esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Results and Discussion
### Profiling of VOCs and Their Distribution
\begin{table}
\begin{tabular}{l l c c c c c} \hline \hline \multicolumn{1}{c}{**No.**} & \multicolumn{1}{c}{**Compound**} & \multicolumn{1}{c}{**RI \({}^{1}\)**} & \multicolumn{1}{c}{**Classification**} & \multicolumn{4}{c}{**DAS**} \\ \cline{4-7}  & & & & **30** & **60** & **70** & **80** \\ \hline
1 & (_E_)-2-Hexanal & 857 & Aldehyde & 0.31 \(\pm\) 0.07 a & 0.25 \(\pm\) 0.02 ab & 0.14 \(\pm\) 0.02 ab & 0.08 \(\pm\) 0.00 b \\
2 & 1-Octen-3-ol & 981 & Fatty alcohol & 0.03 \(\pm\) 0.01 b & 0.04 \(\pm\) 0.00 b & 0.07 \(\pm\) 0.02 b & 0.13 \(\pm\) 0.01 a \\
3 & 6-Methyl-5-hepten-2-one & 986 & Ketones & 0.26 \(\pm\) 0.00 ab & 0.47 \(\pm\) 0.09 a & 0.19 \(\pm\) 0.04 b & 0.13 \(\pm\) 0.02 b \\
4 & (_E_,_E_)-2,4-Heptadien & 1016 & Aldehyde & 0.04 \(\pm\) 0.01 c & 0.02 \(\pm\) 0.00 c & 0.16 \(\pm\) 0.02 b & 0.27 \(\pm\) 0.03 a \\
5 & 4-Methyl benzaldehyde & 1079 & Aldehyde & 1.33 \(\pm\) 0.33 a & 0.42 \(\pm\) 0.01 b & 0.04 \(\pm\) 0.00 b & 0.05 \(\pm\) 0.00 b \\
6 & Linalool & 1101 & Terpene alcohol & 0.25 \(\pm\) 0.03 a & 0.11 \(\pm\) 0.01 b & 0.03 \(\pm\) 0.00 c & 0.02 \(\pm\) 0.01 c \\
7 & Isoneral & 1165 & Monoterpene & 0.37 \(\pm\) 0.01 a & 0.49 \(\pm\) 0.10 a & 0.11 \(\pm\) 0.01 b & 0.14 \(\pm\) 0.01 b \\
8 & Rose furan oxide & 1178 & Furans & 0.37 \(\pm\) 0.01 a & 0.49 \(\pm\) 0.10 a & 0.02 \(\pm\) 0.01 b & 0.01 \(\pm\) 0.00 b \\
9 & Estragole & 1198 & Phenylpropene & 2.14 \(\pm\) 0.22 a & 1.01 \(\pm\) 0.11 a & 0.08 \(\pm\) 0.01 a & 1.66 \(\pm\) 1.43 a \\
10 & (_Z_)-Neral & 1243 & Monoterpene & 40.46 \(\pm\) 0.30 b & 64.96 \(\pm\) 6.69 a & 10.56 \(\pm\) 2.21 c & 5.79 \(\pm\) 1.74 c \\
11 & (_E_)-Nerol & 1258 & Terpene alcohol & 1.65 \(\pm\) 0.32 ab & 2.40 \(\pm\) 0.73 a & 0.72 \(\pm\) 0.13 a & 0.06 \(\pm\) 0.01 b \\
12 & Methyl citromellate & 1262 & Esters & ND \({}^{2}\) & ND & ND & 0.01 \(\pm\) 0.01 \\
13 & Geraiani & 1272 & Monoterpene & 118.38 \(\pm\) 2.69 a & 143.62 \(\pm\) 11.78 a & 22.85 \(\pm\) 5.01 b & 12.10 \(\pm\) 3.74 b \\
14 & Methyl genarian & 1325 & Monoterpene & 0.05 \(\pm\) 0.00 b & 0.34 \(\pm\) 0.04 a & 0.05 \(\pm\) 0.01 b & 0.04 \(\pm\) 0.01 b \\
15 & Caryophyllene & 1423 & Sesquiterpene & 0.19 \(\pm\) 0.01 b & 0.83 \(\pm\) 0.11 a & 0.05 \(\pm\) 0.00 b & ND \\
16 & (_E_)-a-Ionone & 1426 & Ketones & 0.07 \(\pm\) 0.01 b & 0.02 \(\pm\) 0.00 b & 0.17 \(\pm\) 0.01 a & 0.04 \(\pm\) 0.01 b \\
17 & Nerolidol & 1557 & Terpene alcohol & 0.03 \(\pm\) 0.00 b & 0.08 \(\pm\) 0.01 a & ND & ND \\
18 & \(\gamma\)-Dodecalactone & 1678 & Lactones & 0.03 \(\pm\) 0.01 a & 0.03 \(\pm\) 0.01 a & 0.01 \(\pm\) 0.00 a & 0.02 \(\pm\) 0.00 a \\ \hline \hline \multicolumn{1}{c}{Total} & \multicolumn{1}{c}{165.95 \(\pm\) 4.21 a} & 215.58 \(\pm\) 34.08 a & 35.24 \(\pm\) 12.63 b & 20.56 \(\pm\) 11.08 b \\ \hline \hline \end{tabular}
\end{table} 
Table 4: VOCs’ profiling change (ng/mg) of MO following the DAS. \begin{table}
\begin{tabular}{l l c c c c c} \hline \hline \multicolumn{1}{c}{**No.
# Clustering of LMS Use Strategies with Autoencoders
## 2 Materials and Methods
### Data Preprocessing  
We collected data about all official face-to-face courses that have corresponding virtual courses in Moodle. An LMS is used as optional support in face-to-face classes. Each teacher decides how to use the virtual campus, resulting in a variety of uses.  
In the first preprocessing stage, courses without students and empty courses were eliminated, leaving a total of 3303 pre-selected courses. Then, we identified the cases with interesting information to maximize efficiency and validity [37]. We selected all cases that met a predetermined criterion of importance, including courses with at least five students enrolled (since this is the minimum number of students required for an optional course to be taught, according to the Academic Management Regulation of the target university). Finally, 3046 courses were selected. We decided to leave in courses with very low use of the LMS to check if the analysis itself could detect them, which is different from other studies [38; 39]. The described preprocessing is common to our previous study [11].  
In addition to course filtering, we transformed and selected the variables to conduct a sound analysis of Moodle usage patterns. A Moodle course can integrate and configure resources (such as files, links, labels), activities (such as forums, assignments, quizzes, glossaries, workshops, wikis) as well as management tools (such as the event calendar and the gradebook) [40]. From these data, 17 numerical variables were selected to count resources, activities and actions, as indicated in Table 1. All variables about students' interactions were normalized to the number of students enrolled in the course. The role of the actor for the recorded data is also shown. For example, resources and activities are uploaded and created by teachers, while students are responsible for submissions and views. We grouped together data on resources and some activities of very limited use, as detailed in our previous study [11].  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable Name** & **Counted Data** & **Role** \\ \hline Resources & Resources (html, pdf documents) & Teacher \\ ResourceViews & Resource views or downloads & Student \\ Forums & Discussion forums & Teacher \\ ForumNews & Teachers’ forum posts & Teacher \\ ForumInteractions & Students’ forum views and posts & Student \\ Assigns & Assignments & Teacher \\ AssignsShmissions & Assignment submissions & Student \\ Quizzes & Quizzes & Teacher \\ QuizSubmissions & Quiz submissions & Student \\ AdvActivities & Advanced activities & Teacher \\ AdvActivitySubmissions & Advanced activity submissions & Student \\ GradeItems & Gradebook items & Teacher \\ GradeFeedbacks & Feedbacks of gradebooks & Teacher \\ GradeAdvanced & Manual or calculated gradebook items & Teacher \\ Basichinteractions & Entries (glossary, database, chat) & Student \\ Feedbacks & Feedback activities (surveys) & Teacher \\ CalendarEvents & Manual calendar events & Teacher \\ \hline \hline \end{tabular}
\end{table}
Table 1: Description of numerical variables.
## 3 Networks and Protocols of Communication  
The wireless industry has experienced rapid growth in recent years, with the development of several new applications and technologies, such as personal communication services, satellite communications, broadcasting, high-definition TV, wireless networks, Bluetooth, and others. Some of the most recent leading technologies that are being used in wireless applications, are presented below.
# A Novel Cooperative Opportunistic Routing Scheme for Underwater Sensor Networks
## 3 Opportunistic Void-Avoidance Routing Protocol
### Routing Algorithm
#### 3.5.4 Reliability and Energy Consumption Trade-Off  
Sometimes, especially in a dense network, there are too many nodes in a cluster resulting in wasting of energy. Hence, we introduce a new metric, expected energy and packet advancement (EEPA), to balance energy efficiency and routing efficiency. To consume energy more efficiently, it is assumed that nodes can only listen to a transmitted packet if the packet is destined for them [43]. This is achieved by equipping the nodes with a low power receiver to wake them up to participate in the packet forwarding only by checking the header of the packets. Thus, the receiving energy consumption can be reduced by decreasing the number of receivers in the forwarding set. For instance, if \(E_{rx}\) is considered as the receiving energy at each node, by removing \(n\) nodes from \(F\), we can save \(n*E_{rx}\) units of energy.  
Let \(\mathit{EPA}(F,j)\) and \(E(F,j)\) be the expected packet advancement and energy consumption of the forwarding set, respectively, when \(j\) nodes participate in the packet forwarding. The maximum value for EPA and energy (\(\mathit{EPA}_{max}\) and \(E_{max}\), respectively) can be obtained by involving all of the nodes in the forwarding set, _i.e._, \(\mathit{EPA}(F,r)\) and \(E(F,r)\), where \(r=\left|\,F\,\right|\). In this way, by selecting \(j\) forwarding candidates from \(F\), EEPA can be defined as follows:  
\[\mathit{EEPA}(F,j)=\mu\frac{\mathit{EPA}(F,j)}{\mathit{EPA}_{max}}-\rho\frac{E (F,j)}{\mathit{E}_{max}} \tag{11}\]  
where \(\mu\) and \(\rho\) are defined as the weighting coefficients for EPA and energy, respectively. These coefficients can be set according to the desired criteria and density of the network. For instance, if the network is more interested in the energy saving rather than packet delivery, it can increase the \(\rho\) against the \(\mu\), or _vice versa_.  
The forwarding set should be checked for different numbers of members to achieve the maximum possible value for EEPA. This can be done by examining EEPA for \(j=1,...,r\) and, finally, picking the set with the largest value and, accordingly, removing other extra nodes from the forwarding set, if required. In this way, we start from an empty set and add nodes (ordered by their advancement) to the forwarding set one by one. Eventually, the optimal set is selected to relay the packet. In a sparse network, all nodes are held in the forwarding set to increase the reliability; however, in a dense network, some nodes are removed to control the energy dissipation.
# Energy Sustainability in Wireless Sensor Networks: An Analytical Survey
## 5 Discussion
### Challenges and Open Research Issues in Hardware-Based Methods
Similarly, human-based energy harvesting due to human activity is unpredictable, while due to physiological procedures is both unpredictable and uncontrollable [33]. Likewise, wireless energy transfer is associated with various weaknesses. Specifically, energy transfer requires corresponding cross-layer provision covering the MAC, link, and application layers. The achievement of energy transfer requires the use of specialized equipment thus growing the employment cost [19]. Moreover, in the case that robotic vehicles or other types of mobile nodes are used to charge network nodes special algorithms for their navigation are required. Additionally, by using Inductive Coupling for wireless energy transfer only short transmission distances can be covered [41]. The efficacy achieved is decreased by any misalignment existing between the transmitter coil and the receiver coil. Special actions must be taken to avoid the presence of mutual coupling effect that is the cause of interference among nodes. Wireless energy transfer via Magnetic Resonant Coupling requires not only the attainment of alignment between the coils of the transmitter and the receiver, but also the adjustment of resonant frequency in various nodes [42]. Inwireless energy transfer via Electromagnetic Radiation, line of sight is essential and the presence of radiation triggers various health and safety concerns [43]. In order to provide a synoptic overview of the aforementioned statements, the basic operation along with the main strengths and weaknesses of each one of the hardware-based methods for energy sustainability in WSNs are presented in Table 2.
## 2 Bayesian Functional Mapping
### Structuring the Covariance Matrix  
In longitudinal data analysis, statistical modeling of the covariance structure is generally desirable, given that time-dependent variances and correlations follow a certain pattern. Below, we incorporate two commonly used approaches for the covariance structure in functional mapping into the Bayesian framework.  
Autoregressive model  
When a stationary AR(1) model is used, we specify the structure of covariance matrix \(\mathbf{\Sigma}\) by constant variance and covariance, i.e.,  
\[\mathrm{var}(y(t)) = \sigma^{2},\quad\forall\,\,\,1\leq t\leq T \tag{13}\] \[\mathrm{cov}(y(t_{1}),y(t_{2})) = \sigma^{2}\rho^{[t_{1}-t_{2}]},\quad\forall\,\,\,1\leq t_{1}\
eq t _{2}\leq T. \tag{14}\]We use the inverse gamma prior for \(\sigma^{2}\) and an informative prior restricted on \([-1,1]\) for \(\rho\). Assuming that the priors of these two parameters are independent, the posterior density of \((\lambda,\mathbf{\Theta},\sigma^{2},\rho)\) is given as:  
\[\pi(\lambda,\mathbf{\Theta},\mathbf{Q},\rho,\sigma^{2}|\mathbf{y})\propto\pi( \mathbf{y}|\mathbf{\Theta},\mathbf{Q},\sigma^{2},\rho)\cdot\pi(\mathbf{Q}| \lambda)\cdot\pi(\lambda)\cdot\pi(\sigma^{2})\cdot\pi(\rho)\cdot\prod_{j=0}^{2} \pi(\mathbf{\Theta}_{j}), \tag{15}\]  
where \(\pi(\sigma^{2})=IG(\alpha,\beta)\) and \(\pi(\rho)=Uniform(-1,1)\).  
The closed forms of the full conditional posterior distributions of \(\sigma^{2}\) and \(\rho\) are not available, but the explicit expressions that are proportional to these posteriors can be derived, which are:  
\[\pi(\sigma^{2}|\mathbf{y},\lambda,\mathbf{Q},\mathbf{\Theta},\rho) \propto \pi(\mathbf{y}|\lambda,\mathbf{Q},\mathbf{\Theta},\sigma^{2},\rho )\cdot\pi(\sigma^{2}) \tag{16}\] \[\propto |\mathbf{\Sigma}(\sigma^{2},\rho)|^{-\frac{n}{2}}\cdot\frac{ \beta^{\alpha}}{\Gamma(\alpha)}\cdot\sigma^{2(-\alpha-1)}\] (17) \[\cdot \exp\{-\frac{\beta}{\sigma^{2}}-\frac{1}{2}\sum_{j=0}^{2}\sum_{i =1}^{n_{j}}(\mathbf{y}_{ij}-g(\mathbf{t}|\mathbf{\Theta}_{j}))^{\prime} \mathbf{\Sigma}^{-1}(\sigma^{2},\rho)(\mathbf{y}_{ij}-g(\mathbf{t}|\mathbf{ \Theta}_{j}))\} \tag{18}\]  
for \(\sigma^{2}\), and:  
\[\pi(\rho|\mathbf{y},\lambda,\mathbf{Q},\mathbf{\Theta},\sigma^{2 })\propto\pi(\mathbf{y}|\lambda,\mathbf{Q},\mathbf{\Theta},\sigma^{2},\rho) \cdot\pi(\rho) \tag{19}\] \[= \frac{1}{2}\cdot|\mathbf{\Sigma}(\sigma^{2},\rho)|^{-\frac{n}{2} }\cdot\exp\{-\frac{1}{2}\sum_{j=0}^{2}\sum_{i=1}^{n_{j}}(\mathbf{y}_{ij}-g( \mathbf{t}|\mathbf{\Theta}_{j}))^{\prime}\mathbf{\Sigma}^{-1}(\sigma^{2},\rho )(\mathbf{y}_{ij}-g(\mathbf{t}|\mathbf{\Theta}_{j}))\} \tag{20}\]  
for \(\rho\). Based on these expressions, the corresponding Metroplolis-Hastings steps can be developed to update \(\sigma^{2}\) and \(\rho\) within the MCMC estimation scheme (Appendix B).
# Homogeneity and Trend Analysis of Climatic Variables in Cap-Bon Region of Tunisia
## 2 Materials and Methods
### Homogeneity Tests
#### 2.2.2 Standard Normal Homogeneity Test (SNHT)  
The SNHT is a parametric test that is usually more sensitive to breaks near the boundaries of the time series [35]. [PERSON] et al. [36] defined the T(k) statistic for the SNHT as:  
\[\mathrm{T(k)}=\ k\ \overline{Z_{1}^{2}}+(n-k)\ \overline{Z_{2}^{2}}\ \rightarrow(k=1,\ 2,\ \ldots,\ n) \tag{3}\]  
\[\overline{Z_{1}}=\frac{1}{k}\ \sum_{i=1}^{k}(Y_{i}-\ \overline{Y})/\sigma\ \mathrm{and}\ \overline{Z_{2}}=\frac{1}{k-1}\ \sum_{i=k+1}^{k}(Y_{i}-\ \overline{Y})/\sigma \tag{4}\]  
where  
\(\overline{Z_{1}}\) and \(\overline{Z_{2}}\) are the parameters of T(k) statistic;  
\(\overline{Y}\) is the average of time series;  
\(\sigma\) is the standard deviation.  
The statistical test T(k) is used to compare the mean of the first n observations with the mean of the last (n \(-\) k) observations with n data points. The year k can be considered as a change point and consists of a break where the value of Tk reaches its maximum value. The T0 statistic in the standard normal homogeneity test is defined as:  
\[\mathrm{T}_{0}=\mathrm{max}\mathrm{T}_{k}\quad(1\ \leq\ k\ \leq\ n) \tag{5}\]  
When the statistical test surpasses the critical value tabulated in [37], which depends on the sample size (n), the null hypothesis is rejected.
## 2 Analysis of the FPLG System Working Process
### Linear Motor Model Verification  
Model validation of the linear motor is conducted on an existing linear motor test bench, illustrated in Figure 3. The setup includes two linear motors (one as a motor and the other as a generator), a motor driver, a power supply, host computer software, three sliding rheostats, and a power analyzer. During the experiment, the host computer software generates displacement profiles with specified frequency and stroke. The motor driver ensures the motor drives the generator's mover to follow the reference profile. Once stable operation is achieved, an external three-phase resistor is connected. The power analyzer measures the terminal voltage across the resistor, the three-phase current in the circuit, and the output power at the load. The collected data is then imported into data processing software for analysis. The parameters of each component on the test bench are listed in Table 2.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Design Parameters** & **Parameter** & **Design Parameters** & **Parameter** \\ \hline Mass of moving sub & 3.75 & Maximum travel & \\ component/kg & & distance/mm & 80 \\ Cylinder diameter/m & 0.051 & Cylinder depth/m & 0.029 \\ Line resistance/Ohm & 10.16 & Line inductance/mH & 12.78 \\ Motor thrust & 78.9 & Permanent magnet & \\ constant/N/A & & magnetic flux & 0.24 \\ \hline \hline \end{tabular}
\end{table}
Table 1: System Parameter Matching Design.  
Figure 3: Experimental Bench.  
This test examines the power generation characteristics under an external linear load. The motor mover's displacement reference profile is a standard sine wave, with a stroke of 50 mm and a frequency of 10 Hz. The external load is 50 \(\Omega\). Figure 4 a compares the experimental and simulated load--end voltages under these conditions. It shows the voltage in phases A, B, and C (Figure 4). Within one motor operation cycle, the simulated and experimental load--end voltages closely match in peak value and phase. The peak voltage error is 2.1 V, an error rate of about 2.56%.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Equipment** & **Type** & **Parameter** \\ \hline Drive motor & P10 series & Peak force: 1600 N; Peak speed: 6.5 m/s; \\  & & Peak current: 20 A; \(\pm\)20 \(\upmu\)m \\ Motor driver & E1400 series & 32 bit; 3 \(\times\) 400/480 VAC; Supply voltage: 24 V \\ Power analyzer & Yokogawa DL950 & 200 MS/s Sampling rate; 14 bit; 10 GE Data \\  & & transmission rate; 8 G point memory \\ Current sensor & Yokogawa probes & \(\pm\)150 \(\upmu\)m; 10 MHz; 1\(\%\) Accuracy \\ Voltage sensor & Yokogawa probes & \(\pm\)1000 V peak; 60 MHz; 10: 1 \\ Electromagnetic force sensor & HBM S9N & 1 kN; 0.02\(\%\)FS; 2 MV/V \\ Data acquisition instrument & NI USB-6211 & 250 kS/s; 16 bit \\ \hline \hline \end{tabular}
\end{table}
Table 2: Experimental Bench Instrument Models.  
Figure 4: Verification of output voltage of linear motor.
## 5 Conclusions  
This paper has proposed selective FMS filtering estimation with two kinds of measurement windows using the chi-square test statistic in order to cover the nominal system as well as the temporarily uncertain system. The simple matrix form for the FMS filter has been developed from the conditional density of the current state given finite past measurements. Then, one of the two FMS filters, the primary FMS filter and the secondary FMS filter, with different measurement windows has been operated selectively to obtain the valid estimate according to the presence or absence of uncertainty. The primary FMS filter has been selected for the nominal system and the secondary FMS filter has been selected for the temporarily uncertain system, respectively. A declaration rule has been defined to indicate the presence or absence of uncertainty, operate the suitable one from two filters, and then obtain the valid filtered estimate. The test variables for the declaration rule have been defined using the chi-squared distribution with one degree of freedom. Finally, extensive computer simulations have been performed for an aircraft engine system as well as an electric motor system to verify the proposed selective FMS filtering with two kinds of measurement windows and compare with existing FMS filtering and IMS filtering. Through simulation results, it has been confirmed that the proposed selective FMS filtering estimation works well for both nominal systems and temporarily uncertain systems. It has been also shown that the proposed selective FMS filter can be remarkably better than the IMS filter for the temporarily uncertain system.  
In fact, the research work for the FMS filter is relatively inactive in the case where the system and measurement noises are nonzero-mean Gaussian. Thus, an alternative selective FMS filtering for nonzero-mean noises can be researched as future work.  
This research was funded by National Research Foundation of Korea (NRF-2017R1D1A1B03033024). The APC was funded by Korea Polytechnic University.  
This research was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education (NRF-2017R1D1A1B03033024).  
**Conflicts of Interest:** The author declares no conflict of interest.  
Figure 11: Estimation errors of the proposed selective FMS and IMS filters for the electric motor system.
# Mitigating the Impact of Noise on Nonlinear Frequency Division Multiplexing +
## 5 Improved Modulations
### The Power-Tilt Strategy
Conversely, when increasing the power level, the overall amount of errors decreases (as the SNR increases), and the number of bit errors per symbol starts to flatten, until that on the rightmost symbols become higher than that on the leftmost ones. This happens because, while the average signal power is high, despite the strong tilt, the signal loses energy on the latter symbols, becoming very sensitive to noise. Finally, Figure 7a shows the performance in terms of Q-factor versus launch power obtained with the NFDM system with DF-BNFT detection and NIS modulation with different tilt strengths, for a burst length \(N_{b}=1024\). The figure confirms the intuition provided by Figure 6b: in the linear regime (at low power), the best performance is obtained with a small or zero tilt, while a strong tilt worsens the performance. On the other hand, at higher power, a strong tilt improves the performance. Remarkably, all the tilt strengths considered in Figure 7a improve the peak performance with respect to the case without tilt, with a maximum gain of about 2.7 dB obtained for the 0.9 tilt. The proposed power-tilt strategy is a very simple approach to diminish the detrimental impact of the BNFT operation on the latter information symbols, with a negligible computation cost. As a possible side effect, the power tilt might increase the peak-to-average power ratio (PAPR) of the modulated optical signal, with a subsequent increase of the optical power wasted in the modulation process and of the digital resolution required at the transmitter. Indeed, inducing a power tilt on a linearly modulated systems would clearly increase the PAPR. On the other hand, the modulated signal after the BNFT is already affected by a sort of \"intrinsic power tilt\", which makes the signal power decay from left to right. In this case, the power tilt strategy balances this intrinsic power tilt, possibly reducing the final PAPR. In fact, we have verified by numerical simulations that, compared to the case with no tilt, a tilt of \(\delta=0.9\) slightly increases the PAPR of the optical signal at low power (where the modulation is practically linear and the tilt is actually detrimental), but slightly reduces it around the optimal power (where the tilt is indeed useful). Figure 6: Number of bit errors versus symbol position after the transmission of \(10\) bursts of \(N_{b}=1024\) symbols (**a**) at \(P=-7\) dBm for different tilt strengths, (**b**) at different power levels, for tilt strength \(\delta=0.9\). In principle, the power-tilt strategy can be combined with any of the detection strategies described in the previous section. However, we did not obtain any advantage when combining it with the standard FNFT detection, probably because the performance in this case is limited by the detrimental effect of the FNFT on the noise. On the other hand, the application of a power tilt to different modulation techniques--e.g., b-modulation or bExp--should be properly investigated and tailored.