esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 LBT-Based MAC Protocol for LoRaWAN
### ETSI Regulations on Polite Medium Access Based on LBT  
In this paper, we consider LoRaWAN networks deployed in Europe in which all the EDs work on the channels of the EU868 sub-bands that match the ERC Recommendation 70-03. Table 3 shows the considered sub-bands, the number of 125 kHz-channels available for transmission per each sub-band and the limitations on the maximum transmission power (\(Pow_{TX}^{max}\)) per sub-band.  
The use of the sub-bands shown in Table 3 is ruled by the ETSI regulations EN 300 220. In particular, a MAC protocol based on LBT on these sub-bands must be compliant with the limitations shown in Table 4[59].  
When a channel is sensed busy, a deferral interval applies. Such an interval, here called \(\mathcal{T}_{def}\), shall be longer than or equal to a given value \(\mathcal{T}_{def}^{min}\) that corresponds to the CCA interval. As shown in Table 4, the minimum CCA interval (\(\mathcal{T}_{CCA}^{min}\)) is 160 microseconds, while the minimum timespan between two consecutive deferral intervals, here called \(\Delta_{J\
eq f}^{min}\), is manufacturer-dependent. After the CCA, the EDs shall begin transmitting within a manufacturer-dependent value \(\Theta_{CCA\_{TX}}^{max}\) that is lower than or equal to 5 milliseconds. A single transmission duration shall be lower than or equal to a \(ToA_{TX}^{max}\), i.e., 1 s. The maximum length of a sequence of messages, called a transmission dialogue, shall stop within \(\Lambda_{TX}^{max}\) (whose value, based on the ETSI regulations, is equal to 4 s). After each message transmission an ED shall remain silent for an interval, here called \(\mathcal{T}_{OffTime}^{min}\), longer than or equal to 100 milliseconds.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(\mathcal{T}_{CCA}^{min}\) & 160 \(\upmu\)s \\ \(\mathcal{T}_{def}^{min}\) & CCA interval (\(\mathcal{T}_{CCA}\)) \\ \(\Delta_{J\
eq f}^{min}\) & Manufacturer-dependent \\ \(\Theta_{CCA\_{TX}}^{max}\) & 5 ms \\ \(ToA_{TX}^{max}\) & 1 s \\ \(\Lambda_{TX}^{max}\) & 4 s \\ \(\mathcal{T}_{OffTime}^{min}\) & 100 ms \\ \(ToA_{200\text{Hz}}^{tot/h}\) & 100 s \\ \hline \hline \end{tabular}
\end{table}
Table 4: Timing parameters of polite medium access based on LBT [59].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sub-Band** & \begin{tabular}{c} **Frequency Band** \\ **(MHz)** \\ \end{tabular} & \
\begin{tabular}{c} **Number of** \\ **125 kHz-Channels** \\ \end{tabular} &
\begin{tabular}{c} \(Pow_{TX}^{max}\) (dBm)** \\ \end{tabular} \\ \hline h1.4 & 868.00–868.60 & 3 & 14 \\ h1.5 & 868.70–869.20 & 2 & 14 \\ h1.6 & 869.40–869.65 & 1 & 27 \\ h1.7 & 869.70–870.00 & 1 & 14 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Sub-bands of the EU868 ISM Band that match the ERC Recommendation 70-03.  
Finally, each ED can transmit up to 100 s per hour per 200 kHz spectrum, i.e., \(ToA_{200\text{kHz}}^{tot/h}\)=100 s.
## 3 Results
### Safety and Adherence to Telerehabilitation  
There were neither deaths nor major adverse cardiac events, including hospitalizations due to heart failure exacerbation, associated with participation in the HTR program. We did not observe any episodes of exercise-induced malignant arrhythmias. Additionally, no patient experienced musculoskeletal injuries associated with exercise training. However, a few minor events related to telerehabilitation were noted, with three of the patients reporting mild skin reactions caused by the electrodes. No patient required discontinuation or urgent termination of the rehabilitation program. Patients accepted HTR, including the need for interactive everyday collaboration with the medical team from the monitoring center.  
All patients completed the proposed model of HTR. Adherence during the HTR program was monitored through daily telephone interactions with the monitoring center.  
\begin{table}
\begin{tabular}{c c} \hline Males, n (\%) & 29.0 (97.0) \\ \hline Age (years), median [Q1–Q3] & 59.0 \\  & [50.0–63.0] \\ \hline Body mass index (kg/m\({}^{2}\)), median [Q1–Q3] & 26.2 \\  & [22.2–28.5] \\ \hline Etiology of heart failure, n (\%) & \\ \hline Ischemic & 19.0 (63.0) \\ Non-ischemic & 11.0 (37.0) \\ \hline Left ventricular assist devices (LVAD), n (\%) & \\ \hline Heart Mate III & 21.0 (70.0) \\ Heart Ware & \\ Time between LVAD implantation and home-based & \\ telerehabilitation initiation (months), median 2 Q1: 2 Q3: 2.5 & 9.0 (30.0) \\ (min: 1.5, max: 4.5) & \\ \hline Medical history n (\%) & \\ \hline Diabetes & 12.0 (40.0) \\ Hyperlipidemia & 18.0 (60.0) \\ Hypertension & 7.0 (23.3) \\ Stroke & 2.0 (6.7) \\ \hline Treatment n (\%) & \\ \hline Beta-blockers & 29.0 (96.7) \\ Angiotensin-converting enzyme inhibitors/receptor blockers & 29.0 (96.7) \\ Loop diuretics & 29.0 (96.7) \\ Spironolactone/Eplerenone & 28.0 (93.3) \\ Stating & 19.0 (63.3) \\ Aspirin & 30.0 (100.0) \\ Anticogualants & 30.0 (100.0) \\ Digoxine & 7.0 (23.3) \\ Cordarone & 4.0 (13.3) \\ Implantable cardioverter-defibrillator & 30.0 (100.0) \\ \hline \end{tabular}
\end{table}
Table 1: Baseline characteristics of patients.  
These calls were required for patients to obtain clearance to begin their training sessions and to submit ECG data upon completion.
# Research Status and Progress of All-Position Narrow-Gap GMAW for Pipelines
## 2 Current Status of Research on Narrow-Gap All-Position GMAW
### Molten Pool Behavior in Narrow-Gap GMAW
[34] found that during the GMAW vertical welding process, the size of the molten pool and the peak temperature of the molten metal significantly decrease, leading to an accelerated solidification rate of the molten pool, which is the primary factor responsible for suppressing weld pool sagging. Meanwhile, the upward component of the arc force and the enhanced support from the solidified  
Figure 8: Melt pool characteristics for flat and overhead welding positions. Reprinted with permission from Ref. [26]. Copyright 2019, Authors. Figure 7: Short-circuit transition in the downward-facing weld position. Reprinted with permission from Ref. [26]. Copyright 2019, Authors. Figure 9: Schematic diagram of molten pool flow behavior. Reprinted with permission from Ref. [31]. Copyright 2023, Authors. metal bulge help counteract the downward flow of the liquid metal. [PERSON] [35] and [PERSON] [36] et al. studied the impact of gravity on the behavior of the molten pool at different welding positions through fluid dynamics models of the molten pool. [PERSON] et al. [37; 38] conducted numerical simulations to investigate the molten pool behavior under the one droplet per pulse mode during the GMAW process, as well as the molten pool flow patterns at different welding positions. These studies provide valuable insights into how external forces, for example the gravity, influence the molten pool dynamics and, consequently, the quality and formation of the weld seam.
## 5 Conclusions  
Figure 1 shows that the convergence speed of the multipoint iterative method is faster than the one-point iterative method. As shown in Tables 1 and 2, the results obtained with our methods without memory are better than the other methods without memory. From the results displayed in  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Methods** & \(|x_{1}-a|\) & \(|x_{2}-a|\) & \(|x_{3}-a|\) & \(\rho\) \\ \hline Equation \((42)-PD,\gamma_{0}=-0.01\) & 0.14930E\(-\)1 & 0.54292E\(-\)8 & 0.20342E\(-\)37 & 4.5697804 \\ Equation \((43)-PD,\gamma_{0}=-0.01\) & 0.14930E\(-\)1 & 0.32753E\(-\)9 & 0.16659E\(-\)45 & 4.7387964 \\ Equation \((14)-(17),n=2,\lambda_{0}=-1.5\) & 0.29673E\(-\)2 & 0.10381E\(-\)11 & 0.90169E\(-\)55 & 4.5538013 \\ Equation \((15)-(17),n=2,\lambda_{0}=-1.5\) & 0.29673E\(-\)2 & 0.13370E\(-\)13 & 0.29875E\(-\)67 & 4.7285160 \\ Equation \((14)-(17),n=2,\lambda_{0}=-0.5\) & 0.27276E\(-\)4 & 0.76276E\(-\)20 & 0.21310E\(-\)91 & 4.6005252 \\ Equation \((15)-(17),n=2,\lambda_{0}=-0.5\) & 0.27276E\(-\)4 & 0.62055E\(-\)21 & 0.70672E\(-\)102 & 4.8635157 \\ Equation \((14)-(17),n=3,\lambda_{0}=-1\) & 0.34838E\(-\)7 & 0.12841E\(-\)67 & 0.15487E\(-\)611 & 9.0002878 \\ Equation \((15)-(17),n=3,\lambda_{0}=-1\) & 0.34838E\(-\)7 & 0.34679E\(-\)73 & 0.10151E\(-\)705 & 9.5835521 \\ Equation \((16)-(17),n=3,\lambda_{0}=-1\) & 0.34838E\(-\)7 & 0.41211E\(-\)75 & 0.11560E\(-\)741 & 9.8127640 \\ Equation \((14)-(17),n=3,\lambda_{0}=-0.5\) & 0.11873E\(-\)7 & 0.35119E\(-\)73 & 0.13260E\(-\)661 & 8.9795793 \\ Equation \((15)-(17),n=3,\lambda_{0}=-0.5\) & 0.11873E\(-\)7 & 0.43166E\(-\)77 & 0.67183E\(-\)743 & 9.5883270 \\ Equation \((16)-(17),n=3,\lambda_{0}=-0.5\) & 0.11873E\(-\)7 & 0.45981E\(-\)83 & 0.29759E\(-\)820 & 9.7754885 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Numerical results for \(f_{2}(x)\)by the methods with memory.  
Figure 1: Iterative processes of different methods for the function \(f_{1}(x)\).  
Tables 3 and 4, it can be concluded that the convergence of the tested multipoint Equation (17) with memory is remarkably fast. The \(R\)-order of convergence of the family Equation (17) with memory is increased by applying a self-accelerating parameter given by Equations (14)-(16). In addition, above all, the increase of convergence order is obtained without any additional function evaluations, which indicates a very high computational efficiency of our methods with memory.  
The project supported by the National Natural Science Foundation of China (Nos. 11371071 and 11201037), the PhD Start-up Fund of Liaoning Province of China ( Nos. 20141137 and 20141139), the Liaoning BaiQianWan Talents Program (No.2013921055) and the Educational Commission Foundation of Liaoning Province of China (Nos. L2014443,L201444 and L2015012).
# Research on a Nonlinear Dynamic Incipient Fault Detection Method for Rolling Bearings
## 2 Preliminary
### Adaptive Dynamic Method  
The vibration signal collected during the running of rolling bearings reflects the change of the bearing with the running time [33; 34]. Aiming at this time correlation, a moving window algorithm was used to update the model in real time to achieve adaptive detection. On this basis, combined with the autocorrelation matrix, the online update speed was approximately doubled.  
Figure 1: The flow chart of Kernel Principal Component Analysis (KPCA).  
In the process of the update model, the recursive moving window is 1, and the update window length is \(L\), that is, the covariance matrix is updated every \(L\) data collection. Let the mean value \(\overline{X}_{a}\) and the covariance \(R_{a}\) of the previous matrix block \(X_{a}\) be known then the mean value \(\overline{X}_{m}\) and covariance \(R_{m}\) of \(X_{m}\) is:  
\[\overline{X}_{m}=\frac{L}{L-1}\overline{X}_{a}-\frac{1}{L-1}x_{a} \tag{2}\]  
\[R_{m}=\frac{L-1}{L-2}(R_{a}-\frac{1}{L}x_{a-L-1}x_{a-L-1}^{T}-\sum\
olimits_{ a}^{-1}\Delta\overline{X}_{m}\Delta\overline{X}_{m}{}^{T}\sum\
olimits_{a}^{-1}) \tag{3}\]  
According to \(\overline{X}_{m}\) and \(R_{m}\), the mean value \(\overline{X}_{a+1}\) and covariance \(R_{a}\) of \(X_{a}\) as follows:  
\[\overline{X}_{a+1}=\frac{L-1}{L}\overline{X}_{m}+\frac{1}{L}x_{a+L} \tag{4}\]  
\[R_{a+1}=\frac{L-2}{L-1}R_{m}+\frac{1}{L-1}x_{a+L}x_{a+L}^{T}+\sum\
olimits_{ a+L}^{-1}\Delta\overline{X}_{m(a+L)}\Delta\overline{X}_{m(a+L)}{}^{T}\sum \
olimits_{a+L}^{-1} \tag{5}\]  
where, \(\Delta\overline{X}_{m}=\overline{X}_{m}-\overline{X}_{a}\), \(\Delta\overline{X}_{m(a+1)}=\overline{X}_{a+1}-\overline{X}_{m}\).  
According to Formulas (2)-(5), updating the covariance can avoid the complexity of calculating large block matrices and matrix multiplication, but the calculation steps are still complicated. The online update rate can quickly increased through the autocorrelation matrix:  
\[\sum\
olimits_{a}^{-1}\Delta\overline{X}_{m}\Delta\overline{X}_{m}{}^{T}\sum \
olimits_{a}^{-1}=\frac{1}{L^{2}}x_{a}x_{a}^{T} \tag{6}\]  
\[\sum\
olimits_{a+L}^{-1}\Delta\overline{X}_{m(a+L)}\Delta\overline{X}_{m(a+L) }{}^{T}\sum\
olimits_{a+L}^{-1}=\frac{1}{L^{2}}x_{a+L}x_{a+L}^{T} \tag{7}\]  
Substitute Formulas (3), (6), and (7) into Formula (5) obtaining the Formula (8):  
\[R_{a+1}=R_{a}+\frac{L^{2}+L-1}{L^{2}(L-1)}\big{(}x_{a+L}x_{a+L}^{T}-x_{a}x_{a} ^{T}\big{)} \tag{8}\]  
The improved model only needs to directly calculate \(X_{a+1}\) through \(X_{a}\), which reduces the calculation of the number of steps from four to just two, and the online update rate is improved by double. It saves the storage space of hardware and greatly improves the calculation efficiency.
# Lightweight Violence Detection Model Based on 2D CNN with Bi-Directional Motion Attention
## 2 Related Works
### Attention Mechanism on Temporal Information  
It is critical to capture motion features for violence detection. Attention mechanisms are widely applied to capture motion features effectively in violence detection models.  
Self-attention mechanisms have been proposed for use in the area of computer vision. The authors of [37] presented non-local operations to capture long-range dependencies with deep neural networks. A non-local operation computes the response at a position as a weighted sum of the features at all positions in the input feature maps. Vision transformer (ViT) [38] and StNet [39] are typical self-attention modules modeling the long-range spatiotemporal features in behavior recognition. Though these schemes are effective, they come at the cost of significant computational overhead.  
Some researchers use temporal attention mechanisms to enhance the long-range motion modeling ability of 2D CNNs. In [40], the authors proposed a feature-level motion attention mechanism and performed the channel-wise spatiotemporal fusion so as to improve the action recognition accuracy. In [41] the authors proposed a motion excitation (ME) attention mechanism, which enabled 2D CNNs to capture long-range motion information. The ME primarily focuses on motion-sensitive channels. Compared with [40], the scheme in [41] uses a Multiple Temporal Aggregation structure to recalibrate the features after ME and achieves higher accuracy.  
We propose a bi-directional motion attention mechanism (Bi-LTMA) to boost the violence detection performance. Differently from [41], the Bi-LTMA computes an attention map based on bi-directional motion information in both channel and spatial dimensions. In addition to Bi-LTMA, TSM [20] is also employed in our model to realize temporal feature interaction such that the motion feature modeling capability of the model is enhanced further.
## 2 UAV in Wireless Communication Networks
### Use Cases of UAV Wireless Networks
#### 2.2.2 UAV Relay Station  
UAV RS provides a wireless connectivity to isolated users or user groups, who do not have a direct communication link from a BS or a transmitter, without sacrificing the performance of networks, thereby enhancing the capacity of the overall networks [44]. The UAV relay network (URN) can be constructed with single or multiple UAVs, but the number of UAVs, the topology and the routing protocol for a reliable relay communication, and an efficient power consumption should be optimized for applications [43; 44]. URN is suitable for military communications or emergency responses where the temporary communications between command center and operators are essential. The outage probability of access links should be considered to provide a reliable relay connectivity to mission critical operators [43; 44].
# Detection of Large-Scale Floods Using Google Earth Engine and Google Colab
## 2 Materials and Methods
### Data  
This section provides an overview of the data sources and satellite imagery used in our flood detection methodology. We focus on available HAND datasets, the Sentinel-1 constellation and its operational details, data availability in Google Earth Engine, and the specifics of data used for both calibration and application.
## 4 Communications
### Communication Paradigms
Models (e) and (f) can be implemented in both manners. Figure 3: Synchronous and asynchronous RDMA communications. As can be seen, each paradigm has its own unique characteristic which makes it suitable for a particular environment. Models (a) and (d) share the effort for communication in a fair manner. Model (c) puts the burden of communication on the client side and Model (b) on the server side. Model (a) incurs higher CPU usage in both client and server sides due to polling. Models (b)-(d) generate more network traffic for polling remote side. Models (e) and (f) do not induce a pre-defined memory address but they require synchronization in sending and receiving messages. Each communication paradigm supports a series of connection types according to the adopted RDMA operation. RDMA supports unreliable and reliable connection types. Unlike unreliable, reliable connection guarantees the delivery and the order of the packet through an acknowledgment message from the receiver. Furthermore, RDMA supports unconnected and connected connections. Unlike unconnected, each QP in connected communication connects exactly to one QP of a remote node. This paper only considers the connected connections, i.e, _Reliable Connected (RC)_ and _Unreliable Connected (UC)_. Table 1 compares different communication paradigms according to client and server overheads, network traffic, communication, and connection types. Each model is named according to the operations presented in Figure 4.
## 3 Results
For all outcome measures, there was a significant difference between the mean difference and zero (\(p<0.001\)), indicating a significantly lower value for whole-body fat%, whole-body fat mass and right leg fat mass as well as higher values for whole-body bone mineral content (only in men), right arm lean mass, right leg lean mass (only in women) in BIA compared to DXA. No significant difference was observed for right arm fat mass (\(p\) = 0.09) and right leg lean mass (\(p\) = 0.423) in men, in addition to right arm fat mass (\(p\) = 0.116) and whole-body bone mineral content (\(p\) = 0.069) in women. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Men** & **Women** & **Fisher r- to z-Transformation** \\  & **(\(n\) = 47)** & **(\(n\) = 36)** & **\(p\)-Value** \\  & & & **(Z-Value)** \\ \hline
**Body fat (\%)—Whole-body** & 0.90 *\({}^{\circ}\) & 0.90 *\({}^{\circ}\) & 1.00 (0.00) \\
**Fat mass (kg)—Whole-body** & 0.93 *\({}^{\circ}\) & 0.96 *\({}^{\circ}\) & 0.21 (\(-\)1.25) \\
**Lean mass (kg)—Whole-body** & 0.97 *\({}^{\circ}\) & 0.91 *\({}^{\circ}\) & 0.01 (2.45) * \\
**Bone mineral content (kg)—Whole-body** & 0.85 *\({}^{\circ}\) & 0.81 *\({}^{\circ}\) & 0.58 (0.56) \\
**Fat mass (kg)—Right arm** & \(-\)0.018 *\({}^{\circ}\) & 0.26 *\({}^{\circ}\) & 0.22 (\(-\)1.23) \\
**Fat mass (kg)—Right leg** & \(-\)0.029 *\({}^{\circ}\) & 0.43 *\({}^{\circ}\) & 0.03 (\(-\)2.12) * \\
**Lean mass (kg)—Right arm** & 0.87 *\({}^{\circ}\) & 0.61 *\({}^{\circ}\) & 0.01 (2.71) * \\
**Lean mass (kg)—Right leg** & 0.80 *\({}^{\circ}\) & 0.65 *\({}^{\circ}\) & 0.16 (1.40) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Pearson’s r correlation coefficients between BIA and DXA outcome measures for men and women separately. Figure 1: Bland–Altman plots showing the mean value plotted against the mean difference (DXA vs. BIA) for whole-body outcome measures. Figure 2: Bland–Altman plots showing the mean value plotted against the mean difference (DXA vs. BIA) for segmental outcome measures.
# Numerical Study of Mixed Convection and Heat Transfer in Arc-Shaped Cavity with Inner Heat Sources
###### Abstract
A series of simulation studies have been carried out for the mixed convection of different forms of heat sources and different shapes of cavities [21; 22; 23; 24]. Although a large number of studies have been conducted on in-depth studies on the problem of convective heat transfer in cavities, there are few studies on mixed convection in the cavity with an opening. Some previous research model structures are relatively more basic and simplified and lack the exploration of unsteady characteristics and a comprehensive consideration of ventilation and heat dissipation efficiency. However, this is closely related to the comfort of the actual engineering structure environment. Especially in recent years, the environmentally friendly coal shed has been widely used. The heat release of coal piles causes local overheating of the environment, which affects the comfort level and the health of the operators. Therefore, this study takes the current large-span coal shed as the engineering background and simplifies its structure into a curved cavity. The two-dimensional numerical simulation is adopted to conduct a transient study on the fluid flow and the heat transfer inside the curved cavity. This paper discusses the influence of different Re on the flow structure, heat transfer efficiency, heat dissipation efficiency and transient flow characteristics in the fully developed stage of the curved cavity. It is of important practical significance to create a good indoor wind and thermal environment.
# Achievable Rate Maximization for Multi-Relay AF Cooperative SWIPT Systems with a Nonlinear EH Model
## 2 System Model
### Asymptotic Analysis for the Maximum Achievable End-to-End Rate
#### 3.3.2 Asymptotic Analysis for the TS Scheme  
Let \(\alpha^{*}\) be the optimal TS ratio. Then, from (11) and (25), the maximum achievable information rate can be expressed as:  
\[R_{\max-\text{TS}}=\frac{1-\alpha^{*}}{2}\text{log}_{2}\left(1+\sum_{l=1}^{L} \frac{2\alpha^{*}C_{4,l}C_{5,l}}{2\alpha^{*}C_{4,l}+(C_{5,l}+1)(1-\alpha^{*})} \right)\, \tag{30}\]  
where \(C_{4,l}\) and \(C_{5,l}\) are given as (36) and (37) in Appendix, respectively.  
Case 1 (Low Input SNR) with \(P_{s}\to 0\): when \(P_{s}\to 0\), it can be obtained from (37) that \(C_{5,l}\to 0\). Then, from (30), the practical maximum achievable information rate is equal to zero for both the nonlinear and linear EH models. Similarly to the PS scheme, when \(P_{s}\) is so small that the input RF power does not saturate the EH receiver, the same optimal TS ratios can be obtained, leading to the same maximum achievable information rate for both the linear and nonlinear EH models.  
Case 2 (High Input SNR) with \(P_{s}\to\infty\): When \(P_{s}\to\infty\), it can be obtained from (19), (36) and (37) that \(C_{4,l}=C_{3,l}\) and \(C_{5,l}\to\infty\). Then from (30), the practical maximum achievable information rate can be expressed as:  
\[R_{\max-\text{TS}}=\frac{1-\alpha^{*}}{2}\text{log}_{2}\left(1+\sum_{l=1}^{L} \frac{2\alpha^{*}}{1-\alpha^{*}}C_{3,l}\right). \tag{31}\]  
Let \(x^{*}\) and \(y^{*}\) be the optimal TS ratios \(\alpha^{*}\) when the linear and nonlinear EH models are used, which can be obtained by solving the optimal problem (25) and given as:  
\[x^{*}=\underset{0\leq x\leq 1}{\arg\min}\frac{x-1}{2}\logand:  
\[y^{*}=\operatorname*{arg\,min}_{0\leq y\leq 1}\frac{y-1}{2}\log_{2}\left(1+\sum_{l=1 }^{L}\frac{2 yC_{4,l}C_{5,l}}{2 yC_{4,l}+(C_{5,l}+1)(1-y)}\right), \tag{33}\]  
where \(C_{4,l}^{linear}=\eta_{l}P_{s}|h_{S,R_{l}}|^{2}\big{|}h_{R_{l},D}\big{|}^{2} \big{/}N_{0}\). When \(P_{s}\to\infty\), it can be obtained that \(C_{4,l}^{linear}\to\infty\), \(C_{5,l}\to\infty\), and \(C_{4,l}=M_{l}|h_{R_{l},D}\big{|}^{2}\Big{/}N_{0}\ll C_{5,l}\). Then, (32) and (33), respectively, can be rewritten as:  
\[x^{*}=\operatorname*{arg\,min}_{0\leq x\leq 1}\frac{x-1}{2}\log_{2}\left(1+ \sum_{l=1}^{L}C_{5,l}\right)=0 \tag{34}\]  
and:  
\[y^{*}=\operatorname*{arg\,min}_{0\leq y\leq 1}\frac{y-1}{2}\log_{2}\left(1+ \frac{2y}{1-y}\sum_{l=1}^{L}\frac{M_{l}|h_{R_{l},D}|^{2}}{N_{0}}\right), \tag{35}\]  
Let \(R_{\max-\mathrm{TS}}^{linear}\) and \(R_{\max-\mathrm{TS}}^{nonlinear}\) be the practical maximum achievable information rates for the linear and nonlinear EH models, which can be obtained from (31) by substituting \(\alpha^{*}\) with \(x^{*}\) and \(y^{*}\), respectively. From (34) and (35), it can be obtained that when \(P_{s}\to\infty\), \(x^{*}\to 0\) and thus \(R_{\max-\mathrm{TS}}^{linear}\to 0\), whereas \(y^{*}\) does not changes with \(P_{s}\) such that \(R_{\max-\mathrm{TS}}^{nonlinear}\) is invariable when \(P_{s}\) changes.