Orthogonal time frequency space as a sixth generation enabler: A comprehensive analysis in high-mobility vehicular networks

The orthogonal time frequency space (OTFS) system with two-dimensional (2-D) modulation technique is an attractive technology to show the better performance than the conventional orthogonal frequency division multiplexing (OFDM) system, particularly in the high-speed vehicle communications and high-level dimensions of multiple-input multiple-output systems. However, the OTFS system has high peak-to-average power ratio (PAPR), like OFDM system. In this paper, we analyze the PAPR characteristics of the OTFS signal and propose a concept of discrete Fourier transform (DFT)-Spread OTFS system to reduce the PAPR efficiently. The key idea of the DFT precoding technique is to spread the energy of a subcarrier throughout the subcarriers. Therefore, the PAPR is decreased. In the practical wireless communication systems, the power efficiency could become worse, or the bit error rate (BER) is seriously degraded by the high peak signal power in a high power amplifier (HPA). So, by reducing the PAPR, the efficiency of the HPA can be significantly improved and the nonlinear distortion caused by HPA can be decreased, too. We evaluate the spectrum characteristics of conventional OFDM and OTFS schemes and the proposed DFT-Spread OTFS scheme according to the different nonlinear conditions of HPA. Simulation results demonstrate that the power spectrums of the proposed system are less sensitive than the conventional schemes in HPA nonlinear environments. In addition, we compare the uncoded BER performance among the different schemes over the AWGN and delay-Doppler channels according to the several HPA nonlinear conditions for the different mobility speeds of user equipment. The BER performance of the conventional OFDM system breaks down completely in high-mobility scenarios for both HPA linear and nonlinear conditions. The proposed scheme improves the BER performance over AWGN and delay-Doppler channels in HPA nonlinear environments, as compared to the conventional OTFS system. In high-mobility scenarios and at BER of $$1 \times 10^{ - 3}$$ , simulation results verify that the OTFS and our proposed scheme can achieve a gain of 12.8 dB compared to OFDM scheme. Moreover, the proposed DFT-Spread OTFS scheme can be reduced PAPR by 2.2 dB and 1.8 dB compared to OFDM and OTFS schemes, respectively.

High mobility wireless communication systems have been proposed to be robust to channel-induced Doppler shift using Orthogonal Time Frequency Space (OTFS) modulation. The OTFS modulation technique is described in this paper. In addition to being in the delay-Doppler (DD) domain, OTFS has a unique and important feature. The OTFS modulation offers maximum diversity over frequency and time when coupled with an equalizer. This technique converts fading, time-varying wireless channels into time-independent, non-fading interactions that reveal their underlying geometry. Even in challenging 5G deployment settings, OTFS achieves Massive MIMO throughput gains by scaling throughput linearly with MIMO order. An analysis of peak to average power ratio (PAPR) of OFTS modulation wave forms is presented in this paper. OTFS with rectangular pulses is characterized analytically using the complementary cumulative distribution function (CCDF). The simulated CCDF for the PAPR of OTFS is compared with that for orthogonal frequency division multiplexing (OFDM) for different pulse shapes. The results show that OTFS has a better PAPR than OFDM.

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.

PAPR analysis in OTFS using the centre phase sequence matrix based PTS method

Discrete FBMC-based orthogonal time frequency space in wireless communications considering different prototype filters

Nonlinear companding transforms for reducing the PAPR of OTFS signal

In this letter, we devise a discrete cosine transform (DCT)-based orthogonal time frequency space (OTFS), offering reduced peak-to-average power ratio (PAPR) and lower complexity without compromising on bit error rate (BER) performance. The proposed system adopts a DCT-based inverse discrete Zak transform (IDZT) to directly convert 2D information symbols to the delay-time domain. Under such a setting, we provide a comprehensive analysis of PAPR. We derive an upper bound on PAPR for DCT-OTFS, and show a reduction of about 20% in the maximum PAPR of traditional OTFS. We also provide a complementary cumulative distribution function (CCDF) analysis of PAPR for this system. Finally, simulations compare the performance of the proposed scheme with orthogonal time sequency multiplexing (OTSM) and OTFS in terms of CCDF of PAPR and BER. We observe that three schemes have similar BER performance, while DCT-OTFS demonstrates an approximate reduction of 0.5 dB in CCDF of PAPR, compared to traditional OTFS and OTSM. We remark that this PAPR reduction is obtained without using any specific PAPR reduction techniques.

Orthogonal time frequency space (OTFS) is a new multi-carrier modulation technology emerging in recent years. Like orthogonal frequency division multiplexing (OFDM), OTFS also has the problem of high peak to average power ratio (PAPR). Because of the high PAPR, OTFS signals are easy to enter the nonlinear region of the power amplifier (PA), and result in nonlinear distortion. In this paper, we study the PAPR problem for OTFS system and propose an improved algorithm by jointly exploiting the traditional selective mapping (SLM) scheme and the imperialist competition algorithm (ICA), namely ICA-SLM. The simulation results shown that the proposed novel PAPR reduction method is capable of achieving better performance compared to conventional SLM for OTFS systems.

This paper presents methods for reducing the peak‐to‐average power ratio (PAPR) of the orthogonal time frequency space (OTFS) signal. These methods mainly consist of two operations: symbol interferometry (SI) and either ‐law or ‐law companding. SI spreads the data of one OTFS symbol onto all symbols and is implemented using a simple inverse fast Fourier transform operation on each OTFS symbol. During the second operation, the PAPR of the OTFS signal is significantly reduced. For our performance analysis, the complementary cumulative distribution function, probability density function, and bit error rate are illustrated through simulations performed in MATLAB. The performance is also analyzed using a solid‐state power amplifier at the transmitter and compared with OTFS, ‐law‐based OTFS, and SI OTFS systems. The results indicate that the proposed OTFS system achieves a low PAPR.

We provide a detailed comparison between orthogonal time frequency space (OTFS) and orthogonal frequency division multiplexing (OFDM) modulation schemes, focusing on peak-to-average power ratio (PAPR), spectral efficiency (SE), and resistance to frequency dispersion. First experimental research of OTFS is achieved in a photonics-aided D-band indoor wireless communication system. We compare the performance of OTFS and OFDM schemes in real frequency-selective (static) and partially emulated doubly-selective (mobile) channels, using the same experimental setup and indoor environment. OTFS scheme exhibits superior bit error rate (BER) performance and >2 dB power sensitivity improvement over OFDM in both static and mobile channels. Moreover, due to the reduction in overheads, OTFS-4QAM achieves a SE of 2 bit/s/Hz, which is 15% higher than that of OFDM-4QAM. The improvement in SE of OTFS supports the transmission of massive amounts of data for future indoor wireless networks.

Orthogonal Time Frequency Space (OTFS) modulation has emerged as a leading candidate for 6G wireless systems due to its exceptional robustness against high mobility and frequency-selective fading channels. However, its multicarrier structure inherently generates a high Peak-to-Average Power Ratio (PAPR), making OTFS signals highly susceptible to nonlinear distortions introduced by High Power Amplifiers (HPAs). This paper investigates the impact of HPA nonlinearity on OTFS transmission in terrestrial radio environments, using the Rapp model to characterize amplifier behavior. We evaluate key performance metrics including PAPR, Complementary Cumulative Distribution Function (CCDF), Bit Error Rate (BER), Adjacent Channel Power Ratio (ACPR), and amplifier efficiency under varying Input Back-Off (IBO) values (0.5 dB to 4 dB). Our results demonstrate that OTFS exhibits a significantly higher PAPR than conventional 16-QAM, necessitating a larger IBO to avoid saturation. While increasing IBO improves linearity and reduces BER particularly in realistic Rayleigh fading channels it comes at the cost of drastically reduced amplifier efficiency, dropping from 70% at IBO = 0 dB to below 15% at IBO = 6 dB. Furthermore, nonlinear amplification severely degrades spectral purity: ACPR deteriorates from -37 dB (before amplification) to -15 dB (after amplification), indicating a 22 dB increase in out-of-band emissions and a substantial risk of interference with adjacent channels.

Multiple waveforms should be supported by the new generation wireless communication systems, in order to satisfy the requirements for various mobility scenarios. Orthogonal frequency division multiplexing (OFDM) has been extensively adopted by various wireless communication systems, but it faces great challenges in high mobility scenarios due to large Doppler shift and Doppler spread effects. To overcome this challenge, orthogonal time frequency space (OTFS) has been recently proposed to exploit delay and Doppler diversities, which leads to superior performance to OFDM in high mobility scenarios. This excellent property empowers OTFS to become a promising waveform for high-mobility wireless communication systems (HMWCS). However, in low mobility scenarios, OTFS does not exhibit obvious performance superiority, and suffers from some additional processing complexity. In this paper, considering multi-mobility scenarios, we study the co-existence of OTFS and OFDM waveforms to achieve good tradeoffs between performance and complexity. By regarding OTFS as precoded OFDM, we design multi-waveform downlink transmission systems. We also study two schemes for the co-existence of OTFS and OFDM waveforms. The time division multiplexing (TDM) scheme enables OTFS users with high mobility and OFDM users with low mobility to be multiplexed in the time domain, while the frequency division multiplexing (FDM) scheme multiplexes OTFS users and OFDM users in the frequency domain. The simulation results show that both the FDM and TDM schemes improve the bit error rate (BER) performance of high mobility users. The results also show that the TDM scheme achieves superior BER performance to the FDM scheme.

The vision for 6th-generation (6G) wireless communication systems emphasizes the need for robust and reliable communication in extremely high-mobility scenarios, while also addressing critical demands for energy and spectral efficiency. Under such scenarios, doubly time-frequency selective fading channels often significantly degrade the performance of orthogonal frequency-division multiplexing (OFDM) based systems due to the impact of large delay and Doppler shifts. Recently, orthogonal time frequency space (OTFS) modulation has emerged as a promising alternative. By processing signals in the delay-Doppler (DD) domain, OTFS offers several advantages, including quasi-static channel characteristics, full-time-frequency diversity, and low peak-to-average power ratio (PAPR), making it a promising candidate for high-mobility communications. Reconfigurable intelligent surfaces (RIS) are being further integrated to enhance the performance of OTFS systems cost-effectively. With their ability to dynamically reconfigure the wireless environment, the integration of RIS can offer significant performance improvements for OTFS systems. This survey offers a comprehensive review of RIS-assisted OTFS systems, including the fundamental principles, recent advances, and future research directions. Specifically, we first introduce the background of RIS-assisted OTFS systems, outlining the opportunities and challenges of their integration. To ensure the survey is self-contained, we provide a brief overview of the fundamental principles of OTFS and RIS technologies. Building on these foundations, we present a general input-output relationship and capacity characterization for RIS-assited MIMO-OTFS systems. Then, this survey further explores cutting-edge research in areas such as input-output analysis, RIS phase shift design, channel estimation, detection techniques, RIS-assisted integrated sensing and communication (ISAC), and other novel technologies. Finally, we outline some future research directions.

Orthogonal time frequency space (OTFS) modulation shows significant advantages over orthogonal frequency division multiplexing (OFDM), specially in environments with high frequency dispersion. However, high peak-to-average power ratio (PAPR) has been one of the major drawbacks of OTFS systems, which impairs the efficiency of the power amplifier. To resolve the problem, we propose a PAPR reduction method based on the autoencoder (AE) architecture through deep learning (DL) techniques, where the encoder is trained to reduce the PAPR and the decoder is trained to reconstruct the original signal. By carefully designing the loss function, the bit error rate (BER) and the PAPR are simultaneously minimized, and a hyper-parameter is introduced to achieve a good compromise between BER and PAPR in the proposed scheme. Simulation results validate the advantages of the proposed scheme as compared to the other conventional schemes.

Peak-to-average power ratio (PAPR) in orthogonal time frequency space (OTFS) is vital for optimizing signal efficiency, minimizing distortion, and enhancing the performance of a beyond fifth-generation (B5G) system. The paper focuses on lowering the PAPR while retaining the bit error rate (BER) and power spectral density (PSD) for 64 and 256 sub-carriers. The PAPR is minimized by using a fractal optimization process known as selective mapping (SLM) and partial transmission sequence (PTS) at the transmitting block of the OTFS framework. The combination of SLM and PTS reduces peak power by selectively modifying the phase of transmitted symbols. SLM generates multiple versions of the signal, while PTS allocates power to these versions optimally, collectively mitigating amplitude peaks and minimizing PAPR. According to the simulation results, the suggested SLM+PTS works better than the traditional SLM and PTS, achieving low spectrum leakage and PAPR improvements of 5.5 dB and 4.9[Formula: see text]dB as well as SNR gains of 2.4[Formula: see text]dB and 2.1[Formula: see text]dB. In the future, SLM+PTS may work on lowering PAPR by making computers faster, researching adaptive algorithms, and combining machine learning methods for real-time optimization in various communication settings. Complex modeling, including fractal-based SLM and PTS approaches, provides a detailed understanding of waveform behavior and interference patterns, enabling more accurate and effective hybrid PAPR reduction techniques. This combination enhances the ability to manage to mitigate non-linear distortion across various sub-carriers, crucial for the performance and efficiency of 6G OTFS modulation.