Orthogonal time frequency space (OTFS) modulation is a recently proposed waveform for reliable communication in high-speed vehicular communication scenarios. It has better resilience to inter-carrier interference (ICI) than orthogonal frequency division multiplexing (OFDM). In this work, we describe OTFS as block-OFDM with a cyclic prefix and time interleaving. This interpretation helps one visualize OTFS in the light of OFDM as well as it also helps in analyzing the gain obtained by OTFS over OFDM. Further, we compare the performance of OTFS with its contender 5G new radio (NR)'s OFDM configuration of variable subcarrier bandwidth (VSB-OFDM) while considering practical forward error correction codes and 3GPP high-speed channel model. This provides realistic performance comparison, which is highly desired for technology realization. Considering practical channel estimation, we find that OTFS outperforms VSB-OFDM with 5G NR parameter by about 5dB. We also present results on peak to average power ratio (PAPR) due to specific pilot structure used in OTFS for channel estimation.
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…
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…
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…
Orthogonal time frequency space (OTFS) is being pursued in recent times as a suitable wireless transmission technology for use in high mobility scenarios. In this work, we propose nonorthogonal multiple acess (NOMA) based OTFS which may be called NOMA-OTFS system and evaluate its performance from system level and link level perspective. The challenge lies in the fact that while OTFS transmission technology is known for its resilience to high mobility conditions, while NOMA is known to yield high spectral efficiency in low mobility scenarios in comparison to orthogonal multiple access (OMA). We…
We consider a joint radar estimation and communication system using orthogonal frequency division multiplexing (OFDM) and orthogonal time frequency space (OTFS) modulations. The scenario is motivated by vehicular applications where a vehicle equipped with a mono-static radar wishes to communicate data to its target receiver, while estimating parameters of interest related to this receiver. By focusing on the case of a single target, we derive the maximum likelihood (ML) estimator and the Cramér-Rao lower bound on joint velocity and range estimation. Numerical examples demonstrate that both dig…
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…
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…
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 …
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…
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 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 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…
We investigate the relationship between Orthogonal Time Frequency Space (OTFS) modulation and Orthogonal Short Time Fourier (OSTF) signaling. OTFS was recently proposed as a new scheme for high Doppler scenarios and builds on OSTF. We first show that the two schemes are unitarily equivalent in the digital domain. However, OSTF defines the analog-digital interface with the waveform domain. We then develop a critically sampled matrix-vector model for the two systems and consider linear minimum mean-squared error (MMSE) filtering at the receiver to suppress inter-symbol interference. Initial comp…
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…
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 …
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 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 …
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 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…
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…
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…
For broadband wireless communication systems, Orthogonal Frequency Division Multiplexing (OFDM) has been combined with Multi-Input Multi-Output (MIMO) techniques. Bit-Interleaved Coded Multiple Beamforming (BICMB) can achieve both spatial diversity and spatial multiplexing for flat fading MIMO channels. For frequency selective fading MIMO channels, BICMB with OFDM (BICMB-OFDM) can be applied to achieve both spatial diversity and multipath diversity, making it an important technique. However, analyzing the diversity of BICMB-OFDM is a challenging problem. In this paper, the diversity analysis o…
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 …
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…
In orthogonal time frequency space (OTFS) modulation, Zak transform approach is a natural approach for converting information symbols multiplexed in the DD domain directly to time domain for transmission, and vice versa at the receiver. Past research on OTFS has primarily considered a two-step approach where DD domain symbols are first converted to time-frequency domain which are then converted to time domain for transmission, and vice versa at the receiver. The Zak transform approach can offer performance and complexity benefits compared to the two-step approach. This paper presents an early …
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…
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…
Multi-Input Multi-Output (MIMO) techniques have been incorporated with Orthogonal Frequency Division Multiplexing (OFDM) for broadband wireless communication systems. Bit-Interleaved Coded Multiple Beamforming (BICMB) can achieve both spatial diversity and spatial multiplexing for flat fading MIMO channels. For frequency selective fading MIMO channels, BICMB with OFDM (BICMB-OFDM) can be employed to provide both spatial diversity and multipath diversity, making it an important technique. In our previous work, the subcarrier grouping technique was applied to combat the negative effect of subcar…
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-…
Orthogonal time frequency space (OTFS) modulation outperforms orthogonal frequency division multiplexing (OFDM) in high-mobility scenarios. One challenge for OTFS massive MIMO is downlink channel estimation due to the large number of base station antennas. In this paper, we propose a 3D structured orthogonal matching pursuit algorithm based channel estimation technique to solve this problem. First, we show that the OTFS MIMO channel exhibits 3D structured sparsity: normal sparsity along the delay dimension, block sparsity along the Doppler dimension, and burst sparsity along the angle dimensio…
We provide the first-ever performance evaluation of orthogonal time frequency space (OTFS) modulation in cell-free massive multiple-input multiple-output (MIMO) systems. To investigate trade-off between performance and overhead, we apply embedded pilot-aided and superimposed pilot-based channel estimation methods. We then derive a closed-form expression for the individual user downlink and uplink spectral efficiencies as a function of the numbers of APs, users and delay-Doppler domain channel estimate parameters. Based on these analytical results, we also present new scaling laws that the AP's…
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) 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…
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…
In this paper, we investigate the impact of Forward Error Correction (FEC) codes namely Cyclic Redundancy Code and Convolution Code on the performance of OFDM wireless communication system for speech signal transmission over both AWGN and fading (Rayleigh and Rician) channels in term of Bit Error Probability. The simulation has been done in conjunction with QPSK digital modulation and compared with uncoded resultstal modulation. In the fading channels, it is found via computer simulation that the performance of the Convolution interleaved based OFDM systems outperform than that of CRC interlea…
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…
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…
