Time-frequency Space Research Articles

A High-Impedance Fault Detection Method for Active Distribution Networks Based on Time–Frequency–Space Domain Fusion Features and Hybrid Convolutional Neural Network

Traditional methods for detecting high-impedance faults (HIFs) in distribution networks primarily rely on constructing fault diagnosis models using one-dimensional zero-sequence current sequences. A single diagnostic model often limits the deep exploration of fault characteristics. To improve the accuracy of HIF detection, a new method for detecting HIFs in active distribution networks is proposed. First, by applying continuous wavelet transform (CWT) to the collected zero-sequence currents under various operating conditions, the time–frequency spectrum (TFS) is obtained. An optimized algorithm, modified empirical wavelet transform (MEWT), is then used to denoise the zero-sequence current signals, resulting in a series of intrinsic mode functions (IMFs). Secondly, the intrinsic mode functions (IMFs) are transformed into a two-dimensional spatial domain fused image using the symmetric dot pattern (SDP). Finally, the TFS and SDP images are synchronized as inputs to a hybrid convolutional neural network (Hybrid-CNN) to fully explore the system’s fault features. The Sigmoid function is utilized to achieve HIF detection, followed by simulation and experimental validation. The results indicate that the proposed method can effectively overcome the issues of traditional methods, achieving a detection accuracy of up to 98.85% across different scenarios, representing a 2–7% improvement over single models.

Pulsed Orthogonal Time Frequency Space: A Fast Acquisition and High-Precision Measurement Signal for Low Earth Orbit Position, Navigation, and Timing

The recent rapid development of low Earth orbit (LEO) constellation-based navigation techniques has enhanced the ability of position, navigation, and timing (PNT) services in deep attenuation and interference environments. However, existing navigation modulations face the challenges of high acquisition complexity and do not improve measurement precision at the same signal strength. We propose a pulsed orthogonal time frequency space (Pulse-OTFS) signal, which naturally converts continuous signals into pulses through a special delay-Doppler domain pseudorandom noise (PRN) code sequence arrangement. The performance evaluation indicates that the proposed signal reduces at least 89.4% of the acquisition complexity. The delay measurement accuracy is about 8 dB better than that of the traditional binary phase shift keying (BPSK) signals with the same bandwidth. It also provides superior compatibility and anti-multipath performance. The advantages of fast acquisition and high-precision measurement are verified by processing the real signal in the developed software receiver. As Pulse-OTFS occupies only one time slot of a signal period, it can be easily integrated with OTFS-modulated communication signals and used as a navigation signal from broadband LEO satellites as an effective complement to the global navigation satellite system (GNSS).

Research on an Algorithm for High-Speed Train Positioning and Speed Measurement Based on Orthogonal Time Frequency Space Modulation and Integrated Sensing and Communication

The Doppler effect caused by the rapid movement of high-speed rail services has a great impact on the accuracy of train positioning and speed measurement. Existing train positioning algorithms require a large number of trackside equipment and sensors, resulting in high construction and maintenance costs. Aiming to solve the above two problems, this article proposes a train positioning algorithm based on orthogonal time–frequency space (OTFS) modulation and integrated sensing and communication (ISAC). Firstly, based on the OTFS, the positioning and speed measurement architecture of communication awareness integration is constructed. Secondly, a two-stage estimation (TSE) algorithm is proposed to estimate the delay Doppler parameters of HST. In the first stage, a low-complexity coarse grid search is used, and in the second stage, a refined off-grid search is used to obtain the delay Doppler parameters. Then, the time difference of arrival/frequency difference of arrival (TDOA/FDOA) algorithm based on multiple base stations is used to locate the target, the weighted least square method is used to calculate the location, and the Cramér–Rao lower bound (CRLB) for positioning and speed measurement is derived. The simulation results demonstrate that, compared to GNSS/INS and OFDM radars, the algorithm exhibits enhanced positioning and speed measurement accuracy.

Signal detection of M-MIMO-orthogonal time frequency space modulation using hybrid algorithms: ZFE + MMSE and ZFE + MF

Orthogonal Time Frequency Space (OTFS) modulation, coupled with Massive Multiple Input Multiple Output (Massive-MIMO) technology, presents a promising avenue for enhancing the efficiency and reliability of fifth-generation (5G) and beyond fifth-generation (B5G) systems. OTFS modulation offers robust communication in high-mobility environments by converting signals into the delay-Doppler domain, ensuring better performance over fading channels. MIMO enhances wireless networks by using large antenna arrays to boost capacity, spectral efficiency, and reliability, making both technologies vital for next-generation radio systems. In this study, we explore the detection of (8 × 8, 16 × 16, 64 × 64, and 256 × 256) Massive-MIMO-OTFS signals utilizing two prominent detection algorithms: zero forcing equalization (ZFE) with matched filter (MF) known as (ZFE + MF) and Zero Forcing with minimum mean square error (MMSE) known as (ZFE + MMSE). The combination of Massive MIMO and OTFS offers improved spectral efficiency, robustness against fading, and enhanced spatial multiplexing capabilities. The parameters such as bit error rate (BER) and power spectral density (PSD) are analyzed and estimated for the proposed hybrid and conventional algorithms. The proposed algorithms obtained the SNR and PSD gain of 3.2 dB, 3.2 dB, 4.8 dB, and 6.1 dB gain, respectively, for 8 × 8, 16 × 16, 64 × 54, and 256 × 256 MIMO systems. Further, the PSD gain of -390 is obtained for the 256 × 256 system, resulting in high spectral efficiency.

Enhanced Spatial Modulation Based Orthogonal Time Frequency Space System

Enhanced Spatial Modulation Based Orthogonal Time Frequency Space System

ENHANCING OTFS MODULATION FOR 6G THROUGH HYBRID PAPR REDUCTION TECHNIQUE FOR DIFFERENT SUB-CARRIERS

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.

Lowering the PAPR of the optical OTFS-based 6G radio with a hybrid PTS-PSO genetic approach

Orthogonal Time Frequency Space (OTFS) is regarded as one of the best contenders for sixth-generation (6G) radio systems due to its ability to obtain excellent performance in high-speed scenarios. Peak-to-average power ratio (PAPR) significantly impacts and degrades the efficiency of the power amplifier used in OTFS-based 6G systems. The proposed article presents a genetic hybrid algorithm, Partial transmission sequence-particle swarm optimization (PTS-PSO), obtaining an optimal PAPR performance with low computation complexity. The PSO generates the best phase factor compared to the conventional phase generation method of PTS, making PTS-PSO more effective. The impacts such as PAPR, bit error rate (BER), power spectral density (PSD), and complexity of the proposed PTS-PSO are compared with the conventional selective mapping (SLM) and PTS methods for 64, 256, and 512 OTFS sub-carriers. The projected PTS-PSO attained a PAPR and PSD gain of 1–6 dB and − 540 while preserving the BER performance. The experimental results demonstrate that the projected PTS-PSO outperforms the conventional SLM and PTS algorithms with trivial intricacy.

PEAK TO AVERAGE POWER COMPUTING AND OPTIMIZATION OF OPTICAL OTFS 5G WAVEFORM USING HYBRID FRACTAL-BASED SIGNAL PROCESSING ALGORITHM

Optical orthogonal time frequency space (OTFS) is better at handling Doppler shifts and multipath fading, making signals more reliable and valuable in places with much movement beyond the fifth generation (B5G). Using practical power amplifiers at the transmitter causes power inefficiency and signal distortion because of the OTFS system’s high peak-to-average power ratio (PAPR), severely reducing system efficiency. Combining partial transmit sequence (PTS) and selective mapping (SLM), a technique known as PTS+SLM, reduces peak power. While SLM generates numerous phase-modulated signal candidates and chooses the one with the lowest PAPR, PTS separates the signal into sub-blocks and optimizes their phases to decrease peak power. With few changes to the signal structure, this dual strategy effectively reduces PAPR while improving power spectral density (PSD) efficiency. As a result, we ensure the accuracy and dependability of the transferred data by maintaining the bit error rate (BER). Fractal optimization methods could be applied to these algorithms. For example, fractal-inspired optimization techniques might be used to explore the phase space more effectively or to discover new phase sequences that result in lower PAPR. According to the simulation findings, the suggested PTS+SLM method works better than the traditional PTS and SLM methods.

Hadamard and Riemann Matrix‐BasedSLMforPAPRReduction inOTFSSignal

ABSTRACTIn this letter, we study the peak‐to‐average power ratio (PAPR) reduction and bit error rate (BER) performances of the Hadamard and Riemann matrix‐based selected mapping (SLM) technique for Orthogonal Time Frequency Space (OTFS) signals. Unlike the conventional phase sequence based on , which requires the entire sequence to extract the original signal at the receiver, the Hadamard and Riemann matrix‐based SLM techniques require only the row index of the matrix, reducing the additional information necessary to extract the signal. Simulation results are presented to verify the PAPR and BER performance. The results are also compared with the existing normalizedμ‐law, rootingμ‐law, and conventional SLM methods. The results demonstrate that the Riemann‐based SLM technique shows significant performance improvement.

Fatigue crack closure assessment by wavelet transform of infrared thermography signals

The occurrence of crack closure significantly impacts the fatigue life of materials and structural components. Whether it is induced by the nature of the loading, the fabrication process or the geometry of the structure, its magnitude and effect should be considered to further improve predictive models of fatigue crack propagation. However, the definition of reliable experimental methods for the observation and assessment of fatigue crack closure, and in particular suited to structure testing, remains a challenge. The present study aims to provide a novel approach for the assessment of fatigue crack closure via the continuous wavelet transform of infrared thermography data. The processing of the temperature signal close to the crack in a coherent time–frequency space allows for the identification of crack closing and opening instants associated with high-frequency components. The method is meant to be suited to any testing configuration (conventional compact tension specimen or full-scale structures) with minimum operator-dependent parameters.

Factorizations for quasi-Banach time–frequency spaces and Schatten classes

We deduce factorization properties for Wiener amalgam spaces WLp,q, an extended family of modulation spaces M(ω,ℬ), and for Schatten symbols spw in pseudo-differential calculus under e.g. convolutions, twisted convolutions and symbolic products. Here M(ω,ℬ) can be any quasi-Banach Orlicz modulation space. For example we show that WL1,r∗WLp,q=WLp,q and WL1,r#spw=spw when r∈(0,1], r≤p,q<∞. In particular we improve Rudin’s identity L1∗L1=L1.

Enhanced parametric detection employing diversified scan and iteration

In this paper, an enhanced parametric detection method employing diversified scan and iteration is proposed for heterogeneous environment. A diversified scan, encompassing both rough scan and intensive scan, is first conducted in the normalized space–time frequency field to acquire the interference’s frequency components, which is conducive to obtaining the outline of interference in the normalized space–time two-dimensional (2-D) frequency field. The intensities of these components are subsequently determined through iteration to reduce the impact brought by the randomness of training samples. Meanwhile, the environment is commonly sparse in most cases, which is fully utilized in the proposed method. Then the cross-correlation matrix and autoregressive (AR) covariance matrix are reconstructed to form the corresponding detector. In the end, the availability and superiority of the proposed method are validated by numerical results. It is shown from numerical results that the proposed method performs well in detection performance compared to several existing typical methods in heterogeneous environment.

DFT-spread OTFS-NOMA for downlink integrated positioning and communication

In this article, a non-orthogonal multiple-access (NOMA) transmission system that incorporates discrete Fourier transform (DFT) spread orthogonal time-frequency space (OTFS) modulation is proposed for the downlink integrated positioning and communication (IPAC). This system is designed to decrease the Peak-to-Average Power Ratio (PAPR) within the OTFS-NOMA system while simultaneously serving both communication user (CU) and positioning user (PU) within the same time-frequency resources. Firstly, we demonstrate the applicability of the proposed DFT-spread OTFS-NOMA (DFT-s-OTFS-NOMA) system for downlink transmission. It efficiently serves both the CU and PU concurrently within the same time and frequency resources, thereby increasing spectrum utilization. Subsequently, we develop a two-stage parameter estimation algorithm focusing on accurate positioning parameter estimation for PU and precise channel estimation for CU. Then, the position of the PU is estimated using the time of arrival (TOA) model and the linear least squares (LLS) approach. Simulation demonstrates a 9 dB PAPR reduction in the proposed system compared to the existing OTFS-NOMA system. Additionally, the proposed two-stage positioning method for the PU achieves centimeter-level accuracy in position estimation and near millimeter-per-second-level accuracy in velocity estimation. What is more, the performance of channel estimation and symbol detection, aided by the PU signal in the DFT-s-OTFS-NOMA system, demonstrates resilience against Doppler effects without the need for reliance on pilots. This ensures sustained an effective Bit Error Rate (BER) even in time-variant high mobility scenarios.

Bit Error Rate Performance Improvement for Orthogonal Time Frequency Space Modulation with a Selective Decode-and-Forward Cooperative Communication Scenario in an Internet of Vehicles System.

Orthogonal time frequency space (OTFS) modulation has recently found its place in the literature as a much more effective waveform in time-varying channels. It is anticipated that OTFS will be widely used in the communications of smart vehicles, especially those considered within the scope of Internet of Things (IoT). There are efforts to obtain customized traditional point-to-point single-input single-output (SISO)-OTFS studies in the literature, but their BER performance seems a bit low. It is possible to use cooperative communications in order improve BER performance, but it is noticeable that there are very few OTFS studies in the area of cooperative communications. In this study, to the best of the authors' knowledge, it is addressed for the first time in the literature that better performance is achieved for the OTFS waveform transmission in a selective decode-and-forward (SDF) cooperative communication scenario. In this context, by establishing a cooperative communication model consisting of a base station/source, a traffic sign/relay and a smart vehicle/destination moving at a constant speed, an end-to-end BER expression is derived. SNR-BER analysis is performed with this SDF-OTFS scheme and it is shown that a superior BER performance is achieved compared to the traditional point-to-point single-input single-output (SISO)-OTFS structure.

A Low-complex OFDM based DCO-OTFS modulation for VLC systems

Visible Light Communication (VLC) has emerged as a promising alternative for indoor and vehicular wireless communication, offering several advantages over traditional radio frequency (RF) technology. With the adoption of optical-orthogonal frequency division multiplexing (O-OFDM) schemes, visible light communication (VLC) has become more robust and adaptable in indoor, outdoor, vehicular, and underwear communications. Recently, an orthogonal time frequency space (OTFS) modulation technique has evolved with better performance than OFDM. The recent finding in the context of VLC shows that the OTFS technique shows remarkable advantages over conventional OFDM techniques except for the modem design complexity. This work introduces a low-complexity direct current-biased optical OTFS (DCO-OTFS) modulation based on OFDM. This paper evaluates the proposed system’s performance through simulations, providing evidence of its bit-error-rate (BER), peak-to-average power ratio (PAPR), and complexity behavior. Comparative assessments against the DCO-OFDM system are presented to understand the advantages of the low-complex DCO-OTFS system. The findings reveal that the proposed system not only provides low computational complexity in modem design but also maintains superior error performance, with a notable 10 dB signal-to-noise ratio (SNR) gain over DCO-OFDM along with a superior PAPR, making it a commendable choice for VLC applications.

Low complexity stationary iteration based approximate inversion for signal detection in OTFS system

Orthogonal time frequency space (OTFS) system offers a high data rate and effectively exploits full diversity compared to orthogonal frequency division multiplexing (OFDM), achieving a seamless trade-off between data rate and processing gain. However, detecting OTFS signals is challenging due to the complex conversion between delay-Doppler (DD) and time domains. In this article, we propose a stationary iteration-based approximate inversion (SIAI) technique for low-complexity detection in uplink OTFS systems.The proposed SIAI detection technique features square-order computational complexity and delivers performance close to that of a linear minimum mean square error (LMMSE) detector. Simulation results demonstrate that the SIAI technique outperforms several state-of-the-art detection methods in terms of both error performance and computational complexity. Additionally, the robustness of the SIAI technique is validated in scenarios with imperfect channel state information at the receiver.

Wireless channel characterizations in UMi scenarios via ray-tracing at 28 GHz: A perspective of asymmetric beams

As a novel communication pattern, the asymmetric beams adopt a strategy of different beamwidths for a specific link to reduce the beam alignment overheads and energy consumption. A good and thorough knowledge of the radio propagation characteristics is pivotal for further network deployment and optimization of wireless mobile communication systems. In this paper, a multiple-bounce beam channel model is proposed based on the ray-tracing considering the beamforming effects. Besides, a space–time–frequency (STF) power density profile reconstruction method is proposed. Relevant simulations are conducted to emulate an urban micro-cellular (UMi) street scenario at 28 GHz under the case of perfect beam alignment. On this basis, the beam-dependent small-scale fading properties (including STF power density profiles, delay spread, Doppler frequency shift spread, and angular spread) together with the large-scale fading characteristics (involving path loss and shadow fading) are fully investigated. Results reveal that the downlink of asymmetric beams presents more dispersions in contrast to the uplink in the STF domains. Furthermore, the shadow fading variances are asymmetric over different transceivers array element numbers.

Progressive Inter-Path Interference Cancellation Algorithm for Channel Estimation Using Orthogonal Time-Frequency Space.

Fractional delay-Doppler (DD) channel estimation in orthogonal time-frequency space (OTFS) systems poses a significant challenge considering the severe effects of inter-path interference (IPI). To this end, several algorithms have been extensively explored in the literature for accurate low-complexity channel estimation in both integer and fractional DD scenarios. In this work, we develop a variant of the state-of-the-art delay-Doppler inter-path interference cancellation (DDIPIC) algorithm that progressively cancels the IPI as estimates are obtained. The key advantage of the proposed approach is that it requires only a final refinement procedure reducing the complexity of the algorithm. Specifically, the time difference in latency between the proposed approach and the DDIPIC algorithm is almost proportional to the square of the number of estimated paths. Numerical results show that the proposed algorithm outperforms the other channel estimation schemes achieving lower normalized mean square error (NMSE) and bit error rate (BER).

Super-resolution delay-Doppler estimation for OTFS-based automotive radar

In this paper, we consider the problem of joint delay-Doppler estimation in an automotive radar based on orthogonal time frequency space (OTFS) modulation. We propose a super-resolution estimation approach that operates in the continuous domain and employs a two-dimensional atomic norm carrying delay and Doppler shift information to mitigate the off grid errors. The estimation task of target parameters is reformulated as a semidefinite program (SDP) problem. To solve this problem in an efficient way, we leverage the alternating direction method of multipliers (ADMM) and adopt an iterative procedure to obtain the optimal solution. The effectiveness of the proposed method is confirmed by theoretical analyses. Numerical results are presented to demonstrate the superior performance of the proposed method in comparison with the state-of-the-arts.

Cooperative transmission of UAV swarm using orthogonal time–frequency space modulation

Unmanned aerial vehicles (UAVs) emerge as versatile aerial nodes capable of dynamically filling coverage gaps and enabling mission-critical communication based on their mobile nature. UAV swarms, characterized by the coordinated operation of multiple drones, are employed for a wide range of applications such as surveillance, environmental monitoring, precision farming, and autonomous delivery. While individual UAVs suffer from limited power, group transmissions of UAV swarms can enhance the data rate, reliability, and energy efficiency. However, their mobility may cause severe Doppler spread. The existing orthogonal frequency division multiplexing (OFDM) system exhibits limitations such as susceptibility to the Doppler effect in high-speed mobile environments. To address this issue, orthogonal time–frequency space (OTFS)-aided cooperative transmission (CT) for UAV swarms is considered, which can surmount the aforementioned limitations. The results show the BER improvement of the order of 103 at the SNR value of 10 dB when OTFS modulation is utilized and even better at the higher SNR values. Furthermore, the analytical framework of OTFS-based CT is presented by identifying the key design considerations on the subcarrier spacing, the number of symbols, and the number of subcarriers, which are subject to the maximum speed of the UAV and the cluster size of the UAV swarm. These results provide a significant platform for advancing research in the field of UAV-based CT, especially with the Doppler-resilient OTFS modulation.