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18 pages, 1050 KB  
Article
An Optimization Model Solution Method for Transient Voltage Stability Emergency Control in High-Voltage DC Receiving End
by Weigang Jin, Tao Lin, Jiawei Zhang, Jiayi Wang, Jun Li and Chen Li
Energies 2026, 19(12), 2926; https://doi.org/10.3390/en19122926 (registering DOI) - 21 Jun 2026
Viewed by 103
Abstract
In the context of the “dual-carbon” target, the large-scale integration of renewable energy sources leads to an increased risk of transient voltage instability at the high voltage direct current (HVDC) transmission receiving end. The HVDC transmission system possesses fast and accurate power regulation [...] Read more.
In the context of the “dual-carbon” target, the large-scale integration of renewable energy sources leads to an increased risk of transient voltage instability at the high voltage direct current (HVDC) transmission receiving end. The HVDC transmission system possesses fast and accurate power regulation capability. After a fault occurs near the inverter station, reducing the DC current enables the reactive power from the compensation devices to be released and injected into the receiving-end power grid, thereby providing emergency voltage support for the receiving-end grid. To reduce control costs, an optimization model constrained by transient voltage violation is established, and the DC current modulation is acquired via an online solution. To maintain system stability and meet the requirements of online applications, it is crucial to rapidly solve the optimization model based on the grid operating mode and contingency information to update the emergency control strategy table in the special protection system (SPS). Conventional global orthogonal collocation (GOC) and adaptive orthogonal collocation (AOC)-based solution methods transform the optimization model in the continuous time domain into a nonlinear programming (NLP) problem for solution, which addresses the low efficiency of traditional rolling optimization. However, the GOC- and AOC-based solution methods improve the discretization accuracy of the model by pursuing global uniform densification of collocation points, making it difficult to balance solution accuracy and solution efficiency. To this end, this paper proposes an efficient interval partition dynamic adaptive orthogonal collocation (IP-DAOC)-based solution method. Firstly, the overall optimization time window is interval-partitioned into multiple initial intervals, and an interval-partitioned transient voltage stability emergency control optimization model is established. Furthermore, the interval length and the number of collocation points are dynamically adjusted according to the curvature of interpolation polynomials at collocation points in different intervals. Finally, after interval adjustment, the dynamic equations discretized in adjacent intervals are made continuous by reconstructing the differential matrix. This solution method reduces the total number of collocation points, thereby decreasing the scale of the NLP problem and narrowing the search space, significantly improving solution efficiency while ensuring solution accuracy. To verify the effectiveness of the proposed solution method, simulations are carried out on a modified IEEE 14-bus system. The results are compared with those of the traditional GOC- and AOC-based solution methods, which further demonstrate the superiority of the proposed solution method. Full article
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27 pages, 4791 KB  
Article
Combining Fast Orthogonal Search with Deep Learning to Improve Low-Cost IMU Signal Accuracy
by Jialin Guan, Eslam Mounier, Umar Iqbal and Michael J. Korenberg
Sensors 2026, 26(8), 2300; https://doi.org/10.3390/s26082300 - 8 Apr 2026
Viewed by 1453
Abstract
Inertial measurement units (IMUs) in low-cost navigation systems suffer from significant drift and noise errors due to sensor biases, scale factor instability, and nonlinear stochastic noise. This paper proposes a hybrid error compensation approach that combines Fast Orthogonal Search (FOS), a nonlinear system [...] Read more.
Inertial measurement units (IMUs) in low-cost navigation systems suffer from significant drift and noise errors due to sensor biases, scale factor instability, and nonlinear stochastic noise. This paper proposes a hybrid error compensation approach that combines Fast Orthogonal Search (FOS), a nonlinear system identification technique, with deep Long Short-Term Memory (LSTM) neural networks to improve IMU signal accuracy in GNSS-denied navigation. The FOS algorithm efficiently models deterministic error patterns (such as bias drift and scale factor errors) using a small training dataset, while the LSTM learns the IMU’s complex time-dependent error dynamics from much longer training data. In the proposed method, FOS is first used to predict the output of a high-end IMU based on that of a low-end IMU, and the trained FOS model is then used to extend the training data for an LSTM-based predictor. We demonstrate the efficacy of this FOS–LSTM hybrid on real vehicular IMU data by training with a limited segment of high-precision reference measurements and testing on extended operation periods. The hybrid model achieves high predictive accuracy for predicting the high-end signal based on the low-end signal, with a mean squared error below 0.1% and yields more stable velocity estimates than models using FOS or LSTM alone. Although long-term position drift is not fully eliminated, the proposed method significantly reduces short-term uncertainty in the inertial solution. These results highlight a promising synergy between model-based system identification and data-driven learning for sensor error calibration in navigation systems. Key contributions include FOS-based pseudo-label bootstrapping for data-efficient LSTM training and a navigation-level evaluation illustrating how signal correction impacts dead reckoning drift. Full article
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16 pages, 3532 KB  
Article
A Fast Method for Estimating Generator Matrixes of BCH Codes
by Shunan Han, Yuanzheng Ge, Yu Shi and Renjie Yi
Electronics 2026, 15(1), 244; https://doi.org/10.3390/electronics15010244 - 5 Jan 2026
Cited by 2 | Viewed by 499
Abstract
The existing methods used for estimating generator matrixes of BCH codes, which are based on Galois Field Fourier transforms, need to exhaustively test all the possible codeword lengths and corresponding primitive polynomials. With the increase of codeword length, the search space exponentially expands. [...] Read more.
The existing methods used for estimating generator matrixes of BCH codes, which are based on Galois Field Fourier transforms, need to exhaustively test all the possible codeword lengths and corresponding primitive polynomials. With the increase of codeword length, the search space exponentially expands. Consequently, the computational complexity of the estimation scheme becomes very high. To overcome this limitation, a fast estimation method is proposed based on Gaussian elimination. Firstly, the encoded bit stream is reshaped into a matrix according to the assumed codeword length. Then, by using Gaussian elimination, the bit matrix is simplified as the upper triangle form. By testing the independent columns of the upper triangle matrix, the assumed codeword length is judged to be right or not. Simultaneously, by using an augmented matrix, the parity check matrix of a BCH code can be estimated from the simplification result in the procedure of Gaussian elimination. Furthermore, the generator matrix is estimated by using the orthogonality between the generator matrix and parity check matrix. To improve the performance of the proposed method in resisting bit errors, soft-decision data is adopted to evaluate the reliability of received bits, and reliable bits are selected to construct the matrix to be analyzed. Experimental results indicate that the proposed method can recognize BCH codes effectively. The robustness of our method is acceptable for application, and the computation required is much less than the existing methods. Full article
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17 pages, 1109 KB  
Review
Birefringence of the Human Cornea: A Review
by Sudi Patel, Larysa Tutchenko and Igor Dmytruk
Vision 2025, 9(4), 90; https://doi.org/10.3390/vision9040090 - 28 Oct 2025
Viewed by 1591
Abstract
Background: This paper aims to provide an overview of corneal birefringence (CB), systematize the knowledge and current understanding of CB, and identify difficulties associated with introducing CB into mainstream clinical practice. Methods: Literature reviews were conducted, seeking articles focused on CB published between [...] Read more.
Background: This paper aims to provide an overview of corneal birefringence (CB), systematize the knowledge and current understanding of CB, and identify difficulties associated with introducing CB into mainstream clinical practice. Methods: Literature reviews were conducted, seeking articles focused on CB published between the early 19th century and the present time. Secondary-level searches were made examining relevant publications referred to in primary-level publications, ranging back to the early 17th century. The key search words were “corneal birefringence” and “non-invasive measurements”. Results: CB was first recorded by Brewster in 1815. Orthogonally polarized rays travel at different speeds through the cornea, creating a slow axis and a fast axis. The slow axis aligns with the pattern of most corneal stromal collagen fibrils. In vivo, it is oriented along the superior temporal–inferior nasal direction at an angle of about 25° (with an approximate range of −54° to 90°) from the horizontal. CB has been reported to (i) influence the estimation of retinal nerve fiber layer thickness; (ii) be affected by corneal interventions; (iii) be altered in keratoconus; (iv) vary along the depth of the cornea; and (v) be affected by intra-ocular pressure. Conclusions: Under precisely controlled conditions, capturing the CB pattern is the first step in a non-destructive process used to model the ultra-fine structure of the individual cornea, and changes thereof, in vivo. Full article
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25 pages, 4050 KB  
Article
A Multi-Objective Optimization Study of Supply Air Parameters in a Supersonic Aircraft Cabin Environment Combined with Fast Calculation
by Guo Yu, Sajawal Nazar, Fei Li, Yuxin Wu, Zhu He and Xiaodong Cao
Atmosphere 2025, 16(9), 1005; https://doi.org/10.3390/atmos16091005 - 25 Aug 2025
Cited by 1 | Viewed by 1134
Abstract
Supersonic cabins are characterized by high heat flux and high occupant density, which can adversely affect passenger comfort, health, and energy efficiency. This study proposed a multi-objective optimization framework for determining supply air parameters in a supersonic aircraft cabin, evaluating the performances of [...] Read more.
Supersonic cabins are characterized by high heat flux and high occupant density, which can adversely affect passenger comfort, health, and energy efficiency. This study proposed a multi-objective optimization framework for determining supply air parameters in a supersonic aircraft cabin, evaluating the performances of different optimization methods. The optimization focused on three design objectives: thermal comfort (PMV), air freshness (air age), and the temperature differential between the supply and exhaust air. Two fast calculation methods—Proper Orthogonal Decomposition (POD) and Artificial Neural Networks (ANN)—were compared alongside two optimization algorithms: Multi-Objective Genetic Algorithm (MOGA) and Pareto search. The results indicate that the POD method has a smaller relative root mean square error compared to the ANN method. The relative root mean square error of the ANN method in predicting PMV is 2.7 times higher than the POD method and 3.9 times higher in air age prediction. The Pareto search algorithm outperformed MOGA in computational efficiency, generating 3.3 times more Pareto-optimal solutions in less time. The entropy weight method was used to assign weight for both optimization algorithms, revealing that neither algorithm achieved universally optimal performance across all objectives. Therefore, selecting the best solution requires aligning optimization outcomes with specific design priorities. Full article
(This article belongs to the Section Atmospheric Techniques, Instruments, and Modeling)
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17 pages, 4256 KB  
Article
An Image-Based Concrete-Crack-Width Measurement Method Using Skeleton Pruning and the Edge-OrthoBoundary Algorithm
by Chunxiao Li, Hui Qin, Yu Tang, Hailiang Zhao, Shengshen Pan, Jinbo Liu and Wenjiang Luo
Buildings 2025, 15(14), 2489; https://doi.org/10.3390/buildings15142489 - 16 Jul 2025
Cited by 3 | Viewed by 2636
Abstract
The accurate measurement of a crack width in concrete infrastructure is essential for structural safety assessment and maintenance. However, existing image-based methods either suffer from overestimation in complex geometries or are computationally inefficient. This paper proposes a novel hybrid approach combining a fast [...] Read more.
The accurate measurement of a crack width in concrete infrastructure is essential for structural safety assessment and maintenance. However, existing image-based methods either suffer from overestimation in complex geometries or are computationally inefficient. This paper proposes a novel hybrid approach combining a fast skeleton-pruning algorithm and a crack-width measurement technique called edge-OrthoBoundary (EOB). The skeleton-pruning algorithm prunes the skeleton, viewed as the longest branch in a tree structure, using a depth-first search (DFS) approach. Additionally, an intersection removal algorithm based on dilation replaces the midpoint circle algorithm to segment the crack skeleton into computable parts. The EOB method combines the OrthoBoundary and edge shortest distance (ESD) techniques, effectively correcting the propagation direction of the skeleton points while accounting for their width. The validation of real cracks shows the skeleton-pruning algorithm’s effectiveness, eliminating the need for a specified threshold and reducing time complexity. Experimental results with both actual and synthetic cracks demonstrate that the EOB method achieves the smallest RMS, MAE, and R values, confirming its accuracy and stability compared to the orthogonal projection (OP), OrthoBoundary, and ESD methods. Full article
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17 pages, 11217 KB  
Article
Research on Feature Extraction Method and Process Optimization of Rolling Bearing Faults Based on Electrostatic Monitoring
by Ruochen Liu, Han Yin, Jianzhong Sun and Lanchun Zhang
Lubricants 2025, 13(4), 178; https://doi.org/10.3390/lubricants13040178 - 12 Apr 2025
Cited by 1 | Viewed by 948
Abstract
Electrostatic detection is a highly accurate way to monitor system performance failures at an early stage. However, due to the weak electrostatic signal, it can be easily interfered with under complex real-world conditions, leading to a reduction in its monitoring capability. During the [...] Read more.
Electrostatic detection is a highly accurate way to monitor system performance failures at an early stage. However, due to the weak electrostatic signal, it can be easily interfered with under complex real-world conditions, leading to a reduction in its monitoring capability. During the electrostatic monitoring of rolling bearings, noise can easily drown out the effective signal, making it difficult to extract fault characteristics. In order to solve this problem, a sparse representation based on cluster-contraction stagewise orthogonal matching pursuit (CcStOMP) is proposed to extract the fault features in the electrostatic signals of rolling bearings. The method adds a clustering contraction mechanism to the stagewise orthogonal matching pursuit (StOMP) algorithm, performs secondary filtering based on atom similarity clustering on the selected atoms in the atom search process, updates the support set, and finally solves the weights and updates the residuals, so as to reconstruct the original electrostatic signals and extract the fault feature components of rolling bearings. The method maintains fast convergence while analysing the extraction effect by comparing the measured signals of rolling bearing outer ring and bearing roller faults with the traditional StOMP algorithm, and the results show that the CcStOMP algorithm has obvious advantages in accurately extracting the fault features in the electrostatic monitoring signals of rolling bearings. Full article
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22 pages, 14988 KB  
Article
Channel Estimation for Underwater Acoustic Communications in Impulsive Noise Environments: A Sparse, Robust, and Efficient Alternating Direction Method of Multipliers-Based Approach
by Tian Tian, Kunde Yang, Fei-Yun Wu and Ying Zhang
Remote Sens. 2024, 16(8), 1380; https://doi.org/10.3390/rs16081380 - 13 Apr 2024
Cited by 11 | Viewed by 4255
Abstract
Channel estimation in Underwater Acoustic Communication (UAC) faces significant challenges due to the non-Gaussian, impulsive noise in ocean environments and the inherent high dimensionality of the estimation task. This paper introduces a robust channel estimation algorithm by solving an [...] Read more.
Channel estimation in Underwater Acoustic Communication (UAC) faces significant challenges due to the non-Gaussian, impulsive noise in ocean environments and the inherent high dimensionality of the estimation task. This paper introduces a robust channel estimation algorithm by solving an l1l1 optimization problem via the Alternating Direction Method of Multipliers (ADMM), effectively exploiting channel sparsity and addressing impulsive noise outliers. A non-monotone backtracking line search strategy is also developed to improve the convergence behavior. The proposed algorithm is low in complexity and has robust performance. Simulation results show that it exhibits a small performance deterioration of less than 1 dB for Channel Impulse Response (CIR) estimation in impulsive noise environments, nearly matching its performance under Additive White Gaussian Noise (AWGN) conditions. For Delay-Doppler (DD) doubly spread channel estimation, it maintains Bit Error Rate (BER) performance comparable to using ground truth channel information in both AWGN and impulsive noise environments. At-sea experimental validations for channel estimation in Orthogonal Frequency Division Multiplexing (OFDM) systems further underscore the fast convergence speed and high estimation accuracy of the proposed method. Full article
(This article belongs to the Special Issue Advancement in Undersea Remote Sensing II)
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14 pages, 456 KB  
Article
Using Feature Extraction to Perform Equipment Health Monitoring on Ship-Radiated Noise
by Nicholas Marasco, Haidy Elghamrawy and Donald McGaughey
Acoustics 2023, 5(4), 1180-1193; https://doi.org/10.3390/acoustics5040067 - 18 Dec 2023
Cited by 2 | Viewed by 2905
Abstract
The current state of the art in hydroacoustics research employs a variety of feature extraction techniques with the goal of accurately classifying a ship based on its radiated noise. These techniques are capable of accuracy in excess of 95%. A question arises as [...] Read more.
The current state of the art in hydroacoustics research employs a variety of feature extraction techniques with the goal of accurately classifying a ship based on its radiated noise. These techniques are capable of accuracy in excess of 95%. A question arises as to whether similar techniques could be applied to a known vessel to identify and monitor individual systems from the ship’s noise. In this paper, the fast orthogonal search algorithm is used as a basis for a feature extraction and classification algorithm. This algorithm is applied to real recordings of ship-radiated noise and is shown to be capable of identifying the running status of a subset of the ship’s systems, providing a proof of concept for the detection and monitoring of a ship’s systems based solely on the ships hydroacoustic noise. Full article
(This article belongs to the Special Issue Vibration and Noise)
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18 pages, 13806 KB  
Article
Transformer-Based Visual Object Tracking with Global Feature Enhancement
by Shuai Wang, Genwen Fang, Lei Liu, Jun Wang, Kongfen Zhu and Silas N. Melo
Appl. Sci. 2023, 13(23), 12712; https://doi.org/10.3390/app132312712 - 27 Nov 2023
Cited by 5 | Viewed by 3227
Abstract
With the rise of general models, transformers have been adopted in visual object tracking algorithms as feature fusion networks. In these trackers, self-attention is used for global feature enhancement. Cross-attention is applied to fuse the features of the template and the search regions [...] Read more.
With the rise of general models, transformers have been adopted in visual object tracking algorithms as feature fusion networks. In these trackers, self-attention is used for global feature enhancement. Cross-attention is applied to fuse the features of the template and the search regions to capture the global information of the object. However, studies have found that the feature information fused by cross-attention does not pay enough attention to the object region. In order to enhance cross-attention for the object region, an enhanced cross-attention (ECA) module is proposed for global feature enhancement. By calculating the average attention score for each position in the fused feature sequence and assigning higher weights to the positions with higher attention scores, the proposed ECA module can improve the feature information in the object region and further enhance the matching accuracy. In addition, to reduce the computational complexity of self-attention, orthogonal random features are introduced to implement a fast attention operation. This decomposes the attention matrix into the product of a random non-linear function between the original query and key. This module can reduce the spatial complexity and improve the inference speed by avoiding the explicit construction of a quadratic attention matrix. Finally, a tracking method named GFETrack is proposed, which comprises a Siamese backbone network and an enhanced attention mechanism. Experimental results show that the proposed GFETrack achieves competitive results on four challenging datasets. Full article
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18 pages, 5688 KB  
Article
Improved GNSS Ambiguity Fast Estimation Reduction Algorithm
by Xinzhong Li, Yongliang Xiong, Weiwei Chen, Shaoguang Xu and Rui Zhang
Sensors 2023, 23(20), 8568; https://doi.org/10.3390/s23208568 - 18 Oct 2023
Cited by 4 | Viewed by 2128
Abstract
The fast and accurate solution of integer ambiguity is the key to achieve GNSS high-precision positioning. Based on the lattice theory of high-dimensional ambiguity solving, the reduction time consumption is much larger than the search time consumption, and it is especially important to [...] Read more.
The fast and accurate solution of integer ambiguity is the key to achieve GNSS high-precision positioning. Based on the lattice theory of high-dimensional ambiguity solving, the reduction time consumption is much larger than the search time consumption, and it is especially important to improve the efficiency of the lattice basis reduction algorithm. The Householder QR decomposition with minimal column pivoting is utilized to pre-sort the basis vectors and reduce the number of basis vector exchanges during the reduction process by partial size reduction and relaxing the basis vector exchange condition to improve the reduction efficiency of the LLL algorithm. The improved algorithm is validated using simulated and measured data, respectively, and the performance advantages and disadvantages of the improved algorithm are evaluated from the perspectives of the extent of reduction basis orthogonality and the quality of reduction basis size reduction. The results show that the improved LLL algorithm can significantly reduce the number of basis vector exchanges and the reduction time consumption. The HSLLL and PSLLL algorithms with the Siegel condition as the basis vector exchange condition have a better reduction effect, but are slightly less stable. The PLLLR algorithm significantly improves the search ambiguity resolution efficiency, which is conducive to the rapid realization of ambiguity resolution. Full article
(This article belongs to the Topic GNSS Measurement Technique in Aerial Navigation)
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18 pages, 5227 KB  
Article
Fast Synthesis Method for High-Dimensional Electromagnetic Bandgap Structure Using Deep Neural Network for Power/Ground Noise Suppression
by Seongbo Sim and Myunghoi Kim
Electronics 2023, 12(11), 2399; https://doi.org/10.3390/electronics12112399 - 25 May 2023
Cited by 2 | Viewed by 1736
Abstract
A deep neural network (DNN)-based method is proposed for the fast synthesis of a high-dimensional electromagnetic bandgap structure (HD-EBG) suppressing the power/ground noise in high-speed packages and printed circuit boards (PCBs). In recent EBG structures, a highly flexible design with high dimensionality is [...] Read more.
A deep neural network (DNN)-based method is proposed for the fast synthesis of a high-dimensional electromagnetic bandgap structure (HD-EBG) suppressing the power/ground noise in high-speed packages and printed circuit boards (PCBs). In recent EBG structures, a highly flexible design with high dimensionality is required, which is challenging to rapidly achieve an optimal solution. The proposed synthesis method is developed to solve this issue efficiently. The DNN hyperparameter optimization (HPO) associated with the HD-EBG structure is devised using the orthogonal array of the Taguchi method. By using this approach, the search space for HPO is reduced. For the efficient synthesis of the HD-EBG structure, an inverse modeling approach based on a DNN forward model and genetic algorithm optimization is proposed. The proposed DNN inverse modeling (DIM) is applied to two design examples where the HD-EBG structures with a constant fractional bandwidth and stopband bandwidth extension are synthesized. In the demonstration cases, the proposed DIM achieves the fast and accurate synthesis of the HD-EBG structures compared to the conventional method. With the proposed method, the synthesis time is maximally reduced up to 99.8% compared to conventional synthesis based on the forward model of full-wave simulation. Full article
(This article belongs to the Section Microwave and Wireless Communications)
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17 pages, 5871 KB  
Technical Note
Passive Location for 5G OFDM Radiation Sources Based on Virtual Synthetic Aperture
by Tong Zhang, Xin Zhang and Qiang Yang
Remote Sens. 2023, 15(6), 1695; https://doi.org/10.3390/rs15061695 - 21 Mar 2023
Cited by 10 | Viewed by 4635
Abstract
Passive location technology has been greatly developed because of its low power consumption, long detection distance, good concealment, and strong anti-interference ability. Orthogonal frequency-division multiplexing (OFDM) is an efficient multi-carrier transmission technology, which is an important signal form of 5G communication. Researching passive [...] Read more.
Passive location technology has been greatly developed because of its low power consumption, long detection distance, good concealment, and strong anti-interference ability. Orthogonal frequency-division multiplexing (OFDM) is an efficient multi-carrier transmission technology, which is an important signal form of 5G communication. Researching passive locations for OFDM signals can realize the location of base stations, which is of great significance in the military. Space-borne passive location technology has a contradiction between wide coverage and high precision. Therefore, a single-satellite passive location algorithm for OFDM radiation sources based on the virtual synthetic aperture is proposed. The algorithm introduces virtual synthetic aperture technology, using antenna movement to accumulate data coherently over a long time period and synthesizing a long azimuth virtual aperture. In addition, it utilizes fast Fourier transform (FFT) to extract phase information at a specific frequency based on the multi-carrier modulation technology of the OFDM signal. Pilot technology of the communication system is used for phase compensation and noise reduction. Thus, the azimuth linear frequency modulation (LFM) signal containing the location information of the radiation source is obtained. The radiation source location can be obtained by range searching and azimuth focusing. Simulation results verify the effectiveness of the algorithm and show that the algorithm can realize high-precision and wide-coverage location for the OFDM radiation sources using a single antenna, turning the hardware structure into software to reduce the cost and complexity of the system. Full article
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17 pages, 676 KB  
Article
Electromagnetic Spectrum Allocation Method for Multi-Service Irregular Frequency-Using Devices in the Space–Air–Ground Integrated Network
by Yongchao Meng, Peihan Qi, Qian Lei, Zhengyu Zhang, Jinyang Ren and Xiaoyu Zhou
Sensors 2022, 22(23), 9227; https://doi.org/10.3390/s22239227 - 27 Nov 2022
Cited by 6 | Viewed by 2434
Abstract
The management and allocation of electromagnetic spectrum resources is the inner driving force of the construction of the space–air–ground integrated network. Existing spectrum allocation methods are difficult to adapt to the scenario where the working bandwidth of multi-service frequency-using devices is irregular and [...] Read more.
The management and allocation of electromagnetic spectrum resources is the inner driving force of the construction of the space–air–ground integrated network. Existing spectrum allocation methods are difficult to adapt to the scenario where the working bandwidth of multi-service frequency-using devices is irregular and the working priorities are different. In this paper, an orthogonal genetic algorithm based on the idea of mixed niches is proposed to transform the problem of frequency allocation into the optimization problem of minimizing the electromagnetic interference between frequency-using devices in the integrated network. At the same time, a system model is constructed that takes the minimum interference effect of low-priority-to-high-priority devices as the objective function and takes the protection frequency and natural frequency as the constraint conditions. In this paper, we not only introduce the thought of niches to improve the diversity of the population but also use an orthogonal uniform crossover operator to improve the search efficiency. At the same time, we use a standard genetic algorithm and a micro genetic algorithm to optimize the model. The global searchability and local search precision of the proposed algorithm are all improved. Simulation results show that compared with the existing methods, the proposed algorithm has the advantages of fast convergence, strong stability and good optimization effect. Full article
(This article belongs to the Special Issue Dynamic Spectrum Sharing for Future Wireless Systems)
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14 pages, 1799 KB  
Article
MLTSP: New 3D Framework, Based on the Multilayer Tensor Spectrum Pyramid
by Roumiana A. Kountcheva, Rumen P. Mironov and Roumen K. Kountchev
Symmetry 2022, 14(9), 1909; https://doi.org/10.3390/sym14091909 - 12 Sep 2022
Cited by 2 | Viewed by 1994
Abstract
A tensor representation structure based on the multilayer tensor spectrum pyramid (MLTSP) is introduced in this work. The structure is “truncated”, i.e., part of the high-frequency spectrum coefficients is cut-off, and on the retained low-frequency coefficients, obtained at the output of each pyramid [...] Read more.
A tensor representation structure based on the multilayer tensor spectrum pyramid (MLTSP) is introduced in this work. The structure is “truncated”, i.e., part of the high-frequency spectrum coefficients is cut-off, and on the retained low-frequency coefficients, obtained at the output of each pyramid layer, a hierarchical tensor SVD (HTSVD) is applied. This ensures a high concentration of the input tensor energy into a small number of decomposition components of the tensors obtained at the coder output. The implementation of this idea is based on a symmetrical coder/decoder. An example structure for a cubical tensor of size 8 × 8 × 8, which is represented as a two-layer tensor spectrum pyramid, where 3D frequency-ordered fast Walsh–Hadamard transform and HTSVD are used, is given in this paper. The analysis of the needed mathematical operations proved the low computational complexity of the new approach, due to a lack of iterative calculations. The high flexibility of the structure in respect to the number of pyramid layers, the kind of used orthogonal transforms, the number of retained spectrum coefficients, and HTSVD components, permits us to achieve the desired accuracy of the restored output tensor, imposed by the application. Furthermore, this paper presents one possible application for 3D object searches in a tensor database. In this case, to obtain the invariant representation of the 3D objects, in the spectrum pyramid, the 3D modified Mellin–Fourier transform is embedded, and the corresponding algorithm is shown. Full article
(This article belongs to the Section Computer)
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