esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Blast Hole Pressure Measurement Experiment
### Experimental Results  
In this experiment, a hydraulic explosive pressure propagation data measurement system was used to measure the pressure in the blast hole, and a comparative analysis was conducted on the blasting pressure behavior of the sand- and STF-based stemming materials. Table 2 presents the results of the blast hole pressure measurements.  
The pressure in the blasting hole is 5.84 MPa for the sand stemming material and 2.80 MPa for the STF-based stemming material. Further, the blasting pressure by sand is two times higher than by STF-based stemming material. This is the pressure transferred to the water tube located above the test stemming material; therefore, a lower measured pressure value means that the loss of explosive pressure in the blast hole due to stemming transfer is lower.  
The time taken from detonation to explosion pressure transfer is 12.24 ms in the sand stemming material and 31.82 ms in the STF-based stemming material; the measured value is significantly lower than that of the sand stemming material. This is the explosive pressure transfer time from the lower part of the blasting hole to the upper part of the blasting hole for the explosive detonation of the stemming material. Thus, the longer the measured explosive pressure delay time, the better the ejection resistance. In addition, the duration of the explosive pressure in the blast hole is 16.82 ms when using the sand stemming material and 21.81 ms when using the STF-based stemming material, an improvement of approximately 5 ms. This implies that the explosive pressure acted longer inside the blast hole, as long as the duration of the explosive pressure. Figure 9 shows the time-pressure hysteresis curve inside the blast hole.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Peak Pressure in Blasting** & **Explosive Pressure Arrival** & **Explosive Pressure Duration** \\
**Hole (MPa)** & **Time after Trigger (ms)** & **in Blasting Hole (ms)** \\ \hline Sand Stemming & 5.84 & 12.24 & 16.82 \\ STF-based stemming & 2.80 & 31.82 & 21.81 \\ \hline \end{tabular}
\end{table}
Table 2: Result of the explosion pressure measurement in blast hole.  
Figure 8: Schematic of the blast hole measurement system.
# Blockchain and IoT Convergence--A Systematic Survey on Technologies, Protocols and Security
## 8 Blockchain and IoT Main Use Cases
### Industry 4.0 Product Tracking  
The manufacturing industry in recent years is experiencing an improvement from automated production to so-called \"smart production\" [103]. Blockchain and IoT can help manage the incredible amount of data from the various supply chains: product design, raw material supply, manufacturing, recycling, distribution, retail and after-sales service. All this data raises a problem of interoperability that can be solved through a secure peer-to-peer standard based on a Blockchain network [104]. The rise of 5G networks provides a tremendous boost to the IoT devices that will run on them. In the Industrial sector many challenges and interesting scenarios are opening for this type of devices running on Blockchain networks [105]. Updating the firmware of the IoT devices is a crucial problem in the industry because these devices need to be updated regularly to remedy security breaches. A classic firmware upgrade scheme involves the use of cloud servers. If the cloud server is compromised, the device update is blocked and in the worst case, it could allow malicious firmware to be uploaded to company components. [PERSON] et al. [106] propose a Blockchain-based solution for managing firmware updates in IoT. It preserves the integrity of firmware by linking the latest version information by previous versions information with the help of a smart contract mechanism.
# Study on Bridge Displacement Monitoring Algorithms Based on Multi-Targets Tracking
## 4 Evaluation  
In this paper, three experiments are conducted to verify the proposed algorithm's accuracy, robustness, real-time, self-adaptability, low-cost, and simplicity mentioned above. The original pictures in the experiments are made by Photoshop and the algorithm is realized by MATLAB language (R2016a, MathWorks, Natick, MA, USA).  
Figure 2: Flowchart of feature recognition.  
In the first experiment, accuracy and self-adaptability can be proved. The accuracy of the algorithm can reach a sub-pixel level and meet the daily needs of bridges. This algorithm can automatically detect the number of target boards without setting a fixed number in advance, reflecting the self-adaptability of the algorithm. This algorithm realizes multi-target simultaneous monitoring and greatly reduces the cost of monitoring and facilitates later data processing, reflecting the low-cost and simplicity of the algorithm. In the second and third experiments, robustness and real-time can be proved respectively. The robustness of the algorithm is reflected in that, when the target board is slightly contaminated, the algorithm can still identify the location of the target board and the accuracy is almost unaffected. The algorithm is implemented in a frequency domain as far as possible and each step is calculated and compared to select the shortest time-consuming sub-algorithm from sub-algorithms that can achieve the same effect. If the displacement exceeds the threshold, real-time warning can be achieved. In the fourth experiment, the algorithm is achieved by C++ language to prove its availability in the actual environment.
## 3 Failure Mode Analysis  
### Fully Redundant  
The fully redundant state means no sensor failure. Substituting Equation (4) into Equation (9) produces:\[\left\{\begin{array}{l}-x+y\theta_{z}-z\theta_{y}-\theta_{z}R_{x1}=d_{x1}\\ x-y\theta_{z}+z\theta_{y}+\theta_{z}R_{x2}=d_{x2}\\ -y-x\theta_{z}+z\theta_{x}+\theta_{z}R_{y1}=d_{y1}\\ y+x\theta_{z}-z\theta_{x}+\theta_{z}R_{y2}=d_{y2}\\ z-x\theta_{y}+y\theta_{x}+R_{z1x}\theta_{y}+R_{z1y}\theta_{x}=d_{z1}\\ z-x\theta_{y}+y\theta_{x}-R_{z2x}\theta_{y}-R_{z2y}\theta_{x}=d_{z2}\\ z-x\theta_{y}+y\theta_{x}+R_{z3x}\theta_{y}-R_{z3y}\theta_{x}=d_{z3}\\ z-x\theta_{y}+y\theta_{x}-R_{z4x}\theta_{y}+R_{z4y}\theta_{x}=d_{z4}\\ \end{array}\right. \tag{10}\]  
After transforming Equation (10), the relative position between the base and the floating platform is represented as:  
\[\left[\begin{array}{l}x\\ y\\ z\end{array}\right]=\left[\begin{array}{ccc}1&-\theta_{z}&\theta_{y}\\ \theta_{z}&1&-\theta_{x}\\ -\theta_{y}&\theta_{x}&1\end{array}\right]^{-1}\left[\begin{array}{l}m_{1} \\ m_{2}\\ m_{3}\end{array}\right] \tag{11}\]  
where:  
\[\left\{\begin{array}{l}m_{1}=\frac{1}{2}[(d_{x2}-d_{x1})-\theta_{z}(R_{x1}+R_ {x2})]\\ m_{2}=\frac{1}{2}[(d_{y2}-d_{y1})+\theta_{z}(R_{y1}-R_{y2})]\\ m_{3}=\frac{1}{4}[(d_{z1}+d_{z2}+d_{z3}+d_{z4})+\theta_{x}(R_{z2y}-R_{z1y}+R_{z 3y}-R_{z4y})+\theta_{y}(R_{z2x}-R_{z1x}+R_{z4x}-R_{z3x})]\\ \\ \left|\begin{array}{ccc}1&-\theta_{z}&\theta_{y}\\ \theta_{z}&1&-\theta_{x}\\ -\theta_{y}&\theta_{x}&1\end{array}\right|=1+\theta_{x}^{2}+\theta_{y}^{2}+ \theta_{z}^{2}\
eq 0 \tag{13}\]  
Based on the small-angle assumption for simplification, the formula for solving the relative position between the base and the floating platform in three degrees of freedom can be represented as:  
\[\left\{\begin{array}{l}x=m_{1}+m_{2}\theta_{z}-m_{3}\theta_{y}\\ y=m_{2}-m_{1}\theta_{z}+m_{3}\theta_{x}\\ z=m_{3}+m_{1}\theta_{y}-m_{2}\theta_{x}\end{array}\right. \tag{14}\]  
Similarly, the relative three-degree-of-freedom angle solution formula between the base and the floating platform is obtained:  
\[\left\{\begin{array}{l}\theta_{x}=\frac{(R_{x3x}+R_{44})(d_{z1}-d_{z2})-(R_ {x11}+R_{x2})(d_{z3}-d_{z4})}{(R_{z1x}+R_{x21})(R_{zy}+R_{z4y})+(R_{z3x}+R_{z4y}) (R_{zy}+R_{z2y})}\\ \theta_{y}=\frac{(R_{x3y}+R_{z4y})(d_{z1}-d_{z2})+(R_{x1y}+R_{z2y})(d_{z3}-d_{z4 })}{(R_{z1x}+R_{z2x})(R_{zy}+R_{z4y})+(R_{z4y}+R_{z4y})(R_{zy}+R_{z2y})}\\ \theta_{z}=\frac{1}{2}\left(\frac{d_{x1}+d_{z2}}{R_{x2}-R_{x1}}+\frac{d_{y1}+d _{z2}}{R_{y1}+R_{z4y}}\right)\end{array}\right. \tag{15}\]
# Effects of Caprolactam Wastewater on Algal Growth and Nutrients Removal by _Arthrospira platensis_
## 2 Materials and Methods
### Effects of Four Main Organic Matters in WCP on the Growth of A. platensis  
CHN and CHL are volatile; therefore, aerated culture is not suitable for testing the effects of these two organic matters on the growth of _A. platensis_. Flask cultures were used for this experiment. First, 100 mL of algal suspension with an initial optical density of 0.3 \(\pm\) 0.05 (corresponding to an initial biomass DW of approximately 0.15 g/L) was incubated in 250 mL conical flasks. The basal growth medium was modified [PERSON]'s medium with 6 g/L of NaHCO3 (Supplementary Table S1). The culture was grown for 4 d at 28 \({}^{\circ}\)C with a light intensity of 80 umol photons/(m\({}^{2}\)-s) and a photoperiod of 14 h/10 h (light/dark). Three parallel cultures were grown for each treatment and control group.  
The cultures were supplemented with four organic substances. The concentrations of the four organic substances were set as follows: CPL: 0, 100, 300, 500, and 1000 mg/L. CHO: 0, 250, 500, 750, 1000, and 1500 mg/L. CHL: 0, 200, 400, 600, 800, and 1000 mg/L. CHN: 0, 400, 800, 1200, 1800, and 2000 mg/L.  
The mouth of the flasks was sealed with sealing film, and no extra air was aerated during cultivation. The flasks were shaken by hand several times daily.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Concentration (mg/L)** \\ \hline NO3\({}^{-}\) & 4820.0 \(\pm\) 20.0 \\ P & 60.8 \(\pm\) 3.0 \\ TOC & 486.0 \(\pm\) 23.0 \\ CHN & 164.5 \(\pm\) 11.0 \\ CHL & 32.8 \(\pm\) 4.0 \\ CHO & 46.0 \(\pm\) 8.0 \\ CPL & / \\ \hline \hline \end{tabular}
\end{table}
Table 1: Physicochemical characteristics of mixed caprolactam wastewater.
# MANET Routing Protocols' Performance Assessment Under Dynamic Network Conditions
## 1 Introduction
### Challenges in MANETs  
Despite their advantages, MANETs face several challenges. The dynamic nature of the network, where nodes move freely, causes frequent changes in network structure, making it difficult to maintain stable communication. Other issues include limited battery life in devices, which restricts the network's operating time, and constrained bandwidth, which affects data transmission speeds. Furthermore, designing efficient routing protocols that address these challenges remains a significant problem [3,4].  
To address these challenges, this study evaluates the performance of eight MANET routing protocols under diverse network conditions.  
This study investigates the performance of eight MANET routing protocols: OLSR, DSDV, AODV, DSR, AOMDV, TORA, ZRP, and GRP. A customized simulation environment in OMNeT++ 6.0.1 with INET-4.5.0 was used to assess these protocols. The simulations assess their performance under varying network conditions, including node densities of 20, 80, 200, and 500. Key performance metrics examined include network load, throughput, delay, energy consumption, jitter, packet loss rate, and packet delivery ratio [5,6].
## 4 Results
### Optimization of the Damping Effect Control Parameters
If the minimum value of the objective function corresponds to the center, a new hypercuboid of reduced size (half the length of the edges) is constructed about this center. The same procedure is repeated in the next iterations. The iteration process is finished if the minimum value of the objective function lies at the center of the hypercuboid and the lengths of its edges are less than the accuracy, with which the solution is required to be obtained. More details on the evolution optimization method and its application can be found in [41]. The notation of the center and the individual corners of the hypercuboid (rectangular for the case of two design variables) are depicted in Figure 13.  
Figure 12: The current decrease. Figure 13: Notation of the hypercuboid significant points. The rotor starts to accelerate at the point of time of 10.20 s. The solution was performed for the phase shift of the excitation effect of 4/3 \(\times\)\(\pi\) rad (240\({}^{\circ}\)). The initial values of the optimum solution were estimated, and the beginning (\(T\)) and duration (\(\Delta T\)) of the current decrease by 10.7 s and 0.4 s, respectively. The time increment was chosen 0.4 s, which is the same for both design variables. The iteration process is summarized in Table 1. \(R\) stands for the objective function value (maximum lateral displacement of the disc center). After performing six iteration steps, the computational procedure gives the optimum values: the time of beginning of the current decrease 10.50 s and the time of duration of this manipulation 0.60 s. As it is easier to measure the angular speed than the time, the beginning of the current decrease corresponds to the angular velocity of 170.2 rad/s. The system response on the optimized decrease in the damping effect is depicted in Figures 14 and 15. Figure 14 shows the time history of the radial displacement of the disc center, and Figure 15 shows the disc center trajectory. The maximum value of the radial displacement reads 395 \(\upmu\)m.  
The same method was applied for calculation of the optimum values of the control parameters related to the current decrease for several different values of the phase shift \(\psi\) of the excitation effect. The results are summarized in Table 2.
## 3 Results and Discussion
### Structural Variation of Treatment Samples
\begin{table}
\begin{tabular}{c c c c c} \hline  & \multicolumn{3}{c}{**(a)**} \\ \hline  & **R.PSD** & **T.PSD** & **A.PSD** & **T.A.PSD** \\ \hline Cumulative pore volume (cm\({}^{3}\)/g) & \(8.3\times 10^{-4}\) & \(1.32\times 10^{-3}\) & \(1.58\times 10^{-3}\) & \(1.88\times 10^{-3}\) \\ Micro (\(<\)2 nm) & \(1.25\times 10^{-5}\) & \(3.60\times 10^{-6}\) & \(1.95\times 10^{-5}\) & \(2.93\times 10^{-5}\) \\ Meso (2\(-\)50 nm) & \(3.79\times 10^{-4}\) & \(5.43\times 10^{-4}\) & \(6.79\times 10^{-4}\) & \(9.69\times 10^{-4}\) \\ Macro (\(>\)50 nm) & \(4.39\times 10^{-4}\) & \(7.74\times 10^{-4}\) & \(8.86\times 10^{-4}\) & \(8.85\times 10^{-4}\) \\ \hline Cumulative surface area (m\({}^{2}\)/g) & 0.19 & 0.174 & 0.39 & 0.541 \\ Micro (\(<\)2 nm) & 0.026 & 0.008 & 0.042 & 0.063 \\ Meso (2\(-\)50 nm) & 0.147 & 0.136 & 0.314 & 0.444 \\ Macro (\(>\)50 nm) & 0.016 & 0.030 & 0.033 & 0.034 \\ \hline  & \multicolumn{3}{c}{**(b)**} \\ \hline  & **[PERSON]** & **[PERSON]** & **[PERSON]** & **[PERSON]** \\ \hline Cumulative pore volume (cm\({}^{3}\)/g) & \(1.97\times 10^{-3}\) & \(1.86\times 10^{-3}\) & \(3.16\times 10^{-3}\) & \(3.10\times 10^{-3}\) \\ Micro (\(<\)2 nm) & \(1.73\times 10^{-5}\) & \(2.83\times 10^{-5}\) & \(4.88\times 10^{-5}\) & \(7.33\times 10^{-5}\) \\ Meso (2\(-\)50 nm) & \(9.36\times 10^{-4}\) & \(9.51\times 10^{-4}\) & \(1.30\times 10^{-3}\) & \(1.97\times 10^{-3}\) \\ Macro (\(>\)50 nm) & \(1.02\times 10^{-3}\) & \(8.79\times 10^{-4}\) & \(1.81\times 10^{-3}\) & \(1.06\times 10^{-3}\) \\ \hline Cumulative surface area (m\({}^{2}\)/g) & 0.528 & 0.568 & 0.731 & 0.997 \\ Micro (\(<\)2 nm) & 0.037 & 0.062 & 0.105 & 0.159 \\ Meso (2\(-\)50 nm) & 0.433 & 0.456 & 0.541 & 0.793 \\ Macro (\(>\)50 nm) & 0.055 & 0.05 & 0.085 & 0.045 \\ \hline \end{tabular}
\end{table} 
Table 2: Quantitative values for pore volume and surface area of PSD samples **(a)** and kenaf samples **(b)** by nitrogen sorption analysis.
## 4 Self-Adaptive Multi-Density Prediction Model
### Adaptive Multi-Density Radius Calculation
#### 4.2.1 Density Radius EPS Calculation  
The density radius EPS calculation is used to evaluate the cluster density of each key point, where a higher density cluster contains more closely spaced points.  
\[r=k\times\Gamma(n)\times\frac{m}{i\times\sqrt{\pi^{n}}}\times\prod_{i=1}^{n}x_{i}. \tag{1}\]  
In the formula, \(r\) represents the radius, \(k\) represents the threshold for core objects, \(\Gamma(n)\) represents the gamma function, and m represents the dimensions of the points.
# A Novel Markerless Lung Tumor-Tracking Method Using Treatment MV Beam Imaging
## 4 Discussion and Conclusions
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Gantry**} & \multirow{2}{*}{**Motion**} & \multicolumn{3}{c}{**Maximum Deviation (mm)**} & \multicolumn{3}{c}{**Average Deviation (mm)**} \\ \cline{3-8}  & **Range (mm)** & **SI** & **Orth** & **2D** & **SI** & **Orth** & **2D** \\ \hline \multirow{4}{*}{30} & 10 & 0.6 & 0.6 & 0.8 & 0.2 & 0.2 & 0.3 \\  & 12 & 0.9 & 0.8 & 0.9 & 0.3 & 0.3 & 0.5 \\  & 14 & 0.9  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Patient \#**} & \multirow{2}{*}{**Fx \#**} & \multicolumn{2}{c}{**Treatment Field**} & \multirow{2}{*}{**Average Position Deviations (mm)**} & \multicolumn{2}{c}{**CP**} & \multicolumn{2}{c}{**CP**} & \multicolumn{2}{c}{**CP**} \\  & & **Gantry Angle (\({}^{\circ}\))** & & & **5 mm** & **10 mm** & **15 mm** \\ \hline \multirow{4}{*}{1} & \multirow{2}{*}{1} & 180 & 1.0 & \(-\)6.4 & 6.7 & 18\% & 100\% & 100\% \\  & & 270 & \(-\)1.2 & \(-\)2.6 & 3.2 & 75\% & 100\% & 100\% \\ \cline{2-8}  & & 180 & 0.4 & \(-\)4.2 & 4.6 & 57\% & 100\% & 100\% \\  & & 270 & \(-\)1.2 & \(-\)2.6 & 3.3 & 88\% & 100\% & 100\% \\ \hline \multirow{4}{*}{2} & \multirow{2}{*}{1} & 180 & \(-\)2.6 & 7.3 & 7.9 & 0\% & 97\% & 100\% \\  & & 210 & 3.6 & \(-\)3.2 & 4.9 & 61\% & 100\% & 100\% \\ \cline{2-8}  & & 180 & \(-\)1.8 & 7.1 & 7.5 & 0\% & 88\% & 100\% \\  & & 210 & 4.5 & \(-\)4.2 & 6.1 & 0\% & 100\% & 100\% \\ \hline \multirow{4}{*}{3} & \multirow{4}{*}{1} & 20 & 3.2 & \(-\)6.3 & 7.2 & 0\% & 100\% & 100\% \\  & & 60 & \(-\)0.2 & \(-\)7.7 & 7.7 & 8\% & 84\% & 100\% \\  & & 120 & 0.4 & 0.6 & 1.2 & 100\% & 100\% & 100\% \\  & & 220 & \(-\)0.3 & 7.6 & 7.6 & 0\% & 97\% & 100\% \\  & & 270 & \(-\)0.6 & 0.3 & 3.9 & 69\% & 100\% & 100\% \\ \hline \multirow{4}{*}{3} & \multirow{4}{*}{2} & 20 & 1.9 & 3.2 & 3.8 & 82\% & 100\% & 100\% \\  & & 60 & 1.6 & 1.6 & 3.1 & 94\% & 100\% & 100\% \\  & & 120 & 0.3 & \(-\)0.5 & 0.7 & 100\% & 100\% & 100\% \\  & & 220 & \(-\)0.3 & \(-\)2.7 & 3.8 & 65\% & 100\% & 100\% \\  & & 270 & \(-\)2.0 & 0.7 & 3.3 & 100\% & 100\% & 100\% \\ \hline \multirow{4}{*}{4} & \multirow{4}{*}{1} & 20 & \(-\)1.7 & \(-\)0.4 & 2.1 & 100\% & 100\% & 100\% \\  & & 60 & 0.0 & \(-\)8.4 & 8.4 & 4\% & 76\% & 100\% \\  & & 120 & \(-\)1.0 & 3.3 & 3.8 & 66\% & 100\% & 100\% \\  & & 220 & \(-\)0.8 & 6.9 & 7.1 & 12\% & 95\% & 100\% \\  & & 270 & 1.7 & \(-\)0.7 & 4.0 & 73\% & 100\% & 100\% \\ \hline \multirow{4}{*}{1} & \multirow{4}{*}{1} & 80 & 1.0 & 9.8 & 9.9 & 80\% & 100\% & 100\% \\  & & 115 & \(-\)3.1 & \(-\)5.1 & 6.0 & 28\% & 100\% & 100\% \\  & & 155 & \(-\)8.1 & 0.5 & 8.2 & 100\% & 100\% & 100\% \\  & & 295 & \(-\)4.3 & 0.5 & 4.3 & 76\% & 100\% & 100\% \\  & & 325 & \(-\)5.3 & 0.1 & 5.4 & 17\% & 100\% & 100\% \\ \hline \multirow{4}{*}{4} & \multirow{4}{*}{2} & 80 & 0.7 & \(-\)3.3 & 3.4 & 80\% & 100\% & 100\% \\  & & 115 & 0.1 & \(-\)1.4 & 2.3 & 98\% & 100\% & 100\% \\  & & 155 & \(-\)2.5 & \(-\)0.2 & 2.7 & 100\% & 100\% & 100\% \\  & & 295 & \(-\)0.8 & 1.7 & 1.8 & 10
# Towards the Feasibility of Long Range Wireless Power Transfer over an Ocean Surface
## 2 Methodology and Materials  
The objective of this work was to realize wireless transmission of power to multiple loads over a seawater surface. The interface along which this energy propagates is an interface between a low-loss dielectric medium and a high-loss dielectric medium. The low-loss dielectric medium is chosen to be air or a rubber, the latter of which is a non-polarsubstance. The high-loss dielectric medium is chosen to be water, which is a well-known polar solvent.
## 2 Optical Uplink Channel Model
### Statistical Properties of Channel Fading Factors
#### 2.1.2 Pointing Errors and AOA Fluctuations  
The continuous motion of satellites introduces significant challenges in maintaining the precise alignment of the optical beam with the receiving aperture. Beam wander effects further exacerbate pointing inaccuracies and AOA fluctuations. As established in prior research [37], the instantaneous pointing errors can be statistically modeled using Rayleigh distribution. In particular, the optical power fading coefficient \(h_{p}\), induced by these pointing errors, demonstrates a parametric dependence on system characteristics including beam divergence angle and receiver aperture diameter. This relationship underscores the necessity for comprehensive system parameter optimization to mitigate power degradation in space optical communications. Considering a Gaussian beam, PDF of \(h_{p}\) is [44]  
\[f_{h_{p}}(h_{p})=\frac{w_{b}^{2}\cos\theta_{a}}{4\sigma_{p}^{2}}\bigg{(}\text{ erf}\bigg{(}\frac{\sqrt{\pi}d_{r}}{2\sqrt{2w_{d}}}\bigg{)}^{-\frac{w_{b}^{2}}{4 \sigma_{p}^{2}}}h_{p}^{\frac{w_{b}^{2}}{4\sigma_{p}^{2}}-1}, \tag{6}\]  
where \(w_{d}\), \(\sigma_{p}^{2}\), and \(\theta_{a}\) are the beam width, normalized variance of pointing errors, and instantaneous AOA, respectively. In addition, erf is the Gaussian error function, and the equivalent beam width \(w_{b}\) is related to \(w_{d}\).  
For AOA fluctuations induced fading coefficient \(h_{a}\), a two-valued distribution can be used, which is [23]  
\[h_{a}\approx\left\{\begin{array}{ll}1,&\theta_{a}<\Omega_{F},\\ 0,&\theta_{a}\geq\Omega_{F},\end{array}\right. \tag{7}\]  
where \(\Omega_{F}\) denotes the angle of FOV. The rationality of this two-valued distribution is discussed here. The intensity of light spot on the APD photon sensing aperture is expressed by the Airy pattern. Let \(d_{Ai}\) be the distance between the center and any point in the airy light spot. When \(d_{Ai}\geq 25\lambda\), the power of circle spot with radius \(d_{Ai}\) accounts for 99% of the total optical power [45]. Taking \(\lambda=1550\) nm as an example, \(25\lambda=3.87\)\(\mu\)m is much smaller than the APD photon sensing aperture. Therefore, when the light beam converges at the APD photon sensing aperture, the total received power can be detected; that is, \(h_{a}=1\). When \(\theta_{a}>\Omega_{F}\), almost no optical power is detected, i.e., \(h_{a}=0\). Figure 3 shows an example for both cases. Instantaneous AOA \(\theta_{a}\) in (7) follows the Rayleigh distribution [44], which is \[f_{\theta_{a}}(\theta_{a})=\frac{\theta_{a}}{\sigma_{\theta}^{2}}\exp(-\frac{ \theta_{a}^{2}}{2\sigma_{\theta}^{2}}), \tag{8}\]  
where \(\sigma_{\theta}^{2}\) is the variance of AOA.