Search

In this study, a classification algorithm based on complex number feature is proposed. Specifically, the SVM framework is reformulated, so each example would be classified in the unitary space. The cost function is redefined by considering the maximum margin of real and imaginary units of the complex number feature at the same time. The cost function is based on the expectation of the hinge loss, and its derivatives can be calculated in closed forms. Using a stochastic gradient descent (SGD) algorithm, this method allows for efficient implementation. For complex number feature, the example uncertainty is modeled by a sample preprocessing method based on within-class Euclidean distance Gaussian distribution sample (DGS). In addition, a complex number feature selection method based on improved hybrid discrimination analysis (HDA) is proposed by considering the correlation between real and imaginary units of complex number feature. The proposed classification algorithm is tested on synthetic data and three publicly available and popular datasets, namely, MNIST, WDBC, and Voc2012. Experimental results verify the effectiveness of the proposed method. The codes are available: https://github.com/luckysomebody/paper-code.

In this article, we consider the problem of planar graph-based simultaneous localization and mapping (SLAM) that involves both poses of the autonomous agent and positions of observed landmarks. We present complex (CPL)-SLAM, an efficient and certifiably correct algorithm to solve planar graph-based SLAM using the complex number representation. We formulate and simplify planar graph-based SLAM as the maximum likelihood estimation on the product of unit complex numbers, and relax this nonconvex quadratic complex optimization problem to convex complex semidefinite programming (SDP). Furthermore, we simplify the corresponding complex SDP to Riemannian staircase optimization (RSO) on the complex oblique manifold that can be solved with the Riemannian trust region method. In addition, we prove that the SDP relaxation and RSO simplification are tight as long as the noise magnitude is below a certain threshold. The efficacy of this work is validated through applications of CPL-SLAM and comparisons with existing state-of-the-art methods on planar graph-based SLAM, which indicates that our proposed algorithm is capable of solving planar graph-based SLAM certifiably, and is more efficient in numerical computation and more robust to measurement noise than existing state-of-the-art methods. The C++ code for CPL-SLAM is available at https://github.com/MurpheyLab/CPL-SLAM. [ABSTRACT FROM AUTHOR]

The computation of the arctangent of a complex number, i.e., the atan2 function, is frequently needed in hardware systems that could profit from an optimized operator. In this brief, we present a novel method to compute the atan2 function and a hardware architecture for its implementation. The method is based on a first stage that performs a coarse approximation of the atan2 function and a second stage that improves the output accuracy by means of a lookup table. We present results for fixed-point implementations in a field-programmable gate array device, all of them guaranteeing last-bit accuracy, which provide an advantage in latency, speed, and use of resources, when compared with well-established fixed-point options. [ABSTRACT FROM PUBLISHER]

We provide a rigorous account of the equivalence between the complex-valued widely linear estimation method and the quaternion involution widely linear estimation method with their vector-valued real linear estimation counterparts. This is achieved by an account of degrees of freedom and by providing matrix mappings between a complex variable and an isomorphic bivariate real vector, and a quaternion variable versus a quadri-variate real vector. Furthermore, we show that the parameters in the complex-valued linear estimation method, the complex-valued widely linear estimation method, the quaternion linear estimation method, the quaternion semi-widely linear estimation method, and the quaternion involution widely linear estimation method include distinct geometric structures imposed on complex numbers and quaternions, respectively, whereas the real-valued linear estimation methods do not exhibit any structure. This key difference explains, both in theoretical and practical terms, the advantage of estimation in division algebras (complex, quaternion) over their multivariate real vector counterparts. In addition, we discuss the computational complexities of the estimators of the hypercomplex widely linear estimation methods. [ABSTRACT FROM AUTHOR]

We propose an In-Memory Computing (IMC) scheme to implement Fast Fourier Transform (FFT) for noise signal processing using flash memory. By taking advantage of the algorithms of complex number calculation and butterfly operation in FFT, the analyses of low-frequency noise (LFN) and random telegraphy noise (RTN) signals using flash-based IMC were demonstrated successfully, showing the frequency properties of 1/ ${f}$ and 1/ ${f}$ 2, respectively, and matching well with the Matlab numerical calculation. An energy efficiency of 2.7 TOPS/W has been achieved with a dynamic power of 27.7 mW. Our proposed IMC scheme provides an efficient way to enable FFT using a hardware solution and is extendable for other important applications such as image processing and voice recognition. [ABSTRACT FROM AUTHOR]

Generating Rayleigh fading is a well investigated subject. However, most existing methods are fundamentally based on a sum-of-sinusoids, hence have a high computational complexity and become impractical when modelling massive MIMO systems. In this letter we present a novel recursive complex number multiplication method to generate Rayleigh fading for discrete signals. The computational complexity of the method is 75-94% less than all prominent sum-of-sinusoid methods. It also preserves the theoretically expected Bessel autocorrelation of a fading channel, zero cross-correlation between different fading channels and the power spectral density. [ABSTRACT FROM AUTHOR]

Reduced biquaternion is a four dimensional hyper–complex number which is commutative algebra and an extension of complex. Due to this property, the corresponding fast algorithm is designed in time frequency analysis which can better fit the convolution theorem than the non-commutative quaternion. In addition, the reduced biquaternion can be interpreted as a single point in 2-dimensional hyperbolic space with its algebraic structure which has more capacity and variable ability than the Euclidean space. However, the algebra properties of the reduced biquaternion have not yet been well explored in the deep convolutional neural network. In this paper, we develop a new deep network structure, namely reduced biquaternion valued convolutional neural network (RQV-CNN). The proposed RQV-CNN includes basic modules of reduced biquaternion convolution layer and fully connection layer. Extensive experiments on color image classification and color image denoising are conducted to evaluate the promising performance of the RQV-CNN framework. The results show that RQV-CNN outperforms the real-valued CNN (RV-CNN), complex-valued CNN (CV-CNN), and quaternion-valued CNN (QV-CNN) with same structures. The source code can be found at https://github.com/tasteimage/RQVCNN. [ABSTRACT FROM AUTHOR]

The determination of complex elastic, piezoelectric, and dielectric coefficients of piezoelectric ceramics is important for precision engineering devices. Here, a novel method for determining the optimal material coefficients is presented. This method minimizes the average relative error in the values of conductance, susceptance, resistance, and reactance obtained from the 1-D model in the IEEE Standard (ANSI/IEEE Std 176-1987) and the experimental measurements of the first and second radial modes. Poisson’s ratio is assumed to be a complex number in addition to the elastic, piezoelectric, and dielectric coefficients in the present method. The global minimum of the average relative error is found by searching the minimum among all local minima of the average relative error, which are obtained with the Levenberg–Marquardt modification of Newton’s method from randomly chosen initial conditions. The optimal material coefficients of an APC 850 disk and an APC 855 disk are calculated with this method. The uncertainties in the optimal material coefficients are evaluated by calculating the minimum average relative error when the real or imaginary part of each coefficient is prescribed. [ABSTRACT FROM AUTHOR]

This article presents a new entry to the class of published algorithms for the fast computation of the arctangent of a complex number. Our method uses a look-up table (LUT) to reduce computational errors. We also show how to convert a large-sized LUT addressed by two variables to an equivalent-performance smaller-sized LUT addressed by only one variable. In addition, we demonstrate how and why the use of follow-on LUTs applied to other simple arctan algorithms produce unexpected and interesting results. [ABSTRACT FROM PUBLISHER]

This article proposes the Mamdani complex fuzzy inference system (Mamdani CFIS) to improve performance of the classical FIS and complex FIS. The applicability of the proposed CFIS is demonstrated by applying it to six commonly available datasets from UCI Machine Learning under the comparison with Mamdani FIS and the Adaptive Neuro Complex Fuzzy Inference System (ANCFIS). It is successfully proven that the proposed Mamdani CFIS is computationally less expensive and presents a more efficient method to handle time-series data and time-periodic phenomena, among all the fuzzy IS found thus far in the literature. Furthermore, the novelty of CFIS mainly lies in its implementation of the complex number throughout the entire procedures of computation. This gives much greater flexibility of implementing unexpected, nonlinear fluctuations. [ABSTRACT FROM AUTHOR]

It has long been known that the ellipse normally used to model the phase space extension of a beam in linear dynamics may be represented by a complex number which can be interpreted similar to a complex impedance in electrical circuits, so that classical electrical methods might be used for the design of such beam transport lines. However, this method has never been fully developed, and only the transport transformation of single particular elements, like drift spaces or quadrupoles, has been presented in the past. In this article, we complete the complex formalism of linear beam dynamics by obtaining a general differential equation and solving it, to show that the general transformation of a linear beam line is a complex Moebius transformation. This result opens the possibility of studying the effect of the beam line on complete regions of the complex plane and not only on a single point. Taking advantage of this capability of the formalism, we also obtain an important result in the theory of the transport through a periodic line, proving that the invariant points of the transformation are only a special case of a more general structure of the solution, which are the invariant circles of the one-period transformation. Among other advantages, this provides a new description of the betatron functions beating in case of a mismatched injection in a circular accelerator. [ABSTRACT FROM AUTHOR]

We propose an impedance-matching technique for metasurfaces generating evanescent fields with complex free-space impedance for subwavelength focusing. The proposed technique is mandatory for the subwavelength focusing far beyond the diffraction limit. First, we theoretically show the fact that the wave impedance becomes a complex number due to the generated evanescent fields and give an explicit form of the wave impedance as a ratio of local electric and magnetic fields. Then, we discuss the impedance-matching technique for the distributed complex wave impedance by a metasurface with a position-dependent impedance matrix. To demonstrate the proposed technique, we design a subwavelength focusing 1-D metasurface with the null-to-null beamwidth of one-twentieth of the free-space wavelength at 2.45 GHz, and its performance is verified by wave propagation simulations based on the equivalent circuit model. In order to further verify the validity of the proposed technique, a metasurface is implemented with the trilayer configuration, and the subwavelength focusing is experimentally demonstrated. [ABSTRACT FROM AUTHOR]

A Gaussian integer is a complex number whose real and imaginary parts are both integers. Meanwhile, a sequence is defined as perfect if and only if it has an ideal periodic auto-correlation function. This paper proposes a method for constructing sparse perfect Gaussian integer sequences (SPGISs) in which most of the sequence elements are zero. The proposed SPGISs are obtained by linearly combining four base sequences or their cyclic-shift equivalents using nonzero Gaussian integer coefficients of equal magnitudes. Each base sequence contains four nonzero elements belonging to the set \\pm 1, \pm j\. The number of nonzero elements of the constructed SPGISs depends on the choice of complex coefficients and cyclic shifts. However, each SPGIS has at most 16 nonzero elements, irrespective of the sequence length. A systematic investigation is performed into the properties of the SPGISs and their Fourier dual equivalents. Finally, a general expression is derived for a perfect Gaussian integer sequence (PGIS) of length $4n$, where $n$ is any positive integer and most of the sequence elements are nonzero. [ABSTRACT FROM AUTHOR]

This research centers on the application of the discrete-time Taylor–Fourier transform (DTTFT) algorithmic implementation for phasor estimation on a field-programmable gate array board. The system employs a finite impulse response structure of a digital Taylor–Fourier filter to extract amplitude and phase information. The hardware description utilizes a multiply accumulator architecture with only forty embedded 9-bit multiplier elements, achieving an 18-bit input–output resolution. Performance assessment involves signal analysis through FPGA-in-the-loop simulation in MATLAB/Simulink. Findings demonstrate that the DTTFT-based phasor estimator can be effectively characterized using VHDL code and implemented on an Intel D2-115 board. [ABSTRACT FROM AUTHOR]

Falcon is one of the promising digital-signature algorithms in NIST’s ongoing Post-Quantum Cryptography (PQC) standardization finalist. Computational efficiency regarding software and hardware is also the main criteria for PQC standardization. In this paper, we present an efficient Falcon software implementation on ARMv8 environment. Until now, most of the software optimization on PQC algorithms have been conducted on 32-bit ARM (Cortex-M4) and typical CPUs (Intel and AMD CPUs). However, ARMv8 including Cortex-A30, 50, and 70 series have been widely used for various IoT (Internet of Things) applications, Edge computing devices, and OBUs (On Board Units) in autonomous driving cars. For optimizing the performance of Falcon, we take full advantage of NEON engine which is a kind of parallel processing unit in ARMv8 MCU. The main computation in Falcon belongs to polynomial multiplications in Complex number domain and Integer domain. Typically, FFT (Fast Fourier Transformation)-based multiplication method and NTT (Number Theoriteic Transform)-based multiplication method have been widely used for efficient polynomial multiplications in Complex number domain and Integer domain, respectively. Thus, in order to enhance the overall performance of Falcon, we improve the FFT-based multiplication method and NTT-based multiplication method by utilizing NEON engine in ARMv8. Specifically, we parallelize the overall process (FFT/NTT transformation, pointwise multiplication, and inverse FFT/NTT transformation) of FFT-based polynomial multiplication method and NTT-based polynomial multiplication method with strategically utilizing the NEON engine and vector instructions. Furthermore, we minimize the number of redundant memory accesses during FFT/NTT-based polynomial multiplication by making the most of available registers in NEON engine. Through the proposed parallel FFT/NTT-based polynomial multiplications, the proposed Falcon software provides 15.1% (resp. 18.1%), 16.5% (resp. 17.1%), and 65.4% (resp. 69.4%) of performance improvement in keypair generation, signing, and verification at security level 1 (resp. 5) compared with the reference Falcon implementation submitted to the final round of NIST PQC competition. Furthermore, as far as we know, this is the first optimized implementation of Falcon on ARMv8 environment.

In this paper, simple methodologies of deep learning application to conventional multiple-input multiple-output (MIMO) communication systems are presented. The deep learning technologies with deep neural network (DNN) structure, emerging technologies in various engineering areas, have been actively investigated in the field of communication engineering as well. In the physical layer of conventional communication systems, there are practical challenges of application of DNN: calculating complex number in DNN and designing proper DNN structure for a specific communication system model. This paper proposes and verifies simple solutions for the difficulty. First, we apply a basic DNN structure for signal detection of one-tap MIMO channel. Second, convolutional neural network (CNN) and recurrent neural network (RNN) structures are presented for MIMO system with multipath fading channel. Our DNN structure for one-tap MIMO channel can achieve the optimal maximum likelihood detection performance, and furthermore, our CNN and RNN structures for multipath fading channel can detect the transmitted signal properly. [ABSTRACT FROM AUTHOR]

Inductive particle sensors are widely used in online wear condition monitoring. Understanding the behavior of a particle magnetized in an alternating current (ac) magnetic field and the associated sensing mechanism is fundamental to identifying the particle size, improving the detection precision and enhancing the sensor performance. Here, we first establish a particle magnetization model related to particle conductivity, permeability, diameter, and field frequency. Next, an expression for particle detection using inductance is derived that consists of a product of the particle volume, complex particle susceptibility, and particle sensor sensitivity. The derived formulas and experiments reveal that the output of the inductive sensor is a complex number. Therefore, a vector analysis method is proposed for inductive particle detection. The sensitivities of various sensors are discussed. Experiments are conducted using milliparticles and microparticles in various positions relative to sensors. A comparison of the calculation results with the experimental results exhibits satisfactory agreement. Consequently, an optimized rectangular cross-section of coils is proposed. This study provides a theoretical basis for the design and optimization of particle sensors based on magnetic principles. [ABSTRACT FROM AUTHOR]

In coherent optics transmission systems, the digital signal processor (DSP) application-specific integrated circuit (ASIC) is the most power-hungry part of the optical transceiver. Already in the edge of transistor technology, to achieve the power budget, we must look for opportunities to further optimize the designs. This letter explores a dynamic duty cycle for reducing the consumption in the pipeline of such DSP ASICs. We exploit the characteristics of estimator algorithms to introduce a dynamic duty cycle, reducing the mean consumption of designs originally constrained only for worst-case scenarios. We present the methodology to implement duty cycle control using the carrier frequency offset estimator (CFE) algorithm as case study, achieving in simulation level from 22% to 74% power consumption reduction in this algorithm, varying on-chip operation conditions. [ABSTRACT FROM AUTHOR]

The detection of metal particles in oil is of great significance to the fault diagnosis of mechanical equipment. Real domain detection methods cannot simultaneously identify the sizes and materials of particles. Because a metal particle in an alternating magnetic field induces a complex domain signal whose strength relates to the particle properties, this article introduces a double lock-in amplifier circuit (DLAC) into a triple-coil inductive particle sensor to detect the complex domain signal under noise interference conditions. Furthermore, various sizes of red copper, brass, aluminum, iron, and type 403 steel particles are chosen as the experimental materials. For the first time, the complex domain signals induced by the five kinds of particles are detected. Hence, in the complex plane, a method is proposed to identify the size and material of a particle based on the amplitude and phase of these signals. With the high sensitivity and strong antinoise ability of the DLAC, this system can detect 25- $\mu \text{m}$ iron particles and 70- $\mu \text{m}$ copper particles. This study presents a new strategy for the online detection of particles in oil. [ABSTRACT FROM AUTHOR]

Noisy intermediate-scale quantum (NISQ) computers face significant reliability challenges because they are vulnerable to quantum noise, which severely limits their fidelity in quantum applications. In particular, deep circuits with a large number of quantum gates are susceptible to errors as they are more likely to lose their states in a deep circuit. In this paper, we propose a quantum circuit for square root operation that generates correct results on NISQ devices. The square root operation is used in many applications such as complex number computations, computer graphics, etc. While there have been limited studies on quantum square root circuits, none of them can be implemented on NISQ devices. In this work, we simplify the structure of an exact quantum square root circuit and reduce the number of quantum gates. The proposed design reduces the complexity of the square root circuit while maintaining the same level of precision in outputs. In addition, we exploit approximate computing to simplify the circuit further and run it on a real quantum computer. Approximate computing is used in classical computers to enhance the power and/or performance in exchange for accuracy. We exploit approximate computing for a different purpose, which is reducing the depth as well as the number of quantum gates in the square root circuit. To validate the effectiveness of our approach, we conduct experiments on an IBM quantum computer, where our circuit produces meaningful results. Furthermore, we present examples of error-resilient applications to demonstrate the validity of our approximate circuit.

Complex division is commonly used in various applications in signal processing and control theory including astronomy and nonlinear RF measurements. Nevertheless, unless reliability and assurance are embedded into the architectures of such structures, the sub-optimal (and thus erroneous) results could undermine the objectives of such applications. As such, in this paper, we present schemes to provide complex number division architectures based on Sweeney, Robertson, and Tocher-division with error detection mechanisms. Different error detection architectures are proposed in this paper which can be tailored based on the eventual objectives of the designs in terms of area and time requirements, among which we pinpoint carefully the schemes based on recomputing with shifted operands to be able to detect faults based on recomputations for different operands in addition to the unified parity (simplified detecting code) and hardware redundancy approach. The design also implements a minimized look up table approach which favors in error detection based designs and provides high fault coverage with relatively-low overhead. Additionally, to benchmark the effectiveness of the proposed schemes, extensive error detection assessments are performed for the proposed designs through fault simulations and field-programmable gate array (FPGA) implementations; the design is implemented on Xilinx Spartan-6 and Xilinx Virtex-6 FPGA families. [ABSTRACT FROM PUBLISHER]

3-D registration has always been performed invoking singular value decomposition (SVD) or eigenvalue decomposition (EIG) in real engineering practices. However, these numerical algorithms suffer from uncertainty of convergence in many cases. A novel fast symbolic solution is proposed in this article by following our recent publication in this journal. The equivalence analysis shows that our previous solver can be converted to deal with the 3-D registration problem. Rather, the computation procedure is studied for further simplification of computing without complex-number support. Experimental results show that the proposed solver does not loose accuracy and robustness but improves the execution speed to a large extent by almost 50%–80%, on both a personal computer (PC) and an embedded processor. Note to Practitioners—3-D registration usually has a large computational burden in engineering tasks. The proposed symbolic solution can directly solve the eigenvalue and its associated eigenvector. A lot of computation resources can then be saved for better overall system performance. The deterministic behavior of the proposed solver also ensures long-endurance stability and can help an engineer better design thread timing logic. [ABSTRACT FROM AUTHOR]

Graph signal processing (GSP) has become an important tool in many areas such as image processing, networking learning and analysis of social network data. In this paper, we propose a broader framework that not only encompasses traditional GSP as a special case, but also includes a hybrid framework of graph and classical signal processing over a continuous domain. Our framework relies extensively on concepts and tools from functional analysis to generalize traditional GSP to graph signals in a separable Hilbert space with infinite dimensions. We develop a concept analogous to Fourier transform for generalized GSP and the theory of filtering and sampling such signals. [ABSTRACT FROM AUTHOR]

The growing number of data privacy breaches and associated financial losses have driven the demand for private database queries. Clients typically submit queries that involve both search and computation operations, such as counting students under a certain age or calculating the BMI of employees above a specific age. Existing protocols often face limitations due to reliance on specific-purpose encryption schemes or multiple communication rounds between clients and servers. In this work, we present a unified framework utilizing fully homomorphic encryption techniques to efficiently and privately process queries with search and computation operations. Our contributions include a homomorphic encryption-based private comparison algorithm, called the layered comparison algorithm, which achieves a 2.6-6.6X performance improvement compared to algorithms from prior work; a fast Fourier transform-based preprocessing method enabling accurate large integer arithmetic operations in the encrypted domain; and a scalable database encoding method. Evaluation results demonstrate the practicality of our system, as it processes an aggregated query for a 1k-row encrypted database in approximately 4.53 seconds. [ABSTRACT FROM AUTHOR]

Sarcasm, sentiment, and emotion are three typical kinds of spontaneous affective responses of humans to external events and they are tightly intertwined with each other. Such events may be expressed in multiple modalities (e.g., linguistic, visual and acoustic), e.g., multi-modal conversations. Joint analysis of humans’ multi-modal sarcasm, sentiment, and emotion is an important yet challenging topic, as it is a complex cognitive process involving both cross-modality interaction and cross-affection correlation. From the probability theory perspective, cross-affection correlation also means that the judgments on sarcasm, sentiment, and emotion are incompatible. However, this exposed phenomenon cannot be sufficiently modelled by classical probability theory due to its assumption of compatibility. Neither do the existing approaches take it into consideration. In view of the recent success of quantum probability (QP) in modeling human cognition, particularly contextual incompatible decision making, we take the first step towards introducing QP into joint multi-modal sarcasm, sentiment, and emotion analysis. Specifically, we propose a QUantum probabIlity driven multi-modal sarcasm, sEntiment and emoTion analysis framework, termed QUIET. Extensive experiments on two datasets and the results show that the effectiveness and advantages of QUIET in comparison with a wide range of the state-of-the-art baselines. We also show the great potential of QP in multi-affect analysis. [ABSTRACT FROM AUTHOR]

To solve practical challenges for implementing deep learning-based algorithm in MIMO signal detector such as handling complex number or designing proper neural network for a specific communication system, (Baek et al., 2019) has proposed candidate implementation methodologies with simple verification experiments. According to (Baek et al., 2019), it was shown that the proposed algorithms can achieve the optimal ML performance. However, due to the lack of explanation on the experimental environment, it is difficult for readers to reproduce the presented experiments and obtain the same results. This document precisely explains on the experimental environments of (Baek et al., 2019) including the exact channel profiles. [ABSTRACT FROM AUTHOR]

Orthogonal frequency division multiplexing with index modulation (OFDM-IM) is a novel multicarrier scheme, which uses the indices of the active subcarriers to transmit data. The OFDM-IM also inherits the high peak-to-average power ratio (PAPR) problem, which induces in-band distortion and out-of-band radiation when OFDM-IM signal passes through high-power amplifier (HPA). In this letter, dither signals are added in the idle subcarriers to reduce the PAPR. Unlike the previous work using single level dither signals, multilevel dither signals are used by exploiting that the amplitudes of the symbols in the active subcarriers are variously distributed for different subblocks. As a result, the proposed scheme gives the dither signals more freedom (a larger radius of dithering) in average while keeping the good demodulation performance. Simulation results show that the proposed scheme can achieve better bit error rate performance than the previous works with consideration of HPA. [ABSTRACT FROM AUTHOR]

Analyzing the harmonic distortions at the point of common coupling is thoroughly addressed in this two-part paper. The main aim of such an analysis is to identify which of the utility and customer sides is significantly responsible for the harmonic distortions at the point of common coupling. In Part I, the meaning of the dominant side is challenged fundamentally. Here, two different definitions for the dominant side are discussed: The side with the larger equivalent harmonic “voltage” or “current” source. It is shown that these definitions are not identical. Subsequently, common methods are categorized in three general concepts based on: the direction of active power flow, the reactive power, and the voltage-current ratio. These three categories as well as their validity are analytically reviewed for both the definitions. The concept based on the voltage–current ratio has been explicitly presented in the original work for identifying the dominant equivalent harmonic voltage source. This concept is developed in this paper for identifying the dominant equivalent harmonic current source as well. In Part II, the application of the methods is illustrated using some common calculation examples. In addition, these methods are described verbally to provide a physical interpretation. Some practical aspects regarding the implementation of the methods are discussed as well. [ABSTRACT FROM AUTHOR]

Discrete memoryless multicast network (DM-MN) is considered in this paper. We analyze the lower bounds of noisy network coding (NNC) and distributed decode-forward (DDF) for DM-MN, and show that both NNC and DDF ignore the channel output observed at the transmitter. Motivated by this observation, new coding schemes are proposed to improve NNC and DDF by exploiting the transmitter’s observation and applying hybrid relaying strategies. We first study a special case when the transmitter’s observation is rate-limited feedback signals, and propose a scheme that strictly improves NNC when feedback rates are sufficiently large. For the relay channel with perfect relay-transmitter feedback, our achievable rate reduces to Gabbai and Bross’s rate, which is strictly larger than NNC, DDF, and all known lower bounds on the achievable rates proposed for the setup without feedback. In our scheme, both relays and receivers compress their received signals like NNC, and the relays decode independent “common” and “private” parts of the source message. The generated compression indices are sent to the transmitter through feedback, from which the transmitter reconstructs the receivers’ and relays’ inputs and can thus cooperate with the receivers and relays. We then extend our idea to DM-MN without feedback. For this case, although the transmitter observes channel output, both NNC and DDF simply ignore it, while our new scheme has the transmitter utilize its channel output to decode a set of relays’ and receivers’ compression indices, which achieves some cooperation levels between the transmitter and the receivers and relays. An enhanced relay channel is introduced to show that our scheme strictly outperforms NNC and DDF. [ABSTRACT FROM AUTHOR]

Radio frequency interference (RFI) has become a serious problem for synthetic aperture radar (SAR) systems. In recent years, numerous methods have emerged for the suppression of RFI. These methods often rely on assumptions regarding the narrowband characteristics and low-rank nature of radar echoes or interference signals. However, these assumptions may not hold true when dealing with complex RFI. To mitigate complex interference in dual-polarization (dual-pol) SAR systems, a proposed method is the utilization of a filtering algorithm based on sidelobe cancellation (SLC) technology. This method leverages the discrepancies in gain and coherence between observed targets and RFI signals in the co-polarization (co-pol) and cross-polarization (cross-pol) channels. It suppresses interference through SLC filtering on a range line by range line basis in the focused image domain, serving as a post-processing step. The method is capable of tackling multiple complex interferences optimally under the least mean square criterion, such as narrowband, wideband, and noise-modulated pulsed interferences. Both simulation and real data experiments show that the method can remove RFI artifacts and effectively recover the desired SAR images. [ABSTRACT FROM AUTHOR]

Ship target recognition is a vital task in synthetic aperture radar (SAR) imaging applications. Although convolutional neural networks have been successfully employed for SAR image target recognition, surpassing traditional algorithms, most existing research concentrates on the amplitude domain and neglects the essential phase information. Furthermore, several complex-valued neural networks utilize average pooling to achieve full complex values, resulting in suboptimal performance. To address these concerns, this letter introduces a complex-valued convolutional neural network (CVGG-Net) specifically designed for SAR image ship recognition. CVGG-Net effectively leverages both the amplitude and phase information in complex-valued SAR data. Additionally, this study examines the impact of various widely used complex activation functions on network performance and presents a novel complex max-pooling (CMaxPool) method, called Complex Area Max-Pooling. Experimental results from two measured SAR datasets demonstrate that the proposed algorithm outperforms conventional real-valued convolutional neural networks. The proposed framework is validated on several SAR datasets. [ABSTRACT FROM AUTHOR]

In inverse synthetic aperture radar (ISAR) imaging of maneuvering targets, traditional high-order phase compensation methods are usually limited by the heavy computational burden of parameter estimation, making it hard to apply in real-time cases. In this letter, an efficient ISAR motion compensation method is proposed based on fast parameter estimation. A novel analytic expression of the image entropy is derived with the help of a compensation matrix based on sinc function interpolation, which can eliminate the high-order phase term. Hence, the parameter estimation is transformed into an optimization problem where the gradient descent algorithm (GDA) can be adopted to accelerate the computation speed. Compared with other recently proposed methods, our method is superior in high robustness and low computing cost. Experiments with simulated and real data have verified that without affecting the image quality, the computing time of our method can be reduced to about 1/4 of the traditional search algorithm. [ABSTRACT FROM AUTHOR]

Moving targets always defocus and shift outside the scene in video synthetic aperture radar (video SAR) image sequences. However, the shadows of moving targets are immune to these issues and can reveal the true position of the moving targets. As such, by tracking the shadows of moving targets in the video SAR image sequence, it becomes feasible to keep track of these targets. Nevertheless, due to the small pixel size and time-varying characteristics of the target shadow, current prevailing tracking methods often prove insufficient for direct tracking of the shadow. In this letter, a shadow-assisted tracking method for moving targets based on a multilevel discriminant correlation filters network (MDCFnet) is proposed. Primarily, we designed a reverse feature pyramid network (RFPN) that integrates multiple high-level features into low-level features to obtain multiple features with higher distinguishability and resolution, thereby enhancing the final tracking accuracy and precision. Furthermore, we devised multilevel discriminant correlation filters (MDCFs) to perform filtering tracking under multiple feature maps. Real dataset processing results are provided to demonstrate that the proposed method outperforms other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Noncooperative bistatic radars (NCBRs) do not transmit electromagnetic waves but use emitters of other host radars as illuminators for target detection. If the noncooperative bistatic radar and the host radar belong to the opposing camps, respectively, the noncooperative bistatic radar will be a great challenge to the host radar. To ensure the electromagnetic information security of host radars, a joint design of host radar waveforms and mismatched filters (MMFs) is proposed to reduce the detection performance of NCBRs. For NCBRs, we raise the autocorrelation function sidelobe levels of the transmitted waveform to deteriorate its detection performance. For host radars, we design an MMF to improve the target detection performance of such transmitted waveforms. The simulation results show that the effects of raising and suppressing the range sidelobes in the model are both achieved. The price is an additional SNR loss (about 2 dB). Two types of transmission waveforms are designed including mainlobe broadening (MLB) waveforms and false peaks (FPs) waveforms, by controlling the autocorrelation function elevated position parameter. The constant false alarm detection results show that the designed waveforms fulfill the requirements of noncooperative bistatic radar countermeasures. [ABSTRACT FROM AUTHOR]

Extraction road from remote sensing (RS) images is a challenging topic because of the inhomogeneous intensity, nonconsistent contrast, and very cluttered background of satellite images. Most previous approaches, relying on convolutions or self-attention, are built on the local operation or global modeling on the spatial domain but are difficult to capture weak and continuous road objects. The spectral representation of road image features and modulation learning on it provides a novel long-range-dependent and fine-grained feature representation mechanism. Based on it, we propose a novel road extraction network on RS images, called an adaptive Fourier filtered U-shaped network (AFU-Net) in this letter, which relies on modulation learning on the Fourier domain. The AFU-Net is composed of modulation learner (MoL) basic blocks and follows the pipeline of the classical U-Net model. The basic MoL block includes a global MoL (GML) block for global spectral modulation learning and an attentive MoL (AML) block which contains two parallel layers, i.e., phase-modulated filter (PMF) and magnitude-modulated filter (MMF), for fine-grained spectral modulation on the Fourier spectrum. The experiments on two public datasets, such as Massachusetts roads and DeepGlobe road datasets have shown the outstanding performance of AFU-Net on the metrics of accuracy, precision, recall, and mean intersection over union (mIoU). [ABSTRACT FROM AUTHOR]

This paper investigates the secrecy performance for simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) assisted downlink multi-carrier non-orthogonal multiple access (NOMA) networks, consisting of multiple legitimate users and eavesdroppers. We propose two STAR-RIS-NOMA schemes for maximizing the secrecy performance by jointly optimizing the transmission and reflection beamforming of the STAR-RIS, the transmit beamforming of the base station (BS), the power allocation coefficients and the user pairing vector under the full channel state information (CSI) and the statistical CSI of the eavesdropping channel, respectively. For the full CSI available to the BS, an alternating beamforming algorithm is proposed for maximizing the secrecy sum rate. Specifically, we first propose a user pairing scheme based on the differences of user’s channel gains. Then the beamforming vectors and the power allocation coefficients are optimized based on the techniques of semidefinite programming and surrogate lower bound approximation, respectively. For the statistical CSI available to the BS, the problem of minimizing the maximum secrecy outage probability (SOP) is investigated. By invoking the subroutines of alternating beamforming algorithm, we first derive an exact SOP given the user pairing. Then, we conceive the beamforming vectors and the power allocation coefficients by linear matrix inequality and linear programming, respectively. Simulation results show that: 1) the secrecy performance of the proposed STAR-RIS-NOMA scheme outperforms the existing conventional RIS-NOMA scheme and RIS assisted orthogonal multiple access (RIS-OMA) scheme; 2) the proposed alternating beamforming algorithm is capable of achieving a near-optimal performance with low complexity compared to the exhaustive search. [ABSTRACT FROM AUTHOR]

The concept of complex Pythagorean fuzzy set $(\mathbf {CPFS})$ is recent development in the field of fuzzy set $(\mathbf {FS})$ theory. The significance of this concept lies in the fact that this theory assigned membership grades $\psi $ and non-membership grades $\hat {\psi }$ from unit circle in plane, i.e., in the form of a complex number with the condition $(\psi)^{2}+ (\hat {\psi })^{2}\le 1$ instead from [0, 1] interval. This is an expressive technique for dealing with uncertain circumstances. The aim of this study is to proceed the classification of the unique framework of $\mathbf {CPFS}$ in algebraic structure that is field theory and examine its numerous algebraic features. Also, we initiate the important examples and results of certain field. Furthermore, we illustrate that every complex Pythagorean fuzzy subfield ( $\mathbf {CPFSF}$ ) generates two Pythagorean fuzzy subfields $(\mathbf {PFSFs})$ . We also prove many useful algebraic aspects of this notion for a $\mathbf {CPFSF}$ . Moreover, we demonstrate that intersection of two complex Pythagorean fuzzy subfields $(\mathbf {CPFSFs})$ is also $\mathbf {CPFSF}$ . Additionally, we discuss the novel idea of level subsets of $\mathbf {CPFSFs}$ and demonstrate that level subset of $\mathbf {CPFSF}$ form subfield. Additionally, we improve the application of this theory to show the concept of the direct product of two $\mathbf {CPFSFs}$ is also a $\mathbf {CPFSF}$ and produce several novel results on direct product of $\mathbf {CPFSFs}$ . Finally, we explore the homomorphic images and inverse images of $\mathbf {CPFSFs}$ .

This article proposes a new grid impedance detection method incorporating the complex coefficient filter (CCF) with full-order capacitor current observer for a T-type three-level grid-connected inverter controlled by the inverter output current feedback. Compared with conventional CCF impedance detection algorithms, the proposed method reduces the number of current sensors and detects the grid impedance accurately. First, based on the sampled inverter output current and grid-connected voltage signals, the grid-connected current is estimated. Then, the CCF method is used to extract harmonics from the grid-connected current and voltage signals to calculate the grid impedance. Finally, the correctness of the full-order capacitor current observer is verified by simulation and the feasibility and effectiveness of the proposed algorithm are verified experimentally based on a laboratory prototype. [ABSTRACT FROM AUTHOR]

This article explores the unification and simplification of the small-signal model for representative inductive power transfer systems. Various famous compensations are included, such as the S–S, LCC–S, and LCC–LCC. Through system decomposition, the uniform model concept is applied to the inverter, rectifier, and resonant tank. Meanwhile, the model complexity and similarity are discussed for various resonant tanks, and proper simplification is used to reduce the model order. The uniform equivalent circuit model is finally proposed for the target systems, based on which the explicit transfer function can be represented by a general polynomial equation. The model order of the S–S, LCC–S, and LCC–LCC systems are five, two, and five, respectively. The experiment shows the model is accurate up to one-fifth of the switching frequency for all the target systems. [ABSTRACT FROM AUTHOR]

Rotating blades are key turbomachinery components with high failure risk due to harsh working conditions. Thus, monitoring the running state of blades is urgently required. Blade tip timing (BTT) is regarded as a potential technology for blade vibration monitoring owing to its noncontact nature and low cost. However, severe undersampling and strict probe layout hinder the application of BTT. As a result of severe undersampling, aliasing and its suppression are the main research topics in BTT. However, in this article, a biprobes method for BTT based on the utilization of aliasing is proposed to identify the natural frequencies of blades. Active aliasing is used in this method to produce aliasing findings at various equivalent sampling frequencies, and the closed-form robust Chinese remainder theorem is used for dealiasing. Unlike the conventional multirate sampling systems for BTT that use a multiprobe configuration or varied speed, the suggested method utilizes varying delay durations to obtain varying equivalent sample frequencies. Furthermore, to ensure that active aliasing and dealiasing form a closed loop, an included angle coprime layout is proposed. Finally, the robustness and effectiveness of the proposed method are verified through numerical and experimental validation. [ABSTRACT FROM AUTHOR]