esa-sceva/satcom-chunk-collection huggingface dataset:
# Ray Tracing Method of Gradient Refractive Index Medium Based on Refractive Index Step
## 2 The Method of Ray Tracing Based on Refractive Index Step
### Space Snell's Law  
[PERSON]'s law in vector form is much more useful in the process of ray tracing in three-dimensional space [18]. According to the reference [6], we can calculate [PERSON]'s law in vector form.  
The plane [PERSON]'s law can usually be expressed as:  
\[n^{\prime}\sin{I^{\prime}}=n\sin{I} \tag{2}\]  
In this formula, \(n\) and \(n^{\prime}\) are the refractive index of the medium on the incident side and refracted side, respectively. \(I\) and \(I^{\prime}\) are the incident angle and refraction angle of the ray, respectively.  
Combined with Figure 1, Formula (2) can be modified as:  
\[n^{\prime}\big{(}\mathbf{A}_{0}^{\prime}\times\mathbf{N}\big{)}=n(\mathbf{A} _{0}\times\mathbf{N}), \tag{3}\]where \(\mathbf{A}_{0}\) is the unit vector along the incident ray, \(\mathbf{A}_{0}^{{}^{\prime}}\) is the unit vector along the refracted light, and \(\mathbf{N}\) is the unit vector along the normal.  
The refracted ray vector with length \(n^{\prime}\) and the incident ray vector with length \(n\) are written as \(\mathbf{A}^{{}^{\prime}}\) and \(\mathbf{A}\), respectively:  
\[\mathbf{A}^{{}^{\prime}}\times\mathbf{N}=\mathbf{A}\times\mathbf{N}\Rightarrow \left(\mathbf{A}^{{}^{\prime}}-\mathbf{A}\right)\times\mathbf{N}=0 \tag{4}\]  
Formula (4) shows that vector \(\mathbf{A}^{{}^{\prime}}\)-\(\mathbf{A}\) and vector \(\mathbf{N}\) are collinear vectors. Rewrite Formula (4) as:  
\[\mathbf{A}^{{}^{\prime}}-\mathbf{A}\ =\ P\mathbf{N}, \tag{5}\]  
where \(P\) is vector deflection constant. Product both sides of Formula (4) with \(\mathbf{N}\)[6]:  
\[P=\mathbf{N}\bullet\mathbf{A}^{\prime}-\mathbf{N}\bullet\mathbf{A}=n^{\prime} \cos I^{\prime}-n\cos I, \tag{6}\]  
when \(n^{\prime}>n\), the vectors \(\mathbf{A}^{\prime}\)-\(\mathbf{A}\) and \(\mathbf{N}\) are parallel as shown in Figure 1b. When \(n^{\prime}<n\), the two vectors are antiparallel as shown in Figure 1c.  
When the refractive index of the two media and the incident angle of the light are known, \(n^{\prime}\cos I^{\prime}\) can be replaced with:  
\[\begin{array}{ll}n^{\prime}\cos I^{\prime}&=\sqrt{\left(n^{\prime}\right)^{ 2}-\left(n^{\prime}\sin I^{\prime}\right)^{2}}\\ &=\sqrt{\left(n^{\prime}\right)^{2}-n^{2}+\left(n\cos I\right)^{2}}\end{array} \tag{7}\]  
Therefore, the refraction law of vector form is [6]:  
\[\mathbf{A}^{{}^{\prime}}\ =\ \mathbf{A}+P\mathbf{N}=\mathbf{A}+(\sqrt{\left(n^{ \prime}\right)^{2}-n^{2}+\ \left(n\cos I\right)^{2}}-\ n\cos I)\mathbf{N} \tag{8}\]
# Contact Fatigue State Identification of Specim Based on Heterogeneous Data and Evidence Theory
## 3 Contact Fatigue State Identification
### Contact Fatigue State Identification of Specim
#### 3.4.2 Image Signal Processing  
Figure 10 shows the defect area calculation process of specimen based on machine vision [31,32]. Firstly, the image is denoised by fast guided filtering. Secondly, the automatic weighted threshold method is used to perform threshold segmentation on the image. Thirdly, the connected domain analysis is carried out and the segmented maximum interesting area is located. Finally, the maximum interest area is obtained by filling the minimum circumscribed rectangle, and then multiplied by the corresponding equivalent pixel \(3.99\times 10^{-4}\)mm2 [31] to obtain the corresponding damage area.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Status Number** & **Specimen Status** & **Damage Area S/mm2** \\ \hline
0 & Normal & S \(\leq\) 0.01 \\
1 & Medium & 0.01 \textless{} S \(<\) 3 \\
2 & Failure & S \(\geq\) 3 \\ \hline \hline \end{tabular}
\end{table}
Table 8: The contact fatigue state of the specimen.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample Type** & \multicolumn{3}{c}{**Number of SDP Images**} \\  & **Normal** & **Medium** & **Failure** \\ \hline Training Samples & 900 & 900 & 900 \\ Test samples & 200 & 200 & 200 \\ Validation samples & 100 & 100 & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 9: SDP image dataset.  
Table 10 shows a group of the vibration signal and the corresponding SDP image, image signal and the corresponding maximum damage area under three states of the specimen in normal, medium and failure.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**Vibration Signal**} & \multicolumn{2}{c}{**Image Signal**} \\
**Specimen** & & **Visual Recognition of** & **Quantification of** \\
**Status** & **Original Vibration Signal** & **SDP Image** & **Maximum Damage** & **Area Values/mm\({}^{2}\)** \\ \hline Normal & & & \\ \hline \hline \end{tabular}
\end{table}
Table 10: A group of vibration and image signals of the specimen in three states.  
Figure 10: Calculation process of specimen damage area.
## 2 Description of the Numerical Tools
### The Hybrid Solver  
The combination of the previously described numerical methods results in a Hybrid Eulerian-Lagrangian solver (from hereon HoPFlow). A typical numerical setup for the hybrid solver can be seen in Figure 2. The computational domain is decomposed in two overlapping parts; the Eulerian one, \(D_{E}\), and the Lagrangian one \(D_{PM}\). In \(D_{E}\) MaPFlow CFD solver is utilized and thus wall boundary conditions on \(S_{B}\) are handled exactly, which particle methods have several difficulties to efficiently implement. For the Eulerian part, boundary conditions are also needed on \(S_{E}\). They are provided by the Lagrangian solver. In this way the two solvers are coupled. Because the two domains are independent and overlapping, a correct communication between them should provide a smooth transition from one solution to the other.  
Coupling is achieved by a two way communication. The Lagrangian solver provides on \(S_{E}\) the boundary conditions needed for the Eulerian solver, and the Eulerian solver provides back the effect of solid boundaries on \(D_{PM}\) by substituting the vorticity-dilatatat distributions over its defining domain \(D_{E}\).
# An Efficient SC-FDM Modulation Technique for a UAV Communication Link
## 2 Related Works
In [14], [PERSON] gives an overview of SC-FDMA. Another research focuses on PAPR reduction of localized SC-FDMA using a partial transmit sequence (PTS) [15]. Actually, there can be localized and distributed modes of subcarrier mapping in SC-FDMA [14; 16]. In localized SC-FDMA, each terminal uses a set of contiguous subcarriers for the transmission of symbols, thereby limiting them to only a portion of the system bandwidth. On the other hand, the subcarriers used by the terminal are propagated throughout the entire bandwidth in the distributed SC-FDMA. Localized SC-FDMA, which is used for uplink transmission of LTE systems, has lower PAPR than distributed SC-FDMA. Furthermore, [PERSON] et al. [17] provided a bargaining model and power optimization framework to solve the problem of subcarrier and power allocation in multiuser SC-FDMA wireless networks. The obtained numerical results and key features of their proposed approach demonstrate that the introduced framework can be a foundation for the supporting heterogeneous services and the  
Figure 1: Hardware architecture. implementation of different users' priorities to access the available resources. Towards this direction, a similar work can be found in [18]. In 2016, [PERSON] et al. [19] studied and examined the various state-of-the-art resource allocation algorithms and frameworks developed to allocate the subcarriers and transmission power of users in the uplink of SC-FDMA wireless networks. [PERSON] and [PERSON] [20] proposed the SC-FDMA-IDMA system model, which is the combination of SC-FDMA and interleaved division multiple access (IDMA) and studied the effect of carrier frequency offset (CFO) on the BER performance of this system model.
# Wake-Up Receiver with Equal-Gain Antenna Diversity +
## 2 Background
### Selection Diversity  
For any incoming signal, a selection diversity system connects the receiver always to the antenna that has the highest RSSI (received signal strength indicator) value. All other signals do not contribute to \(f(t)\), as illustrated in Figure 2[17], which sketches a selection diversity system consisting of three antennas that receive fading signals. The antenna with the highest RSSI value can be determined, for example, by comparing the short term averages of the incoming signals on all antennas. This antenna is then connected to the receiver. The average RSSI value detected at a receiver clearly increases  
Figure 1: Schematic of a receiver with maximal ratio combining diversity for two input channels.  
compared to that of a single branch system. However, selection diversity is not an optimal diversity system, as it does not use all present diversity branches simultaneously [14].
## 4 Calibration of the Camera Array  
Methods of calibrating and rectifying images described in Section 2.4 do not completely cover transformations which need to be performed in order to calibrate and rectify EBCA. Moreover, techniques based on bundle adjustment are also insufficient because they are designed for other kinds of camera locations as presented in Section 2.4, in which work performed by [PERSON] et al. is discussed [52]. In this paper, the stereo camera calibration methods described in Section 2.4 were used. However, in adapting existing stereo camera calibrating methods to EBCA there are two missing steps: The first problem is ensuring that all stereo cameras considered in EBCA will produce a disparity map referring to the same central image, because EBCA is designed to make it possible to easily merge data obtained from different camera pairs. The second problem is calibrating baselines. Solutions for both of these two issues are introduced in Sections 4.1 and 4.2 of the paper.  
A large majority of stereo matching algorithms and calibrating algorithm are designed and implemented with such an assumption that the algorithm will be used with a stereo camera consisting of a left camera and a right camera. Disparities occur in the X dimension. In fact, every stereo matching algorithm can be similarly implemented to process images which were taken by lower and upper camera. However, it requires modifying existing implementations of algorithms for stereo cameras. It is particularly problematic when an there is no open-source implementation. This paper proposes a method in which instead of re-implementing existing software the images are flipped and rotated in such a way that they can be perceived by stereo matching algorithms a pair consisting of a left, reference image and a right, side image. After these operations disparity maps refer to points of the same central image regardless of the side camera used in EBCA. Section 4.1 describe transformations required to achieve this.  
The second problem is calibrating baselines in EBCA. It is beneficial for the quality of disparity maps obtained from EBCA when distances between cameras are as closely similar to each other as possible. However, in real devices inaccuracies occurs. In case of using stereo cameras such a problem does not exist because there is only one baseline in a stereo camera. Therefore, the problem of calibrating baselines appears when images from EBCA are processed. However, all previously performed research on camera arrays such as EBCA described in Section 2.4 did not cover methods of calibrating baselines. Therefore, this paper introduce a method described in Section 4.2.
# A Review on 5G Sub-6 GHz Base Station Antenna Design Challenges
## 3 Challenges in BSA Design
### Port Measurements: Impedance Bandwidth
#### 3.1.1 Wideband Balun  
A generic and the most adopted Balun design is shown in Figure 7. The 50 \(\Omega\) transmission feed is transformed to a balanced feed through an impedance transformer as shown in Figure 7a. This is then fed to the dipole via a series LC resonator. This series LC resonator may be required depending on the impedance presented by the dipole. It is usually not required for a halfwave dipole but is used for longer dipoles. The implementation of the Balun on a microstrip feed or otherwise known as stalk is shown in Figure 7b. The 50 \(\Omega\) feed is connected at the bottom of the stalk, which is underneath the reflector once mounted on the antenna (Figure 7c). The first transmission line (TL) and Open line (OL) at the input side of the transformer is implemented on the front side of the stalk. The backside balanced Short Line (SL), which is also connected to the reflector ground, acts as the ground for TL and OL microstrip lines printed on the front. The balanced Open Line (OL) then has a provision to include two inductors. The dipoles are soldered to one side of the capacitor on the top. The area of the parallel printed metals is adjusted to provide the required capacitance. It should be noted that Figure 7, only shows the feed for one polarization only. Two of such stalks can be combined together to feed a dual polar design.  
The variations of this generic Balun are often used in many designs to achieve wider impedance bandwidths. Some of the reported works include L-probe feed with impedance bandwidth 54% [9], Y shaped feeding line with impedance bandwidth of 45% [10], T probe line [11] with impedance bandwidth of 71.17%, and shorted stub with impedance bandwidth 27.6% in [12]. In [35], microstrip to slot line balun is used to improve impedance matching with return loss better than 14 dB over the operating band 1710-2170 MHz. Slot line impedance is controlled through slot and ground width. The feed point height adjustment is a common parameter used during the Balun design to achieve a broader bandwidth [36].
# True Equalization of Polarization-Dependent Loss in Presence of Fast Rotation of SOP +
## 5 Conclusions  
In this paper, we make clear that a true PDL equalization should include either power equalization or BER recovery, the latter of which, though, is frequently ignored in the literature. Meanwhile, in some extreme scenarios, the ultra-fast RSOP would be induced due to lightning striking and vibration. The fast RSOP in combination with PDL will put a heavy burden on the DSP equalization module. Faced with this dilemma, we proposed a method to implement the true equalization of the combined effect of PDL and ultra-fast RSOP using the Kalman filter and Golden code. First, we simplified the polarization model and then equalized the power imbalance using the 3D Stokes method and tracked the RSOP using the Kalman filter. Finally, we recovered BER asymmetry using the Golden code. The presented approach was evaluated in a 28-GBaud PDM QPSK coherent system and compared with Uncode + CMA and Golden code + TS methods. It was clear that the proposed Golden code + KF scheme provided a significant performance. With an approximate 1.2 dB OSNR penalty, it can compensate up to 7 dB PDL under 1 Mrad/s ultra-fast RSOP, which has the important gain compared to the Uncode + CMA and Golden code + TS schemes and has no coding redundancy.  
Conceptualization, N.C. and X.Z.; methodology, N.C. and W.Z.; software, N.C.; data curation, N.C.; writing--original draft preparation, N.C; writing--review and editing, X.Z.; visualization, X.T.; supervision, L.X. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (61571057, 61527820, 61575082), Fund of State Key Laboratory of IPOC (BUPT) (No. IPOC2019 ZZ02), P. R. China and BUPT Excellent Ph.D. Students Foundation (CX2019317).  
Figure 7: The performance comparison: (**a**) BER vs. OSNR; (**b**) OSNR penalty vs. PDL; (**c**) RSOP tracing curve; (**d**) BER performance under weak impairment condition; (**e**) BER performance under severe impairment condition.
# A Survey of Algorithms and Systems for Evacuating People in Confined Spaces
## 3 Evacuation Wayfinding Algorithms
### Off-Line Evacuation Wayfinding Algorithms
#### 3.1.5 Game Theoretic Model-Based Algorithms  
To model the behavioural reactions of the individuals during an evacuation process explicitly, especially the cooperative and competitive behaviours [73], many of the studies have utilised game theory to mimic the interactive decision-making and strategy-adapting among evacuees. For instance, the research in [54] employed the non-cooperative game theory [74] to mimic evacuees' exit selection process when an emergency occurred in a building with multiple exits; the procedure of the algorithm consisted of two steps: in the first step, all evacuees were considered as a \"whole entity\", which aimed at minimising the overall evacuation time, while a \"virtual entity\" was used to maximise the overall evacuation time by imposing the blockage influence; hence, a two-player zero sum game was envisaged between the evacuees and the virtual entity; the optimal strategy was found when a Nash equilibrium [75] was achieved via optimising the probabilities for the evacuees to choose each exit and the possibilities for the virtual entity to pick each exit (to generate congestion); in the second step, the decision of each individual evacuee was determined by calibrating the evacuees' probabilistic choices in terms of evacuees' distance to exits; this was because, in reality, an evacuee will not pick a farther exit unless the nearer exit is congested. The study in [56] utilised a game-theoretical model to investigate the competitive and cooperative behaviours during an evacuation process from a large single room with one exit; during the evacuation process, when \(N\) evacuees wished to occupy the same desired position, the conflict among evacuees led to a \(N*N\) game; each evacuee could choose to either compete or cooperate: if all the evacuees chose to cooperate, then they would all reach the desired position; if all the evacuees were competitive, they would all be blocked at the initial position; if one evacuee chose to compete and the rest were in a state of cooperation, only the competitive evacuee could reach the desired position; the simulation results showed that: (1) with the increasing urgency of emergency, the cooperation among evacuees decreased; (2) higher cooperation frequency resulted in shorter overall evacuation time; (3) the imitation behaviours among evacuees enhanced the cooperation level, but reduced the efficiency of the evacuation process.
# Analysis of Hydrocarbon Enrichment in Tight Sandstone Reservoirs in the Eastern Baiyun Depression
## 4 Basic Characteristics of Paleogene Reservoir Formation Elements in the Eastern Baiyun Depression  
### Development Characteristics of Source Rock  
The evaluation of source rock quality mainly includes three aspects: abundance, type and maturity of organic matter. The abundance of organic matter directly determines the hydrocarbon generation capacity and quantity of the source rock. The type of organic matter is a parameter to measure the hydrocarbon production capacity of organic matter and determines whether the product is mainly oil or gas. The analysis shows that the source rocks of the Wenchang Formation in the east of Baiyun Juwa reached the mature stage in the late deposition of the Zhuhai Formation (about 23 Ma).
# Q-Pandora Unboxed: Characterizing Resilience of Quantum Error Correction Codes Under Biased Noise
## 1 Introduction
### Contributions  
To our knowledge, this paper presents the first comprehensive study of QECCs in the context of biased noise. Our goal is to explore how QECCs can be customized for specific scenarios, aiming to reduce overhead while maintaining reliability. In this research, we use STIM [31], a fast simulator for quantum stabilizer circuits. According to a recent study [17], STIM does an exceptional job of mimicking the performance of QECCs on real quantum machines. As today's quantum computers do not have enough qubits to run QECCs directly, we find STIM to be the best tool for our study.  
In most cases, however, a code capable of managing both bit-flip and phase-flip errors, like surface codes, is necessary. Among surface codes, our analysis favors rotated surface codes for their superior thresholds, attributed to less complexity and fewer qubit needs. In the context of quantum hardware with predominant error types or noise models, we can arrange the resource requirements of different codes from least to most demanding as follows: reset and readout errors, depolarizing errors, and gate errors for error types; and the phenomenological model, the code-capacity model, and the circuit-level model for noise models. Our experiments reveal that the surface code's error threshold or the point where these codes stop working is at least ten times higher than existing quantum processors. They also have the capability of reducing the logical error rate significantly. This performance can be further enhanced by increasing resources like code distance and rounds, which we validate, to reduce the logical error rate. We also highlight that the highest-performing surface code is not always necessary. By understanding a system's targeted error rate and noise types, we can optimize surface code parameters to reduce surplus qubit and gate overhead. For an in-depth understanding and characterization of these QECCs, refer to the comprehensive analysis presented in Section 6.  
Crosstalk and leakage errors in quantum computing do not typically fall under biased noise because they represent different types of physical interactions rather than biases in error types. Crosstalk involves unintended interactions between qubits, and leakage refers to a qubit's state moving outside the computational space; both represent distinct physical phenomena unrelated to the frequency bias of error occurrences like gate or depolarizing errors. Thus, these two are not considered in this research. We assume that readers have a foundational understanding of QEC including rudimentary principles of classical error correction, repetition codes, stabilizer and encoding circuits, and topological codes, along with an understanding of the distinction between toric and surface codes. For such background information, one can refer to the recent literature on the topic, such as [32].