an extension of the traditional super-resolution problem, which deals with the problem of recovering fine details from coarse measurements. The non-stationary blind super-resolution problem appears in many applications including radar imaging, 3D single-molecule microscopy, computational photography, etc. There is a growing interest in solving non-stationary blind super-resolution task with convex methods due to their robustness to noise and strong theoretical guarantees. Motivated by the recent work on atomic norm minimization in blind inverse problems…
5G cellular communications promise to deliver the gigabit experience to mobile users, with a capacity increase of up to three orders of magnitude with respect to current LTE systems. There is widespread agreement that such an ambitious goal will be realized through a combination of innovative techniques involving different network layers. At the physical layer, the OFDM modulation format, along with its multiple-access strategy OFDMA, is not taken for granted, and several alternatives promising larger values of spectral efficiency are being considered. This paper provides a review of some modu…
In this study, we propose an approach to constructing on-off keying (OOK) symbols for wake-up radios (WURs) by using sequences in the frequency domain. The proposed method enables orthogonal multiplexing of wake-up signals (WUSs) and orthogonal frequency division multiplexing (OFDM) waveforms. We optimize the sequences with a tractable algorithm by considering the reliability of WUSs in fading channels. The proposed algorithm relies on an alternating minimization technique, i.e. cyclic algorithm-new (CAN), which was originally proposed for obtaining a unimodular sequence with good aperiodic co…
Large-scale antenna (LSA) has gained a lot of attention due to its great potential to significantly improve system throughput. In most existing works on LSA systems, orthogonal frequency division multiplexing (OFDM) is presumed to deal with frequency selectivity of wireless channels. Although LSA-OFDM is a natural evolution from multiple-input multiple-output OFDM (MIMO-OFDM), the drawbacks of LSA-OFDM are inevitable, especially when used for the uplink. In this paper, we investigate single-carrier (SC) modulation for the uplink transmission in LSA systems based on a novel waveform recovery th…
Spectral efficiency improvement is a key focus in most wireless communication systems and achieved by various means such as using large antenna arrays and/or advanced modulation schemes and signal formats. This work proposes to further improve spectral efficiency through combining non-orthogonal spectrally efficient frequency division multiplexing (SEFDM) systems with index modulation (IM), which can efficiently make use of the indices of activated subcarriers as communication information. Recent research has verified that IM may be used with SEFDM to alleviate inter-carrier interference (ICI)…
In this paper, we propose modulation diversity techniques for Spatial Modulation (SM) system using Complex Interleaved Orthogonal Design (CIOD) meant for two transmit antennas. Specifically, we show that by using the CIOD for two transmit antenna system, the standard SM scheme, where only one transmit antenna is activated in any symbol duration, can achieve a transmit diversity order of two. We show with our simulation results that the proposed schemes offer transmit diversity order of two, and hence, give a better Symbol Error Rate performance than the SM scheme with transmit diversity order …
The recently proposed orthogonal time frequency space (OTFS) modulation technique was shown to provide significant error performance advantages over orthogonal frequency division multiplexing (OFDM) in Doppler channels. In this paper, we derive the explicit input-output relation describing OTFS modulation and demodulation (mod/demod) for delay-Doppler channels. We analyze the interferences and develop a novel low-complexity yet efficient message passing (MP) algorithm for joint interference cancellation (IC) and symbol detection. The proposed MP algorithm can effectively compensate for a wide …
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…
Non-orthogonal multiple access (NOMA) schemes have been proved to increase the multiple-access achievable rate with respect to orthogonal multiple access (OMA). In this paper we propose a novel communication system that combines multi-level coded modulation and polar codes in a NOMA scenario. Computational complexity decreases with the proposed scheme with respect to state-of-the-art solutions. We also highlight the trade-off between error rate performance and computational complexity.
Filter bank multiple access (FBMA) without subbands orthogonality has been proposed as a new candidate waveform to better meet the requirements of future wireless communication systems and scenarios. It has the ability to process directly the complex symbols without any fancy preprocessing. Along with the usage of cyclic prefix (CP) and wide-banded subband design, CP-FBMA can further improve the peak-to-average power ratio and bit error rate performance while reducing the length of filters. However, the potential gain of removing the orthogonality constraint on the subband filters in the syste…
This letter is the first part of a three-part tutorial on orthogonal time frequency space (OTFS) modulation, which is a promising candidate waveform for future wireless networks. This letter introduces and compares two popular implementations of OTFS modulation, namely the symplectic finite Fourier transform (SFFT)- and discrete Zak transform (DZT)-based architectures. Based on these transceiver architectures, fundamental concepts of OTFS modulation, including the delay-Doppler (DD) domain, DD domain information multiplexing, and its potential benefits, are discussed. Finally, the challenges a…
To accommodate current machine type communications (MTC), an uplink waveform is proposed where MTC nodes use one carrier to transmit signal, and central nodes demodulate different nodes' signal jointly. Furthermore, the carrier bandwidth is variable to fit for the channels of nodes. This waveform may reduce the hardware complexity of low cost MTC nodes, and loose the time and frequency domain synchronization requirements of the entire system. This paper also provides the interference analysis and complexity comparisons of proposed scheme and orthogonal frequency division multiplexing (OFDM).
In this paper, we propose a novel joint coding-modulation technique based on serial concatenation of orthogonal linear transform, such as discrete Fourier transform (DFT) or Walsh-Hadamard transform (WHT), with memoryless nonlinearity. We demonstrate that such a simple signal construction may exhibit properties of a random code ensemble, as a result approaching channel capacity. Our computer simulations confirm that if the decoder relies on a modified approximate message passing algorithm, the proposed modulation technique exhibits performance on par with state-of-the-art coded modulation sche…
One objective of this paper is to propose a novel class of sequence pairs, called "Quasi-orthogonal Z-complementary pairs (QOZCPs)", each depicting Z-complementary property for their aperiodic auto-correlation sums and also have a zero correlation zone when their aperiodic cross-correlation is considered. Construction of QOZCPs based on Successively Distributed Algorithms under Majorization Minimization (SDAMM) is presented. Another objective of this paper is to apply the proposed QOZCPs in fully polarimetric radar systems and analyse the corresponding ambiguity functions. It turns out that QO…
We consider a bistatic vehicular integrated sensing and communications (ISAC) system that employs the recently proposed orthogonal chirp division multiplexing (OCDM) multicarrier waveform. As a stand-alone communications waveform, OCDM has been shown to be robust against the interference in time-frequency selective channels. In a bistatic ISAC, we exploit this property to develop efficient receive processing algorithms that achieve high target resolution as well as high communications rate. We derive statistical bounds for our proposed Sequential symbol decoding and radar parameter estimation …
Fifth generation (5G) wireless systems are expected to combine emerging transmission technologies, such as large-scale multiple-input multiple-output (MIMO) and non-orthogonal multi-carrier waveforms, to improve the spectral efficiency and to reduce out-of-band (OOB) emissions. This paper investigates the efficacy of two promising multi-carrier waveforms that reduce OOB emissions in combination with large-scale MIMO, namely filter bank multi-carrier (FBMC) and generalized frequency division multiplexing (GFDM). We develop novel, low-complexity data detection algorithms for both of these wavefo…
We elaborate on the recently proposed orthogonal time frequency space (OTFS) modulation technique, which provides significant advantages over orthogonal frequency division multiplexing (OFDM) in Doppler channels. We first derive the input--output relation describing OTFS modulation and demodulation (mod/demod) for delay--Doppler channels with arbitrary number of paths, with given delay and Doppler values. We then propose a low-complexity message passing (MP) detection algorithm, which is suitable for large-scale OTFS taking advantage of the inherent channel sparsity. Since the fractional Doppl…
The orthogonal design of a Cyclic Block Filtered Multititone Modulation (CB-FMT) system is addressed. CB-FMT is a filter bank modulation scheme that uses frequency confined prototype pulses, similarly to Filtered Multitone Modulation (FMT). Differently from FMT, where the linear convolution is used, the cyclic convolution is exploited in CB-FMT. This allows to efficiently implement the system via a concatenation of discrete Fourier transforms (DFT). The necessary and sufficient orthogonality conditions are derived in time domain and frequency domain. Then, these conditions are expressed in mat…
Orthogonal time frequency space (OTFS) modulation was proposed to tackle the destructive Doppler effects in wireless communications, with potential applications to many other areas. In this paper, we investigate its application to radar systems, and propose a novel efficient OTFS-based matched filter algorithm for target range and velocity estimation. The proposed algorithm not only exhibits the inherent advantages due to multi-carrier modulation of the existing orthogonal frequency division multiplexing (OFDM-) based radar algorithms but also provides additional benefits to improve radar capa…
In this paper, we investigate the design of a novel multicarrier (MC) modulation on delay-Doppler (DD) plane, to couple the modulated signal with a doubly-selective channel having DD resolutions. A key challenge for the design of DD plane MC modulation is to find a realizable pulse orthogonal with respect to the DD plane's fine resolutions. To this end, we first indicate that a feasible DD plane MC modulation is essentially a type of staggered multitone modulation. Then, we propose an orthogonal delay-Doppler division multiplexing (ODDM) modulation, and design the corresponding transmit pulse.…
In this paper, a novel spatial modulation aided non-orthogonal multiple access (SM-NOMA) system is proposed. We use mutual information (MI) to characterize the achievable spectral efficiency (SE) of the proposed SM-NOMA system. Due to the finite-alphabet space-domain inputs employed by SM, the expression of the corresponding MI lacks a closed-form formulation. Hence, a lower bound is proposed to quantify the MI of the SM-NOMA system. Furthermore, its asymptotic property is also theoretically investigated in both low and high signal-to-noise ratio (SNR) regions. The SE performance and its analy…
Future generations of communications systems will target a very wide range of applications. Each application comes with its own set of requirements in terms of data rate, latency, user density, reliability... Accommodating this large variety of specifications implies the need for a novel physical layer technology. In this regard, the most popular modulation nowadays, namely, the orthogonal frequency division multiplexing modulation, is characterized by a poor time-frequency localization, implying strong limitations. In the light of these limitations, communications using new waveforms, relying…
Non-cooperative communications using non-orthogonal multicarrier signals are challenging since self-created inter carrier interference (ICI) exists, which would prevent successful signal classification. Deep learning (DL) can deal with the classification task without domain-knowledge at the cost of training complexity since neural network hyperparameters have to be extensively tuned. Previous work showed that a tremendously trained convolutional neural network (CNN) classifier can efficiently identify feature-diversity dominant signals while it failed when feature-similarity dominates. Therefo…
Orthogonal time frequency space (OTFS) modulation is a recently proposed multi-carrier transmission scheme, which innovatively multiplexes the information symbols in the delay-Doppler (DD) domain instead of the conventional time-frequency (TF) domain. The DD domain symbol multiplexing gives rise to a direct interaction between the DD domain information symbols and DD domain channel responses, which are usually quasi-static, compact, separable, and potentially sparse. Therefore, OTFS modulation enjoys appealing advantages over the conventional orthogonal frequency-division multiplexing (OFDM) m…
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…
We study the coexistence of different multicarrier waveforms such as orthogonal frequency division multiplexing (OFDM), filter-bank multicarrier (FBMC) and universal-filtered multicarrier (UFMC) waveforms in licensed shared access (LSA) for next-generation communication systems. The fundamental changes required in the existing physical layer using OFDM towards a hybrid physical layer (either OFDM-FBMC or OFDM- UFMC) ensuring backward compatibility are discussed. We also perform mutual interference analysis for the coexisting asynchronous systems sharing the LSA frequency band. Be- cause of the…
Orthogonal Time Frequency Space (OTFS) is a novel modulation scheme designed in the Doppler-delay domain to fully exploit time and frequency diversity of general time-varying channels. In this paper, we present a novel discrete-time analysis of OFDM-based OTFS transceiver with a concise and vectorized input-output relationship that clearly characterizes the contribution of each underlying signal processing block in such systems. When adopting cyclic prefix in the time domain, our analysis reveals that the proposed MIMO OTFS and OFDM systems have the same ergodic capacity despite the well-known…
Multi-antenna non-orthogonal multiple access (NOMA) is a promising technique to significantly improve the spectral efficiency and support massive access, which has received considerable interests from academic and industry. This article first briefly introduces the basic idea of conventional multi-antenna NOMA technique, and then discusses the key limitations, namely, the high complexity of successive interference cancellation(SIC) and the lack of fairness between the user with a strong channel gain and the user with a weak channel gain. To address these problems, this article proposes a novel…
The fundamental concepts and challenges of orthogonal time frequency space (OTFS) modulation have been reviewed in Part I of this three-part tutorial. In this second part, we provide an overview of the state-of-the-art transceiver designs for OTFS systems, with a particular focus on the cyclic prefix (CP) design, window design, pulse shaping, channel estimation, and signal detection. Furthermore, we analyze the performance of OTFS modulation, including the diversity gain and the achievable rate. Specifically, comparative simulations are presented to evaluate the error performance of different …
It is shown that replacing the sinusoidal chip in Golay complementary code pairs by special classes of waveforms that satisfy two conditions, symmetry/anti-symmetry and quazi-orthogonality in the convolution sense, renders the complementary codes immune to frequency selective fading and also allows for concatenating them in time using one frequency band/channel. This results in a zero-sidelobe region around the mainlobe and an adjacent region of small cross-correlation sidelobes. The symmetry/anti-symmetry property results in the zero-sidelobe region on either side of the mainlobe, while quasi…
This paper presents a study of the candidate waveforms for 5G when they are subject to timing and carrier frequency offset. These waveforms are: orthogonal frequency division multiplexing (OFDM), generalized frequency division multiplexing (GFDM), universal filtered multicarrier (UFMC), circular filter bank multicarrier (C-FBMC), and linear filter bank multicarrier (FBMC). We are particularly interested in multiple access interference (MAI) when a number of users transmit their signals to a base station in an asynchronous or a quasi-synchronous manner. We identify the source of MAI in these wa…
Non-orthogonal multiple access (NOMA) is envisioned as an efficient candidate for future communication systems. This letter proposes a novel orthogonal frequency division multiplexing (OFDM) with index modulation (IM)-based NOMA scheme, called OFDM-IM NOMA, for future multi-user communication systems. Inspired by IM and classical OFDM-NOMA, users utilize flexibility by adjusting power allocation factors and subcarrier activation ratios. Our new scheme allows different service users to share available resources as in classical NOMA, more efficiently. It is shown that OFDM-IM NOMA reliably suppo…
This paper proposes orthogonal time sequency multiplexing (OTSM), a novel single carrier modulation scheme that places information symbols in the delay-sequency domain followed by a cascade of time-division multiplexing (TDM) and Walsh-Hadamard sequence multiplexing. Thanks to the Walsh Hadamard transform (WHT), the modulation and demodulation do not require complex domain multiplications. For the proposed OTSM, we first derive the input-output relation in the delay-sequency domain and present a low complexity detection method taking advantage of zero-padding. We demonstrate via simulations th…
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…
Design of Weyl-Heisenberg sets of waveforms for robust orthogonal frequency division multiplex- ing (OFDM) has been the subject of a considerable volume of work. In this paper, a complete parameterization of orthogonal Weyl-Heisenberg sets and their corresponding biorthogonal sets is given. Several examples of Weyl-Heisenberg sets designed using this parameterization are pre- sented, which in simulations show a high potential for enabling OFDM robust to frequency offset, timing mismatch, and narrow-band interference.
As the next generation cellular system, 5G network is required to provide a large variety of services for different kinds of terminals, from traditional voice and data services over mobile phones to small packet transmission over massive machine-type terminals. Although orthogonal-subcarrier based waveform has been widely used nowadays in many practical systems, it can hardly meet the future requirements in the coming 5G networks. Therefore, more flexible waveforms have been proposed to address the unprecedented challenges. In this article, we will provide comprehensive analysis and comparison…
Orthogonal time frequency space (OTFS) modulation is a two-dimensional signaling technique that has recently emerged in the literature to tackle the time-varying (TV) wireless channels. OTFS deploys the Doppler-delay plane to multiplex the transmit data where the time variations of the TV channel are integrated over time and hence the equivalent channel relating the input and output of the system boils down to a time-invariant one. This signaling technique can be implemented on the top of a given multicarrier waveform with the addition of precoding and post-processing units to the modulator an…
The diversity multiplexing tradeoff of a general two-hop asynchronous cooperative network is examined for various relaying protocols such as non-orthogonal selection decode-and-forward (NSDF), orthogonal selection decode-and-forward (OSDF), non-orthogonal amplify-and-forward (NAF), and orthogonal amplify-and-forward (OAF). The transmitter nodes are assumed to send pulse amplitude modulation (PAM) signals asynchronously, in which information symbols are linearly modulated by a shaping waveform to be sent to the destination. We consider two different cases with respect to the length of the shapi…
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…
Orthogonal time-frequency space (OTFS) modulation is a recently proposed waveform for efficient data transfer in high-speed vehicular scenarios. The use of rectangular pulse shape in OTFS results in high out of band (OoB) radiation, which is undesirable for multi-user scenarios. In this work, we present a circular pulse shaping framework for OTFS for reducing the OoB. We also design a low complexity transmitter for such a system. We argue in favor of orthogonal transmission for low complexity transceiver structure. We establish that frequency-localized circulant Dirichlet pulse is one of the p…
Directional modulation (DM) is a physical layer security technique based on antenna arrays and so far the polarisation information has not been considered in its designs. To increase the channel capacity, we consider exploiting the polarisation information and send two different signals simultaneously at the same direction, same frequency, but with different polarisations. These two signals can also be considered as one composite signal using the four dimensional (4-D) modulation scheme across the two polarisation diversity channels. In this paper, based on cross-dipole arrays, we formulate th…
Integrated Sensing and Communication (ISAC) systems are recognised as one of the key ingredients of the sixth generation (6G) network. A challenging topic in ISAC is the design of a single waveform combining both communication and sensing functionalities on the same time-frequency-space resources, allowing to tune the performance of both with partial or full hardware sharing. This paper proposes a dual-domain waveform design approach that superposes onto the frequency-time (FT) domain both the legacy orthogonal frequency division multiplexing (OFDM) signal and a sensing one, purposely designed…
The emerging orthogonal time frequency space (OTFS) modulation technique has shown its superiority to the current orthogonal frequency division multiplexing (OFDM) scheme, in terms of its capabilities of exploiting full time-frequency diversity and coping with channel dynamics. The optimal maximum a posteriori (MAP) detection is capable of eliminating the negative impacts of the inter-symbol interference in the delay-Doppler (DD) domain at the expense of a prohibitively high complexity. To reduce the receiver complexity for OTFS scheme, this paper proposes a variational Bayes (VB) approach as …
