esa-sceva/satcom-chunk-collection huggingface dataset:
# Massive Data Capture Approach for Modeling Existing Building Stocks
## 4 Results  
A general image of the resulting model is shown in Figure 3. The resulting BIM of the building with its surroundings is based on joining all the data, more than 181,553,907 points, with associated data and 22 reality capture alignment points. This model needed 220 min processing time and 170 min capture time.  
As previously mentioned, this final model is the result of joining the data from TIS, the laser scanner (TLS), automatic frame extraction from a UAV video (AFE) and HQ pictures from UAV (HQP), cartography, and LiDAR. The resulting model has controlled precision and is georeferenced. The specific contributions of the technologies applied in this research have been as expected. Satellite LiDAR mainly provides high coverage of the surroundings, which when combined with existing cartography, enhances the inclusion of large areas to the BIM. Image capture from video or high-quality pictures improves the overall point cloud density and roof coverage, as well as obtains high-quality RGB color information. Geometric precision is obtained from the topographic survey, which can be also used to check data integrity. TLS contributes to obtaining large point clouds with high precision and orientation information, and TIS offers sufficient precision and greatly improves the capture time indoors, where TLS is very slow and AFE or HQPs are not possible due to the aforementioned special constrains.  
Figure 3: General view of the model resulting from applying the new approach to the BCN.C2 reference building.
## 4 Performance Analysis
### Bit Error Rate  
Assuming the frequency offset \(w_{if}\) and the phase offset \(\Delta\varphi\) between the signal and the local laser are estimated and compensated ideally, the BER of a BPSK system is expressed as [21]:  
\[P_{e}=\frac{1}{2}{\int_{0}^{\infty}}\mathit{erfc}(\sqrt{\frac{\gamma}{2}})d\gamma \tag{14}\]  
where \(\gamma\) is the SNR described in (10). For an optical communication system with channel fading the bit error rate can be obtained as  
\[P_{e}=\frac{1}{2}{\int_{0}^{\infty}}\mathit{f}(I)\mathit{erfc}(\sqrt{\frac{ \gamma_{0}}{2}I})dI \tag{15}\]  
\(f(I)\) is the probability density function of irradiance \(I\) described by (5). According to (5), (10), (13) and (15), \(P_{e}\) can be expressed as:  
\[P_{e}=\frac{1}{2}{\int_{0}^{\infty}}\frac{1}{\sqrt{2\pi\sigma_{l}^{2}}}\frac{1 }{I}\exp\left\{-\frac{\left[\ln(\frac{I}{I_{0}})-E(I)\right]^{2}}{2\sigma_{l}^ {2}}\right\}\mathit{erfc}(\sqrt{\frac{\gamma_{0}}{2}I})dI \tag{16}\]  
\(f(I)\) is determined by \(\sigma_{l}\), and \(\sigma_{l}\) is influenced by the aperture diameter described in (1).  
If the aperture area is considered as variable as described in (11) and (12), the BER is expressed as:  
\[P_{e}=\frac{1}{2}{\int_{0}^{\infty}}\frac{1}{\sqrt{2\pi\sigma_{l}^{2}}}\frac{ 1}{I}\exp\left\{-\frac{\left[\ln(\frac{I}{I_{0}})-E(I)\right]^{2}}{2\sigma_{l} ^{2}}\right\}\mathit{erfc}(\sqrt{A\frac{\rho_{0}}{2}I})dI \tag{17}\]  
If the frequency offset and the phase offset are not estimated ideally, the constellation of information bits rotates within certain range, and the BER may higher than the above results.
## 3 Numerical Examples
For the case where the boundary condition at one end is free, we have \(F=0\), which means the axial force is zero, leading to the equation  
\[+\rho A\omega^{2}V_{x}(x)+\mu\left[-z_{c}\omega^{2}\Theta_{z}(x)- y_{c}\omega^{2}\Theta_{y}(x)\right]=0,\]3  
Additionally, the boundary conditions given in Equation (23) require  
\[+\rho A\omega^{2}V_{x}(x)+\mu\left[-z_{c}\omega^{2}\Theta_{z}(x)- y_{c}\omega^{2}\Theta_{y}(x)\right]=0,\]4As a result, under these conditions, \(\frac{dV_{x}}{dx}=0\) holds. These requirements are satisfied by taking  
\[ \begin{bmatrix}V_{y}(x)\\ V_{z}(x)\\ \Psi(x)\end{bmatrix} = \begin{bmatrix}C_{V_{y}}\sin(\lambda_{n}x)\\ C_{V_{y}}\sin(\lambda_{n}x)\\ C_{\Psi}\sin(\lambda_{n}x)\end{bmatrix} \quad\text{and}\quad \begin{bmatrix}V_{ x}(x)\\ \Theta_{y}(x)\\ \Theta_{z}(x)\end{bmatrix} = \begin{bmatrix}C_{V_{x}}\lambda_{n}\cos(\lambda_{n}x )\\ C_{\Theta_{y}}\lambda_{n}\cos(\lambda_{n}x)\\ C_{\Theta_{z}}\lambda_{n}\cos(\lambda_{n}x)\end{bmatrix} , \tag{28}\]  
where \(C_{V_{x}},C_{V_{y}},C_{V_{z}},C_{\Theta_{z}},C_{\Theta_{z}}\), and \(C_{\Psi}\) are unknown constants and \(\lambda_{n}=\frac{n\pi}{L}(n=1,2,3,\dots)\). Substituting Equation (28) into Equation (22) gives the six homogeneous differential equations for \(C_{V_{x}},C_{V_{y}},C_{V_{z}},C_{\Theta_{y}},C_{\Theta_{z}}\), and \(C_{\Psi}\). The resulting equation is obtained as follows:  
\[\textbf{B}_{(6\times 6)}\vec{x}_{(6\times 1)}=\vec{0}_{(6\times 1)}, \tag{29}\]  
where \(\vec{x}_{(6\times 1)}=(C_{V_{x}},C_{V_{y}},C_{\Theta_{y}},C_{\Theta_{z}},C_{ \Psi})^{T}\). For details of the matrix **B** form, see Appendix B. This system of linear equations cannot have \(\vec{x}_{(6\times 1)}\) being identically equal to zero, thus leading to the equation  
\[\det[\textbf{B}_{(6\times 6)}]=0, \tag{30}\]  
\[b_{1}(\omega^{2})^{6}+b_{2}(\omega^{2})^{5}+b_{3}(\omega^{2})^{4}+b_{4}(\omega ^{2})^{3}+b_{5}(\omega^{2})^{2}+b_{6}(\omega^{2})^{1}+b_{7}=0. \tag{31}\]  
The coefficients \(b_{1},b_{2},b_{3},b_{4},b_{5},b_{6}\), and \(b_{7}\) are derived from the system of Equation (29). These coefficients imply that for each \(n\), which defines an external vibration mode of the beam's axis as a whole, there exist six internal modes of vibration within the cross-sections. For \(n=1,2,3\), six natural frequencies of a simply supported thin-walled beam, corresponding to three different cross-sectional types, were determined. These six numerical values characterize six distinct internal vibration modes: axial vibration along the \(x\)-direction, bending vibration along the \(y\)-direction and \(z\)-direction, and torsional vibration modes along the \(x\)-, \(y\)-, and \(z\)-directions. In this section, three numerical examples are used to validate the effectiveness and accuracy of the proposed Timoshenko-Vlasov beam model in comparison to traditional beam models. For each example, beams with lengths of 3 m, 10 m, and 50 m are calculated and compared.
# Numerical Phase-Field Model Validation for Dissolution of Minerals
## 5 PF Modelling Methodology and Numerical Implementation
### Finite Element Implementation  
Numerical implementation of the PF model is carried out by using finite element method in the framework of multiphysics object-oriented simulation (MOOSE) environment [28]. Transient solver with preconditioned Newton's method was used. In this case, the full and accurate Jacobian was calculated. The backward Euler algorithm was employed. Adaptive time stepping was used to improve computational efficiency. The time step would grow or shrink according to the number of iterations taken and needed to obtain a converged solution in the last converged step. The maximum number of non-linear iterations per time step was also set to provide optimal solution efficiency. For 2D simulation, the triangular element type was chosen to mesh the geometry.  
In addition, an adaptive mesh refinement (AMR) was used [97]. Based on the error estimated from the FEM results, the global and local mesh errors were calculated, and then the mesh size was automatically adjusted to the changing morphology of the grain boundaries at each time step. This is very effective for the numerical solution of partial differential equations in regions of arbitrary shape. In order to ensure numerical stability and simulation accuracy, at least 5 nodes on the diffusion interface were used to describe the boundary morphology, while coarser grids were used for solutions and solids that were far from the boundary (Figure 3). This does not only provide an accurate representation of the boundary evolution, but also improved the computational efficiency. The relative and absolute error tolerance was set to \(10^{-8}\).
# Analysis of Multi-Antenna GNSS Receiver Performance under Jamming Attacks
## 3 Simulation Results and Discussion
### Tracking Domain Analysis
Figure 5: Tracking performance of PRN 6 with CW interference. Figure 6: Carrier tracking performance of PRN 6 with chirp interference. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Single Antenna**} & \multicolumn{3}{c}{**PM**} & \multicolumn{3}{c}{**MPDR**} \\ \cline{2-10}
**PRN** & **RMSE Doppler** & \multicolumn{2}{c}{**C/N\({}_{\text{B}}\)**} & **RMSE Doppler** & \multicolumn{2}{c}{**PLI**} & \multicolumn{2}{c}{**C/N\({}_{\text{B}}\)**} & **RMSE Doppler** & \multicolumn{2}{c}{**PLI**} & \multicolumn{2}{c}{**C/N\({}_{\text{B}}\)**} \\  & **(Hz)** & **PLI** & **(dB-Hz)** & **(Hz)** & **PLI** & **(dB-Hz)** & **(Hz)** & **PLI** & **(dB-Hz)** \\ \hline PRN 3 & 0.45 & 0.99 & 36.6 & 0.32 & 0.99 & 48.9 & 0.26 & 0.99 & 54.9 \\ PRN 6 & 0.40 & 0.99 & 36.6 & 0.36 & 0.99 & 48.0 & 0.28 & 0.99 & 54.7 \\ PRN 10 & 0.46 & 0.99 & 36.7 & 0.78 & 0.99 & 45.8 & 0.36 & 0.99 & 54.4 \\ PRN 16 & 0.74 & 0.99 & 36.7 & 0.61 & 0.99 & 45.9 & 0.51 & 0.99 & 54.4 \\ PRN 18 & 0.43 & 0.99 & 36.7 & 0.40 & 0.99 & 47.3 & 0.35 & 0.99 & 54.4 \\ PRN 21 & 0.42 & 0.99 & 36.7 & 0.35 & 0.99 & 48.5 & 0.33 & 0.99 & 54.8 \\ PRN 24 & 0.48 & 0.99 & 36.6 & 0.46 & 0.99 & 47.6 & 0.36 & 0.99 & 54.0 \\ PRN 25 & 0.47 & 0.99 & 36.7 & 0.43 & 0.99 & 47.0 & 0.33 & 0.99 & 54.9 \\ PRN 29 & 0.55 & 0.99 & 36.7 & 0.49 & 0.99 & 45.4 & 0.46 & 0.99 & 54.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Tracking performance of different PRNs in the presence of chirp interference. Figure 7: Carrier tracking performance of PRN 6 with Band limited white Gaussian noise.
# Non-Thermal Methods for Ensuring the Microbiological Quality and Safety of Seafood
## 3 Ultrasound--US
### Effects of US on the Quality of Fish and Seafood  
As mentioned before, US treatment can be used in combination with other methods or individually to improve the physical properties [121; 123; 124] and the sensory quality [122; 128] of fish and seafood products. Alternatively, it can be used to evaluate the fat content's measurement in live carps as a non-invasive method as reported by [PERSON] et al. (2019) [129]. They used ultrasound at 5 MHz to measure the backfat thickness of carp (_Cyprinus carpio_) for the first time to ensure product quality and to achieve high customer acceptance. Shrimps are commonly blamed for causing allergic reactions [130; 131], and high-intensity ultrasounds have been proved that can be used as a treatment to influence the allergenicity showing positive effects with a 76% reduction in tropomyosin [123]. Regarding the effectivity of US to improve the physical properties of cod fillets, [PERSON] et al. (2021) [120] proposed the use of US to improve hydration and reduce the processing times. [PERSON] et al. (2019) [128] combined US at 60 or 80 W with chitosan nanocomposite water-retaining agent (WRA) to study their cryoprotective effect on crayfish during frozen storage at \(-18\)\({}^{\circ}\)C. They resulted in significant differences in the soaking weight gain, thawing loss, water content, and water activity between the control and WRA treated groups of frozen crayfish. Finally, they reported that US at 60 W and WRA improved the overall quality of the frozen crayfish at \(-18\)\({}^{\circ}\)C.
# An Enhanced YOLOv5 Model for Greenhouse Cucumber Fruit Recognition Based on Color Space Features
## 3 Results
### Comparison of Detection Effects  
The recognition effect of the original YOLOv5s model and the enhanced YOLOv5s model are compared in Figures 9 and 10.  
The detection results of the original YOLOv5s model are shown in Figure 9, where only relatively intact fruit are identified. The recognition ability for occluded fruits is poor, and small fruits cannot be distinguished. Figure 10 shows the test results using the enhanced YOLOv5s model. Most cucumber fruits are accurately identified, and incomplete fruits can also be accurately classified. The result is significantly better than that of the original model. From the comparison, the enhanced YOLOv5 method has a good recognition ability and high confidence for intact cucumber fruit, partially occluded cucumber fruit, and sliced cucumber fruit in a relatively complex background. At the same time, labeling the negative samples of leaves and stems as the background can greatly avoid identifying green leaves or stems as cucumber fruits and improve the recognition accuracy.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & & **F1** & **Precision** & **Recall** & **mAP** & **FPS** \\ \hline \multirow{3}{*}{SSD} & original & 0.41 & 53.65\% & 26.11\% & 42\% & 28.3 \\  & enhanced & 0.41 & 55.16\% & 26.11\% & 42\% & 28.9 \\ \multirow{3}{*}{Faster R-CNN} & original & 0.50 & 51.66\% & 48.23\% & 46\% & 21.7 \\  & enhanced & 0.54 & 54.75\% & 53.54\% & 51\% & 22.5 \\ \multirow{3}{*}{YOLOv5s} & original & 0.63 & 83.70\% & 52.21\% & 53\% & 53.2 \\  & enhanced & 0.67 & 85.19\% & 54.03\% & 58\% & 53.3 \\ \multirow{3}{*}{YOLOv5m} & original & 0.64 & 80.54\% & 52.21\% & 53\% & 38.6 \\  & enhanced & 0.65 & 83.69\% & 53.10\% & 56\% & 39.1 \\ \multirow{3}{*}{YOLOv5l} & original & 0.64 & 80.54\% & 53.10\% & 54\% & 24.4 \\  & enhanced & 0.66 & 81.17\% & 55.31\% & 57\% & 24.5 \\ \multirow{3}{*}{YOLOv5x} & original & 0.61 & 78.95\% & 52.21\% & 55\% & 13.2 \\  & enhanced & 0.64 & 81.38\% & 53.10\% & 55\% & 14.7 \\ \hline \end{tabular}
\end{table}
Table 3: Comparison of evaluation indexes of enhanced YOLOv5s model.  
Figure 9: Detection effect of the original YOLOv5s models.  
For prediction, 100 images of cucumber fruits were divided into 10 groups, each consisting of 10 images. The comparison results of the number of fruits in each image group counted by the enhanced YOLOv5s model and manual statistics can be found in Table 4.  
According to Table 4, both the intact fruit in the image and the partially occluded fruit were correctly identified by the enhanced YOLOv5s model, with an average recognition precision of 80.3%. The missing detections are due to cucumbers with few pixels and those that are far from the lens, which have no influence in automated harvesting.
## 3 Results and Discussion
On this point, we steadily increased \(P_{1}\) to 229 mW (maximum) while \(P_{2}\) was fixed at a maximum of 200 mW. For \(\Delta\)T = 0 \({}^{\circ}\)C, an overall nonlinear conversion efficiency of \(\sim\)20.3%/W was calculated using the relation \(\eta_{SFG}=P_{SFG}/(P_{1}P_{2})\), where \(P_{SFG}\) is the sum frequency power. This is, however, lower than the theoretical value of \(\sim\)33.4%/W calculated approximately from \(P_{SFG}=32\pi^{2}d_{eff}^{2}P_{1}P_{2}L/n_{SFG}\varepsilon_{0}\lambda_{SFG}^{2 }c(n_{1}\lambda_{2}+n_{2}\lambda_{1})\)[29], where \(c\) is the speed of light in vacuum, \(\varepsilon_{0}\) is the permittivity in vacuum, and \(d_{eff}=2d_{33}/\pi\) is the effective nonlinear coefficient of MgO:PPLN \(n_{SFG}\), \(n_{1}\), and \(n_{2}\) are refractive indices at \(\lambda_{SFG}\), \(\lambda_{1}\), and \(\lambda_{2}\), respectively. We noted a reduced SFG power measured to be \(\sim\)22% of its maximum (at \(\Delta\)T = 0 \({}^{\circ}\)C) when the SFG bandwidth is maximum (at \(\Delta\)T = 22.1 \({}^{\circ}\)C). The reduction in conversion efficiency is attributable to fabrication errors of the crystal structure. However, the efficiency of the up-converted output can be increased by using different approaches, for instance, use of high power fundamental lasers, focusing the two incident beams at the same point in the crystal, and/or by anti-reflection (AR) coating the crystal facets to minimize Fresnel reflection losses. The spatial profile of the orange light beam was measured with the knife-edge method using Beamage (Ophir-Spiricon, Inc., Jerusalem, Israel) laser beam analyzer at a distance of \(\sim\)20 cm from the output face of the crystal. The horizontal and vertical M\({}^{2}\) factors were measured to be \(\sim\)1.9 and \(\sim\)2.1 respectively. The degradation of the beam quality could be attributed to the use of a non-achromatic lens which leads to different focus positions inside the MgO:PPLN crystal. Figure 5 shows the time dependence of the orange light output power at triple-wavelength operation over a period of 30 mins measured using the StarLab 2.11 software from Ophir, Incl., Jerusalem, Israel, indicating \(<\)2.5% fluctuation about 9.3 mW. This fluctuation can be attributed to the stability of both input lasers, fluctuation in temperature of the MgO:PPLN crystal, air currents and mechanical vibrations of the laboratory environment (Ophir-Spiricon Inc.). Figure 4: Measured SFG output power (green circles) as a function of the product of input fundamental power at \(\Delta\)T = 0 \({}^{\circ}\)C. The solid red curve is a quadratic fit to the SFG data using \(P_{SFG}=\eta_{SFG}P_{1}P_{2}\), where \(\eta_{SFG}\) = 20.3%/W is the SFG normalized conversion efficiency determined from power measurements. The error bars include the uncertainty in the output power measurements.
# A Phase Angle-Modulated Bat Algorithm with Application to Antenna Topology Optimization
## 2 Background
### Binary Bat Algorithm  
The emergence of the bat algorithm was as a means to solve the continuous numerical optimization problem and to find the necessary 0/1 string in the feature selection problem. Additionally, the BBA introduces the transfer function to change the position update equation [22]. The velocity and frequency of the BBA are defined in continuous space. Compared with BA, BBA was additionally modified as follows:  
* A transformation function was added to map a continuous position vector to a discrete bit vector.
* The random walk Equation (4) that improves the local search ability was deleted, as it is not suitable for the binary optimization algorithm.  
In the BBA, using Equation (8) as the transfer function, the probability of the individual velocity of the BBA population is mapped to its position vector element flip. The greater the absolute value of the independent variable speed, the greater the dependent variable result, and the greater the probability of element flipping. The location update rules are as follows:  
\[f(v_{i}^{k}(t))=|\frac{2}{\pi}\text{arctan}(\frac{2}{\pi}v_{i}^{k}(t))| \tag{8}\]\[X_{i}^{k}(t+1)=\left\{\begin{array}{ll}\left(X_{i}^{k}(t)\right)^{-1},&rand\leq f (v_{i}^{k}(t+1))\\ X_{i}^{k}(t),&rand>f(v_{i}^{k}(t+1))\end{array}\right. \tag{9}\]  
where \(X_{i}^{k}(t)\) and \(V_{i}^{k}(t)\) indicate the \(k\)-th dimension position and velocity of the \(i\)-th bat at iteration \(t\), and \(\left(X_{i}^{k}(t)\right)^{-1}\) indicates the complement of \(X_{i}^{k}(t)\).
## 3 Results and Discussion
### Experimental Results for the Four Typical Crack Models
#### 3.3.2 Fixed Axial Pressure  
The flow rate change curves of different crack modes and confining pressure values with axial pressures of 40 MPa and 10 MPa are shown in Figure 29. The flow rate change rule was similar under axial pressures of 40 MPa and 10 MPa, but the flow rate value was significantly higher under 10 MPa compared to 40 MPa. This indicates that the flow rate decreases with an increase in axial pressure. The seepage flow rate was, in order from large to small, type III, type II, type Y, 70-degree, and then type I. As the confining pressure decreased, the seepage flow rate gradually increased and the increment of the seepage flow rate also increased.
# It Is Our Turn to Get Cannabis High: Put Cannabinoids in Food and Health Baskets
## 7 Phytocannabinoids
### Phytoannabinoids Biosynthesis and Its Gene Networks  
Pityocannabinoids are mainly produced in glandular hairs called trichomes [99; 100; 101; 102], although some of the secondary metabolites such as THC and CBD have also been tracked in pollen [35], seeds [103; 104], stem [105; 106], leaves [73; 106], and roots [106] in a low quantity [35; 103; 107]. However, trichomes covering the female flower are the major site of phytocannabinoids production [105; 106; 108].  
Cannabinoids are synthesized through either the polyketide pathway or deoxyxylulose phosphate/methylribitol phosphate (DOXP/MEP) pathway which lead to the production of olivetolic acid (OLA) and geranyl diphosphate (GPP), respectively [109; 110], and these biosynthetic pathways were well-reviewed in [PERSON], 2008, [PERSON] et al., 2011 and [PERSON] et al., 2016 (Figure 3). OLA production is catalyzed by polyketide synthase (PKS) and an olivetolic acid cyclase (OAC) [111]. The next stage giving rise to CBGA, the central precursor of \(\Delta\)9- tetrahydroccannabinolic acid (\(\Delta\)9-THCA), CBDA, and cannabichromeic acid (CBCA) includes  
Figure 2: Cannabinoids receptors CB1 and CB2 and their natural distribution in the human body.  
alkylation of OLA with GPP which is catalyzed by geranylpyrophosphate:olivetolate geranyltransferase (GOT) ([PERSON] and [PERSON], 1998). In the MEP pathway, however, the preenyl side-chain originates provide substrates for GPP synthesis which lead to the production of CBGA by an aromatic prenyltransferase (PT) [112]. The enzymatic reactions encompass THCA synthase (THCAS), CBDA synthase (CBDAS) and CBCA synthase (CBCAS) which convert CBGA to THCA, CBDA, and CBCA, respectively [113; 114]. The last stage includes a nonenzymatic reaction during storage or smoking (heat) through decarboxylation of THCA and CBDA into THC and CBD (Figure 3) [108].
# Survey of Dense Video Captioning: Techniques, Resources, and Future Perspectives
## 3 Techniques for Dense Video Captioning
### Encoder-Decoder Based Approaches
#### 3.1.3 Attention-Based Encoder-Decoder Models  
To overcome the limitations of basic encoder-decoder models, attention mechanisms have been introduced. These mechanisms enable the model to focus on salient parts of the video while generating captions by dynamically adjusting the weight assigned to different video frames based on their relevance to the currently generated caption. [PERSON] et al. [23] proposed a hierarchical RNN with an attention mechanism to encode videos at multiple temporal scales. The overall structure of this hierarchical RNN-based attention encoder-decoder framework is illustrated in Figure 4.  
Building on this, [PERSON] et al. [24] introduced a spatio-temporal attention model that captures both spatial and temporal attention, further enhancing the model's ability to focus on important video features. Despite these advancements, attention-based models still face challenges in capturing long-range dependencies and generating diverse captions. Ongoing research continues to explore solutions to these remaining issues.
# Wireless Energy Harvesting for Internet-of-Things Devices Using Directional Antennas
## 3 System Model  
### Architecture of RF Energy Harvesting  
Figure 1 shows the architecture of RF energy harvesting. There are two components in the RF energy-harvesting architecture: rechargeable devices, and the access point (AP). The rechargeable devices are equipped with an omnidirectional antenna and RF-DC converter around the AP. The omnidirectional antenna receives RF energy from the AP, and the RF-DC converter converts received RF energy to electricity. We assume that there are \(N\) devices located under the radio coverage of the AP. Due to the limitations of our model, the charge level of devices too close to the AP will be distorted, so there will be no devices within a range of 1 m. The AP is a base station that receives data from devices, and it is also a charging station equipped with an antenna array which can transmit RF energy to devices. The devices whose battery level is higher than a threshold value can transmit data to the AP. The AP and devices share the same frequency band by means of a time division duplex (TDD); namely, wireless energy transfer and data transmission do not take place at the same time.  
In practice, beamforming requires accurate channel state information (CSI). Therefore, the AP needs to know the accurate CSI to achieve large energy beamforming gain. We assume that the AP may consume energy to estimate the CSI from a dedicated device.