esa-sceva/satcom-chunk-collection huggingface dataset:
# Enhanced Epileptic Seizure Detection through Wavelet-Based Analysis of EEG Signal Processing
## 3 Methodology
### Support Vector Machine (SVM)  
SVM is a supervised binary classification model based on constructing a hyperplane \(H\) to maximize the margin between data points from distinct classes [36]. The function \(H\) is defined as:  
\[H=w^{\top}\cdot x_{i}+b=0, \tag{8}\]  
where \(w\) represents the weight vector, \(x_{i}\) denotes the input feature vector of the \(i\)-th observation, and \(b\) is the bias coefficient. Depending on its class, each observation is labeled as \(1\) or \(-1\), forming a label vector \(y_{i}\). The margin distance between the nearest opposing observations can be maximized, which is written as a minimization problem in the form:  
\[\begin{split}\min_{w,b}&\frac{1}{2}\left(w^{\top} \cdot w\right),\\ s.t.& y_{i}(w^{\top}\cdot x_{i}+b)-1\geq 0.\end{split} \tag{9}\]  
This problem is known as a primal problem and can be solved as a Lagrange optimization problem, such that:  
\[\mathcal{L}p(w,b,\alpha)=\frac{1}{2}\left(w^{\top}\cdot w\right)-\sum_{i=1}^{ n}\alpha_{i}[y_{i}(w^{\top}\cdot(x_{i}+b)-1], \tag{10}\]  
where \(\alpha_{i}\) denotes the Lagrange coefficients and \(n\) denotes the total number of vectors. Resolving this problem is complex given its dependency on \(w\), \(b\), and \(\alpha\). By applying the Karush-Kuhn-Tucker (KKT) conditions, we reach a dual problem exclusively dependent on \(\alpha\), as expressed below:  
\[\mathcal{L}d(\alpha)=-\frac{1}{2}\sum_{i=1}^{n}\sum_{j=1}^{n}\alpha_{i}y_{i}( x_{i}^{\top}\cdot x_{j})y_{j}\alpha_{j}+\sum_{i=1}^{n}\alpha_{i}. \tag{11}\]  
Once the coefficients \(\alpha_{i}\) are obtained, the weight vector can be calculated through the  
The classifier determines which of the two classes an observation belongs to using the sign function, which results from evaluating the new observation \(x_{k}\) in the model. Ultimately, the decision function of the classifier, denoted as \(y_{k}\), is expressed as:  
\[y_{k}=\text{sign}(w^{\top}\cdot x_{k}+b). \tag{14}\]  
For cases where the sets cannot be completely separated, a penalty parameter \(C\) and slack variables \(\xi_{i}\) are introduced. Therefore, the primal problem is now expressed as:  
\[\begin{split}\min_{w,b}&\quad\frac{1}{2}\left(w^{ \top}\cdot w\right)+C\sum_{i=1}^{n}\xi_{i},\\ s.t.&\quad y_{i}(w^{\top}\cdot x_{i}+b)-1+\xi_{i} \geq 0,\\ &\xi_{i}\geq 0.\end{split} \tag{15}\]  
Expressing in primal Lagrangian form and KKT conditions, the procedure in this case remains identical to the previous case, with the addition of a new single constraint given by \(0\leq\alpha_{i}\leq C\).  
In instances where separation of the set is not feasible, a kernel function is utilized to project the feature space into a higher dimension. The weight vector is now redefined as:  
\[w_{k}=\sum_{i=1}^{n}\alpha_{i}y_{i}K(x_{i},x_{j}), \tag{16}\]  
where \(K(x_{i},x_{j})\) involves applying the kernel function [36]. Commonly used kernel functions are linear, perceptron, polynomial, radial basis function (gaussian), and sigmoid kernels.
## 1 Introduction
It is divided into four sections. The second section formulates a scientific problem related to the positioning accuracy of SV with the selected methods based on measurements made with onboard navigation equipment and a measurement system based on an omnidirectional camera. The third section describes a simulation study involving the generation of navigational measurement results with errors (including gross errors). The method is used to position an SV sailing along a given trajectory in the vicinity of three beacons. The fourth section presents an extensive analysis of the simulation results, indicating that the GRA and EKF methods as the best for positioning the SV. It provides a proposal for the index to select the most accurate one under specific measurement conditions. The final section provides generalised conclusions from the study and guidance on the interchangeable use of EKF and GRA methods.
## 3 Proposed Receiver
### Channel Estimation
The information from the BEM of channel in the frequency and frequency Doppler domains are found compactly in the doubly-indexed matrix:  
\[\mathbf{\Phi}_{q,r}^{k}=\mathbf{FB}_{q,r}^{k}\mathbf{F}^{H}, \tag{11}\]  
with  
\[\left[\mathbf{B}_{r,q}^{k}\right]_{n,n^{\prime}}=\phi_{q}{}^{I}[n+(k+1)(N+N_{S })]\phi_{r}{}^{II}[(n-n^{\prime})_{N}] \tag{12}\]  
and the BEM coefficients given by:  
\[\rho_{q,r}=\sum_{m=0}^{3N-1}\sum_{l=0}^{L-1}h[m,l]\tilde{\phi}_{q}^{I}[m]\tilde {\phi}_{r}^{II}[l]. \tag{13}\]  
Substituting the channel for its BEM in (6) yields the expression:  
\[\mathbf{u}^{k}=\sum_{q=0}^{M_{D}-1}\sum_{r=0}^{M_{\mathrm{r}}}\rho_{q,r}\mathbf{ \Phi}_{q,r}^{k}\mathbf{s}^{k}+\mathbf{z}^{k}, \tag{14}\]  
Annezing this representation of the channel to the Equation (7) and considering only the positions where the transmitted and received pilots are found, yields the following:  
\[\mathbf{u}_{\mathcal{P}}=\mathbf{\Lambda}\mathbf{\rho}+\mathbf{\epsilon}_{\mathcal{P}}, \tag{15}\]  
where:  
\[\mathbf{\Lambda}^{T} =\left[\mathbf{\Lambda}^{k-1}{}^{T}\quad\mathbf{\Lambda}^{k}{}^{T}\quad \mathbf{\Lambda}^{k+1}{}^{T}\right]^{T}, \tag{16}\] \[M_{\mathrm{T}} =\lceil F_{\mathrm{s}}\tau_{max}\rceil+1, \tag{9}\]0 (17) \[M_{\mathrm{T}} =\lceil F_{\mathrm{s}}\tau_{max}\rceil+1, \tag{9}\]1 (18) \[M_{\mathrm{T}} =\lceil F_{\mathrm{s}}\tau_{max}\rceil+1, \tag{9}\]2  
the subscript \(\mathcal{P}\) refers to the sub-sample of the vectors and matrices in the rows and columns corresponding to the pilots' position. For reasons of simplification in the notation, the indexed variable \(i=q+M_{D}(r-1)\) was used, where \(0\leq r\leq M_{\tau}\) and \(0\leq q\leq M_{D}-1\). \(\mathbf{\epsilon}_{\mathcal{P}}\) is the vector that concentrates the noise contributions, modeling error and intersymbol interference in order to simplify the expressions. It is assumed that the receiver has matrix \(\mathbf{\Lambda}\) and the received vector \(\mathbf{u}_{\mathcal{P}}\), such that the calculation of the channel's estimated coefficient vector can be obtained by the least-squares (LS) algorithm [23]:  
\[M_{\mathrm{T}} =\lceil F_{\mathrm{s}}\tau_{max}\rceil+1, \tag{9}\]3  
Once these coefficients are obtained, any of the representations, such as the time-varying impulse response and the channel transfer function, can be calculated directly by computing the weighted sum of the base functions. In this way, the frequency-Doppler and frequency response matrix can be calculated by using the expression:  
\[M_{\mathrm{T}} =\lceil F_{\mathrm{s}}\tau_{max}\rceil+1, \tag{9}\]4
# Low-Complexity QRD-\(M\) with Path Eliminations in MIMO-OFDM Systems
###### Abstract  
The QR decomposition-\(M\) algorithm (QRD-\(M\)) is a popular signal detector which has similar error performance with maximum likelihood (ML) in multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) systems. The QRD-\(M\) uses \(M\) candidates at each layer, unlike the ML. However, the complexity of the QRD-\(M\) is high in huge MIMO-OFDM systems due to unnecessary survival paths at each layer. In this paper, a low-complexity QRD-\(M\) with variable number of survival paths at each layer is proposed. In the conventional QRD-\(M\), path eliminations at the previous layer reduce the number of calculations for accumulated squared Euclidean distance (ASED) in subsequent layers. The proposed QRD-\(M\) eliminates unnecessary survival paths by comparing the ASED and the calculated threshold at each layer. The simulation results show that the proposed QRD-\(M\) maintains the error performance for the conventional QRD-\(M\) and has a very low complexity.  
MIMO-OFDM; QRD-\(M\); survival path; path elimination +
Footnote †: journal: Applied Sciences  
_Applied_  
_Acticle_
# Bearing Fault Diagnosis Based on Small Sample Learning of Maml-Triplet
## 5 Conclusions and Prospect  
This paper aims at the low frequency of faults during equipment operation and the small amount of fault data that is not easy to cause by collecting fault signals. A small  
Figure 12: Four-way \(k\)-shot classification result.  
Figure 13: Five-way \(k\)-shot classification result.  
sample-bearing fault diagnosis framework based on the Maml-Triplet model is proposed, and the validity of the proposed framework in identifying new artificial bearing faults is verified using CWRU datasets.  
When the Maml-Triplet model has 20 samples in each fault type, its accuracy can reach about 99% and its effect is better than that of the triplet model, Maml-CNN model, and CNN model. When there are less than 20 samples per fault type, the accuracy of the Maml-Triplet model increases with the number of samples. Furthermore, when increasing the number of fault types, the accuracy of the Maml-Triplet model is relatively stable, which is significantly better than that of the Maml-CNN model and CNN model. In conclusion, the Maml-Triplet model is significantly superior to other models under small sample conditions.  
Of course, there are still some shortcomings in the Maml-Triplet model. For example, during the training of the Maml neural network, there are disadvantages such as an unstable secondary gradient and slow training speed. For the Maml training process, [PERSON] et al. proposed an improved method in the literature [37]. The Maml-Triplet model can only be used for supervisory tasks, but it cannot process data without a label or with an incomplete label and cannot use the signal without a label at the early stage of equipment, which results in a certain degree of data waste.  
Future work will study semi-supervised learning in the case of small sample data and missing labels based on the maml meta learning method  
Conceptualization, Q.C.; Data curation, Z.H.; Formal analysis, Z.H.; Funding acquisition, Q.C. and Z.Z.; Methodology, Z.H.; Project administration, Z.L.; Resources, Q.C. and Z.Z.; Software, Z.H. and Z.Z.; Supervision, Z.L.; Validation, Y.L.; Visualization, Y.L.; Writing--original draft, T.Z.; Writing--review and editing, T.Z. All authors have read and agreed to the published version of the manuscript.  
This research is supported by JCKY2020203B016 and the National Natural Science Foundation of China (grant no. 51975012, grant no. 52275230, grant no. 51905334).  
Not applicable.  
The authors have no conflict of interest to declare.  
The following abbreviations are used in this manuscript:  
CWRU Case Western Reserve University  
CNN convolutional neural network  
AE automatic encoder  
RNN recurrent neural network  
GAN generative adversarial network  
DQNN deep quantum inspired neural network  
FFT fast Fourier transform  
CBLSTM convolutional bidirectional long short-term memory  
FTNN feature-based transfer neural network  
MAML model-agnostic meta-learning
# A Review of Modular Multilevel Converters for Stationary Applications
## 3 Mathematical Modeling and Control of Three-Phase MMC
### Circulating Current Control  
The voltage difference between the upper and lower arms of the MMC legs results in the circulating current. The circulating current has little influence on the output voltages and currents at the AC side. However, it distorts the arm current, leading to extra power losses, a higher rating of devices, and submodule voltage ripples [96]. Therefore, the circulating current is expected to be eliminated. The arm inductors can suppress the circulating current to some extent [97]. Furthermore, the elimination controller is required to be employed. Since the circulating current is dominated by even-order harmonic components, especially second-order harmonics, the control objective of the elimination controller mainly focuses on the elimination of second-order harmonics [98]. The circulating current elimination approaches are based on decoupling control in the rotating \(dq\)-frame or resonant control in the stationary \(abc\)-frame. In terms of decoupling control, the second-order circulating  
Figure 12: SoC balancing control: (**a**) Leg SoC balancing control; (**b**) Arm SoC balancing control; (**c**) Individual SoC balancing control.  
Figure 13: Flow chart of sorting balancing control.  
current is converted into a \(d\)-axis and \(q\)-axis as DC components, which can be controlled easily and independently by PI regulators, as shown in Figure 14a [99; 100]. In the case of unbalanced conditions where the circulating currents have positive, negative, and zero sequence components, the repetitive controller [101; 102] can be applied to regulate multiple circulating current harmonics. Compared to decoupling methods, the proportional resonant controller has some advantages under unbalanced conditions with an easier implementation of multiple resonant controllers to eliminate a wider bandwidth of circulating current harmonics [103; 104]. The resonant control structure to eliminate second-order, fourth-order, and sixth-order harmonics is described in Figure 14b [92; 104]. In addition, for the sake of control robustness, the improved quasi proportional resonant controller is adopted to eliminate the circulating current, as shown in Figure 14c [105; 106]. Except for eliminating the circulating current, the circulating current injection method is developed to reduce the submodule voltage ripple. Circulating current injection can be realized by the lookup table method [107] or the online calculation method based on instantaneous data [108].
## 4 Case II: Active Eavesdropper
### Bit-Error-Rate (BER) Performance  
#### 4.4.1 BER at the Legitimate Receiver User A  
The BER performances versus \(SNR_{A}\) at user A for different values of the jamming-to-noise ratio from user E (\(\rho_{EA}\)) are illustrated in Figure 19a,b for both the blind feedback scheme and the semi-blind scheme at user A, respectively. The self-interference-to-noise ratio at user A (\(\rho_{AA}\)) is set at 30 dB. We can observe that the BER increases as the jamming-to-noise ratio of user E (\(\rho_{EA}\)) increases, and the increase in the BER is bigger for larger \(SNR_{A}\) values compared with the passive case. We can also remark that the semi-blind scheme is less sensitive to the jamming from user E than the blind feedback scheme, and it also converges faster to the error floor than the other. In particular, when maintaining \(BER_{A}=10^{-5}\) and increasing the jamming-to-noise ratio \(\rho_{EA}\) from 0 to 30 dB, the blind feedback scheme needs about 5 dB in \(SNR_{A}\), while the semi-blind feedback scheme requires only 2.5 to 3 dB to reach that result. Therefore, the semi-blind feedback scheme is suitable in the case of an active eavesdropper because the increase in jamming power from the active user E has less influence on the BER performance at the legitimate receiver user A. In fact, it can considerably improve the reliability factor of secrecy in FD wiretap transmission in the case of an active eavesdropper.
# RST Resilient Watermarking Scheme Based on DWT-SVD and Scale-Invariant Feature Transform
## 2 SIFT Algorithm
### Scale-Space Peak Selection  
The basic theory of the scale-space approach [31] is to introduce a scale parameter in the visual information processing model and obtain visual processing information on different scales by continuously changing scale parameters. Then, the information is integrated to explore essential characteristics of the image. For achieving the scale transformation, Gaussian convolution kernel [32] is the only linear kernel applied. The scale-space kernel \(f_{\text{out}}\) can be defined as Equation (1):  
\[f_{\text{out}}=K_{\text{n}}*f_{\text{in}}, \tag{1}\]  
where \(K_{\text{n}}\) is the kernel, \(f_{\text{in}}\) is the input signal, and \(*\) represents the convolutional calculation.  
The scale-space \(S(x,y,\sigma)\) of the image \(I(x,y)\) is shown as Equation (2):  
\[S(x,y,\sigma)=G(x,y,\sigma)*I(x,y),\ G(x,y,\sigma)=\frac{1}{2\pi\sigma^{2}} \text{e}^{-(x^{2}+y^{2})/2\sigma^{2}}, \tag{2}\]  
where \(G(x,y,\sigma)\) is the scale variable Gaussian function, \((x,y)\) is the spatial coordinates, and \(\sigma\) is the scale-space factor, which decides the smoothness of the image. The large value of \(\sigma\) represents smoother image overview features of large scales, and the small value of \(\sigma\) describes the abundant image detailed features of small scales.  
To detect stable points in scale-space effectively, [PERSON] [20] proposed the difference of Gaussian (DOG) scale-space presented as Equation (3):  
\[D(x,y,\sigma)=[G(x,y,k\sigma)-G(x,y,\sigma)]*I(x,y)=S(x,y,k\sigma)-S(x,y, \sigma), \tag{3}\]  
where \(I(x,y)\) is the input image and \(k\) is the multiple between two neighboring scale-spaces.  
With the help of DOG scale-space image, all extreme points can be detected as keypoints in the candidate points.
# Low-Latency Bit-Accurate Architecture for Configurable Precision Floating-Point Division
## 2 Background  
Very high-radix class algorithm is similar to non-restoring digit-recurrence algorithm. Their differences lie in hardware and logic arrangements for quotient selection and partial remainder generation. A simple basic schematic of very high-radix class algorithm is presented in Figure 1.  
Proposed by [PERSON] and [PERSON], fast division [18] is the earliest high-radix algorithm. Fast division requires hardware with at least one look-up table of size \(2^{m-1}\times m\) bits and three multipliers, a carrying assimilation multiplier of size \((m+1)\times n\) for the divisor's initial multiplications and a carry-save multiplier of size \((m+1)\times m\) for the quotient segments computation. As for the basic version of fast division, the look-up table has \(m=11\), i.e., \(2^{(11-1)}=1024\) entries, each 11 bits wide, so in total, 11 K bits are required in the look-up table. As for the advanced version, 736 K bits are required in the look-up table when \(m=16\).  
The high-radix algorithm proposed by [PERSON] and [PERSON] [19] shows the construction of a radix-\(2^{K}\) divider for implementing a radix-10 divider whose quotient digit is decomposed into two parts, one in radix-5 and the other in radix-2. In radix-5, the quotient digit is represented as values \(\{-2,\,-1,\,0,\,1,\,2\}\), requiring three multipliers. Radix-2 is used to perform division on the most significant slice. It uses an estimation technique in the quotient selection component, which requires the use of a redundant digit format.  
In brief, high-radix division algorithm works with a scaling dividend and divisor by correct initial approximation of the reciprocal, followed by quotient selection logic with a multiplier and subtraction. Beyond this, high-radix dividers are almost the same as SRT-based radix dividers.  
When it comes to ways to implement higher radix dividers, prior works focus on enhancing the complexity and criticality of SRT-based radix dividers [37; 38]. Moreover, a combination of two or more alternatives together could be another way. Many works are going on to provide different standpoints for high-radix dividers. Use of different look-up tables along with quotient-digit selection logic look-up table [39; 40; 41], speculating quotient digit and using arithmetic functions to multiplicative iterations rather than subtractive iterations [42], pre-scaling operands [43; 44; 45], using Fourier division [46; 47], using alternative digit codes such as binary-coded decimal (BCD) digits instead of decimal and basic binary digits [48], cascading multiple stages of lower radix dividers [49], overlapping two or more stages of low radix [50; 51], a truncated schema of exact cell binary shifted adder array [52; 53; 54], on-line serial and pipelined operand division [55], parallel implementation of the low-radix dividers [8], array implementation [56], these are some of the possible ways applicable for high-radix dividers.
## 2 Preliminaries
### Intel SGX  
A trusted execution environment (TEE) allows an arbitrary code to be executed in an isolated environment, providing integrity and confidentiality protection on the executed codes, stored data, and runtime states, such as sensitive I/O, CPU registers, and memory. Intel SGX, one of the main prevailing and representative TEEs, is a set of extended Intel's x86 instructions providing isolated execution environments, called enclaves [7]. The enclave is the trusted component located in a dedicated memory portion of the physical RAM, called the enclave page cache (EPC). During system boot-up, a total of 128 MB is typically reserved for the Intel SGX, out of which 96 MB is allocated to the EPC; this EPC is shared among all the running enclaves on the system. The untrusted part is executed as an ordinary process, and can trigger the enclave under a securely defined process. When the data are loaded inside the enclave, the SGX-enabled processors protect their integrity and confidentiality by isolating them from the outside untrusted environment, including the operating systems and hypervisor. The enclave can access the entire virtual memory of its untrusted host process, but the untrusted host or any other enclave cannot directly access any code or data in the enclave.  
When an enclave is required to communicate with other instances, an attestation mechanism is executed for authentication before exchanging the data. There are two forms of attestation: local attestation and remote attestation. Local attestation is used for authenticating two enclaves running on the same physical machine, and is conducted using the EREPORT and EGETKEY instructions, which generate signed reports for verification. Remote attestation is used when an enclave attests its identity (usually represented by its initial code and data) to another enclave running on a remote physical machine. The remote enclave uses a quote generated by the quoting enclave (QE), and verifies the signature by sending it to the Intel attestation server. Through the attestation service, a secure channel is established between them.