esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 5G and TSN Integrated Networks for VPP
### Semi-Persistent Scheduling with Reserved Bandwidth Sharing and Pre-Emption  
The frames in the TSN and 5G integrated networks are forwarded independently according to the QoS framework of their specific technologies. However, considering the time criticality of VPP applications, it is recommended to jointly schedule traffic flows in both 5G and TSN. This section proposes a semi-persistent scheduling with reserved bandwidth sharing and pre-emption (SPS-RBSP) mechanism. It reduces the transmission delay of VPP traffic, especially the event-triggered (ET) traffic, in the 5G and TSN integrated network. In the 5G system, the stream configuration is transmitted in the form of a QoS profile that includes QoS parameters such as 5 QI. The SMF determines the appropriate resource allocation for QoS flows according to the QoS profile. The TSN can be used as a 5G transmission network to provide deterministic low-latency communication services for traffic through the gate control list (GCL).
## 4 Implementation and Application Scenarios
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No** & **Time** & **Air Temperature** & **Air Humidity** & **Soil Moisture** & **Soil pH Range** \\ \hline
1 & 08:38:07 + 02:00 & Normal & Normal & High & Normal \\
2 & 09:53:45 + 02:00 & Normal & Normal & High & Normal \\
3 & 11:45:23 + 02:00 & Normal & Normal & Normal & Normal \\
4 & 13:02:04 + 02:00 & Normal & Normal & Normal & Normal \\
5 & 14:34:36 + 02:00 & High & Low & Normal & Normal \\
6 & 16:10:11 + 02:00 & High & Low & Normal & Low \\
7 & 17:26:18 + 02:00 & High & Low & Normal & Normal \\
8 & 18:46:13 + 02:00 & High & Normal & High & High \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Random sample sets of high-level contextual data. Figure 16: Indicative Python source code for classification to high-level contextual data. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No** & **Date** & **Time** & **Air Temperature (°C)** & **Air Humidity (\%)** & **Soil Moisture (\%)** & **Soil pH** \\ \hline
1 & 2019-06-20 & 08:38:07 + 02:00 & 27.6 & 53 & 62.4 & 6.4 \\
2 & 2019-06-20 & 09:53:45 + 02:00 & 30.2 & 51 & 65.8 & 6.8 \\
3 & 2019-06-20 & 11:45:23 + 02:00 & 31.6 & 51 & 60.7 & 6.1 \\
4 & 2019-06-20 & 13:02:04 + 02:00 & 32.4 & 48 & 60.2 & 6.1 \\
5 & 2019-06-20 & 14:34:36 + 02:00 & 33.8 & 42 & 58.3 & 6.0 \\
6 & 2019-06-20 & 16:10:11 + 02:00 & 34.2 & 42 & 57.4 & 5.9 \\
7 & 2019-06-20 & 17:26:18 + 02:00 & 33.2 & 43 & 61.1 & 6.5 \\
8 & 2019-06-20 & 18:46:13 + 02:00 & 31.5 & 46 & 63.5 & 7.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Random sample sets of agricultural raw data acquired in a maize field. Information concerning the profile characteristics of the cultivation is stored in the context repository served by a suitable Azure data source while log entries of unusual instances are also stored with corresponding timestamps. For the purposes of this research, two application scenarios where studied during the implementation process of the system.
# Learning-Based Traffic Scheduling in Non-Stationary Multipath 5G Non-Terrestrial Networks
## 2 Materials and Methods
### Channel Model
If we let \(L_{g}\) and \(L_{b}\) denote the mean length (in meters) of the G and B states, respectively, as derived in [24], and let \(\
u\) be the speed in meters per second (m/s) of a moving vehicle, and we then assume that the packets transmitted by the vehicle have a length of \(l\) bits, with \(R\) being the bit rate in bits per second (bps), then the state time durations \(D_{b}\) and \(D_{g}\) are given by \(D_{g}=1/b\) and \(D_{b}=1/g\), respectively, equal to  
\[D_{b}=\frac{R}{\
u\cdot l}L_{g};D_{g}=\frac{R}{\
u\cdot l}L_{b}. \tag{6}\]  
Then, it follows that  
\[b=(\frac{R}{\
u\cdot l}L_{g})^{-1};g=(\frac{R}{\
u\cdot l}L_{b})^{-1} \tag{7}\]  
According to [5], \(L_{b}\) and \(L_{g}\) can be computed as follows:  
\[L_{G,B}=exp\left(\mu_{G,B}+\frac{\sigma_{G,B}^{2}}{2}\right)\frac{erfc\left( \frac{logdur_{min,G,B}-(\mu_{G,B}+\sigma_{G,B}^{2})}{\sigma\sqrt{2}}\right)} {erfc\left(\frac{logdur_{min,G,B}-\mu_{G,B}}{\sigma\sqrt{2}}\right)} \tag{8}\]  
where \((\mu,\sigma)_{G,B}\) and \(dur_{min}\) are the mean, standard deviation and minimum state lengths in meters, respectively, of the channel states. These parameters (\((\mu,\sigma)_{G,B}\) and \(dur_{min}\)) are provided in [5] for urban, suburban and rural environments at different elevation angles and transmission frequencies as reported in Table 1. \begin{table}
\begin{tabular}{c c c c} \hline
**Elevation** & \(\mu_{G,B}\) & \(\sigma_{G,B}\) & \(dur_{min,G,B}\) \\ \hline
20\({}^{\circ}\) & 2.0042, 3.6890 & 1.2049, 0.9796 & 3.9889, 10.3114 \\
30\({}^{\circ}\) & 2.7332, 2.7582 & 1.1030, 1.2210 & 7.3174, 5.7276 \\
45\({}^{\circ}\) & 3.0639, 2.9108 & 1.6980, 1.2602 & 10.0, 6.0 \\
60\({}^{\circ}\) & 2.8135, 2.0211 & 1.9595, 0.6568 & 10.0, 1.9126 \\
70\({}^{\circ}\) & 4.2919, 2.1012 & 2.4703, 1.0341 & 118.3312, 4.8569 \\ \hline \end{tabular}
\end{table} 
Table 1: Satellite link parameters for the dense urban area in France at 2.2 GHz [5]. For the purpose of this work, we used the parameters for an urban environment at 2.2 GHz to compute the mean lengths of the channel states \(L_{g}\) and \(L_{b}\) using Equation (7). We then used Equation (6) to calculate the corresponding transition probabilities \(g\) and \(b\) for our channel model as reported in Table 2. We then used these transition matrices to create Markov link state traces for training our model. We assumed successful traffic reception only if there was an LOS (i.e, it was in a good state). We also assumed that the UAV received some feedback reports as described in [3], indicating the traffic reception status and the link state.
# Numerical and Experimental Studies of the LK Type Shaped Charge
## 1 Introduction
Therefore, high explosive burn, the Jones-Wilkins-Lee equation of state (JWL-EOS), elastic-plastic hydrodynamic analysis, and the Mei-Gruneisen EOS are the basic constitutive models currently used to describe the material in numerical simulations [34; 35; 36]. The issue of cumulative jet formation is now analyzed with various numerical methods, usually using smoothed-particle hydrodynamics (SPH) [37; 38; 39]. The problem of the formation of an effective jet is still a field that requires researchers to seek solutions in the sphere not only of modern materials for liners or innovative high-energy materials. Knowledge of the problem from the physical side allows the possibility of jet optimization by directing the detonation wave front of the explosion in an appropriate way. It allows a better use of the Birkhoff phenomenon. In this regard, computer simulation methods based on hybrid methods are helpful. Figure 1: Speeds of the resulting individual components of the collapsing liner. The authors of this paper present analysis of two types of the Polish LK cumulative charge, differing only in the explosive detonation-initiation system. The purpose of this analysis was to strengthen the cumulative jet by shaping the front of the detonation wave acting on the liner. By introducing additional inserts between the explosive and the liner into the LK charge, it was possible to influence the way the collapsing liner spreads over a part of the slug and the jet. This task was accomplished by means of numerical simulations. The results of simulations shown that mechanical properties as well as hybrid combinations of the materials used in production of the cumulative liner had influence to stability of the cumulative jet. The obtained results were compared with experimental results. The experimental tests were limited to the execution of test batches of shaped charges with an additional aluminum insert and without an insert in order to compare their effectiveness on the armor plate. On this basis, conclusions pertaining to the impact of the geometry of the insert on the durability of the cumulative jet speed were formulated.
## 2 General Introductions to Field Measurements
### Testing Principle of the Rotation Accelerometer  
The mathematical representation of the mathematical model of the rotation accelerometer is shown in Figure 6. The motion differential equation of model RA013 rotation accelerometer can be expressed as follows ([PERSON], et al., 2015 [29]):  
\[K_{1}\ddot{\theta}+b\dot{\theta}+k\theta+G_{1}i_{1}=-\sum m_{i}H_{i}\times\ddot {y}-K_{1}\ddot{\varphi} \tag{1}\]  
where \(K_{1}\) is the moment of the inertia of the double pendulum swinging about the rotational axis. \(b\) refers to the damping coefficient. \(k\) denotes the angular stiffness. \(\theta\) represents the displacement. \(\ddot{y}\) is the ground translation acceleration. \(\ddot{\varphi}\) is the ground rotational acceleration. \(G_{1}\) is the electric constant of the damping coil. \(i_{1}\) is the current flowing into the damping coil.  
Figure 1: Moving track of typhoon Sarika and the exterior view of the measured building: (**a**) moving track of typhoon Sarika; (**b**) exterior view of the measured building; and (**c**) field installation of anemometer atop the building.  
Figure 4: Measuring point layouts of the translation and rotation accelerometer.  
Figure 3: Rotation sensitive axis of the rotation accelerometer.  
Figure 2: Building plan of the measured high-rise building.  
The solution of the equation can be expressed by ([PERSON], et al., 2015 [29])  
\[\theta(s)=\frac{-s^{2}}{s^{2}+2 Dns+n^{2}}(\frac{1}{l_{0}}y-\varphi) \tag{2}\]  
where \(l_{0}\) is the equivalent pendulum length. \(s\) is the operator. \(n\) is the circular frequency of self-vibration. \(D\) is the damping ratio.  
Figure 5: Layout of the translation and rotation accelerometers on different floors: X axis; Y axis; Z rotation axis.  
Figure 6: Schematic representation of the mathematical model of the rotation accelerometer ([PERSON], et al., 2015).  
Furthermore,  
\[n^{2}=\frac{k}{K_{1}},\ \ \ 2 Dn=\frac{b}{K_{1}},\ \ \ l_{0}=\frac{K_{1}}{\sum m_{i}H_{i} }=\frac{K_{1}}{m_{1}-m_{2}H_{2}}\]  
where \(m_{1}\), \(m_{2}\) are the effective masses of the double pendulum. \(H_{1}\), \(H_{2}\) are the distances between the two centers of mass and the rotational axis. Likewise, when \(m_{1}H_{1}=m_{2}H_{2}\), \(l_{0}=\infty\), the instrument will only reflect the rotational angle, and not the translation; the solution of the equation can be expressed by ([PERSON], et al., 2015)  
\[\theta(s)=-\frac{s^{2}\theta}{s^{2}+2 Dns+n^{2}} \tag{3}\]  
It can be seen from Equation (3) that the angle of rotation accelerometer is in proportion to the rotation accelerometer of ground \(s^{2}\varphi\).
# Study on the Combustion Behavior and Kinetic Characteristics of Semi-Coke from Oil Shale
## 3 Results and Discussion
### Combustion Characteristics of Oil Shale Semi-Coke
#### 3.1.2 Extraction of Combustion Characteristic Parameters  
To further analyze the combustion behavior of oil shale semi-coke, key combustion characteristic parameters were extracted from the thermogravimetric analysis (TGA) and derivative thermogravimetric analysis (DTG) curves. These parameters include ignition temperature (\(T_{i}\)), peak temperature (\(T_{p}\)), burnout temperature (\(T_{f}\)), and mass loss ratio. They reflect the thermal and chemical characteristics of the combustion process, including its initiation, main reaction phase, and completion. In this study, the extrapolation method was used to analyze the TG-DTG curves and determine the combustion characteristic parameters (\(T_{i}\), \(T_{p}\), and \(T_{f}\)) of the oil shale semi-coke. Taking the heating rate of 25 \({}^{\circ}\)C/min as an example, the calculation is shown in Figure 3.  
Thermogravimetric analysis (TGA) reveals the staged characteristics of the combustion process of oil shale semi-coke, providing experimental data to support subsequent kinetic modeling. The ignition temperature and peak temperature reflect the thermal stability and reaction rate characteristics of semi-coke combustion. Higher ignition and peak temperatures indicate better combustion stability. The combustion characteristic parameters of oil shale semi-coke at different heating rates are shown in Table 4.  
Figure 3: Schematic diagram for calculating combustion characteristic parameters of oil shale semi-coke.  
As shown in Table 4, with the increase in heating rate, the ignition temperature (\(T_{i}\)), peak temperature (\(T_{p}\)), and final combustion temperature (\(T_{f}\)) of the sample all show a gradual upward trend. This indicates that the thermal stability of the sample improves with higher heating rates, and the reaction rate characteristics of the combustion process also change. A higher heating rate leads to more intense combustion reactions at elevated temperatures, demonstrating better thermal stability and faster reaction rates. Using a higher heating rate can help improve the combustion efficiency of oil shale semi-coke and enhance its energy conversion efficiency.
# Mapping a Guided Image Filter on the HARP Reconfigurable Architecture Using OpenCL
## 6 Experimental Results
### Impact of the OpenCL Cache  
When the input parameters are not marked by the keyword volatile, the OpenCL compiler adds a software implemented cache. The performance of the OpenCL cache is shown in the cache hit rates of the profiling report, see Table 6. The cache hit rate for the filtering input equals 81.5 %. This can be explained by considering the size of the struct that is used, which equals 12 B, and the size of the OpenCL cache lines, which is 64 B. Data is read from memory as 64 B cache lines. If one struct element is read, the remaining 52 B of the same cache line reside in cache memory. This leads to a cache hit ratio of 52/64 = 81.5%. Moreover, as a separate cache is created for the filtering input and the guidance input, both cache reads do not interfere with each other. The same reasoning can be applied to the cache hit ratio of the guidance image input.
# An Optimal Online Resource Allocation Algorithm for Energy Harvesting Body Area Networks
## 3 System Model
### Collecting Rate and Utility  
In time slot \(t\), let \(c_{n}(t)\) represent the collecting rate of sensor \(n\) carried by the patient in BAN. \(c_{n}(t)\) follows an independent and identical distribution. We assume that the collected data have a finite maximum \(c^{max}\), so that  
\[0\leq c_{n}(t)\leq c^{max},\forall n\in N. \tag{1}\]  
The collecting rate is associated with a user utility function \(U_{n}(c_{n}(t))\), which is a concave function over the interval \(0\leq c_{n}(t)\leq c^{max}\) with a bounded first derivative \(U_{n}^{\prime}(c_{n}(t))\) and \(U(0)=0\)[23]. We assume that utility function \(U_{n}(c_{n}(t))\) has a finite maximum slope of \(v\).
# Computational Modeling of Passive and Active Cooling Methods to Improve PV Panels Efficiency
## 3 Results and Discussion
### Comparison of the Implemented Methods  
When a comparison is performed between the three implemented alternatives (perforated panel, active panel, and hybrid panel), it was possible to establish that the greatest decrease in temperature is achieved with the hybrid solar panel. In absolute values, with the hybrid panel, an average decrease of 17.24 \({}^{\circ}\)C was obtained compared to 15.01 \({}^{\circ}\)C for the active panel and 4.46 \({}^{\circ}\)C for the perforated panel (See Table 11). In percentage terms, with the hybrid solar panel, a decrease of 287% in operating temperature was obtained compared to the passive solar panel and 15% compared to the active solar panel.  
In terms of the output power of the solar panels, with the decrease in the operating temperature, better results were obtained. Obviously, with the hybrid solar panel higher power was obtained on average (17.92 W) compared to the active solar panel (16.29 W) and the passive solar panel (4.65 W) (Table 12). In percentage terms, the hybrid panel  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Time**} & **Std. Panel (W)** & **Hyb. Panel Wat.** & **Diff. Hyb.—Act. Panel Wat.** \\  & **Panel (\({}^{\circ}\)C)** & **Amb. T. (W)** & **Amb. T. (W)** \\ \hline
10:00 & 67.61 & 77.24 & 9.63 \\
11:00 & 63.98 & 76.04 & 12.06 \\
12:00 & 50.16 & 75.38 & 25.22 \\
13:00 & 50.76 & 75.12 & 24.36 \\
14:00 & 54.80 & 75.23 & 20.43 \\
15:00 & 59.65 & 75.46 & 15.81 \\ Prom. & 57.83 & 75.75 & 17.92 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Power values of the PV panels for different hours of the day (standard—hybrid).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Time**} & **Diff. Std.—Perf.** & **Diff. Std.—Act. Panel** & **Diff. Std.—Hyb. Panel** \\  & **Panel (\({}^{\circ}\)C)** & **Wat. Amb. T. (\({}^{\circ}\)C)** & **Wat. Amb. T. (\({}^{\circ}\)C)** \\ \hline
6:00 & 1.45 & 1.86 & 2.73 \\
7:00 & 4.45 & 9.15 & 9.80 \\
8:00 & 4.40 & 10.95 & 11.05 \\
9:00 & 5.21 & 12.55 & 12.77 \\
10:00 & 5.56 & 14.86 & 17.69 \\
11:00 & 4.70 & 16.57 & 19.12 \\
12:00 & 5.34 & 28.38 & 31.70 \\
13:00 & 4.74 & 28.31 & 32.19 \\
14:00 & 6.06 & 24.31 & 28.24 \\
15:00 & 5.61 & 20.49 & 23.63 \\
16:00 & 3.91 & 13.92 & 17.30 \\
17:00 & 3.28 & 9.14 & 11.18 \\
18:00 & 3.24 & 4.68 & 6.66 \\ Prom. & 4.46 & 15.01 & 17.24 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Temperature differences between the solar panels evaluated.  
obtained 286% more power compared to the passive panel and 10% more compared to the active panel.  
This situation shows that the hybrid solar panel has better performance in terms of power output. However, it is noteworthy that both the active panel and the passive panel improve the performance of the standard solar panel.
# A Novel RBFNN-CNN Model for Speaker Identification in Stressful Talking Environments
## 4 Model Architecture
### Deep Learning Experiments
#### 4.3.7 Attention-BILSTM BI-GRU  
The proposed Attention-BILSTM model consists of three BI-GRU layers. Each of these three GRU layers has 32 filters. We added a dropout layer, which helps in avoiding overfitting; we set a dropout ratio of 30%. Finally, we added a fully connected layer and a dense layer that has activation function Softmax with 16 nodes.
## 3 Results  
In total, nineteen sequences of _MECPS_ gene promoters from seven selected model plants were analyzed. The details of the analyzed sequences are provided in Supplementary File S1 and Table S1.  
Analyses of _Zm00001d051458_ (_MECPS1_) were performed on the promoters and defined using the PlantPAN3.0 database in relation to different transcripts of _Zm00001d051458_, described as _Zm00001d0514587002-T008_. Among the observed sequences of RSREs (**G/A/C)CGCG(C/G/T)** and spacers, the sequence **ACGCG**ACGCG**ACCCG**ACCCG**CC**CC**, was most often noted (_Zm00001d051458/MECPS1_7002_, _T005_, _T006_, _T007_, and _T008_). The sequence **CCGCG**ACCCG**TT**CCGC**GT** was observed only in _Zm00001d051458 T003_ (Supplementary File S1, Table S1). A different sequence **CCGCG**ACGAAT**CCGC** was found in the gene _Zm00001d017608/MECPS2_T001_ (Table S1). Although spacer sequences are different in the two _ZmMECPS1_ and _ZmMECPS2_ genes, they are both 7 nt long. Moreover, they are localized in the 5'UTR region of the _ZmMECPS1_ and \(2\) genes (File S1, Table S1). Sequences of closely spaced RSRE repetitions within _Zea maysMECPS_ genes are presented in Table 1.  
\begin{table}
\begin{tabular}{c c c} \hline
**Nr** & **Sequence of Closely Spaced RSRE Repetitions** & **Gene ID/Name** \\ \hline
1 & **ACGCG**ACGCG**ACGCG**CC & _Zm00001d051458_T002/MECPS1_ \\
2 & **CCGCG**AT**CCGT**TT**CCGC**GT** & _Zm00001d051458_T003/MECPS1_ \\
3 & **ACGCG**ACGCG**ACCCG**CC** & _Zm00001d051458_T005/MECPS1_ \\
4 & **ACGCG**ACGCG**ACGCG**CC** & _Zm0001d051458_T006/MECPS1_ \\
5 & **ACGCG**ACGCG**ACGCG**CCGC** & _Zm0001d051458_T007/MECPS1_ \\
6 & **ACCGG**ACGCG**ACGCG**CCGC** & _Zm00001d051458_T008/MECPS1_ \\
7 & **CCGCG**ACGAAT**CCGCGC** & _Zm0001d017608_T001/MECPS2_ \\ \hline \end{tabular}
\end{table}
Table 1: Sequences of closely spaced RSRE repetitions found in _Zea maysMECPS_ and _MECPS2_ genes. Sequences of RSREs are written in bold.  
The closely spaced RSEe sequences of MEP pathway genes other than _ZmMECPS1_ and _ZmMECPS2_ were observed in _Zm00001d012197/CMS_ (Supplementary File S2, Table S2). The same sequence **GCGCGCCTGGCGCGC** was noted in _Zm00001d012197/CMS_T001_, _T005_, _T006_,and _T007_. The spacing is 4 nt (TGGT), which is much less when compared to the _ZmMECPS1_ and \(2\) genes (Supplementary File S2, Table S2). These repetitions are localized in the proximal promoter, within 317 nt from the putative transcription start site. Moreover, the _Os030t0732000-00/HDR_ gene contains **CCGCGCGC**CCAGAGCT**CCGCGC**. However, the 10 nt long spacing between two RSEs in _Os03t0732000-00/HDR_ is relatively long, exceeding the limit of 8 nt value [34]. Therefore, the potential to induce CAMTA dimerization should be interpreted carefully. The sequences of closely spaced RSE repetitions found in _Zea maysCMS_ gene are presented in Table 2.
## 2 System Model
### Array Model  
Consider an antenna array consisting of a uniform linear array (ULA) with \(M\) elements spaced \(d\) distance apart. The array receives one OFDM signal and \(L\) DME signals at time \(k\). The received data of the array can be obtained as  
\[\mathbf{x}(k)=\mathbf{x}_{0}(k)+\mathbf{x}_{i}(k)+\mathbf{x}_{n}(k), \tag{3}\]  
where \(\mathbf{x}_{0}(k)=\mathbf{a}_{0}s_{0}(k)\), \(\mathbf{x}_{i}(k)=\sum\limits_{i=1}^{L}\mathbf{a}_{i}s_{i}(k)\), \(\mathbf{x}_{n}(k)\) represent the OFDM signal, DME signals and Gaussian white noise, respectively. \(s_{0}(k),\mathbf{a}_{0}\), respectively, represents the waveform and SV of the OFDM signal. \(s_{i}(k),\ i=1,\cdots,L\) is the waveform of the \(i\)th DME signal at time \(k\), and \(\mathbf{a}_{i},\ i=1,\cdots,L\) is the SV associated with the \(i\)th DME signal. Assuming that the DOA of the \(m\)th signal is \(\theta_{m}\), and the speed of light is \(c\), then the time delay caused by the signal impinging on adjacent array elements is  
\[\tau_{m}=(d\sin\theta_{m})/c,\ m=0,1,\cdots,L. \tag{4}\]  
The output of the beamformer is \(y(k)=\mathbf{w}^{H}\mathbf{x}(k)\), where \(\mathbf{w}=\left[w_{1},w_{2},\ldots,w_{M}\right]^{T}\) denotes the weight vector of the beamformer. The optimal weight vector can be obtained by maximizing the output signal-to-interference-plus-noise ratio (SINR) of the beamformer. This optimization problem can be expressed as  
\[\min\limits_{\mathbf{w}}\mathbf{w}^{H}\textbf{R}_{i+n}\mathbf{w}\ \text{s.t.}\ \mathbf{w}^{H}\mathbf{a}_{0}=1, \tag{5}\]  
where \(\textbf{R}_{i+n}=\sum\limits_{i=1}^{L}\sigma_{i}^{2}\mathbf{a}_{i}\mathbf{a}_{i}{}^{H }+\sigma_{n}^{2}\textbf{I}=\textbf{R}_{i}+\textbf{R}_{n}\) is the theoretical value of the INCM, \(\sigma_{i}^{2}\) and \(\sigma_{n}^{2}\) represent the \(i\)th DME signal power and noise power, while \(\textbf{R}_{i}\) and \(\textbf{R}_{n}\) are the theoretical ICM and noise covariance matrix (NCM), respectively. As a result, the optimal weight vector can be expressed as  
\[\mathbf{w}_{opt}=\frac{\textbf{R}_{i+n}^{-1}\mathbf{a}_{0}}{\mathbf{a}_{0}{}^{H}\textbf{R} _{i+n}^{-1}\mathbf{a}_{0}}, \tag{6}\]  
which is called the minimum variance distortionless response (MVDR) beamformer.  
In practical applications, the SCM \(\textbf{R}_{x}=\frac{1}{K}\sum\limits_{k=1}^{K}\mathbf{x}(k)\mathbf{x}^{H}(k)\) is often used in place of the theoretical INCM, where \(K\) represents the number of snapshots of the sample data. When the number of snapshots is small and the DOA estimation is inaccurate, the conventional beamforming algorithm based on INCM reconstruction suppresses the desired signal as interference, especially at high SNRs, resulting in a degradation of the beamformer's performance.