esa-sceva/satcom-chunk-collection huggingface dataset:
# Complex-Order Models: A System Identification Point of View
## 5 Identification Results
Figure 9: Comparison of the frequency responses of the fitted high-order ARX model and the complex-order model (first transfer function). **Remark 1**. : _In order to point out the advantages of the proposed complex-order schema, the results obtained for the second transfer function (39) are compared with the frequency responses of the following transfer functions:_  
\[ \begin{split} G_{2,1}(s)&=K\frac{\left[(\frac{s}{ \gamma_{1,1}})^{2}-2\frac{s}{\gamma_{1,1}}\gamma_{1,2}+1\right]^{\gamma_{1,3}} \prod_{i=1}^{3}(\frac{s}{\omega_{1,i}}+1)^{\alpha_{1,i}}}{(1-\frac{s}{\omega_{ 2}})^{\alpha_{2}}}\;,\\ G_{22}(s)&=K\frac{\left[(\frac{s}{\gamma_{1,1}})^{2}-2 \frac{s}{\gamma_{1,1}}\gamma_{1,2}+1\right]^{\gamma_{1,3}}\prod_{i=1}^{3}( \frac{s}{\omega_{1,i}}+1)^{\alpha_{1,i}}}{\prod_{j=1}^{3}(\frac{s}{\omega_{2,j }}+1)^{\alpha_{2,j}}}\;.\end{split}  \tag{40}\]  
_The parameters of all transfer functions have been obtained optimally, applying the same procedure described in Section 5. Transfer function \(G_{2,1}\) contains the same number of poles and zeros as transfer function (39), but as real-order elements (\(12\) parameters), while \(G_{2,2}\) has the same number of unknown parameters (\(16\) parameters) as structure (39). The obtained simulation results are shown in Figure 11, while the obtained optimal parameters are specified in Tables 3 and 4. It is not hard to notice that the approximated transfer function with complex-order elements gives more accuracy in fitting both the phase and magnitude of the high-order ARX model._ \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & \(K\) & \(\omega_{1,1}\) & \(\alpha_{1,1}\) & \(\beta_{1,1}\) & \(\omega_{2,1}\) & \(\alpha_{2,1}\) & \(\beta_{2,1}\) & \\ \hline \(16\) pars. & \(0.0004\) & \(0.0923\) & \(1.0031\) & \(0.1744\) & \(0.2450\) & \(1.9615\) & \(0.1708\) & \\ \hline  & \(\omega_{1,2}\) & \(\alpha_{1,2}\) & \(\beta_{1,2}\) & \(\omega_{1,3}\) & \(\alpha_{1,3}\) & \(\beta_{1,3}\) & \(\gamma_{1,1}\) & \(\gamma_{1,2}\) & \(\gamma_{1,3}\) \\ \hline  & \(-26.4457\) & \(0.3644\) & \(0.0000\) & \(-35.7210\) & \(0.6965\) & \(0.0003\) & \(167.7741\) & \(0.0484\) & \(1.0395\) \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters of the fitted \(16\)-parameter complex-order model. Figure 10: Comparison of the frequency responses of the fitted high-order ARX model and the complex-order model (second transfer function).
# Multi Stage Retrieval for Web Search During Crisis
## 2 Related Works
### Text Retrieval
While these neural network-based approaches often yield significant improvements, they typically require substantial computational resources for both indexing (in the case of dense retrieval) and inference. This can be a challenge for deployment in real-time crisis scenarios. Furthermore, while powerful, if such models were extended or coupled with abstractive components for tasks like summarization, they could introduce the risk of \"hallucinations\"--generating plausible but factually incorrect information [13]. Hybrid approaches, which combine traditional lexical-based methods with neural retrieval models, have been explored to balance between efficiency and accuracy [26]. A common strategy involves a two-step retrieval process: an initial candidate selection using an efficient lexical model, followed by a more computationally intensive neural reranker to refine the results [25; 27]. While this is an established practice, a single pass of retriever and reranker can inherently lose many relevant documents, so we propose a double pass of retriever and reranker to better process a smaller set of potentially relevant documents. Additionally, topic modeling was already explored in retrieval [28], but to assign a topic to a query rather than filtering the corpus from noise, as we conversely propose in our approach. Our extractive multi-stage pipeline, which avoids abstractive generation, offers a promising avenue to meet the demands of crisis responders by maximizing recall of potentially relevant information in early stages while systematically refining precision and ensuring factual grounding in later stages without sacrificing scalability.
# Speckle Noise Reduction in Digital Holography Using a DMD and Multi-Hologram Resampling
## 2 Digital Holography with a DMD
### Digital Micro-Mirror Device  
A Digital micromirror Device (DMD) is a versatile mechanism for passive light manipulation. It offers attractive experimental characteristics such as fast switching of the modulated signal, direct use avoiding any calibration, low spectrum sensitivity, and polarization invariance. Its main principle is to control the way light reflects on it through millions of small switchable mirrors that can be electronically set to two specific orientations [20]. The resultant operation is that of a multiplication of the incoming wave by a binary transmittance function composed by the lateral aggregation of all micromirrors, resulting in an amplitude-only control. However, a Lee Hologram [21] can be used to modulate phase and amplitude using a DMD as well. This Lee hologram is projected on the DMD and the emanating light is transferred to a Fourier filtering scheme, where by selecting the appropriate diffraction order the desired wave modulation is obtained. [PERSON] (2010) proposed to generate such hologram using the following expression [20],  
\[L(x,y)=\frac{1}{2}+\frac{1}{2}sgn\left\{cos\left[2\pi x\
u_{x}-\phi(x,y)\right]+ cos\left[\pi\omega(x,y)\right]\right\}, \tag{2}\]  
where \(\
u_{x}\) is the carrier frequency, and \(\omega(x,y)\) is a function related to the target complex wave \(A(x,y)exp(i\phi(x,y))\) by  
\[\omega(x,y)=\frac{1}{\pi}arcsin\left[A(x,y)\right]. \tag{3}\]  
Therefore, any desired complex wave can be obtained by designing the functions \(\phi\) and \(\omega\), and selecting an appropriate carrier spatial frequency. We consider the quality of this phase modulation technique to be sufficient for our application, despite the diffraction produced by the periodicity of the DMD and the diffraction noise inherent to the binary nature of the Lee holograms, as the Fourier filtering effectively isolates the desired modulated light beam [22].  
Figure 1 shows our optical set-up. Light from a blue laser \(\lambda=473\) nm is split into the object and reference arms necessary for the holographic register. The object arm is directed towards the functioning DMD. The DMD diffracts this wave in multiple diffraction orders. One of those is inputted into a Fourier filtering system producing a single complex wave with a phase function designed according to the pattern displayed on the DMD. This filtered wave strikes the reflective object creating the object wave for the holographic recording. The camera records the combination of the object and reference waves, namely, the hologram, for subsequent digital reconstruction.
## 2 Proposed Framework
### NN Design via Hankelization-Based Preprocessing
The boldfaced values indicate the SNR points where the proposed methods achieve the highest mean detection rate among all evaluated methods. From 0 dB and above, the proposed method (with the FFT-processed signal) demonstrates superiority, yielding the highest detection rates across all conditions in this range. These results collectively validate that the proposed framework, particularly when combined with FFT preprocessing, achieves superior classification performance compared to baseline methods, demonstrating robustness and stability across various SNR conditions. Figure 5: Confusion matrices (SNR = 10 dB). (**a**) Proposed method (with original signal). (**b**) Proposed method (with FFT-processed signal). (**c**) Deep learning (CNN with real and imaginary values of signal). (**d**) SCNN2. (**e**) CLDNN. (**f**) LSTMDAE. Figure 6: Detection rate according to the number of training datasets. (**a**) SNR = 4 dB. (**b**) SNR = 10 dB. (**c**) SNR = 16 dB. Figure 7 shows the test error curves across training epochs. The proposed method (with FFT-processed signal), shown in orange, consistently exhibits the fastest convergence and lowest test error across all SNR levels. Notably, under the SNR condition of 4 dB, as shown in Figure 7a, the proposed method (with FFT-processed signal) achieves a near-minimal test error within 30 epochs. The results highlight that the FFT-based method achieves faster convergence and learns robust, discriminative features effectively across varying conditions. Figure 8 shows the detection performance of the proposed method under various SNR levels, with respect to the number of retained singular values. The Hankelized matrix is constructed to be approximately square, while the number of singular values is varied to assess its influence on classification accuracy. Across all SNR conditions, the
## 4 Use Case Evaluation
### Semantic Reasoning with CYPHER Queries
#### 4.3.1 Co-Location Social Relationships  
To identify _co-location_ relationships between entities, we use the _geofronttext_ function in Cypher to calculate the distance between entities locations. We then use a threshold value to determine whether the sensors are close enough to be considered co-located. Here, is an example of the Cypher query used to identify _co-location_ relationships:  
```
MATCH(e1: Entity),(s2: Entity) WHEREe1<e2 AND distance(point(latitude: s1.hasLocationLat, longitude: e1.hasLocationLong)),point({latitude: e2.hasLocationLat, longitude: 2.hasLocationLong})) < 500 CREATE(e1)-[CO_LOCATED]>(e2)
```  
This query matches all pairs of _Entity_ nodes that are not identical and have a distance less than 500 m between their respective locations. The query then creates a CO_LOCATED relationship between the two sensors.
## 5 Conclusions
Future research should focus on developing more efficient algorithms, enhancing data security, and creating cost-effective solutions to make these advanced systems more accessible and practical for widespread use. By overcoming these obstacles, the full potential of integrating EEG, VR, RL, and robotics can be unlocked, leading to advancements in various fields. Ultimately, the synergy of these technologies promises to significantly improve human-robot collaboration, fostering a future where machines not only assist but empathize and intuitively interact with their human counterparts, making technology more humane and effective. The path forward is promising, and with continued interdisciplinary efforts, the vision of emotionally aware, responsive, and adaptive collaborative robots can become a reality, revolutionizing industries and enhancing the quality of human life. Conceptualization, A.G.-S. and J.-I.V. ; Methodology, A.G.-S. and J.-I.V. ; Data curation, A.G.-S.; Validation, J.-I.V. and A.E. ; Writing--original draft, A.G.-S.; Writing--review and editing, A.E., J.-I.V. and A.G.-S.; Supervision, J.-I.V. and A.E. All authors have read and agreed to the published version of the manuscript. This research was supported by the project ACROBA, which has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 101017284, and the project EGIA which has received funding from the ELKARTEK programme from the Basque Government. Data Availability Statement: Not Applicable. Conflicts of Interest: The authors declare no conflicts of interest. Abbreviations  
The following abbreviations are used in this manuscript: \begin{tabular}{l l} AR & Augmented Reality \\ BCI & Brain-Computer Interface \\ BDI & Beck Depression Inventory \\ BVP & Blood Volume Pulse \\ CNN & Convolutional Neural Network \\ ECG & Electrocardiography \\ EEG & Electroencephalography \\ EOG & Electro-oculograph \\ ErrP & Error Potential-Related Event \\ ERP & Error-Related Potential \\ GSR & Galvanic Skin Response \\ HAR & Human-Robot Recognition \\ HDT & Human Digital Twin \\ HRI & Human-Robot Interaction \\ ICA & Independent Component Analysis \\ KNN & K-Nearest Neighbor \\ MR & Mixed Reality \\ PSS & Perceived Stress Questionnaire \\ RL & Reinforcement Learning \\ RSP & Respiration Rate \\ SVM & Support Vector Machine \\ VR & Virtual Reality \\ \end{tabular}
# AI-Driven Phishing Detection: Enhancing Cybersecurity with Reinforcement Learning
## 5 Model Ongoing Training
### Detection Latency and Performance Trade-Off
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{\
\begin{tabular}{c} **Accuracy** \\ **(\%)** \\ \end{tabular} } & \multirow{2}{*}{**Precision (\%)**} & \multirow{2}{*}{**Recall (\%)**} & \multirow{2}{*}{
\begin{tabular}{c} **False Positive** \\ **Rate (\%)** \\ \end{tabular} } \\ \hline SVM & 85 & 84 & 83 & 12 \\ Random Forest & 87 & 86 & 85 & 10 \\ Our RL-Based Model & 95 & 96 & 94 & 2 \\ K-Nearest Neighbors & 80 & 79 & 79 & 14 \\ Naive Bayes & 78 & 79 & 79 & 16 \\ Logistic Regression & 83 & 84 & 83 & 11 \\ Deep Learning (CNN) & 96 & 97 & 96 & 5 \\ XGBoost & 92 & 93 & 91 & 5 \\ BERT-Based Model & 97 & 98 & 97 & 3 \\ PCA-RF & 89 & 87 & 87 & 8 \\ BRNN [25] & 91 & 90 & 89 & 7 \\ DDQN [27] & 95 & 94 & 93 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparative performance metrics across phishing detection models (table format). Figure 5: Comparative bar chart illustrating the F1 scores of phishing detection models. The RL-based model achieved the highest F1 score (0.94), followed by CNN ([PERSON] et al., 1998) at 0.91, and DDQN [27] at 0.89. Traditional models, including Logistic Regression ([PERSON], 1958) and Naive Bayes ([PERSON], 1961), performed moderately, while PCA-RF ([PERSON], 2019) recorded the lowest score (0.72), indicating reduced effectiveness for complex phishing scenarios. In Figure 5 below provides a comparative bar chart illustrating the F1 scores of various phishing detection models. Our RL-based model leads with the highest F1 score (0.94), followed by CNN (0.91), DDQN [27] (0.89), and Random Forest (0.87). Classical models like Naive Bayes and PCA-RF [24] show lower F1 scores of 0.78 and 0.72, respectively, highlighting their limited effectiveness in handling complex phishing patterns. These results demonstrate the superior classification balance achieved by reinforcement learning and deep learning models.
# Auto-Encoder Learning-Based UAV Communications for Livestock Management
### Motivation  
The use of UAVs for livestock location, detection, activity monitoring, anomaly detection and rearing requires onboard sensors operating at radio frequencies (RF) of 2.4 and 5.8 GHz for reliable data transfer between the UAVs and the ground stations [1; 4]. However, due to traffic of the target-related UAV data, the tasks become more strenuous and demanding as the resolution of the onboard sensors becomes higher, specifically in the backbone network [14]. Accordingly, this imposes enormous demands on the communication system as well as the challenge of decoding the transmitted data with minimum error probability at the user end. Livestock farming requires extensive farmland, located mainly in rural areas. It is known that many rural areas, even in developed countries, are significantly under-connected with mobile wireless technology. Therefore deploying 5G test beds in rural areas can motivate service providers to improve internet connectivity. Recently, the United Kingdom (UK) launched a project called 5G Rural Integrated Test bed (5 GRIT) to create test beds for 5G in rural areas [3]. The project seeks to demonstrate the role 5G networks can play in consolidating farming and tourism sectors using an integrated system of UAVs and AI technologies. Therefore, designing a robust communication system that will provide reliable data transfer between UAVs and the GCS is necessary for UAV-based livestock farming.
## 4 Experimental Settings and Results
### Results of LSTM
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Wrongly Inserted, Deleted, and Substituted Characters** & **TP** & **FN** & **FP** & **TN** & **Precision** & **Recall** \\
**and Substituted Characters** & **0** & **32** & **15** & **4618** & **0.0** & **0.0** \\ \hline \multirow{3}{*}{ /} & 23 & 0 & 0 & 4642 & 100 & 100 \\  & 4 & 0 & 0 & 4661 & 100 & 100 \\ : & 10 & 0 & 0 & 4655 & 100 & 100 \\  a & 60 & 1 & 0 & 4604 & 100 & 98.4 \\  c & 24 & 1 & 0 & 4640 & 100 & 96 \\  i & 59 & 0 & 1 & 4605 & 98.3 & 100 \\  k & 9 & 0 & 0 & 4656 & 10 & 100 \\  l & 50 & 1 & 0 & 4614 & 100 & 98 \\ \multirow{3}{*}{!} & 1 & 0 & 0 & 4664 & 100 & 100 \\  & 445 & 3 & 0 & 4217 & 100 & 99.3 \\  & 121 & 1 & 0 & 4543 & 100 & 99.2 \\ \(\_\)\(\_\)\(\_\) & 129 & 1 & 2 & 4533 & 98.5 & 99.2 \\ \(\_\)\(\_\)\(\_\) & 31 & 1 & 0 & 4633 & 100 & 96.9 \\ \(\_\)\(\_\) & 43 & 2 & 0 & 4620 & 100 & 95.6 \\ \(\_\)\(\_\) & 234 & 1 & 0 & 4430 & 100 & 99.6 \\ \(\_\)\(\_\) & 71 & 1 & 0 & 4593 & 100 & 98.6 \\ \(\_\)\(\_\) & 44 & 0 & 3 & 4618 & 93.6 & 100 \\ \(\_\)\(\_\) & 1 & 1 & 0 & 4663 & 100 & 50 \\ \(\_\)\(\_\) & 29 & 0 & 1 & 4635 & 96.7 & 100 \\ \(\_\)\(\_\) & 69 & 3 & 0 & 4593 & 100 & 95.8 \\ \(\_\)\(\_\) & 171 & 1 & 6 & 4487 & 96.6 & 99.4 \\ \(\_\)\(\_\) & 188 & 0 & 1 & 4476 & 99.5 & 100 \\ \(\_\)\(\_\) & 162 & 0 & 1 & 4502 & 99.4 & 100 \\ \(\_\)\(\_\) & 187 & 1 & 1 & 4476 & 99.5 & 99.5 \\ \(\_\)\(\_\) & 63 & 0 & 1 & 4601 & 98.4 & 100 \\ \(\_\)\(\_\) & 246 & 0 & 5 & 4414 & 98 & 100 \\ \(\_\)\(\_\) & 6 & 0 & 1 & 4658 & 85.7 & 100 \\ \(\_\)\(\_\) & 4 & 1 & 1 & 4659 & 80.0 & 80 \\ \(\_\)\(\_\) & 1 & 1 & 2 & 4661 & 33.3 & 50 \\ \(\_\)\(\_\) & 1 & 0 & 1 & 4663 & 50 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Confusion matrix of nearly 4680 characters of test set, font Calibri and size 14 (the characters with 100% of accuracy are not shown). Figure 8: Testing BINA using a real image. Figure 9: Output of the Figure 8 using proposed model. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Font** & **Number of Images** & **Size 14** \\ \hline Arial & 2 & 97.03 \\ Calibri & 1 & 92.38 \\ Mitra & 12 & 88.55 \\ Nazanin & 2 & 90.41 \\ Tahoma & 1 & 83.68 \\ Times New Roman & 2 & 91 \\ \hline Average of Accuracy & - & 90.51 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Proposed model accuracy on real test set, size 14.
## 5 Formulation of the LMI Stability Criterion
### Design of the LMI Condition
#### 5.2.3 LMI Approach with Fixed Parameter \(\epsilon\) and Unknown Parameter \(\delta\)
It is clear that this condition (88) can be recast like so:  
\[\theta_{2}-\lambda-m_{3}^{-1}>0 \tag{89}\]  
Using the Schur complement for expression (89), we can establish the subsequent LMI condition:  
\[\left[ \begin{array}{cc}\theta_{2}-\lambda&1\\ \star&m_{3}\end{array} \right]>0 \tag{90}\]  
where \(\lambda>0\). Following the past outcomes, we can hence establish the subsequent Theorem subject to two LMI conditions. Theorem 3: Suppose that there exist matrices \(\mathcal{S}>0\), \(\mathcal{R}\) and \(\mathcal{M}_{1}>0\), along with scalars \(m_{2}>0\), \(m_{3}>0\), \(\gamma>0\), \(\lambda>0\), and \(\theta_{2}>0\). Therefore, the subsequent LMI minimization task is posed for a given constant \(\zeta\geq 0\) and a fixed parameter \(\epsilon>0\). \[\begin{array}{llll}&\min~{}\theta_{2}\\ &\text{s.t. }\\ &\left[ \begin{array}{cc}\Xi_{33}&\mathcal{S}&\mathcal{O}&\mu_{3}\mathcal{S} \mathcal{C}_{1}^{\mathrm{T}}&\mathcal{O}&\mathcal{O}\\ \star&-\gamma\mathcal{I}&\mathcal{O}&\mathcal{O}&\mathcal{O}\\ \star&\star&\frac{\gamma}{\epsilon^{2}}\mathcal{D}_{1}\mathcal{D}_{1}^{ \mathrm{T}}-\mathcal{M}_{1}&\frac{\gamma}{\epsilon^{2}}\mathcal{D}_{1}&\frac{ \gamma}{\epsilon^{2}}\mathcal{D}_{1}\mathcal{B}^{\mathrm{T}}&\mathcal{O}\\ \star&\star&\star&\frac{\gamma}{\epsilon^{2}}\mathcal{I}-\left(\sigma\big{(} \frac{1}{\epsilon_{3}}-1\big{)}^{2}+\frac{1}{\epsilon_{3}}\right)m_{2}&\frac{ \gamma}{\epsilon^{2}}\mathcal{B}^{\mathrm{T}}&\mathcal{O}\\ \star&\star&\star&\star&\frac{\gamma}{\epsilon^{2}}\mathcal{B}^{\mathrm{T}}- \lambda\mathcal{I}&\lambda-m_{3}\\ \star&\star&\star&\star&\star&\frac{\gamma}{\epsilon^{2}}\mathcal{B}^{ \mathrm{T}}-\lambda\mathcal{I}&\lambda-m_{3}\\ \star&\star&\star&\star&\star&\frac{\gamma}{\epsilon^{2}}\mathcal{B}^{ \mathrm{T}}\\ \end{array} \right]<0 \tag{91b}\] \[\left[ \begin{array}{cc}\phi_{2}-\lambda&1\\ \star&m_{3}\end{array} \right]>0 \tag{91c}\]  
where \(\Xi_{33}=(\mathcal{AS}+\mathcal{BR})+(\mathcal{AS}+\mathcal{BR})^{\mathrm{T}}+ \mathcal{M}_{1}+m_{2}\mathcal{D}_{2}\mathcal{D}_{2}^{\mathrm{T}}+m_{3} \mathcal{I}+\zeta\mathcal{S}\). As a result, the joint-knee rehabilitation exoskeleton robot's nonlinear dynamics (5) are stabilized at the intended position by the affine state-feedback controller (25). Relation (78) is used to compute the controller's gain \(\mathcal{K}\). Moreover, the parameter \(\bar{\delta}\) of the lumped disturbance \(\Delta_{t}\) meeting condition (10) can have its maximum value, \(\bar{\delta}_{max}\), determined as follows:  
\[\bar{\delta}_{max}=\sqrt{\frac{m_{3}}{\lambda}} \tag{92}\]  
The two LMI conditions resulting from this process are represented by formulas (91b) and (91c). They involve the unknown variables \(\mathcal{S}\), \(\mathcal{R}\), \(\mathcal{M}_{1}\), \(m_{2}\), \(m_{3}\), \(\gamma\), \(\lambda\), and \(\theta_{2}\).
# Optimization Techniques for Design Problems in Selected Areas in WSNs: A Tutorial
## 18 Dispatching of Mobile Sensor Nodes in a WSN to Sense a Region of Interest
### Fusion of Delay Sensitive Noise Perturbed Data Sensed by Different Nodes in a Given Cluster  
#### System Model and Design Objectives  
A cluster of a WSN was considered in [14] where sensor nodes collect and transmit data to the fusion center of the cluster directly or through relay nodes. Relay nodes amplify and forward data to the fusion center or the next relay node. Synchronous TDMA based MAC was considered in [14]. The total energy consumed by the sensor is related to the transmission power and the duration of transmission as the following equation shows:  
\[E_{k}=\left[\left(1+\alpha_{k}\right)P_{tk}+P_{ck}\right]T_{tk}+P_{0k}T_{0k} \tag{36}\]where \(P_{tk}\) is the data transmission power, \(\alpha_{k}\) is the ratio of power consumption by RF power amplifier to transmission power, \(P_{ck}\) is the circuit power in the transceiver baseband parts, \(T_{tk}\) is the duration of the transmitting mode which is inversely proportional to the transmission rate, \(P_{0k}\) and \(T_{0k}\) are the power consumption and duration for the sleep and transient modes. The time delay per frame considered in [14] is the sum of transmission durations from the sensor nodes to the fusion center.  
There are \(L\) physical phenomena sources to be observed in the given cluster by \(K\) sensors. The sensed data is in analogue format in each sensor which was considered as the weighted sum of all the original data being observed and the sensor's noise which was assumed to be Gaussian. The analogue signal is quantized at the sensor and then digitized and sent on a noisy channel to the fusion center as shown in Figure 20. The fusion center uses the least square error method to estimate the original data from the received signals of the sensors with prior knowledge of the weighting coefficients. Since the battery life is limited and the data considered was delay sensitive, optimization of the transmission power allocation strategy and the delay of each node was considered to minimize the mean distortion of the measured information.