Orthogonal time frequency space (OTFS) modulation is a recent modulation scheme designed in the delay-Doppler domain. It has been shown to achieve superior performance compared to conventional multicarrier modulation schemes designed in the time-frequency domain. In this paper, we consider OTFS based multiple access (OTFS-MA), where delay-Doppler bins serve as the resource blocks for multiple access. Different delay-Doppler resource blocks (DDRBs) in the delay-Doppler grid are allocated to different users for multiple access. We consider three different DDRB allocation schemes. While Scheme 1 multiplexes the users along the delay axis, Scheme 2 multiplexes them along the Doppler axis. In both these schemes, each user's signal spans the entire time-frequency plane. Scheme 3 allocates the DDRBs in such a way that each user's signal is limited to span only over a subset of the time-frequency plane. We study the performance of OTFS-MA in high mobility environments on the uplink and compare it with those of OFDMA and SC-FDMA. Our results show that OTFS-MA (with maximum-likelihood detection in small dimension systems and with a message passing based detection in large dimension systems) achieves better performance compared to OFDMA and SC-FDMA. We also present the performance of a multiuser channel estimation scheme using pilot symbols placed in the delay-Doppler grid.
Orthogonal time frequency space (OTFS) modulation is a recently introduced multiplexing technique designed in the 2-dimensional (2D) delay-Doppler domain suited for high-Doppler fading channels. OTFS converts a doubly-dispersive channel into an almost non-fading channel in the delay-Doppler domain through a series of 2D transformations. In this paper, we focus on MIMO-OTFS which brings in the high spectral and energy efficiency benefits of MIMO and the robustness of OTFS in high-Doppler fading channels. The OTFS channel-symbol coupling and the sparse delay-Doppler channel impulse response enab…
Orthogonal time frequency space (OTFS) modulation is a 2-dimensional (2D) modulation scheme designed in the delay-Doppler domain, unlike traditional modulation schemes which are designed in the time-frequency domain. Through a series of 2D transformations, OTFS converts a doubly-dispersive channel into an almost non-fading channel in the delay-Doppler domain. In this domain, each symbol in a frame experiences an almost constant fade, thus achieving significant performance gains over existing modulation schemes such as OFDM. The sparse delay-Doppler impulse response which reflects the actual ph…
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…
Orthogonal time frequency space (OTFS) modulation was shown to provide significant error performance advantages over orthogonal frequency division multiplexing (OFDM) in delay--Doppler channels. In order to detect OTFS modulated data, the channel impulse response needs to be known at the receiver. In this paper, we propose embedded pilot-aided channel estimation schemes for OTFS. In each OTFS frame, we arrange pilot, guard, and data symbols in the delay--Doppler plane to suitably avoid interference between pilot and data symbols at the receiver. We develop such symbol arrangements for OTFS ove…
Orthogonal time frequency space (OTFS) modulation has recently emerged as an effective waveform to tackle the linear time-varying channels. In OTFS literature, approximately constant channel gains for every group of samples within each OTFS block are assumed. This leads to limitations for OTFS on the maximum Doppler frequency that it can tolerate. Additionally, presence of cyclic prefix (CP) in OTFS signal limits the flexibility in adjusting its parameters to improve its robustness against channel time variations. Therefore, in this paper, we study the possibility of removing the CP overhead f…
In this paper we introduce a new 2D modulation technique called OTFS (Orthogonal Time Frequency & Space) that transforms information carried in the Delay-Doppler coordinate system to the familiar time-frequency domain utilized by traditional modulation schemes such as OFDM, CDMA and TDMA. OTFS converts the fading, time-varying wireless channel into a non-fading, time-independent interaction revealing the underlying geometry of the wireless channel. In this new formulation, all QAM symbols experience the same channel and all Delay-Doppler diversity branches of the channel are coherently combine…
Orthogonal time frequency space (OTFS) is a 2-dimensional (2D) modulation technique designed in the delay-Doppler domain. A key premise behind OTFS is the transformation of a time varying multipath channel into an almost non-fading 2D channel in delay-Doppler domain such that all symbols in a transmission frame experience the same channel gain. It has been suggested in the recent literature that OTFS can extract full diversity in the delay-Doppler domain, where full diversity refers to the number of multipath components separable in either the delay or Doppler dimension, but without a formal a…
Reconfigurable intelligent surfaces (RIS) and orthogonal time-frequency space (OTFS) modulation have gained attention in recent wireless research. RIS technology aids communication by reflecting the incident electromagnetic waves towards the receiver, and OTFS modulation is effective in high-Doppler channels. This paper presents an early investigation of RIS-aided OTFS in high-Doppler channels. We derive the end-to-end delay-Doppler (DD) domain input-output relation of a RIS-aided OTFS system, considering rectangular pulses and fractional delay-Doppler values. We also consider a Zak receiver f…
In this paper, we introduce a new 2D modulation scheme referred to as OTFS (Orthogonal Time Frequency & Space) that multiplexes information QAM symbols over new class of carrier waveforms that correspond to localized pulses in a signal representation called the delay-Doppler representation. OTFS constitutes a far reaching generalization of conventional time and frequency modulations such as TDM and FDM and, from a broader perspective, it establishes a conceptual link between Radar and communication. The OTFS waveforms couple with the wireless channel in a way that directly captures the underly…
Although the combination of the orthogonal time frequency space (OTFS) modulation and the massive multiple-input multiple-output (MIMO) technology can make communication systems perform better in high-mobility scenarios, there are still many challenges in downlink channel estimation owing to inaccurate modeling and high pilot overhead in practical systems. In this paper, we propose a channel state information (CSI) acquisition scheme for downlink massive MIMO-OTFS in presence of the fractional Doppler, including deterministic pilot design and channel estimation algorithm. First, we analyze the…
Extensive work has demonstrated the excellent performance of orthogonal time frequency space (OTFS) modulation in high-mobility scenarios. Time-variant wideband channel estimation serves as one of the key compositions of OTFS receivers since the data detection requires accurate channel state information (CSI). In practical wideband OTFS systems, the Doppler shift brought by the high mobility is frequency-dependent, which is referred to as the Doppler Squint Effect (DSE). Unfortunately, DSE was ignored in overall prior estimation schemes employed in OTFS systems, which leads to severe performan…
The recent proposed orthogonal time frequency space (OTFS) modulation shows signifcant advantages than conventional orthogonal frequency division multiplexing (OFDM) for high mobility wireless communications. However, a challenging problem is the development of effcient receivers for practical OTFS systems with low complexity. In this paper, we propose a novel delay-Doppler reversal (DDR) technology for OTFS system with desired performance and low complexity. We present the DDR technology from a perspective of two-dimensional cascaded channel model, analyze its computational complexity and als…
Orthogonal time frequency space (OTFS) modulation is a recently proposed delay-Doppler (DD) domain communication scheme, which has shown promising performance in general wireless communications, especially over high-mobility channels. In this paper, we investigate DD domain Tomlinson-Harashima precoding (THP) for downlink multiuser multiple-input and multiple-output OTFS (MU-MIMO-OTFS) transmissions. Instead of directly applying THP based on the huge equivalent channel matrix, we propose a simple implementation of THP that does not require any matrix decomposition or inversion. Such a simple i…
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…
Orthogonal time frequency and space (OTFS) modulation is a promising technology that satisfies high Doppler requirements for future mobile systems. OTFS modulation encodes information symbols and pilot symbols into the two-dimensional (2D) delay-Doppler (DD) domain. The received symbols suffer from inter-Doppler interference (IDI) in the fading channels with fractional Doppler shifts that are sampled at noninteger indices in the DD domain. IDI has been treated as an unavoidable effect because the fractional Doppler shifts cannot be obtained directly from the received pilot symbols. In this pap…
This paper introduces a Compressed Sensing (CS) estimation scheme for Orthogonal Time Frequency Space (OTFS) channels with sparse multipath. The OTFS waveform represents signals in a two dimensional Delay-Doppler (DD) orthonormal basis. The proposed model does not require the assumption that the delays are integer multiples of the sampling period. The analysis shows that non-integer delay and Doppler shifts in the channel cannot be accurately modelled by integer approximations. An Orthogonal Matching Pursuit with Binary-division Refinement (OMPBR) estimation algorithm is proposed. The proposed…
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 the past few years, some alternatives to the Orthogonal Frequency Division Multiplexing (OFDM) modulation have been considered to improve its spectral containment and its performance level in the presence of heavy Doppler shifts. This paper examines a novel modulation, named Doppler-Resilient Universal Filtered MultiCarrier (DR-UFMC), which has the objective of combining the advantages provided by the Universal Filtered MultiCarrier (UFMC) modulation (i.e., better spectral containment), with those of the Orthogonal Time Frequency Space (OTFS) modulation (i.e., better performance in time-var…
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…
Orthogonal time frequency space (OTFS) modulation has attracted substantial attention recently due to its great potential of providing reliable communications in high-mobility scenarios. In this paper, we propose a novel hybrid signal detection algorithm for OTFS modulation. By characterizing the input-output relationship of OTFS modulation, we derive the near-optimal symbol-wise maximum a posteriori (MAP) detection algorithm for OTFS modulation, which aims to extract the information of each transmitted symbol based on the corresponding related received symbols. Furthermore, in order to reduce…
Orthogonal time frequency space (OTFS) is a framework for communication and active sensing that processes signals in the delay-Doppler (DD) domain. This paper explores three key features of the OTFS framework, and explains their value to applications. The first feature is a compact and sparse DD domain parameterization of the wireless channel, where the parameters map directly to physical attributes of the reflectors that comprise the scattering environment, and as a consequence these parameters evolve predictably. The second feature is a novel waveform / modulation technique, matched to the D…
Orthogonal time frequency space (OTFS) modulation is a recently developed multi-carrier multi-slot transmission scheme for wireless communications in high-mobility environments. In this paper, the error performance of coded OTFS modulation over high-mobility channels is investigated. We start from the study of conditional pairwise-error probability (PEP) of the OTFS scheme, based on which its performance upper bound of the coded OTFS system is derived. Then, we show that the coding improvement for OTFS systems depends on the squared Euclidean distance among codeword pairs and the number of ind…
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…
As a promising technique for high-mobility wireless communications, orthogonal time frequency space (OTFS) has been proved to enjoy excellent advantages with respect to traditional orthogonal frequency division multiplexing (OFDM). However, a challenging problem is to design efficient systems to further improve the performance. In this paper, we propose a novel block-wise index modulation (IM) scheme for OTFS systems, named Doppler-IM with OTFS (DoIM-OTFS), where a block of Doppler resource bins are activated simultaneously. For practical implementation, we develop a low complexity customized …
In this paper, we investigate the impacts of transmitter and receiver windows on orthogonal time-frequency space (OTFS) modulation and propose a window design to improve the OTFS channel estimation performance. Assuming ideal pulse shaping filters at the transceiver, we first identify the role of window in effective channel and the reduced channel sparsity with conventional rectangular window. Then, we characterize the impacts of windowing on the effective channel estimation performance for OTFS modulation. Based on the revealed insights, we propose to apply a Dolph-Chebyshev (DC) window at ei…
We provide a performance evaluation of orthogonal time frequency space (OTFS) modulation in cell-free massive MIMO (multiple-input multiple-output) systems. By leveraging the inherent sparsity of the delay-Doppler (DD) representation of time-varying channels, we apply the embedded pilot-aided channel estimation method with reduced guard intervals and derive the minimum mean-square error estimate of the channel gains from received uplink pilots at the access points (APs). Each AP applies conjugate beamforming to transmit data to the users. We derive a closed-form expression for the individual u…
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…
Orthogonal time frequency space (OTFS) modulation has been confirmed to provide significant performance advantages against Doppler in high-mobility scenarios. The core feature of OTFS is that the time-variant channel is converted into a non-fading 2D channel in the delay-Doppler (DD) domain so that all symbols experience the same channel gain. In now available literature, the channel is assumed to be quasi-static over an OTFS frame. As for more practical channels, the input-output relation will be time-variant as the environment or medium changes. In this paper, we analyze the characterization…
In this paper, we present a deep neural network (DNN) based transceiver architecture for delay-Doppler (DD) channel training and detection of orthogonal time frequency space (OTFS) modulation signals along with IQ imbalance (IQI) compensation. The proposed transceiver learns the DD channel over a spatial coherence interval and detects the information symbols using a single DNN trained for this purpose at the receiver. The proposed transceiver also learns the IQ imbalances present in the transmitter and receiver and effectively compensates them. The transmit IQI compensation is realized using a…
This paper proposes an off-grid channel estimation scheme for orthogonal time-frequency space (OTFS) systems adopting the sparse Bayesian learning (SBL) framework. To avoid channel spreading caused by the fractional delay and Doppler shifts and to fully exploit the channel sparsity in the delay-Doppler (DD) domain, we estimate the original DD domain channel response rather than the effective DD domain channel response as commonly adopted in the literature. OTFS channel estimation is first formulated as a one-dimensional (1D) off-grid sparse signal recovery (SSR) problem based on a virtual samp…
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…
Orthogonal Time Frequency Space (OTFS) is a $\text{2-D}$ modulation technique that has the potential to overcome the challenges faced by orthogonal frequency division multiplexing (OFDM) in high Doppler environments. The performance of OTFS in a multi-user scenario with orthogonal multiple access (OMA) techniques has been impressive. Due to the requirement of massive connectivity in 5G and beyond, it is immensely essential to devise and examine the OTFS system with the existing Non-orthogonal Multiple Access (NOMA) techniques. In this paper, we propose a multi-user OTFS system based on a code-…
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…
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…
In this paper, we analyze the performance of orthogonal time frequency space (OTFS) modulation with antenna selection at the receiver, where $n_s$ out of $n_r$ receive antennas with maximum channel Frobenius norms in the delay-Doppler (DD) domain are selected. Single-input multiple-output OTFS (SIMO-OTFS), multiple-input multiple-output OTFS (MIMO-OTFS), and space-time coded OTFS (STC-OTFS) systems with receive antenna selection (RAS) are considered. We consider these systems without and with phase rotation. Our diversity analysis results show that, with no phase rotation, SIMO-OTFS and MIMO-O…
Orthogonal time-frequency space (OTFS) has been confirmed to take advantage of full time-frequency diversity to significantly improve error performance in high-mobility scenarios. We found that the proposed message passing (MP) and variational Bayes (VB) detectors can achieve approximate maximum a posteriori (MAP) detection, the interferences cannot be completely eliminated in the absence of noise. To achieve near-optimal MAP detection, this letter proposes a novel detection method based on sum-product algorithm (SPA) with low complexity. Leveraging subtly factorized posteriori probabilities, …
This paper investigates the massive connectivity of low Earth orbit (LEO) satellite-based Internet-of-Things (IoT) for seamless global coverage. We propose to integrate the grant-free non-orthogonal multiple access (GF-NOMA) paradigm with the emerging orthogonal time frequency space (OTFS) modulation to accommodate the massive IoT access, and mitigate the long round-trip latency and severe Doppler effect of terrestrial-satellite links (TSLs). On this basis, we put forward a two-stage successive active terminal identification (ATI) and channel estimation (CE) scheme as well as a low-complexity …
