esa-sceva/satcom-chunk-collection huggingface dataset:
# Evaluation of Forward Models for GNSS Radio Occultation Data Processing and Assimilation
## Appendix A Abel Integral Algorithms
### Abel Integral
#### a.2.1 Direct Algorithm  
To solve the singularity of \(x=a\) in Equation (2), [22] used hyperbolic transformation, and this formula is called the direct Abel integral method (hereafter direct). First, \(d\ln(n)\) in Equation (2) is replaced with the Abel integral inversion (Details have been given in Appendix B in [37])  
\[n(r)=\exp\left[\frac{1}{\pi}\int_{a}^{\infty}\frac{\alpha(x)dx}{\sqrt{x^{2}-a^ {2}}}\right] \tag{2}\]  
Then the Equation (A1) becomes  
\[\alpha(a)=2a\int_{x=a}^{x=\infty}\frac{d^{2}\ln(n(a))}{dx^{2}}\ln\left\{\frac{x }{a}+\sqrt{\left(\frac{x}{a}\right)^{2}-1}\right\}d \tag{3}\]  
in which hyperbolic transformation can solve the singularity.  
\[z=ar\cosh\left(\frac{x}{a}\right)=\ln\left[\frac{x}{a}+\sqrt{\left(\frac{x}{a }\right)^{2}-1}\right] \tag{4}\]  
This method is the most accurate solution among all other pure mathematics to the Abel integral [41]. However, pure mathematics relies on high-quality input, whose order of magnitude should be larger, or it will become less representative. We test the exact number in experiment 1.  
It is also the algorithm of the early version of the End-to-End GNSS Occultation Performance Simulation and Processing System (EGOPS) software developed by the Wegener Center/the University of Graz (WEGC) [42]. This Abel integral method closely resembles the Abel integral and is widely used in all fields concerning the Abel integral. For example, it maps three dimensional images into its two dimensional objection [41]. [PERSON] also developed an open-access project named Pyabel in GitHub (Available online at [[https://github.com/luli/hedp/blob/master/hedp/math/abel.py](https://github.com/luli/hedp/blob/master/hedp/math/abel.py)]([https://github.com/luli/hedp/blob/master/hedp/math/abel.py](https://github.com/luli/hedp/blob/master/hedp/math/abel.py)), accessed on 8 June 2021), which was also used in our experiment.
# Analyzing Multiscale Spatial Relationships between the House Price and Visual Environment Factors
## 2 Framework
### Model Construction
#### 2.4.2 Multiscale Geographically Weighted Regression  
Spatial nonstationarity is another common phenomenon in geographic distribution. However, the HPM neglects the spatial impacts of variables, and it cannot reveal the spatial dynamics of the relationship between spatial variables. The multiscale geographically weighted regression (MGWR) model can solve this problem. Therefore, we build the MGWR model to investigate the spatial nonstationarity and to investigate the influences on house prices. The MGWR model is an extended model of the GWR and semi-parametric geographically weighted regression (SGWR). Whereas both GWR and SGWR constrain the local relationships within each model to vary at the same spatial scale, MGWR allows the conditional relationships between the response variable and the different predictor variables to vary at different spatial scales. The calculation formula of MGWR is as follows:  
\[\ln(P_{i})=\beta_{0}(u_{i},v_{i})+\sum_{j=1}^{k}\beta_{bwj}(u_{i},v_{i})x_{ij} +\varepsilon_{i} \tag{8}\]  
where \((u_{i},v_{i})\) stand for the coordinates of the \(i\)th neighborhood unit, \(bwj\) in \(\beta_{bwj}\) indicates the bandwidth used for calibration of the \(j\)th conditional relationship, \(x_{ij}\beta_{bwj}\) is the coefficient of the \(j\)th independent variables \(x_{ij}\) at location \((u_{i},v_{i})\), and \(\varepsilon_{i}\) is the \(i\)th error term.
## 2 Double-Ridged Waveguide Rotman Lens Design in the K/K\({}_{\text{a}}\)-Band
### Rotman Lens Design
For this reason, the phase error  
Figure 4: Simulated scattering parameters in amplitude (left) and adjacent port phase difference (right) of the double-ridged waveguide 10 \(\times\) 10 Rotman lens design for (**a**) port 1, (**b**) port 3 and (**c**) port 5 (reflection coefficient in _black_; coupling coefficients in _shades of blue_; transmission coefficients in _shades of red_; operating frequency bands in _light grey_). was slightly worse at the lower frequencies. It is also noted that the phase error was fairly stable across the focal arc, confirming the excellent stability of the Rotman lens across the scanning range. Port 1, which is one of the off-axis focal points, has phase errors similar to those of the other ports, although slightly worse in the upper band, confirming the phase errors are dominated by implementation aspects such as transitions and reflections within the cavity not accounted for in the simplified ray-tracing model of the Rotman lens [20; 38]. Overall, it is noted that the operation could be extended with acceptable performance up to 31 GHz to include the governmental band allocated to broadband satellite communications, confirming the very wide band operation of the beamformer. The electric field distribution obtained with the full-wave model at 20 and 30 GHz are reported for ports 1, 3 and 5 in Figure 6.  
Figure 5: Simulated RMS and peak-to-peak phase error for selected ports of the double-ridged 10 \(\times\) 10 Rotman lens design (operating frequency bands in _light grey_). Figure 6: Simulated electric field distribution in the 10 \(\times\) 10 Rotman lens design at 20 GHz (**left**) and 30 GHz (**right**) for port 1 (**top**), port 3 (**middle**) and port 5 (**bottom**). To extend slightly the scanning range while avoiding grating lobes in the visible domain, the scaling factor was set to \(\gamma\approx 1.33\), such that the 10 beams produced cover a range of 27\({}^{\circ}\) with a beam-to-beam angular spacing of 6\({}^{\circ}\). The linear array considered has an element spacing of 6.28 mm, corresponding to 0.63 \(\lambda_{0}\) at 30 GHz. Here, we focus on the quasi-optical beamformer design and assume the output ports are connected via equal-length coaxial cables to the elements of the linear array using adequate transitions. Section 3 discusses the Rotman lens design adaptation to additive manufacturing and associated experimental results.
## 3 Results
### Individual Electron Density Profile Comparison
GNSS-RO profiles were not shifted in altitude, such that the ionosonde and RO profiles perfectly align at the \(fmin\) altitude. The average distance the profiles were shifted (i.e., the average altitude difference at \(fmin\)) is displayed in Table 3. Examples of the shifted profiles are presented in Figure 4, which are the shifted profiles corresponding to the examples given in Figure 3.  
Once the ionosonde profile has been shifted, the GNSS-RO profiles are nearly the same in the E-region, and the difference in \(N_{e}\) below \(fmin\) between the ionosonde and the GNSS-RO profile is much more apparent. Another noteworthy feature of the GNSS-RO profiles that will be discussed in more detail in Sections 3.3 and 4 is the lack of a clear E-region peak in many of the profiles. This is observed in the Gakona RO profile in Figures 3 and 4, where the profile shows a minor change in slope with respect to altitude near 110 km, but it does not show a clear E-region peak or E- to F-region valley. All following statistical comparisons aside from the frequency of the E-region peak (\(foE\)) and \(hmE\) comparison will be performed for both the original unshifted profile and the shifted profile. In Section 3.5, the direct virtual height measurements from the ionosondes are used to compare against virtual heights calculated from the RO profiles, which removes the uncertainty in the ionogram inversion process and eliminates the need to shift profiles for comparison.
# Co-Design of Mechanical and Vibration Properties of a Star Polygon-Coupled Honeycomb Metamaterial
## 4 Comparison and Analysis of the Bandgap Properties
### Calculation of Bandgap Properties  
It is assumed that the damping and body forces are not considered; the propagation of elastic waves in two-dimensional structures can be expressed by Equation (1) according to the elastic dynamics [44].  
\[\rho(\mathbf{p})\ddot{\mathbf{L}}(\mathbf{p})= \
abla[\lambda(\mathbf{p})+2\mu(\mathbf{p})][\
abla\mathbf{L}( \mathbf{p})]-\
abla\times[\mu(\mathbf{p})\
abla\times\mathbf{L}(\mathbf{p})] \tag{1}\]  
where \(\rho\) represents the mass density, \(\mathbf{L}\) is the displacement vector, \(\mathbf{p}=(x,y)\) denotes the position vector, and \(\
abla\) indicates the differential operator. \(\lambda\) and \(\mu\) are constants and can be used to express [PERSON]'s modulus \(E\) and [PERSON]'s ratio \(v\) as:  
\[E=\frac{\mu(3\lambda+2\mu)}{\lambda+\mu},v=\frac{\lambda}{2(\lambda+\mu)} \tag{2}\]  
\(\mathbf{L}\) can be further extended in accordance with the [PERSON]'s theorem as:  
\[\mathbf{L}(\mathbf{p},\mathbf{k})= \mathbf{L}(\mathbf{p})e^{\beta(\omega t-\mathbf{p}\mathbf{k})} \tag{3}\]  
in which \(\omega\) and \(t\) represent the angular frequency and time, accordingly. \(\mathbf{k}\) denotes the wave vector of the lattice, \(\delta=\sqrt{-1}\).  
Since the proposed structures are periodic, \(\mathbf{L}\) is a periodic function that has the same periodicity with the proposed structures, and the following relationship is possessed:  
\[\mathbf{L}(\mathbf{p},\mathbf{k})=\mathbf{L}(\mathbf{p},\mathbf{k}+\mathbf{R}) \tag{4}\]  
where \(\mathbf{R}\) stands for the lattice vector. Combining Equations (3) and (4), we have:  
\[\mathbf{L}(\mathbf{p}+\mathbf{R},\mathbf{k})= \mathbf{L}(\mathbf{p})e^{\beta(\omega t-\mathbf{p}\mathbf{k})} \tag{5}\]  
Substituting Equation (5) into Equation (1), after some manipulations, the following eigenvalue equation is derived:  
\[\Big{(}\mathbf{K}-\omega^{2}\mathbf{M}\Big{)}\mathbf{Y}=0 \tag{6}\]  
in which \(\mathbf{K}\) stands for the stiffness matrix, \(\mathbf{M}\) denotes the mass matrix, and \(\mathbf{Y}\) is the displacement vector of the nodes.
# Verification Methodology for Simulation Models of the Synchronous Generator on Transients Analysis
## 2 Modeling Methods for Transients Calculation
### Sudden Short-Circuit by a Dynamic Model  
The node-voltage matrix Equation (4) is used to determine electromagnetic events in windings of the machine [1]:  
\[[\text{U}]=[\text{R}]\cdot[\text{i}]+[\text{L}]\cdot\frac{\text{d}[\text{i}]} {\text{dt}}+\omega_{\text{el}}\cdot\frac{\text{d}[\text{L}]}{\text{d}\gamma} \cdot[\text{i}], \tag{4}\]  
where  
[U] is the matrix of voltage,  
[i] is the matrix of current,  
[R] is thermatrix of resistance,  
[L] is the matrix of inductance,  
\(\omega_{\text{el}}\) is the electric angle velocity of rotor, and  
\(\gamma\) is the electric angle between the axis of stator phase \"a\" and the d-axis of rotor. The practice is to make the transformations of variables in the two-phase rotors \"dq0\" coordinate system instead of in the primary three-phase \"abc\" system, in order to eliminate the mutual inductance connection placed between the windings with axes that are not perpendicular to each other, as well as the interrelation of inductance on the angular position of the rotor. The transformation matrices used for the substitution of a three-phase electrical machine to a two-axis model are elaborated upon in (2). In order to prepare the system for suitability with computer modeling, the matrix in Equation (4) is disassembled into a system of differential equations. That system introduces current substitution and mutual magnetic fluxes.
## 5 MUD-Enhanced Bootstrapping
### Smart Object Authentication  
The first phase of the MUD-enhanced bootstrapping is the _smart object authentication_ based on the use of PANA to transport the required EAP-PSK messages. Therefore, this process is initiated by the smart object (acting as the PaC) with a PANA-Client-Initiation message (message 1) to the Authentication Agent, which acts as the PAA. Then, this entity sends a PANA-Auth-Request (PAR) (message 2) including the set of supported PRF and integrity algorithms, which are required for key derivation purposes. The smart object selects a PRF and integrity algorithm, and it includes them into a PANA-Auth-Answer (PAN) (message 3). After these parameters are agreed, the Authentication Agent requests the smart object identity, which is sent to the AAA Server. Toward this end, the smart object, Authentication Agent, and AAA server perform an EAP message exchange (messages 4-10) in which a specific EAP method is selected (EAP-PSK in our case). Then, the EAP-PSK exchange [31] is carried out for the authentication of the smart object. For this exchange (messages 11-18), PAR and PAN messages are used to transport EAP Request and EAP Response messages between the smart object and the Authentication Agent. Furthermore, this entity forwards EAP packets through a RADIUS Access-Request and RADIUS Access-Challenge messages to the AAA Server. If the process is successfully completed, the Authentication Agent receives an EAP Success packet, which is included in a RADIUS Access-Accept message (message 19). In our proposal, this message contains the MUD URL of the smart object's MUD file that is included as a RADIUS attribute _Vendor-Specific_[41]. Such attribute is intended to allow vendor to support their own extended attributes. This message also contains the Master Session Key (MSK), which is derived between the smart object (acting as EAP peer) and AAA server (acting as EAP server), and exported by the EAP-PSK exchange.
## 2 Channel Model and Signal-to-Noise Ratio
### Channel Impulse Response  
To evaluate the impulse response of the indoor IR channel, a Monte Carlo ray-tracing algorithm was implemented. In general, the impulse response of the IR channel for arbitrary emitter \(E\) and receiver \(R\) positions can be expressed as an infinite sum of the form [14]:  
\[h(t;E,R)=h^{(0)}(t;E,R)+\sum_{k=1}^{\infty}h^{(k)}(t;E,R) \tag{2}\]where \(h^{(0)}(t;E,R)\) represents the LOS impulse response and \(h^{(k)}(t;E,R)\) is the impulse response of the light undergoing \(k\) reflections, i.e., the multiple-bounce impulse responses. Given an emitter \(E\) and receiver \(R\) in an environment free of reflectors (Figure 1), with a large distance d between both, the LOS impulse response is approximately:  
\[h^{(0)}(t;E,R)=\frac{1}{d^{2}}R_{E}(\theta,n)A_{eff}(\psi)\delta\left(t-\frac {d}{c}\right) \tag{3}\]  
where \(R_{E}(\theta,n)\) represents the generalized Lambertian model used to approximate the radiation pattern of the emitter, c is the speed of light and \(A_{eff}(\psi)\) is the effective signal-collection area of the receiver [14]. In general, a bare detector, commonly called a single-element detector, achieves an effective signal-collection area of:  
\[A_{eff}^{barr}(\psi)=A_{R}cos(\psi)\ rect\left(\frac{\psi}{FOV}\right),\ where\ rect\left(x\right)= \begin{cases}1,&\left|x\right|\leq 1\\ 0,&\left|x\right|>1\end{cases}  \tag{4}\]  
where \(A_{R}\) is the physical area of the receiver, and FOV is the receiver field of view (semi-angle from the surface normal). In an environment with reflectors, however, the radiation from the emitter can reach the receiver after any number of reflections (see Figure 2). In the algorithm, to calculate the impulse response due to multiple reflections, many rays are generated at the emitter position with a probability distribution equal to its radiation pattern. The power of each generated ray is initially \(P_{E}/N\), where \(N\) is the number of rays used to discretize the optical source. When a ray impinges on a surface, the reflection point becomes a new optical source, thus a new ray is generated with a probability distribution provided by that surface's reflection pattern. The process continues throughout the maximum simulation time, \(t_{max}\). After each reflection,  
Figure 1: Emitter and receiver geometry without reflector. Figure 2: Emitter and receiver geometry with reflector. Reflection pattern of the surface is described by [PERSON]’s model. the power of the ray is reduced by the reflection coefficient of the surface, and the reflected power reaching the receiver (\(p_{i,k}\), \(i\)-th ray, \(k\)-th time interval) is computed by:  
\[p_{i,k}=\frac{1}{d^{2}}R_{S}(\varphi,\varphi^{\prime})A_{eff}(\psi) \tag{5}\]  
where \(R_{S}(\varphi,\varphi^{\prime})\) is the model used to describe the reflection pattern. In this work, [PERSON]'s model is used [17]. In this model, the surface characteristics are defined by three parameters: the reflection coefficient \(\rho\), the percentage of incident signal that is reflected diffusely \(rd\), and the directivity of the specular component of the reflection \(m\).
# Machine Learning Techniques for Non-Terrestrial Networks
## 4 Non-Terrestrial Network Architectures
### NTN Architectures
#### 4.2.2 Regenerative NTN Architecture  
In Figure 5, the regenerative NTN architecture is reported. In this case, the gNB is mounted on-board to the NTE, thus improving the NTN performance. Differently from the transparent NTN case in Figure 2, where the satellite radio interface (SRI) in the feeder link is based on 5G-Uu, for regenerative NTN, the SRI is a transport link used to transmit both user and control data from the NTE to the NTN gateway on the ground.  
The structure of the protocol stack for regenerative NTN is reported in Figures 6 and 7 for UP and CP, respectively. The NTE is not transparent, and the typical processing of the gNB is performed on-board, where the access stratum protocols close. The NTN gateway is transparent, and it does not affect the GTP tunnel from the gNB to UPF.  
Figure 4: Protocol stack of the control plane in the transparent NTN architecture [27].  
Figure 5: Regenerative NTN architecture.  
Figure 6: Protocol stack of the user plane in the regenerative NTN architecture [27].
## 2 Materials and Methods
### Spectral Measurements  
Reflectance measurements were acquired in the laboratory with a Spectra Vista Cooperation (SVC) HR1024i field spectrometer ranging from 350 nm to 2500 nm. The SVC field spectrometer consists of three diffraction grating spectrometers ranging from 350 nm to 1000 nm, 1000 nm to 1890 nm and from 1890 nm to 2500 nm with a spectral resolution (FWHM, full width at half maximum) of \(\leq\)3.5 nm, \(\leq\)9.5 nm and \(\leq\)6.5 nm, respectively. All measurements were taken with a 14\({}^{\circ}\) nominal foreoptic (FOV) and a scan time of 3 s relative to a standardized Spectralon panel. Two 75 W halogen lamps mounted on either side of the spectrometer were used to illuminate the target at an incident angle of 30\({}^{\circ}\). The distance between sensor and sample surface was approximately 80 cm resulting in a measurement spot diameter of about 20 cm (Figure 2).  
All spectra were resampled to 1 nm and smoothed using a Savitzky Golay filter [15] with a filter size of 32 and a smoothing polynomial of 4. Before analysis, noisy bands on either side of the spectral range below 400 nm and above 2450 nm were removed.  
Measurements with the SVC field spectrometer were carried out on all 11 days of the experiment. In addition, every second day starting on 9 July hyperspectral image data were acquired using a mobile hyperspectral imaging system [16]. The Specim IQ camera measures reflectance in 204 spectral bands between 400 nm and 1000 nm with a spectral resolution of 7 nm (FWHM). The camera was mounted approximately 36 cm above the pots' surface resulting in a field of view of 20 cm \(\times\) 20 cm in the centre of the pots.
## 3 Methodology
### Channel Coding/Decoding  
In the Channel Coding block, the video is converted into binary data, represented as binary information. In channel coding, redundant bits are added to the original data to enhance the robustness of the transmission. Moreover, various combinations of code pairs are utilized to further enhance the robustness of the transmission by channel coding. The RS-CONV and BCH-LDPC are codes applied sequentially. Initially, an external encoder (RS and BCH) adds redundancy to the binary information; subsequently, a second layer of redundancy is added by the internal encoder (LDPC and CONV), as presented in Figure 3. The Channel Decoding block decodes the received information by performing the inverse operations of the RS-CONV and BCH-LDPC, thus obtaining the binary information corresponding to the received video.  
A brief description of the codes is presented below.  
* BCH (Bose-Chaudhuri-Hocquenghem): BCH codes represent block codes that function on multiple bits instead of individual ones. Employing a BCH(n,k) code enables the encoding of k message bits and the generation of encoded n-bit data, where \(n\) is equal to \(2^{m}-1\) with \(m\geq 3\)[31];
* LDPC (low-density parity check): LDPC codes utilize a binary parity check matrix characterized by numerous elements with values of 1 and 0. In particular, LDPC coding encompasses diverse methodologies, including the implementation of matrices and graphs [32];
* RS (Reed-Solomon): RS codes are systematic cyclic linear block codes that operate on symbols with width of \(m\) bits, where m is \(m>2\). In RS codes, the codes are designed in such a way that every possible m-bit word is indeed a valid symbol [33];
* CONV (convolutional codes): Unlike block encoding, the output of the convolutional encoder is not in block format but in the form of a coded sequence generated from an input information sequence. The encoder generates redundancy through convolutions. The decoder utilizes the redundancy in the coded sequence to determine which message sequences are sent through an error correction action. Thus, in this type of error-correcting code, a set of \(m\) symbols is transformed into a set of \(n\) symbols [34].  
Table 2 lists the parameters of the channel encoders and the transmission and reception process of the OFDM systems. These parameters are based on the standards defined in [35; 36].  
\begin{table}
\begin{tabular}{c c} \hline Resolution & 4K (3840 \(\times\) 2160) \\ \hline Frame rate & 50 FPS (frames per second) \\ \hline Number of frames & 500 \\ \hline Length of GOP (Group of Pictures) & 20 \\ \hline B-frames per GOP & 3 \\ \hline Quantization parameter (QP) & 37 \\ \hline \end{tabular}
\end{table}
Table 1: Parameters of codification.  
Figure 3: Concatenated BCH-LDPC coding scheme.
# Elevation Angle Characterization for LEO Satellites: First and Second Order Statistics
### Contributions
#### 1.1.2 Contribution 2  
The PDF and CDF of the elevation angle can be obtained as proposed in [1; 2]. Nonetheless, this document describes a methodology to obtain the PDF and CDF parameters of the elevation angle distribution for different orbit configurations and ES locations using a well-known random variable. The proposed random variable facilitates analytical manipulation as well as computation of the probabilities of occurrence of the elevation angle at  
Figure 1: Elevation angle cases for LEO satellite systems: (**a**) The values of \(\theta_{min}\) and \(\theta_{max}\) are usually related to the best and worst case of the received power, \(P_{R}\), at an ES; nonetheless, those cases are rare and represent the extremes of \(\theta\). (**b**) The elevation angle of a LEO satellite system as observed from an ES is always-varying; then, it is more convenient to analyze its behavior through statistical tools.  
specific values. A small table containing the resultant parameters to characterize multiple LEO orbits configurations as observed from multiple ES's is included.