esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 System Framework Overview
### Middleware Layer
#### 3.2.2 Context Management
An example of mapping in terms of the proposed system's entities is illustrated in Figure 10. According to this, the root of the tree structure in the top level is context while in the following level there are the four nodes which correspond to the main entities of the modeling structure. The nodes which have no children are in the lowest level of the tree. As a respective tree structure represents the services, through the mapping operation similar paths between the two context trees are identified. Figure 9: Distributed Context Management Module. Finally, agricultural stakeholders into the services cloud can provide rules for control actions regarding several operational aspects of the PF facility. Nevertheless, in this framework, control actions do not derive only by the services cloud, as in certain cases the context-aware middleware cloud may also provide action rules through detecting, associating, and coordinating already existing services. This process of the system is characterized as service discovery. According to the service discovery process, centralized, or distributed repositories are employed for the storage of corresponding service profiles involving parameters, attributes, and locations which are required for the execution of further queries. On the subject of service discovery several protocols are taken into consideration as for instance the Service Discovery Service (SDS) [98] or the Simple Service Discovery Protocol (SSDP) [99].
## 4 Model Predictive Control for Power Optimization and DDPG-Based Optimization Scheduling
### DDPG-Based Optimization Scheduling
#### 4.2.2 DDPG Algorithm Training Process  
(1) Neural network initialization Based on the state space and action space, a policy network (P network) and a value network (Q network) are established, as shown in Figure 6. Except for the input layer, the P network and Q network have 11 and 10 layers, respectively. The P network has four inputs (state) and one output (action), with the activation function of the output layer being Sigmoid to map the output to the range of 0-1, facilitating the scaling and restoring of actions. The Q network has five inputs (state + action) and one output (reward). FC represents fully connected layer, and LN represents layer normalization.  
Algorithm parameter settings  
Training parameter settings: Set the learning rates of the network \(\alpha^{P}\) and \(\alpha^{P}\), target network update coefficient \(\tau\), scheduling period \(T\), number of training episodes \(e_{\max}\), discount factor \(\gamma\), experience replay Memory, and training batch size _Batch size_.  
OU noise parameter settings: Value regression rate \(\theta\), mean \(\mu\), volatility \(\sigma\), maximum fluctuation \(\sigma_{\max}\), minimum fluctuation \(\sigma_{\min}\), and noise decay period \(T_{Nd}\).  
Reward function parameter settings: Coefficients \(\alpha\) and \(l_{1}\).
3. Training scenario setup  
Before the start of each training episode, a normal random fluctuation of no more than 10% is added to the mean of the load source data within the typical day scenario and the feasible operating domain of the equipment. This approach continuously generates new typical day training scenarios until the training process is complete.  
The total number of training episodes is set to 200, necessitating the random generation of 200 unique training scenarios. An example illustrating the electrical power mean and fluctuation range is presented in Figure 7, where the solid line represents the load mean, and the shaded area depicts the range of data fluctuation.  
(4) MDP training loop  
Before each training begins, the initial state \(S_{0}\) of the system is obtained. For each time step, given the state \(s_{t}\), the policy network outputs an action \(P\big{(}s_{t}\big{|}\theta^{P}\big{)}\). After the system executes the action, a reward \(r_{t}\) is obtained, and the next state \(s_{t+1}\) is determined. The training experience \((s_{t},a_{t},r_{t},s_{t+1})\) is stored in the experience replay pool, the current state is updated, and the MDP is repeated until the final time step, completing one training episode.  
Figure 6: Schematic diagram of the DDPG policy network and value network structure.  
Figure 7: Mean and range of random operating conditions.  
(5) Network parameter update  
When the experience replay pool accumulates sufficient experiences to meet the batch size requirement, the network parameters are updated at each time step. This process involves updating the policy network and value network, while the target network undergoes updates using a soft update mechanism.
# From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
## Appendix A Compendium of Mappings and Compilations
### Controlled-Bit-Flip (\(\Lambda_{f}(X)\)) Mixers
#### a.2.4 MaxSetPacking  
**Problem:** Given a universe \([n]\) and \(m\) subsets \(\mathcal{S}=\big{(}S_{j}\big{)}_{j=1}^{m}\), \(S_{j}\subset[n]\), find the maximum cardinality subcollection \(\mathcal{S}^{\prime}\subset\mathcal{S}\) of pairwise disjoint subsets.  
**Approximability:** As difficult as MaxClique [50]. Cannot be efficiently approximated within any constant factor unless \(P=NP\)[75]. The best known algorithm gives an \(O(\sqrt{n})\)-approximation [76]. APX-complete with the restriction \(|S_{j}|\leq k\) (Max-\(k\)-Set-Packing).  
**Constraint graph:** Vertices \(V=[m]\) corresponding to elements of \(\mathcal{S}\), edges \(E\) corresponding to pairs of intersecting subsets.  
**Domain:** Subcollections containing mutually disjoint subsets, \(\Big{\{}\mathbf{x}:\bigwedge_{\{i,j\}\in E}\bar{x}_{i}\vee\bar{x}_{j}\Big{\}}\).  
**Objective:**\(\max\ |\mathcal{S}^{\prime}|=\sum_{j=1}^{m}x_{j}\)  
**Initial state:**\(|s\rangle=|0\rangle^{\otimes m}\), i.e., \(\mathcal{S}^{\prime}=\emptyset\).  
**Mixing rule:** Swap \(S_{j}\) in or out of \(\mathcal{S}^{\prime}\) if \(S_{j}\) is disjoint from the other subsets in \(\mathcal{S}^{\prime}\), i.e., \(\mathbf{x}_{\text{nbhd}(j)}=\mathbf{0}\).  
**Partial mixing Hamiltonian:**\(H_{\mathcal{C}\times j}=2^{-D_{j}}X_{j}\prod_{i\in\text{nbhd}(j)}(I+Z_{i})=X_{j}H_{ \text{NOR}(x_{\text{nbhd}(j)})}\).  
**Phase separator:**\(U_{P}(\gamma)=\exp(-i\gamma\sum_{j=1}^{m}Z_{j})\).  
**Resource count:**  
\(\bullet\) **Controlled-bit-flip mixers:** Each partial mixer \(H_{\mathcal{C}\times j}\) is implemented as a controlled-\(R_{X}\) gate with \(D_{j}\) control qubits. Partial mixer depth at most \(m\).  
\(\bullet\) **Phase separator:**\(m\) single-qubit \(Z\)-rotations. Depth 1.  
\(\bullet\) **Initial state:** Depth 0.  
**Variants:** Also called MaxHypergraphMatching. Equivalent to MaxClique under a PTAS-reduction [50].
# Efficient Inorganic Stabilization Materials for Chromium and Arsenic Pollution in Water and Soil
## 2 Inorganic Stabilization Materials
### MXenes  
Mxenes were identified as a new class of two-dimensional materials with a layered structure [57], which was usually composed of multiple connected layers. Its basic chemical composition could be expressed as M\({}_{n+1}\)X\({}_{n}\)T\({}_{x}\) (M = transition metal element, x = C and/or n, and T = surface termination, e.g., -O, -OH, -F) [58]. The interlayer spacing of Mxenes was adjustable [59], which provided a feasible channel for the diffusion of ions and small  
Figure 7: (**a**) The effect of PEI loading on Cr(VI) adsorption capacity in GO-PEI [56]; (**b**) High-resolution XPS spectra of Cr 2p after GO-PEI adsorption [56].  
molecules between their layers. The Mxenes were mainly prepared from their parent materials by selective etching [60]. Ammonium fluoride (NH\({}_{4}\)F) was used by [PERSON] et al. [61] as an etchant to produce Mxenes. A clear layered structure was generated (Figure 8a). The adsorption capacity of Cr(VI) reaches 59.8 mg/g. Ti\({}_{3}\)AlC\({}_{2}\) was used by [PERSON] et al. [62] as a precursor to prepare Ti\({}_{3}\)C\({}_{2}\), which was then complexed with FES, polyimide (PEI), and polydopamine (PDA) to generate Ti\({}_{3}\)C\({}_{2}\)@FeFe-PDA/PEI composites, removing 107.2 mg/g of Cr(VI). Titanium aluminum carbide (Ti\({}_{3}\)AlC\({}_{2}\)) and multi-walled carbon nanotubes (MWCNTs) were dispersed by [PERSON] et al. [63] into FeSO\({}_{4}\).7H\({}_{2}\)O solution to produce nZVI/MXene@CNTs. The maximum adsorption capacity for As(III) is 443.32 mg/g. The entire process involves adsorption, catalytic oxidation, and co-precipitation (Figure 8c). [PERSON] et al. [64] doped MXenes with Fe and Zn. Used for actual wastewater treatment, all meet the discharge standards, and remove over 80% of As(III) at 0.1-1 mg/L (Figure 8d). [PERSON] et al. [65] obtained layered MXenes. For Cr adsorption, ultraviolet photocatalytic synergy was carried out, contributing to the greatly improved removal efficiency of Cr. Compared with pure adsorption, it was increased by 3.1-28.9% (Figure 8b).  
Figure 8: (**a**) SEM image of Mxenes [61]; (**b**) Comparison of Cr(VI) removal by MXenes through adsorption and photocatalytic-assisted adsorption [65]; (**c**) Ti\({}_{3}\)C\({}_{2}\)@FeS-PDA/Li the stability mechanism towards As(III) [63]; (**d**) The effect of iron- and zinc-doped MXenes on As removal in different water bodies [64].
## 3 Experiments and Results
### Results
#### 3.2.1 No Noise Condition
Moreover, the motion displacement of the object in each frame is greater at 1.5 Hz. As a result, the optical flow method calculation produces larger errors, and these errors are mainly concentrated in the vicinity of the peak values. The calculation results of the accuracy of the region of interest for the vibration curve with a frequency of 1.5 Hz are shown in Table 3. The accuracy remains stable at 97.0%, which is much higher than that using the traditional LK method. The average error of the calculation results across all frames is 2.0%. \begin{table}
\begin{tabular}{c c c c c} \hline
**ROI** & **Max Pt Region1** & **Min Pt Region1** & **Max Pt Region2** & **Min Pt Region2** \\ \hline Traditional LK & 95.7\% & 95.9\% & 95.9\% & 96.05\% \\ Improved LK & 97.0\% & 97.1\% & 97.3\% & 96.9\% \\ \hline \end{tabular} Marginal notes: ROI (region of interest) refers to the region of interest. “Max pt region1” and “Min pt region2” represent the region near the maximum extreme-value point and the region near the minimum extreme-value point, respectively, and the numbers 1 and 2 denote the first or second (region).  
\end{table} 
Table 2: Accuracy Comparison of Region of Interest Computation: Traditional LK Method vs. Improved LK Method with a Threshold of 0.3\(\times\sigma\) (at 0.5 Hz). Figure 8: Comparison of Data Errors Calculated by the Optical Flow Method at Each Temporal Moment: Before and After the Improvement (at 0.5 Hz).
## 4 Experimental Results
### Comparison with Other Methods
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type** & **Method** & **Recall \(\uparrow\)** & **FI Score \(\uparrow\)** & **Error Rate \(\downarrow\)** & **MIoU \(\uparrow\)** \\ \hline \multirow{8}{*}{Day} & U-Net [41] & 80.39\% & 85.99\% & 10.86\% & 77.99\% \\  & Att-UNet [42] & 87.23\% & 89.66\% & 8.17\% & 82.91\% \\  & Swin-UNet [43] & 88.82\% & 90.70\% & 7.60\% & 84.40\% \\  & UNeXt [44] & 89.78\% & 91.00\% & 7.31\% & 84.80\% \\  & MA-SegCloud [45] & 87.59\% & 90.45\% & 7.59\% & 84.20\% \\  & Laplacian [46] & 89.37\% & 90.67\% & 7.58\% & 84.50\% \\  & CSWin-UNet [47] & 88.05\% & 90.82\% & 7.82\% & 84.52\% \\  & Rolling-UNet [48] & 87.66\% & 90.27\% & 7.91\% & 83.69\% \\  & Ours & **92.02\%** & **92.22\%** & **6.38\%** & **86.72\%** \\ \hline \multirow{8}{*}{Night} & U-Net & 68.90\% & 76.24\% & 15.53\% & 65.03\% \\  & Att-UNet & 78.74\% & 83.67\% & 12.65\% & 73.65\% \\  & Swin-UNet & 85.87\% & 85.80\% & 11.27\% & 76.72\% \\  & UNeXt & 81.75\% & 84.98\% & 12.04\% & 75.71\% \\  & MA-SegCloud & 77.21\% & 82.77\% & 12.31\% & 72.70\% \\  & Laplacian & 76.69\% & 83.39\% & 12.56\% & 73.62\% \\  & CSWin-UNet & 71.26\% & 80.57\% & 13.16\% & 70.06\% \\  & Rolling-UNet & 83.51\% & 83.69\% & 12.69\% & 74.33\% \\  & Ours & **91.72\%** & **88.69\%** & **9.21\%** & **80.39\%** \\ \hline \multirow{8}{*}{Day + Night} & U-Net & 79.18\% & 84.97\% & 11.35\% & 76.62\% \\  & Att-UNet & 83.71\% & 87.91\% & 8.99\% & 80.60\% \\ \cline{1-1}  & Swin-UNet & 88.51\% & 90.19\% & 7.98\% & 83.59\% \\ \cline{1-1}  & UNeXt & 88.93\% & 90.36\% & 7.81\% & 83.84\% \\ \cline{1-1}  & MA-SegCloud & 86.23\% & 89.55\% & 8.22\% & 82.85\% \\ \cline{1-1}  & Laplacian & 88.04\% & 89.91\% & 8.10\% & 83.36\% \\ \cline{1-1}  & CSWin-UNet & 86.28\% & 89.74\% & 8.38\% & 83.00\% \\ \cline{1-1}  & Rolling-UNet & 87.22\% & 89.58\% & 8.41\% & 82.71\% \\ \cline{1-1}  & Ours & **91.99\%** & **91.85\%** & **6.67\%** & **86.05\%** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance comparison between our algorithm and the other eight cloud image segmentation algorithms. Bold indicates the best option. algorithm. The AUC value of the proposed method is the largest, indicating that it has the highest accuracy and robustness in the cloud image segmentation task. The above results are shown in Figure 9.
# Hybrid Renewable Systems for Small Energy Communities: What Is the Best Solution?
## 3 Case Study
### Results and Discussion
#### 3.2.2 SA2--PV + Wind + PSH + BESS  
The second stand-alone solution, SA2, introduces a battery energy storage system (BESS) to investigate its influence on the system's behavior and ascertain whether it is advantageous by reducing the necessary power installations of other energy sources. The optimized power results were distributed as 55 kW in the PV system, 100 kW in wind turbine, 35 kW in pump, 40 kW in turbines, and 40 kW in batteries, making the total power equal to 270 kW.  
Figure 11 shows the annual balance with the integration of a battery energy storage system (BESS). The incorporation of the BESS into the stand-alone setup resulted in a slight decrease in the solar and wind energy sources. However, the total power installation increased, due to an increase in pump power resulting from the optimization preference for installing more solar energy. The surplus energy generated from solar sources exceeds that from wind sources. Consequently, a higher pump nominal power is required to enable its usage in the pumped-storage process, as the solar surplus is characterized by higher peaks than wind surplus due to their distinct generation patterns. The BESS plays a relatively inferior role in the SA2 solution. Even if its storage capacity was to increase to a hypothetical 1 MWh, the power installation of the other energy sources would not undergo a notable reduction.  
During the winter months, maximum loads occur over consecutive hours on various days, which presents a challenge for the performance of an electric battery under the power ranges of the presented small energy solution. Figure 12 shows the battery state of charge variation along the analyzed year and the solar + wind generation profile for three different days of the year.  
Figure 11: _Cont._  
increasing the initial investment by more than double. Figure 13 illustrates the annual balance of the grid-connected solar power solution with PSH.  
Compared to the stand-alone configurations, the grid-connected setup with solar power is more suitable for meeting the total load demand, with a total solar energy production of 134 MWh for an annual energy consumption of 97 MWh. In the stand-alone setup, both configurations demonstrated a primary renewable energy production level that was approximately three times greater than the demand. The import of grid energy is permitted solely during the peak winter months.  
Figure 13: GC1—PV + PSH + Grid yearly balance: (**a**) energy balance, (**b**) water balance, (**c**) energy by sources, (**d**) power data, and (**e**) statistics (between percentile 25 and 75%).
## Abbreviations  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} E2E & end-to-end \\ MEC & Multi-access Edge Computing \\ IoT & Internet of Things \\ mmWave & millimeter-wave \\ MIMO & Multiple-Input Multiple-Output \\ eMBB & enhanced Mobile Broadband \\ mMTC & massive Machine Type Communications \\ URLLC & Ultra-Reliable and Low Latency Communications \\ ITU-R & International Telecommunication Union \\ MVNO & Mobile Virtual Network Operator \\ MNO & Mobile Network Operator \\ RAN & Radio Access Networks \\ ETSI & European Telecommunications Standards Institute \\
3 GPP & The 3 rd Generation Partnership Project \\ UPF & User Plane Function \\
5 GC & 5G Core \\ B5G & Beyond 5G \\ QoS & Quality of Service \\ QoE & Quality of Experience \\ PoC & Proof of Concept \\ SOTA & State-of-the-Art \\ ASP & Application Service Provider \\ API & Application Programming Interface \\ COTS & Commercial Off-The-Shelf \\ GTP-U & GPRS Tunneling Protocol User plane \\ ICN & Information-Centric Networking \\ C-V2X & Cellular-Vehicle to Everything \\ NFVI & Network Functions Virtualization Infrastructure \\ MANO & Management and Orchestration \\
5G PPP & 5G Infrastructure Public Private Partnership \\ RU & Radio Unit \\ CU & Centralized Unit \\ DU & Distributed Unit \\ VIM & Virtualized Infrastructure Management \\ CC & Component Carrier \\ \end{tabular}
## 6 Conclusions and Prospects
\begin{table}
\begin{tabular}{c l c c c c c c} \hline \hline  & **Group** & \multicolumn{2}{c}{**Unpruned DeepESN**} & \multicolumn{4}{c}{**Pruned DeepESN**} \\ \cline{3-8}  & **Method** & - & \multicolumn{1}{c}{**ED-IPMA**} & **PC-IPMA** & **SC-IPMA** & **KC-IPMA** & **IPMA** \\ \hline \multirow{3}{*}{\(MG:4\times 100\)} & \(NRMSE_{test}\) (Mean) & 0.036 105 & **0.036 046** & 0.036 240 & 0.036 206 & 0.036 243 & 0.036 380 \\  & \(NRMSE_{test}\) (Std.) & 0.000 483 & 0.000 388 & 0.000 221 & 0.000 281 & 0.000 144 & 0.000 291 \\  & Neuron number & 120 & 120 & 80 & 120 & 120 & 120 \\ \hline \multirow{3}{*}{\(MG:8\times 50\)} & \(NRMSE_{test}\) (Mean) & 0.035 544 & **0.035 238** & 0.035 350 & 0.035 516 & 0.035 427 & 0.036 030 \\  & \(NRMSE_{test}\) (Std.) & 0.000 699 & 0.000 346 & 0.000 516 & 0.000 533 & 0.000737 & 0.000 338 \\  & Neuron number & 160 & 200 & 240 & 280 & 280 & 240 \\ \hline \multirow{3}{*}{\(LZ:4\times 100\)} & \(NRMSE_{test}\) (Mean) & 0.184 285 & 0.148 812 & 0.152 775 & 0.164 455 & **0.140 930** & 0.155 667 \\  & \(NRMSE_{test}\) (Std.) & 0.043 201 & 0.026 072 & 0.024 417 & 0.022 953 & 0.031 862 & 0.027 816 \\  & Neuron number & 400 & 200 & 160 & 280 & 240 & 200 \\ \hline \multirow{3}{*}{\(LZ:8\times 50\)} & \(NRMSE_{test}\) (Mean) & 0.251 535 & 0.198 581 & 0.189 230 & 0.210 376 & 0.193 678 & **0.186 933** \\  & \(NRMSE_{test}\) (Std.) & 0.044 484 & 0.027 631 & 0.024 995 & 0.033 404 & 0.029 164 & 0.024 092 \\ \cline{1-1}  & Neuron number & 320 & 160 & 120 & 160 & 160 & 120 \\ \hline \hline \end{tabular} Red bold values indicate the best validation performance of all methods.  
\end{table} 
Table 1: Minimum testing NRMSE condition of each experiment group. **Author Contributions:** Methodology, Q.S. ; software, Q.S. ; validation, Q.S. ; investigation, Q.S. ; resources, Q.S. ; writing--original draft, Q.S. ; writing--review and editing, Q.S. and H.Z. ; supervision, Y.M. ; funding acquisition, Y.M. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the National Natural Science Foundation of China--grant number: 62271109. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The data presented in this research and relevant resources are available upon request; please send your request message to [EMAIL_ADDRESS]. **Conflicts of Interest:** The authors declare no conflict of interest.
# Design of A Parallel Decoding Method for LDPC Code Generated via Primitive Polynomial
## 2 Motivation
### LDPC Codes Generated via Primitive Polynomial  
Consider an LFSR with connected primitive polynomial \(f(x)=x^{k}+x^{p}+1\), where \(k,\ p\) are positive integers such that \(k>p\). Denote trace function \(tr_{1}^{k}(\cdot)\) as a mapping from field \(\mathbf{GF}(2^{k})\) to field \(\mathbf{GF}(2)\)[11]. Let \(\alpha\) be a root of \(f(x)\) and \(\beta\) be the initial phase of the LFSR. Then, the m-sequence \((a_{i})\) generated by the register can be described as  
\[a_{i}=tr_{1}^{k}(\beta\alpha^{i})\;\alpha,\beta\in\mathbf{GF}(2^{k}) \tag{1}\]  
For the m-sequence, \(f(x)\) further gives the following parity-check constraints  
\[a_{i}+a_{i+p}+a_{i+k}=0,i=0,1,\ldots. \tag{2}\]  
With (2), it has been proven that given integer \(n(>k)\), we can construct an LDPC matrix for all segments \((a_{i})_{i=0}^{n-1}\) truncated from \((a_{i})\)[1]. That is, \((a_{i})_{i=0}^{n-1}\) is a codeword of an LDPC code.  
The parity-check matrix of an m-sequence code has two types of check rows. One is obtained from parity-check constraints in (2). The other is derived from the conjugate primitive elements \(\alpha^{2m},\;m=1,\;2,\cdots,M\) of \(\alpha\), where \(M\) is the maximum integer such that \(2^{M}k<n\). Consider the m-sequence \((a_{i}^{(m)})\) generated by conjugate primitive element \(\alpha^{2m}\), it can be written as  
\[a_{i}^{(m)}=tr_{1}^{k}(\beta(\alpha^{2m})^{i})=tr_{1}^{k}(\beta\alpha^{2m})=a _{2^{m}i}. \tag{3}\]  
Note that \(\alpha^{2m}\) is the root of \(f(x)\)[11]. As a result, sequence \((a_{i}^{(m)})\) can be also checked by (2), i.e.,  
\[a_{i}^{(m)}+a_{i+p}^{(m)}+a_{i+k}^{(m)}=0. \tag{4}\]  
Combining (3) and (4), the following parity-check constraints for codeword \((a_{i})_{i=0}^{n-1}\) are derived  
\[a_{i}+a_{i+2^{m}p}+a_{i+2^{m}k}=0,\;i=0,1,\cdots,n-2^{m}k-1. \tag{5}\]  
Finally, the parity-check matrix can be 4-cycle free if the factors \(k,p\) satisfy the conditions derived in [1], i.e.,  
\[\begin{cases}k\
eq(1+2^{m})p\\ k\
eq 2^{m}p\\ k\
eq(1-2^{-m})p\\ k\
eq(1+2^{-m})p\end{cases} \tag{6}\]  
In this paper, the matrix constructed by (2) and (5) is called the basic parity-check matrix.
## 3 Simulation Results
### BLER in Same Subcarrier Spacing  
Let all subcarriers in the channel bandwidth have an identical subcarrier spacing of 480 kHz. In order to reduce the interference between subbands in GFB-OFDM, the first-level IFFT is oversampled with the double bandwidth, i.e., a 2048-point IFFT. Traditional CP-OFDM is adopted. Figure 6 presents the BLER of CP-OFDM and GFB-OFDM, showing that the BLER performance of the two waveforms are almost the same. This result confirms that the inter-subband interference can be ignored and that there is no degradation in the BLER of GFB-OFDM when \(L\geq 4\).  
Figure 5: The out-of-band leakage of CP-OFDM and GFB-OFDM is evaluated. Specifically, the number of the subbands are 8 and 1 in the corresponding (**a,b**). The results demonstrate that the out-of-band leakage of GFB-OFDM is lower than the OFDM because of the polyphase filter operation.  
Figure 6: The The BLER of CP-OFDM and GFB-OFDM is evaluated for the same subcarrier spacing scenario. The rate-\(\frac{3}{4}\) LDPC channel coding, the 64 QAM modulation and the AWGN channel are employed. The result demonstrates that GFB-OFDM maintains a nearly identical BLER performance compared to CP-OFDM.