Dual-Input Multi-Layered Attention Model for Enhanced Path Loss Prediction

Dual-Input Multi-Layered Attention Model for Enhanced Path Loss Prediction | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Dual-Input Multi-Layered Attention Model for Enhanced Path Loss Prediction Mamta Tikaria, Vineeta Saxena This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6732837/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Path loss prediction is crucial for optimizing base station placement in cellular networks. Traditional methods rely on extensive field testing, which is time-consuming and resource-intensive. Machine learning (ML)-based approaches offer an alternative, yet most existing models use unimodal systems, limiting predictive accuracy. To address this, we propose a Bimodal Path Loss Prediction System that integrates environmental data with visual information extracted from satellite images. We introduce the Dual-Input Integrative Attention Model (DIIAM), a multi-layered architecture designed for improved path loss prediction. DIIAM consists of three key layers: Dual-Input Feature Extraction Layer (DIFEL), Feature Weighted Attention Layer (FWAL), and Learning Layer (LL). DIFEL extracts environmental features using data imputation, normalization, and statistical feature selection, while visual features are obtained using the ResNet50 transfer learning model. FWAL applies an attention mechanism to enhance feature relevance, and LL employs six different learning models—SVR, RFR, BPNN, LSTM, BiLSTM, and GRU—to effectively capture complex feature relationships. Evaluated on four publicly available datasets, DIIAM achieves an average RMSE of approximately 1.5 dB, outperforming state-of-the-art methods. The results demonstrate the effectiveness of integrating environmental and visual data for path loss prediction, offering a more accurate and computationally efficient alternative to traditional and unimodal ML approaches. Path loss 5G wireless communication machine learning bimodal Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 1 Introduction The telecommunication industry is experiencing rapid growth due to rising use of mobile devices and the increasing demand for higher capacity in modern networks. It is projected that by the end of 2025, there will be over 20 billion connected devices [ 1 ] [ 2 ]. To address the challenges of rising demand and ca-pacity limitations, advancements in wireless technol-ogy have led to the establishment of new standards. Today, faster data services are required by users that definetely requires more bandwidth [ 3 ]. With this need for more bandwidth is challenging mobile net-works and led to the development of 5th generation (5G) mobile technology for enhanced network capa-bilities [ 4 ]. This 5G revolutionized the communica-tion system by providing 50 times higher data rates than current standards with reduced latency and energy costs [ 5 ]. This advancement builds on the existing LTE systems and involves enhancing spec-tral efficiency and capacity [ 6 ]. It also encourages the use of previously underutilized frequency bands to enhance efficiency of communication models [ 7 ]. The move of LTE into unlicensed bands may disrupt Wi-Fi and other technologies. The success of 5G in densely populated areas centers on deploying small-cell technology to tackle its limited range and suscep-tibility to interference at mm. Wave frequencies. This challenge explored the importance of radio frequen-cy (RF) propagation analysis while optimizing 5G network performance and reliability[ 8 ]. RF propaga-tion explores how radio waves interact with external factors that makes it essential for optimizing signal strength and reliability for 5G networks [ 9 ]. RF mod-elling and planning optimize the 5G network for real-world deployments by balancing cost, coverage, and quality [ 10 ]. Optimizing the 5G spectrum involves using beamforming to focus signals and overcome obstructions. Beamforming and accurate propaga-tion models are key to mitigating path loss in 5G networks by focusing signals and predicting trans-mission behaviors [ 11 ]. Path loss in communical models will increases with the distance between transmitter and receiver. These are influenced by several factors like transmission power, antenna gains, frequency, etc. [ 12 ]. To understand the rela-tionship between received power level and path loss, the concept of the path loss exponent factor (PLE) is introduced. The PLE helps to quantify the rate at which path loss increases with distance. However, this simple relationship is complicated by the multi-path effect, where signals take multiple paths to reach the receiver, leading to variations in the PLE value. The multipath effect necessitates adjustments to the path loss exponent rule, resulting in different PLE values that reflect the complex nature of real-world signal propagation. Path loss prediction has various models depending on frequency distance, various environmental specific parameters, applica-tion area such as rural, suburban, urban etc. Free space path loss (FSPL) models are presented in [ 13 ] [ 14 ] [ 15 ]. In telecommunication, FSPL is attenua-tion of the radio energy between two antennas that communicate through free space without any obsta-cle. But as it is one of the basic models of path loss it has several disadvantages. In [ 16 ] it assumes a per-fect free-space environment without obstacles or reflections, which is rarely the case in real-world sce-narios. In [ 17 ] it ignores the impact of terrain, build-ings, and other obstacles on signal propagation and in [ 18 ] it has limited applicability in environments with high obstacles or complex structures. Another method such as log-distance path loss model [ 19 ] [ 20 ] for path loss prediction for densely populat-ed areas considering distance as factor but it as-sumes a simplistic power-law relationship between distance and path loss, which may not capture the complexities of real-world propagation. Also, it re-quires a path loss exponent (n) that may not be uni-versally applicable across different environments and frequencies and it has limited accuracy in sce-narios with non-line-of-sight (NLOS) conditions. Hata-Okumura model [21] [ 22 ] [ 23 ] for path loss pre-diction is another conventional radio propagation model for predicting the path loss for dense envi-ronment with frequency range of 150 to 1500 MHz. Empirical model that incorporates frequency, dis-tance, and various environment-specific parameters [ 24 ] [ 25 ] [ 26 ]. It was developed based on extensive measurements in urban, suburban, and rural environments. The telecommunications sector has adopted a more flex-ible and data-driven approach by utilizing machine learning, ensuring optimal performance in a variety of changing propagation situations. Therefore, this paper presented the bimodal machine learning based path loss prediction models by combining the loca-tion specific information and the satellite image data. The key contributions of the paper are: The methodology integrates environmental or channel features with visual satellite image data by utilizing advanced machine learning models to capture a more detailed and accurate repre-sentation of the factors influencing path loss. The paper presents a dual-input (bimodal) sys-tem that processes both environmental/channel information and visual data simultaneously that will explore more diverse informations for robust path loss prediction model. The paper presents a multi-layered model dual-input integrative attention model (DIIAM) that incorporating attention mechanisms into the model architecture for path loss prediction. By dynamically focusing on the most relevant fea-tures from both input streams, the model can improve its prediction accur acy and efficiency, making it a significant advancement for wireless communication. The application of DIIAM across different learning models such SVR, RFR, BPNN, LSTM, BiLSTM, GRU for the learning layer demon-strates the versatility and adaptability of the ap-proach. This flexibility allows for extensive test-ing and optimization across various algorithms to identify the most effective solution for path loss prediction. Rest of the paper is organized as: Section 2 de-scribes’ mathematical description of path loss. Sec-tion 3 presents the role of machine learning ap-proaches for prediction of path loss. Section 4 pre-sents the proposed methodology for prediction of path loss. Section 5 presents the implementation de-tails and result analysis with comparative state-of-art. Finally, in section 6 conclusion and future scope is presented. 2 Mathematical Modelling of Path Loss Path loss indicates the path gain increase and decrease in decibel as linear function. It is evaluated by using logarithmic distribution function around mean path loss [ 27 ] [ 28 ] [ 29 ] [ 30 ] [31]. Mathematically, it is represented as: $$\:PL\left(dB\right)=20\:{log}_{10}\frac{4\pi\:d}{\lambda\:}$$ 1 Where, d is the distance between the transmitter and receiver and λ is the wavelength of the signal. This equation highlights that the received power level at the receiver is dependent on the path loss, indicat-ing the importance of understanding and managing path loss for effective communication. The received powe at distance d from transmitter is represented as: $$\:{P}_{r}=\:{P}_{t}{G}_{r}{G}_{r}\:{\left(\frac{\lambda\:}{4\pi\:d}\right)}^{2}$$ 2 The ratio of transmitting power to received power is represented as path loss: $$\:\frac{{P}_{t}}{{P}_{r}}=\:{\frac{1}{{G}_{r}{G}_{r}\:{\left(\frac{\lambda\:}{4\pi\:d}\right)}^{2}}}_{.}$$ 3 If the antenna gains are assumed to be unity, then expression of path loss should be given by: $$\:PL\left(dB\right)=20\:{log}_{10}\frac{4\pi\:d}{\lambda\:}$$ 4 In the original form, path loss is given by: $$\:PL\left(dB\right)=10\:{log}_{10}{\left(\frac{4\pi\:d}{\lambda\:}\right)}^{2}$$ 5 Path loss (PL) is determined by the square of the signal frequency and the distance between the transmitter and receiver. Higher path loss results in lower received power levels. The goal is to minimize path loss to enhance the power available at the re-ceiver. The path loss equation, when expressed in decibels (dB), quantifies this relationship and helps in optimizing communication system performance as: $$\:{P}_{r}\left(dB\right)={P}_{t}\left(dB\right)+\:{G}_{t}\left(dB\right)+\:{G}_{r}\left(dB\right)-\:20\:{log}_{10}\frac{4\pi\:d}{\lambda\:}$$ $$\:{P}_{r}\left(dB\right)={P}_{t}\left(dB\right)+\:{G}_{t}\left(dB\right)+\:{G}_{r}\left(dB\right)-PL\:\left(dB\right)$$ 6 Thus, $$\:PL\:\left(dB\right)=\:{P}_{t}\left(dB\right)+\:{G}_{t}\left(dB\right)+\:{G}_{r}\left(dB\right)\--\:{P}_{r}\left(dB\right)$$ 7 From Eq. ( 7 ), it can be inferred that increasing transmission power or using high gain antennas can reduce path loss in communications, which is rele-vant for line-of-sight or near line-of-sight systems like microwave and satellite communications. However, technologies such as commercial AM radio broad-casting and WLAN communications do not neces-sarily require line-of-sight to function effectively. 3. Machine Learning Modelling for Path Loss Machine learning offers a promising approach to predict path loss in wireless communications by overcoming limitations of traditional empirical and deterministic models [ 27 ]. These models are essential for network planning, affecting coverage, frequency allocation, and interference prediction. Machine learning techniques, such as neural networks [ 28 ], support vector regression [ 30 ], and random forest [31], etc. provide more accurate and computational-ly efficient predictions. This advancement makes machine learning a viable alternative for enhancing network planning and optimization by accurately forecasting path loss [ 32 ]. Below Table 1 presents the recent research contributions for path loss prediction using machine learning [33] [ 34 ]. 3.1 ANN based path loss predictionPaper [ 32 ] demonstrated that multilayer per-ceptron (MLP) neural networks in artificial neural networks (ANNs) provide high-accuracy path loss (PL) predictions, outperforming conventional models. Emphasized the agreement of ma-chine-learning-based models (ANN, SVR, RF) with measured data, introducing data expansion schemes to enhance training data use. [ 35 ] as-sessed machine learning methods for rural path loss prediction, highlighting the effectiveness of a three-layered ANN with 51 neurons. [ 37 ] investigated neural network parameters for VHF band path loss prediction, showing ANN models' su-perior accuracy and generalization over empirical models. Artificial Neural Networks (ANNs) are effec-tively utilized for solving nonlinear regression prob-lems. ANNs is designed by concatenating input layer, one or more hidden layers, and an output layer. All layers are composed of neurons that are connected to neurons of subsequent layer with varying weights. This architecture is referred as multi-layer perceptron. These networks are preferred algorithm for learning from complex data patterns or behaviors such as path loss in wireless communications. The presence of number of hidden layers influence the efficacy of ANN. But sometimes, the complex ANN architecture results in overfitting. 3.2 SVR based path loss prediction [ 32 ] proposed support vector regres-sion (SVR) for path loss prediction for urban envi-ronemnt. SVR presented similar outcome as MLP based ANN but it has lower computational complexi-ty. SVR is a supervised learning technique that can be applied for classification and regression applica-tions. Path loss model is a type of regression task therefore SVR can be applied here. It operates by devising a hyperplane, or multiple hyperplanes in expansive-dimensional spaces, which can classify or predict data points. The primary objective of SVM is to determine the ideal hyperplane that establishes the largest gap between distinct categories, ensuring im-proved adaptability and resilience. To do this, SVM elevates input data into a more comprehensive fea-ture domain and seeks the most suitable separating plane. Through kernel functions, this elevation is accomplished, with linear, polynomial, and radial basis functions (RBF) being the most prevalent. SVMs excel in managing data with numerous dimen-sions and can adapt to non-linear decision bounda-ries by harnessing kernel functions. Mathematical Description of SVM are: Hyperplane: Defined by the W^T x + b = 0, where w is the weight vector and b is the bias. Support Vectors: Data points that are closest to the hyperplane and influence its position and orientation. Margin: The distance between the nearest points (support vectors) of separate classes to the hyper-plane. The margin is given by 2/(||w||). The solution to the optimal hyperplane is a con-strained optimization problem, which can be written as: Minimize $$\:Minimize\:\frac{1}{2}{\left|\left|W\right|\right|}^{2}+C{\sum\:}_{i=1}^{n}{\xi\:}_{i}subject\:to\:{y}_{i}\left({W}^{T}x+b\ge\:1\right)-\:{\xi\:}_{i}\:and\:{\xi\:}_{i}\ge\:0.$$ 8 Where,ξi are slack variables. C is a regularization parameter controlling the trade-off between maxim-izing the margin and minimizing the error. 3.3 Random Forest based path loss prediction [36] explored clustering and regres-sion algorithms (random forest, AdaBoost, K-nearest neighbors) for path loss prediction, comparing them against other regression techniques through extensive simulation and tenfold cross-validation. [ 39 ] introduced an environment features-based model (EFBM) using Random Forest for direct path loss prediction, reducing RMSE significantly at 6 and 28 GHz. Random Forest, an ensemble technique, aggregates multiple decision trees to deduce predic-tions. Suitable for classification and regression, it formulates predictions by amalgamating the individ-ual tree outcomes. Each tree in this ensemble learns from distinct data portions, and while determining splits, a random feature subset is chosen. Key strengths of Random Forests include their resilience against data irregularities, competence in high-dimensional datasets, and capability to rank feature significance. The Random Forest algorithm has key hyperparameters to set, including node size, the number of trees, and the number of features sam-pled. Random Forest is composed of decision trees, each built on a bootstrap sample from the training data. It introduces randomness through feature bag-ging to reduce tree correlation. For regression, the trees are averaged. For path loss prediction using decision trees, the predicted value for new samples is obtained by averaging the predictions from all indi-vidual decision trees. Mathematically, the output decision is evaluated as y = 1/T ∑_(t = 1)^T▒〖h ̂_t (x)〗. Here, total number of trees used as learning is represented as T and its respective predicted out-come is represented as h ̂_t (x). This method aggre-gates the outcomes of various decision trees to im-prove prediction accuracy. 3.4 RNN based path loss prediction [40] proposed a RNN-LSTM model for path loss prediction. [ 41 ] also used RNN based path loss model for urban environ-ment model. Recurrent Neural Network (RNN) is also a type of machine learning that learns patterns from temporal data and predict the temporal dependent outcomes. In path loss predictive models RNN pro-vides high data rate with low latency and improved reliability. The path loss data contains informations such as obstacles, terrain types, weather conditions, and other environmental factors that makes the learning process difficult [ 49 ]. But the architecture of RNN to utilize the output from the previous state as input to the current state makes it an efficient learner. Therefore, RNN models can be efficiently chosen over traditional ANNs. But conventional RNN face issues while handling long sequences. This lead to development of more efficient RNN models such as Long Short-Term Memory (LSTM) and Gated Re-current Unit (GRU) to address these challenges. Un-like traditional ANN, RNN relies on feed-forward connections, LSTM, or GRU incorporate an internal state or memory that allows them to consider both the current input and information from previous in-puts. This feature makes RNNs particularly suitable for analyzing time-dependent data. The text high-lights the adaptability of RNNs to handle variable-length sequences of inputs thanks to their dynamic behavior and memory capabilities. 3.5 Deep Learning based path loss prediction [31] compared state-of-the-art sto-chastic and ray-tracing models, finding that satellite images and model-aided techniques can improve path loss predictions by approximately 0.8 dB and 1 dB, respectively. A deep learning (DL) model showed improvements of about 1 dB at 811 MHz and 4.7 dB at 2630 MHz. T. T. [ 44 ] presented a model-aided deep learning technique for 7 GHz path loss prediction in urban environments, showing supe-rior performance to empirical models. [ 42 ] proposed a deep learning-based path loss prediction considering obstacles and weather in V2V commune-cation, achieving accurate predictions. Improved modality fusion results through transfer learning and image augmentation, achieving lower mean absolute error (MAE) values. Convolu-tional Neural Networks (CNNs) are a type of deep neural network that was initially used in computer vision tasks. Recently, CNNs have expanded their application to other domains, including human-computer interfaces, due to their ability to detect feature localities. CNNs are distinguished from feed-forward networks by their capability to extract and process features from both 2-dimensional and 3-dimensional data, which is organized into matrices for processing. The more advanced and powerful type of CNN models are transfer learning. Transfer learning leverages a model developed for one task as a foundation for a model on a second task, signifi-cantly benefiting deep learning by utilizing pre-trained models to save on computational resources and time. This approach offers two main ad-vantages: enhanced learning speed and performance due to the transfer of learned features, and a reduced need for large datasets, making it especially valuable when data availability is limited. By employing pre-trained models familiar with complex image features, transfer learning improves accuracy and detection capabilities, which are vital for diagnosing medical conditions with limited specific data. Therefore, this paper have adopted the transfer learning for design-ing a bimodal methodology for path loss. Table 1 Recent Research Contribution for path loss prediction using machine learning Ref Year Modularity Frequency (in MHz) Environment type Technique Used RMSE [31] 2020 Bimodal 811/2630 University Campus DNN ~ 4dB [ 32 ] 2020 Unimodal 2500 Urban/Suburban/Rural ANN ~ 4-6dB [ 34 ] 2019 Unimodal 2021.4 Urban SVR, RF, ANN ~ 4dB [ 35 ] 2021 Unimodal 3700 Rural SVR, RF, k-NN ~ 4dB [36] 2019 Unimodal 600 Urban SVR, RF, k-NN, ANN ~ 6-6.5dB [ 37 ] 2019 Unimodal 189.25/479.25 Urban ANN ~ 2-21dB [ 38 ] 2020 Unimodal 2140 Urban SVR, RF, k-NN ~ 2-4dB [ 39 ] 2021 Bimodal 900 Urban CNN ~ 4dB [40] 2022 Unimodal - Urban Wavelet-GA ~ 2-4dB [ 41 ] 2022 Unimodal 6000–28000 Urban RF ~ 0.33–0.89 dB [ 42 ] 2023 Unimodal 60000 Urban DNN ~ 1-4dB [43] 2023 Unimodal 7000 Urban CNN ~ 4dB [ 44 ] 2024 Unimodal - - Ensemble NN ~ 2-5dB 4 Methodology Used In this paper, a multi-level and bimodal approach is presented for path loss prediction. The paper introduces a network termed as Dual-Input Integrative Attention Model (DIIAM) for path loss detection based on image and environmental or channel parameters. The model is termed as Dual-input because it is processing image features and environmental features together with attention layer to generate weighted features. DIIAM integrates channel features using machine learning models and visual features from pre-trained CNN architectures like ResNet50. By merging these features and using attention mechanisms, DIIAM can dynamically focus on crucial data points, offering a comprehensive solution for identifying path loss. This model architecture is presented in Fig. 1 for path loss prediction involves a multi-layered approach that integrates both environmental or channel features with visual satellite image data. Each layer of the model are described below sub-sections. The algorithm of the proposed methodology is presented below in algorithm 1. Algorithm 1: Dual-Input Integrative Attention Model (DIIAM) Input: Environmental or channel informations \(\:{EI}_{i}\:\) and satellite images \(\:{VI}_{i}\) Output: Path loss \(\:Pl\) Begin Pass \(\:{EI}_{i}\:and\:{VI}_{i}\) to DIFEL Extract Environemental Feature Vector \(\:{F}_{{EI}_{p}}=\text{D}\text{N}\left[\text{D}\text{I}\left\{{\text{E}\text{I}}_{i}\right\}\right]\) {eq. ( 12 )} Select Relevant Features \(\:{F}_{{EI}_{p}}=\{{T}_{test}\left({F}_{{EI}_{p}}\right)\oplus\:{Z}_{test}\left({F}_{{EI}_{p}}\right)\}\) {eq. ( 13 )} Extract visual Feature Vector \(\:{F}_{{VI}_{p}}=\text{R}\text{e}\text{s}\text{N}\text{e}\text{t}50\left[{\text{V}\text{I}}_{i}\right]\) {eq. (14)} \(\:{F}_{DI}=concat\{{F}_{{EI}_{p}},{F}_{{VI}_{p}}\}\) \(\:FWAL\underset{{F}_{DI}}{\leftarrow\:}DIFEL\) Extract attention weight \(\:{\widehat{a}}_{i}\) Evaluate weighted feature vector \(\:{{F}_{DI}}_{w}\) {eq. ( 18 )} \(\:LL\underset{{{F}_{DI}}_{w}}{\leftarrow\:}FWAL\) For \(\:m=1\:to\:max\_iter\) \(\:Model=build\_model\left(x\right)\) {Where, x can be SVR, RFR, etc.} \(\:Traine{d}_{model\underset{\text{m}\text{i}\text{n}\left(loss\right)}{\leftarrow\:}}Train(x,m,{{F}_{DI}}_{w})\) End for \(\:Pl\leftarrow\:Predict({Trained}_{model},{{F}_{DI}}_{w})\) End 4.1 Input Layer This is the first layer dual input are taken, one is environmental or channel informations and other as visual informations. The environmental or channel informations is represented as EI={e_1,e_2,….e_n}. The visual information comprises satellite images that provide a visual representation of the terrain and surrounding environment and represented as VI={v_1,v_2,….v_n }. 4.2 Dual-Input Feature Extraction Layer (DIFEL) It is mentioned that the input is bimodal or dual input in nature as F={EI,VI}. In this step, environmental or channel informations EI as well as visual information VI features are extracted. The EI feature matrix is generated by following steps: Data Imputation (DI): Depending on the context and significance of missing data, data imputation is applied to handle missing data. Imputation is a method used to handle missing values in a dataset by replacing them with substitute values, thereby allowing for more complete analysis without discarding data. For data imputation, K-Nearest Neighbors (KNN) is used. Missing values are imputed using the values of the k most similar instances (neighbors), based on other, non-missing attributes. The similarity between instances is usually measured using a distance metric such as Euclidean distance. The imputed value is the mean (for numerical variables) or mode (for categorical variables) of the k nearest neighbors. Data Normalization (DN): Scaling numerical features to a specific range, typically between 0 and 1, helps with model convergence and interpretation. For this z-score normalization is adopted stated as: $$\:{Data}_{i}=\frac{{x}_{i}-\stackrel{-}{x}}{std}$$ 9 Where, xi = The data value at instance \(\:i\) and \(\:\stackrel{-}{x}\) = mean value $$\:\stackrel{-}{x}=\frac{1}{n}\sum\:_{i=1}^{n}{x}_{i}$$ 10 std = standard deviation $$\:std=\sqrt{\frac{1}{n}\sum\:_{i=1}^{n}({x}_{i}-\stackrel{-}{x}})$$ 11 Then, relevant features are selected by applying combine T-Test and Z-Test statistical tests. Those features who shows high T-Test and Z-Test values are considered further and others are neglected. Then final pre-processed feature matrix \(\:\:{F}_{{EI}_{p}}\) is generated as: $$\:{F}_{{EI}_{p}}=DN\left[DI\left\{{EI}_{i}\right\}\right]\:\:\:\:\:\:\:\:\:\:\:where\:\{i=\text{1,2},\dots\:n\}$$ 12 $$\:{F}_{{EI}_{p}}=\{{T}_{test}\left({F}_{{EI}_{p}}\right)\oplus\:{Z}_{test}\left({F}_{{EI}_{p}}\right)\}$$ 13 For, visual feature extraction pre-trained Resnet50 model is used because it captures more distinct and characteristic visual features. For example, a given image \(\:I\) , pre-trained learning model are used to derive feature maps from second-to-last pooling layer and reporesented as: $$\:{F}_{{VI}_{p}}=ResNet50\left[{VI}_{i}\right]\left(14\right)$$ The core component of the ResNet50 is convolution layer and each convolution layer perform convolution operation over \(\:{\text{V}\text{I}}_{i}\:\) as: $$\:{F}_{{VI}_{p}}(i,j)=\left(g*h\right)(i,j)\sum\:_{p}\sum\:_{q}g\left(p,q\right)*h(i-p)(j-q)$$ 15 Where, \(\:{F}_{{VI}_{p}}(\text{i},\text{j})\) is the output visual feature map, \(\:g\) represents the input image or feature map from previous layer of model. The kernal filter is represented as \(\:h\) with convolution operation \(\:\text{*}\) . 4.3 Feature Weighted Attention Layer (FWAL) To combine the environmental features \(\:{F}_{{EI}_{p}}\:\) and visual features \(\:{F}_{{VI}_{p}}\) effectively, it is require to combine these features together. Mathematically, dual-input feature \(\:{F}_{DI}\) is presented as: $$\:{F}_{DI}=\left(\begin{array}{cc}{F}_{{EI}_{p}}&\:{F}_{{VI}_{p}}\end{array}\right)$$ 16 The more detailed visual description for generation of \(\:{F}_{DI}\) to \(\:{{F}_{DI}}_{w}\) is represented in Fig. 2 . Then \(\:{F}_{DI}\) is passed to attention layer to generate a weighted feature vector for efficient learning. For this attention mechanism is used. Machine learning are often seen as “black boxes” because it is difficult to understand their internal workings. The attention mechanism improves its interpretability by allowing the learning process to focus on specific parts of an input, like certain pixels in images or specific feature in input. This method assigns “attention weights” to elements, indicating their importance for a given task. The attention feature vector is passed through a linear layer to produce a vector \(\:\widehat{m}\) . This operation is typically a linear transformation represented as: \(\:\widehat{m}={W}_{m}\bullet\:{F}_{DI}+{b}_{m}\) . Where, \(\:{W}_{m}\) is the weight matrix of the linear layer, and \(\:{b}_{m}\) ​ is the bias. The importance of each feature row \(\:F{R}_{i}\) ​ in the feature matrix \(\:{F}_{DI}\) is determined by computing the attention weights \(\:{\widehat{a}}_{i}\) ​. This is done by measuring the similarity between \(\:\widehat{m}\) and \(\:{F}_{DI}\) ​, typically using a dot product, and applying a softmax or a sigmoid function to normalize the weights. The mathematical expression for calculating each attention weight \(\:{\widehat{a}}_{i}\) ​ is given by: $$\:{\widehat{a}}_{i}=\frac{1}{1+exp(F{R}_{i}\bullet\:\widehat{m})}\:$$ 17 The output \(\:{{F}_{DI}}_{w}\:\) of the attention layer is a weighted sum of the rows in the \(\:{F}_{DI}\:\) feature matrix, with the weights being the attention scores \(\:{\widehat{a}}_{i}\) ​. Mathematically it is represented as: $$\:{{F}_{DI}}_{w}=\sum\:({\widehat{a}}_{i}\times\:F{R}_{i})$$ 18 Where, \(\:{{F}_{DI}}_{w}\) is the output weighted feature matrix. 4.4 Learning Layer For learning, the weighted feature vector \(\:{{F}_{DI}}_{w}\) is taken as input and passed to six different learning models, i.e., SVR, RFR, BPNN, LSTM, BiLSTM, and GRU. These models are described in detail in previous section. 5 Results and Discussion In this section, results are presented for implementation of proposed methodology for path loss prediction. The entire model is simulated on python platform over google colab with facility of Tesla P100-PCIE GPU. After the training, the testing performance of the proposed model is evaluated. Subsection 5.1 presents the description about dataset. Parameters are described in sub-section 5.2 . The result analysis of the proposed model is presented in subsection 5.3 and comparative analysis is presented in sub-section 5.4 . 5.1 Datasets Used In this paper the performance is evaluated on four datasets, as described in Table 2 . Table 2 Statistical Analysis for Dataset D1 Dataset Modularity Description Features No. of Samples Dataset-1 (D1) [ 45 ] Unimodal This dataset has been generated using NYUSIM 3.0 mm-Wave channel simulator software with environmental factors. T-R Separation Distance (m), Time Delay (ns), Received Power (dBm), Phase (rad), Azimuth AoD (degree), Elevation AoD (degree), Azimuth AoA (degree), Elevation, AoA (degree), RMS Delay Spread (ns), Season, Frequency and Path Loss (dB) 2835 Dataset-2 (D2) [ 46 ] Unimodal This dataset was created for smart campus environment from drive tests along three routes within Covenant University, Nigeria. Environmental details were obtained from a Digital Terrain Map to support the modeling, focusing on an 1800 MHz frequency band. Longitude, Latitude, Elevation (m), Altitude (m), Clutter height (m), Distance (m), Path Loss (dB) 937 Dataset-3 (D3) [47] Unimodal This dataset is composed of geolocation information as well as satellite images for path loss prediction on 2630 MHz frequency band. Local coordinates 60000 Dataset-4 (D4) [47] Bimodal Local coordinates, Satellite images 3000 5.2 Parameters Used Mean Squared Error (MSE): It is evaluated by measuring the averaged square of the error between actual ( \(\:{A}_{i}\) ) and predicted ( \(\:{P}_{i})\) value. $$\:MSE=\frac{\sum\:_{i=1}^{n}{({P}_{i}-{A}_{i})}^{2}}{n}$$ 19 Mean Absolute Error (MAE): It is used to represent the error between actual ( \(\:{A}_{i}\) ) and predicted ( \(\:{P}_{i})\) value. $$\:MAE=\frac{\sum\:_{i=1}^{n}|{P}_{i}-{A}_{i}|}{n}$$ 20 Where, n = Number of tested samples. Root Mean Square Error (RMSE): It measures the square root of the average squared differences between the predicted path loss and the actual measured path loss. $$\:RMSE\:=\:\sqrt{MSE}$$ 21 Mean Absolute Percentage Error (MAPE): It is used to evaluate the average absolute percentage errors between the predicted and actual values. $$\:MAPE=\frac{100}{n}\sum\:_{i=1}^{n}\frac{|{P}_{i}-{A}_{i}|}{{A}_{i}}$$ 22 Maximum Prediction Error (MaxPE): It identifies the maximum absolute difference between the predicted and actual path loss values. $$\:MaxPE={max}|{P}_{i}-{A}_{i}|$$ 23 Error Sum of Squares (ESD): It calculates the sum of the squared differences between the predicted and actual values. $$\:ESD=\sum\:_{i=1}^{n}{({A}_{i}-{P}_{i})}^{2}$$ 24 R-Squared ( \(\:{R}^{2}\) ): It is used to evaluate the variation of dependant variables with independent variables. $$\:{R}^{2}=1-\frac{{UE}_{variation}}{{T}_{variation}}$$ 25 Where, \(\:{UE}_{variation}\) = Unexplained variation and \(\:{T}_{variation}\) = Total variation. 5.3 Statistical Analysis of Unimodal System Table 3 Statistical Analysis for Dataset D1 Features T-Test Z-Test P-Value Simulation Run Number 4.123 4.343 1.40E-05 T-R Separation Distance (m) 20.514 20.644 0 Time Delay (ns) 19.598 19.615 0 Received Power (dBm) -30.537 -30.525 0 Phase (rad) -1.898 -1.898 5.77E-02 Azimuth AoD (degree) 4.009 4.009 6.10E-05 Elevation AoD (degree) -1.185 -1.184 2.36E-01 Azimuth AoA (degree) 4.994 4.995 5.89E-07 Elevation AoA (degree) -2.744 -2.744 6.08E-03 RMS Delay Spread (ns) 5.371 5.373 7.76E-08 Season 0.861 0.848 3.97E-01 Frequency 20.408 22.906 0 Table 3 presents the result of T-Test, Z-Test and P-Value for each feature of D1 dataset. The T-Test, Z-Test are evaluated as in Eq. ( 26 ) and Eq. ( 27 ) respectively: $$\:T-Test=\frac{\sum\:{x}_{1}-{x}_{2}}{\sigma\:\sqrt{1/n}}$$ 26 $$\:Z-Test=\frac{{\stackrel{-}{x}}_{1}-{\stackrel{-}{x}}_{2}}{\sqrt{\frac{{{\sigma\:}_{1}}^{2}}{{n}_{1}}+\frac{{{\sigma\:}_{2}}^{2}}{{n}_{2}}}}$$ 27 Where, \(\:{\stackrel{-}{x}}_{1}and\:{\stackrel{-}{x}}_{2}\) are mean of two features, \(\:{\sigma\:}_{1}and\:{\sigma\:}_{2}\:\) are represents the standard deviations and \(\:{n}_{1}and\:{n}_{2}\) are sample size of respective features. The p-value depends on the specific test being conducted (T-test or Z-test). The p-value represents the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed, assuming the null hypothesis is true. These metrics are fundamental in statistical hypothesis testing and are significant for determining the relevance and significance of features for further machine learning analysis. A higher absolute value of T-Test or Z-Test indicates a more significant difference. The P-Value quantifies the probability of observing the given results. A low P-Value (< 0.05) suggests rejecting the null hypothesis and that the feature is statistically significant. In D1, features such as Simulation Run Number, T-R Separation Distance (m), Time Delay (ns), Received Power (dBm), Azimuth AoD (degree), Azimuth AoA (degree), RMS Delay Spread (ns), and Frequency have very low P-Values indicating that they are statistically significant with both T-Test and Z-Test. They are highly relevant for further analysis in machine learning models. Phase (rad), Elevation AoD (degree), and Season features show higher P-Values therefore they are not statistically significant. Features with significant T-Test and Z-Test and low P-Values are strong candidates for inclusion in machine learning models. They have shown a significant effect, suggesting a strong relationship with the outcome variable. Table 4 Statistical Analysis for Dataset D2 Features T-Test Z-Test P-Value Longitude 25.789 25.801 0 Latitude 25.789 25.801 0 Elevation (m) 19.418 21.365 0 Altitude (m) 17.589 21.029 0 Clutter height (m) -10.143 -7.214 0 Distance (m) 25.789 25.801 0 For D2 dataset, Table 4 presents the statistical T-test, Z-Test, and P-value metrices for each feature. These metrics are essential for evaluating the statistical significance of each feature and its potential relevance for machine learning models. Longitude, Latitude, Elevation (m), Altitude (m), and Distance (m) features show very high absolute values for both T-Test and Z-Test indicating extremely strong statistical significance. The high T and Z values suggest these features have a strong effect size. For Clutter Height (m), the T-Test and Z-Test are negative, indicating a negative effect size. But the P-Value is still extremely low that makes this feature statistically significant. The negative values indicate that as the clutter height increases, the dependent variable might decrease (or vice versa), but further domain-specific analysis is needed to interpret this relationship properly. Therefore, Longitude, Latitude, Elevation (m), Altitude (m), and Distance (m) are evidently significant predictors due to their statistical metrics. These features are likely to have a strong relationship with the outcome variable and should be considered for any predictive modelling efforts. Table 5 Statistical Analysis for Dataset D3 Features T-Test Z-Test P-Value Longitude -66.096 -66.094 0 Latitude 20.638 20.639 0 Speed (m/s) 35.2360 35.238 0 Distance (m) 227.400 227.400 0 Distance_x (m) 20.638 20.639 0 Distance_y (m) -66.096 -66.094 0 PCI 24.766 24.740 0 For the D3 dataset, Table 5 presents the statistical analysis employing T-test, Z-test, and P-value metrics for each feature. The features Longitude, Latitude, Speed (m/s), Distance (m), Distance_x (m), Distance_y (m), and PCI show very high absolute values for both the T-test and Z-test, indicating an extremely strong statistical significance. The P-value for all features is 0 which means all features are highly significant. 5.4 Unimodal Performance Evaluation The results presented in Table 6 for dataset D1 for proposed DIIAM model with six different learning models. Support Vector Regression (SVR) shows moderate performance with a relatively high MSE and RMSE. Random Forest Regressor (RFR) exhibits the best performance across almost all metrics. It has the lowest MSE, MAE, MAPE, MaxPE, and RMSE, alongside the highest R² value. This indicates that RFR is both accurate and reliable. Backpropagation Neural Network (BPNN) shows good performance with lower errors compared to SVR, LSTM, BILSTM, and GRU but not as low as RFR. Its R² value is also high. LSTM has higher errors in terms of MSE, MAE, RMSE as compared to RFR and BPNN but its R² value is good but not more than RFR and BPNN. Bidirectional LSTM (BiLSTM) shows similar performance as LSTM. Gated Recurrent Unit (GRU) shows better performance than both LSTM and BILSTM in terms of errors but not more than RFR. Therefore, it can be concluded that the RFR is most effective model for this dataset. Table 6 Performance Evaluation on Dataset D1 Models MSE MAE MAPE MaxPE ESD RMSE R 2 SVR 58.151 5.319 3.410 41.310 49486.824 7.626 0.746 RFR 24.763 3.413 2.108 14.515 21073.695 4.976 0.892 BPNN 44.336 5.155 3.172 18.523 37729.867 6.659 0.807 LSTM 56.784 5.826 3.610 21.708 48323.270 7.536 0.752 BILSTM 57.519 5.788 3.583 21.802 48948.427 7.584 0.749 GRU 50.757 5.331 3.297 19.483 43194.097 7.124 0.779 Table 7 presents the performance of propose DIIAM model on dataset D2. SVR shows high values in MSE, MAE, and RMSE. However, its R 2 value of 0.872. RFR present excellent performance across all metrics. This indicates very accurate predictions with minimal error and high reliability in capturing the variance in the data. BPNN has significantly worse performance compared to other models as it shows highest values in MSE, MAE, MAPE, and RMSE, and a negative R 2 value. LSTM networks show good performance with moderate errors and a high R 2 value of 0.970. BILSTM shows the best performance with D2. Gated Recurrent Unit (GRU) also performs well with low error metrics and a high R 2 of 0.991. Therefore, for dataset D2, BILSTM and RFR models outperform the others in terms of predictive accuracy and reliability. The RFR shows better performance in path loss prediction due to its robust ensemble learning method that effectively reduces overfitting and improves prediction accuracy by combining multiple decision trees. The BiLSTM model outperforms others because of its ability to understand and process temporal dependencies in both forward and backward directions. This makes it highly effective for capturing complex patterns in time-series data. Table 7 Performance Evaluation on Dataset D2 Models MSE MAE MAPE MaxPE ESD RMSE R 2 SVR 14.369 1.024 0.875 24.268 4052.038 3.791 0.872 RFR 0.436 0.094 0.088 6.875 123.014 0.660 0.996 BPNN 161.926 9.345 6.399 23.092 45663.140 12.725 -0.446 LSTM 3.397 1.284 0.907 7.837 957.832 1.843 0.970 BILSTM 0.435 0.497 0.357 1.524 122.597 0.659 0.996 GRU 1.035 0.774 0.555 2.935 291.916 1.017 0.991 Table 8 presents the performance of propose DIIAM model on dataset D3. SVR shows a significantly improved performance with a low MSE of 0.828 and a R 2 of approx. 0.993. RFR shows best performance with least MSE, MAE, MAPE, MaxPE, ESD and RMSE and highest R 2 of approx. 1. BPNN, LSTM, BiLSTM and GRU also shows good performance on D3 but not that much RFR. Therefore, from all dataset’s results RFR are considered to be the first choice. Table 8 Performance Evaluation on Dataset D3 Models MSE MAE MAPE MaxPE ESD RMSE R2 SVR 0.828 0.232 0.245 13.682 14311.801 0.910 0.993 RFR 0.000 0.001 0.001 0.246 0.310 0.004 1.000 BPNN 0.212 0.317 0.276 3.646 3655.888 0.460 0.998 LSTM 0.007 0.044 0.040 1.588 119.740 0.083 1.000 BILSTM 0.006 0.036 0.034 1.455 106.504 0.079 1.000 GRU 0.005 0.042 0.037 0.960 77.813 0.067 1.000 5.5 Bimodal Performance Evaluation Table 9 Performance Evaluation on Dataset D4 Models MSE MAE MAPE MaxPE ESD RMSE R2 SVR 0.406 0.192 0.193 8.104 366.247 0.638 0.996 RFR 0.000 0.008 0.007 0.119 0.260 0.017 1.000 BPNN 6.612 1.943 1.716 11.160 5957.699 2.571 0.940 LSTM 2.107 1.039 0.948 7.572 1898.039 1.451 0.981 BILSTM 2.986 1.270 1.138 9.680 2690.502 1.728 0.973 GRU 2.029 1.024 0.932 7.846 1828.523 1.425 0.981 Table 9 presents the performance evaluation on dataset D4. DIIAM with different learning models are used for evaluation. Among them SVR shows a significantly improved performance with a low MSE of 0.406 and a R 2 of approx. 0.996. RFR shows best performance with least MSE, MAE, MAPE, MaxPE, ESD and RMSE and highest R 2 of approx. 1. BPNN, LSTM, BiLSTM and GRU also shows good performance on D4 but not that much RFR. Therefore, RFR is considered to be the best regression model for proposed bimodal approach. 5.6 Comparative Analysis In this section, performance of Proposed DIIAM Model with all learning models are presented for average result on all datasets i.e., D1, D2, D3 and D4. Figure 3 presents the comparative MSE evaluation for various learning models i.e., SVR, RFR, BPNN, LSTM, BiLSTM, and GRU. The graph shows that lowest MSE is achieved by RF learning model in proposed DIIAM model. This is due to the ensemble learning approach of RFR. Whereas second least MSE was achieved by GRU and then by BiLSTM model. Figure 4 presents the average MAE evaluation of DIIAM Model. The least MAE was also achieved by RFR and then followed by SVR and GRU. Figure 5 presents the average MAPE evaluation of DIIAM Model. The least MAPE was also achieved by RFR and then followed by SVR and GRU. Figure 6 presents the average RMSE evaluation on all datasets. In this graph RFR have also achieved the least RMSE and then followed by GRU and BiLSTM. Figure 7 presents the average MaxPE evaluation on all dataset. The performance of average MaxPE shows similar pattern as RMSE. Figure 8 presents the average ESD evaluation on all dataset. The performance of average ESD shows similar pattern as RMSE. In Fig. 9 average R2 is presented and highest R2 was also achieved by RVR and then followed by GRU and BiLSTM. The benefit of integrating the proposed DIIAM model with RFR learning model have shown best performance due to its ensemble learning approach that limit overfitting. Whereas, DIIAM model can be integrated with GRU and BiLSTM as second choice that can efficiently capture dependencies for time-series data with less computational resources than other models. The Fig. 10 presents the comparative state-of-art in terms of RMSE for different approaches with proposed DIIAM. Lower RMSE presents that model is more predictive robust. Bimodal and unimodal approaches have been applied to different environment types, with techniques ranging from DNN[ 42 ], CNN[43], ANN [31], RF[ 35 ], Wavelet-GA [40] and Ensemble NN [ 44 ]. The performance in terms of RMSE varies from 4-6dB under urban environment. The DIIAM (proposed) which is a bimodal system has a significantly lower RMSE of 1.4. The comparatively lower RMSE for the proposed DIIAM model indicates that it substantially outperforms the existing approaches. The efficacy of the DIIAM model is evident as it provides more accurate predictions across diverse environments which can be particularly challenging due to varying signal interferences and complexities. The bimodal approach of DIIAM, possibly integrating two different types of data or models, seems to enhance the predictive accuracy, making it a potentially more robust and adaptable system in varying environmental conditions compared to the unimodal systems. 6. Conclusion The proposed methodology for path loss prediction is considered as significant advancement in wireless communication that will make the communication system more accurate and reliable. In this paper, the limitations of conventional approaches for path loss prediction models are removed. From detailed literature review, it can be concluded that most of the path loss prediction models are unimodal in nature that means they are only dependent on different environmental or channel factors. But these unimodal system results in high error during prediction. To mitigate these issues, the paper presented a dual-input (bimodal) system for path loss prediction. In this approach environmental or channel information with satellite images are considered to provide more comprehensive information for learning a model. Therefore, the methodology is multi-layered with dual input based path loss prediction model. To process environmental data, the methodology extracted important and relevant features by applying T-Test and Z-Test approach. And to process the visual data a pre-trained transfer learning model such as ResNet50 is used to reduce computational complexity and that will make the entire system lightweight. Further these features are fused together and then passed to attention layer to generate weighted feature vector for learning models. The key aspect of the proposed model is that it integrated the benefits of machine learning and attention mechanism for robust and accurate prediction model. The multi-layered model architecture, combined with advanced preprocessing and integration techniques, enables the effective utilization of complex data types, leading to superior prediction outcomes. The result analysis was presented on four datasets each for unimodal as well as bimodal systems. The results analysis shows better prediction performance as compared to existing approaches. Future research direction will motivate to design more fine-tuned model to incorporate wider range of environmental and visual data, and applying the methodology to a broader set of scenarios to validate its effectiveness and adaptability to different geographic and urban conditions. Declarations Funding This research recieved no external funding . Data availability: available on request Conflicts of interest : The author declare no conflict of interest. Author Contribution Mamta Tikaria conceptualized the study, performed the experiments, and wrote the main manuscript text. Dr. Vineeta Saxena (Nigam) supervised the research, contributed to the methodology, and reviewed the manuscript. All authors reviewed and approved the final version of the manuscript. Acknowledgement The authors, Mamta Tikaria and Dr. Vineeta Saxena (Nigam), would like to express their gratitude to the Department of Electronics and Communication Engineering, University Institute of Technology, Bhopal, for their continuous support and for providing the necessary facilities for this research. They also thank their colleagues who provided valuable feedback during the development of this work. References Ma, Y., & Zhou, J. (2024). Effects of mixed aerosol on the path loss of NLOS UV communication system. Optoelectronics Letters , 20 (9), 549–559. Oladimeji, T. 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Tikaria","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBElEQVRIiWNgGAWjYPACCQMGBsYGhoQfNkAOY+MBAspBSqFaHvakgQWI0cJgAGY9YDsMFsKrRbf9dPqDnz8sjPlnH278kMBz3m5t+2GgLTU20bi0mJ3J3djYkyBhJnEusVkiweJ28rYziUAtx9JyG3BpOZC7sYEnQcKG4Qxjg0QCz+1kswNALYwNh3FrOf92Y+MfoBb5M4zNPxLYziWbnX9IQMuN3I3NQFvMDM4wtkkksB2wM7tByJYbbzfOlkmTMDYEarFI7ElOMLsBtCUBn1/O5274+MamznDeGfbHN3/8sLM3O5/+8MGHGhucWjBAIlhlArHKQcCeFMWjYBSMglEwMgAA7hxp9YJtzP0AAAAASUVORK5CYII=","orcid":"","institution":"University Institute of Technology","correspondingAuthor":true,"prefix":"","firstName":"Mamta","middleName":"","lastName":"Tikaria","suffix":""},{"id":474811839,"identity":"c1854b4c-ca77-4af1-8a4b-d9c9358e5e60","order_by":1,"name":"Vineeta Saxena","email":"","orcid":"","institution":"University Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Vineeta","middleName":"","lastName":"Saxena","suffix":""}],"badges":[],"createdAt":"2025-05-23 12:23:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6732837/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6732837/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":85348675,"identity":"d4ed51da-9c6d-4c2a-b1bb-de2f99401cca","added_by":"auto","created_at":"2025-06-25 02:27:29","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":199955,"visible":true,"origin":"","legend":"\u003cp\u003eProposed Dual-Input Integrative Attention Model\u003c/p\u003e","description":"","filename":"Picture1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6732837/v1/2e205cebd458b5d8909fbd2b.jpg"},{"id":85348673,"identity":"5dfae936-ffe2-45d0-b5c1-3c77dbab508f","added_by":"auto","created_at":"2025-06-25 02:27:29","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":74010,"visible":true,"origin":"","legend":"\u003cp\u003eThe architecture of Feature Weighted Attention Layer\u003c/p\u003e","description":"","filename":"Picture2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6732837/v1/06d2c7ea6e101aa89d1b5825.jpg"},{"id":85348677,"identity":"4c276aba-2c8e-4a48-b575-62492f1186af","added_by":"auto","created_at":"2025-06-25 02:27:29","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":425407,"visible":true,"origin":"","legend":"\u003cp\u003eAverage MSE Comparison of Learning Models with Proposed DIIAM Model\u003c/p\u003e","description":"","filename":"Picture3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6732837/v1/3726bb169e20421a3ce384db.jpg"},{"id":85348679,"identity":"1198f714-3a5c-41a2-970b-4b34ed36bd66","added_by":"auto","created_at":"2025-06-25 02:27:29","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":386777,"visible":true,"origin":"","legend":"\u003cp\u003eAverage MAE Comparison of Learning Models with Proposed DIIAM Model\u003c/p\u003e","description":"","filename":"Picture4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6732837/v1/cfc6b598c3d6309705bd1625.jpg"},{"id":85349141,"identity":"b3f4a50a-825a-4d78-9bb7-f20fb03416ad","added_by":"auto","created_at":"2025-06-25 02:35:29","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":369110,"visible":true,"origin":"","legend":"\u003cp\u003eAverage MAPE Comparison of Learning Models with Proposed DIIAM Model\u003c/p\u003e","description":"","filename":"Picture5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6732837/v1/d290591af7e53056f01bc7ad.jpg"},{"id":85348682,"identity":"a66eca48-5ca4-43df-ab04-01610e58f460","added_by":"auto","created_at":"2025-06-25 02:27:29","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":369192,"visible":true,"origin":"","legend":"\u003cp\u003eAverage RMSE Comparison of Learning Models with Proposed DIIAM Model\u003c/p\u003e","description":"","filename":"Picture6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6732837/v1/e5a2277ab7e04e8b843c20ef.jpg"},{"id":85348690,"identity":"877ebf55-964b-417f-828a-d4eece3e8f80","added_by":"auto","created_at":"2025-06-25 02:27:29","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":381956,"visible":true,"origin":"","legend":"\u003cp\u003eAverage MaxPE Comparison of Learning Models with Proposed DIIAM Model\u003c/p\u003e","description":"","filename":"Picture7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6732837/v1/27e8bc6823f661b0d6cca6f8.jpg"},{"id":85348683,"identity":"bbca910e-3398-464b-bfaa-91513c485464","added_by":"auto","created_at":"2025-06-25 02:27:29","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":365503,"visible":true,"origin":"","legend":"\u003cp\u003eAverage ESD Comparison of Learning Models with Proposed DIIAM Model\u003c/p\u003e","description":"","filename":"Picture8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6732837/v1/3b078642b603ee23a94804a3.jpg"},{"id":85349861,"identity":"c8f9418d-5efd-4ec3-8254-4ef9ea52539a","added_by":"auto","created_at":"2025-06-25 02:43:29","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":348891,"visible":true,"origin":"","legend":"\u003cp\u003eAverage R2 Comparison of Learning Models with Proposed DIIAM Model\u003c/p\u003e","description":"","filename":"Picture9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6732837/v1/cacadf70ef7f4901030d1e58.jpg"},{"id":85348688,"identity":"f5317ccb-a749-48f7-9658-12c605ba381e","added_by":"auto","created_at":"2025-06-25 02:27:29","extension":"jpg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":219385,"visible":true,"origin":"","legend":"\u003cp\u003eComparative State-of-Art\u003c/p\u003e","description":"","filename":"Picture10.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6732837/v1/66083492c4826bea34c0816f.jpg"},{"id":86631752,"identity":"985cd0ed-2f0d-4184-9a24-535e7d5f6ecb","added_by":"auto","created_at":"2025-07-14 06:24:40","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4442393,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6732837/v1/6ba74658-a56c-443c-81c1-01fc7b6bbf28.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Dual-Input Multi-Layered Attention Model for Enhanced Path Loss Prediction","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eThe telecommunication industry is experiencing rapid growth due to rising use of mobile devices and the increasing demand for higher capacity in modern networks. It is projected that by the end of 2025, there will be over 20\u0026nbsp;billion connected devices [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. To address the challenges of rising demand and ca-pacity limitations, advancements in wireless technol-ogy have led to the establishment of new standards. Today, faster data services are required by users that definetely requires more bandwidth [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. With this need for more bandwidth is challenging mobile net-works and led to the development of 5th generation (5G) mobile technology for enhanced network capa-bilities [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. This 5G revolutionized the communica-tion system by providing 50 times higher data rates than current standards with reduced latency and energy costs [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. This advancement builds on the existing LTE systems and involves enhancing spec-tral efficiency and capacity [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. It also encourages the use of previously underutilized frequency bands to enhance efficiency of communication models [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. The move of LTE into unlicensed bands may disrupt Wi-Fi and other technologies. The success of 5G in densely populated areas centers on deploying small-cell technology to tackle its limited range and suscep-tibility to interference at mm. Wave frequencies. This challenge explored the importance of radio frequen-cy (RF) propagation analysis while optimizing 5G network performance and reliability[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. RF propaga-tion explores how radio waves interact with external factors that makes it essential for optimizing signal strength and reliability for 5G networks [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. RF mod-elling and planning optimize the 5G network for real-world deployments by balancing cost, coverage, and quality [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Optimizing the 5G spectrum involves using beamforming to focus signals and overcome obstructions. Beamforming and accurate propaga-tion models are key to mitigating path loss in 5G networks by focusing signals and predicting trans-mission behaviors [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Path loss in communical models will increases with the distance between transmitter and receiver. These are influenced by several factors like transmission power, antenna gains, frequency, etc. [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. To understand the rela-tionship between received power level and path loss, the concept of the path loss exponent factor (PLE) is introduced. The PLE helps to quantify the rate at which path loss increases with distance. However, this simple relationship is complicated by the multi-path effect, where signals take multiple paths to reach the receiver, leading to variations in the PLE value. The multipath effect necessitates adjustments to the path loss exponent rule, resulting in different PLE values that reflect the complex nature of real-world signal propagation. Path loss prediction has various models depending on frequency distance, various environmental specific parameters, applica-tion area such as rural, suburban, urban etc. Free space path loss (FSPL) models are presented in [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. In telecommunication, FSPL is attenua-tion of the radio energy between two antennas that communicate through free space without any obsta-cle. But as it is one of the basic models of path loss it has several disadvantages. In [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] it assumes a per-fect free-space environment without obstacles or reflections, which is rarely the case in real-world sce-narios. In [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] it ignores the impact of terrain, build-ings, and other obstacles on signal propagation and in [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] it has limited applicability in environments with high obstacles or complex structures. Another method such as log-distance path loss model [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] for path loss prediction for densely populat-ed areas considering distance as factor but it as-sumes a simplistic power-law relationship between distance and path loss, which may not capture the complexities of real-world propagation. Also, it re-quires a path loss exponent (n) that may not be uni-versally applicable across different environments and frequencies and it has limited accuracy in sce-narios with non-line-of-sight (NLOS) conditions. Hata-Okumura model [21] [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] for path loss pre-diction is another conventional radio propagation model for predicting the path loss for dense envi-ronment with frequency range of 150 to 1500 MHz. Empirical model that incorporates frequency, dis-tance, and various environment-specific parameters [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. It was developed based on extensive measurements in urban, suburban, and rural environments. The telecommunications sector has adopted a more flex-ible and data-driven approach by utilizing machine learning, ensuring optimal performance in a variety of changing propagation situations. Therefore, this paper presented the bimodal machine learning based path loss prediction models by combining the loca-tion specific information and the satellite image data.\u003c/p\u003e \u003cp\u003eThe key contributions of the paper are:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe methodology integrates environmental or channel features with visual satellite image data by utilizing advanced machine learning models to capture a more detailed and accurate repre-sentation of the factors influencing path loss.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe paper presents a dual-input (bimodal) sys-tem that processes both environmental/channel information and visual data simultaneously that will explore more diverse informations for robust path loss prediction model.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe paper presents a multi-layered model dual-input integrative attention model (DIIAM) that incorporating attention mechanisms into the model architecture for path loss prediction. By dynamically focusing on the most relevant fea-tures from both input streams, the model can improve its prediction accur acy and efficiency, making it a significant advancement for wireless communication.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe application of DIIAM across different learning models such SVR, RFR, BPNN, LSTM, BiLSTM, GRU for the learning layer demon-strates the versatility and adaptability of the ap-proach. This flexibility allows for extensive test-ing and optimization across various algorithms to identify the most effective solution for path loss prediction.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eRest of the paper is organized as: Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e de-scribes\u0026rsquo; mathematical description of path loss. Sec-tion 3 presents the role of machine learning ap-proaches for prediction of path loss. Section \u003cspan refid=\"Sec9\" class=\"InternalRef\"\u003e4\u003c/span\u003e pre-sents the proposed methodology for prediction of path loss. Section \u003cspan refid=\"Sec14\" class=\"InternalRef\"\u003e5\u003c/span\u003e presents the implementation de-tails and result analysis with comparative state-of-art. Finally, in section 6 conclusion and future scope is presented.\u003c/p\u003e"},{"header":"2 Mathematical Modelling of Path Loss","content":"\u003cp\u003ePath loss indicates the path gain increase and decrease in decibel as linear function. It is evaluated by using logarithmic distribution function around mean path loss [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e] [31]. Mathematically, it is represented as:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:PL\\left(dB\\right)=20\\:{log}_{10}\\frac{4\\pi\\:d}{\\lambda\\:}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, d is the distance between the transmitter and receiver and λ is the wavelength of the signal. This equation highlights that the received power level at the receiver is dependent on the path loss, indicat-ing the importance of understanding and managing path loss for effective communication. The received powe at distance d from transmitter is represented as:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{P}_{r}=\\:{P}_{t}{G}_{r}{G}_{r}\\:{\\left(\\frac{\\lambda\\:}{4\\pi\\:d}\\right)}^{2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe ratio of transmitting power to received power is represented as path loss:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:\\frac{{P}_{t}}{{P}_{r}}=\\:{\\frac{1}{{G}_{r}{G}_{r}\\:{\\left(\\frac{\\lambda\\:}{4\\pi\\:d}\\right)}^{2}}}_{.}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIf the antenna gains are assumed to be unity, then expression of path loss should be given by:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:PL\\left(dB\\right)=20\\:{log}_{10}\\frac{4\\pi\\:d}{\\lambda\\:}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the original form, path loss is given by:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:PL\\left(dB\\right)=10\\:{log}_{10}{\\left(\\frac{4\\pi\\:d}{\\lambda\\:}\\right)}^{2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ePath loss (PL) is determined by the square of the signal frequency and the distance between the transmitter and receiver. Higher path loss results in lower received power levels. The goal is to minimize path loss to enhance the power available at the re-ceiver. The path loss equation, when expressed in decibels (dB), quantifies this relationship and helps in optimizing communication system performance as:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{P}_{r}\\left(dB\\right)={P}_{t}\\left(dB\\right)+\\:{G}_{t}\\left(dB\\right)+\\:{G}_{r}\\left(dB\\right)-\\:20\\:{log}_{10}\\frac{4\\pi\\:d}{\\lambda\\:}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:{P}_{r}\\left(dB\\right)={P}_{t}\\left(dB\\right)+\\:{G}_{t}\\left(dB\\right)+\\:{G}_{r}\\left(dB\\right)-PL\\:\\left(dB\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThus,\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\:PL\\:\\left(dB\\right)=\\:{P}_{t}\\left(dB\\right)+\\:{G}_{t}\\left(dB\\right)+\\:{G}_{r}\\left(dB\\right)\\--\\:{P}_{r}\\left(dB\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eFrom Eq.\u0026nbsp;(\u003cspan refid=\"Equ7\" class=\"InternalRef\"\u003e7\u003c/span\u003e), it can be inferred that increasing transmission power or using high gain antennas can reduce path loss in communications, which is rele-vant for line-of-sight or near line-of-sight systems like microwave and satellite communications. However, technologies such as commercial AM radio broad-casting and WLAN communications do not neces-sarily require line-of-sight to function effectively.\u003c/p\u003e"},{"header":"3. Machine Learning Modelling for Path Loss","content":"\u003cp\u003eMachine learning offers a promising approach to predict path loss in wireless communications by overcoming limitations of traditional empirical and deterministic models [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. These models are essential for network planning, affecting coverage, frequency allocation, and interference prediction. Machine learning techniques, such as neural networks [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], support vector regression [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e], and random forest [31], etc. provide more accurate and computational-ly efficient predictions. This advancement makes machine learning a viable alternative for enhancing network planning and optimization by accurately forecasting path loss [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. Below Table \u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents the recent research contributions for path loss prediction using machine learning [33] [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e34\u003c/span\u003e].\u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 ANN based path loss predictionPaper\u003c/h2\u003e \u003cp\u003e[\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] demonstrated that multilayer per-ceptron (MLP) neural networks in artificial neural networks (ANNs) provide high-accuracy path loss (PL) predictions, outperforming conventional models. Emphasized the agreement of ma-chine-learning-based models (ANN, SVR, RF) with measured data, introducing data expansion schemes to enhance training data use. [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e35\u003c/span\u003e] as-sessed machine learning methods for rural path loss prediction, highlighting the effectiveness of a three-layered ANN with 51 neurons. [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e37\u003c/span\u003e] investigated neural network parameters for VHF band path loss prediction, showing ANN models' su-perior accuracy and generalization over empirical models. Artificial Neural Networks (ANNs) are effec-tively utilized for solving nonlinear regression prob-lems. ANNs is designed by concatenating input layer, one or more hidden layers, and an output layer. All layers are composed of neurons that are connected to neurons of subsequent layer with varying weights. This architecture is referred as multi-layer perceptron. These networks are preferred algorithm for learning from complex data patterns or behaviors such as path loss in wireless communications. The presence of number of hidden layers influence the efficacy of ANN. But sometimes, the complex ANN architecture results in overfitting.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 SVR based path loss prediction\u003c/h2\u003e \u003cp\u003e[\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] proposed support vector regres-sion (SVR) for path loss prediction for urban envi-ronemnt. SVR presented similar outcome as MLP based ANN but it has lower computational complexi-ty. SVR is a supervised learning technique that can be applied for classification and regression applica-tions. Path loss model is a type of regression task therefore SVR can be applied here. It operates by devising a hyperplane, or multiple hyperplanes in expansive-dimensional spaces, which can classify or predict data points. The primary objective of SVM is to determine the ideal hyperplane that establishes the largest gap between distinct categories, ensuring im-proved adaptability and resilience. To do this, SVM elevates input data into a more comprehensive fea-ture domain and seeks the most suitable separating plane. Through kernel functions, this elevation is accomplished, with linear, polynomial, and radial basis functions (RBF) being the most prevalent. SVMs excel in managing data with numerous dimen-sions and can adapt to non-linear decision bounda-ries by harnessing kernel functions. Mathematical Description of SVM are:\u003c/p\u003e \u003cp\u003eHyperplane: Defined by the W^T x\u0026thinsp;+\u0026thinsp;b\u0026thinsp;=\u0026thinsp;0, where w is the weight vector and b is the bias.\u003c/p\u003e \u003cp\u003eSupport Vectors: Data points that are closest to the hyperplane and influence its position and orientation.\u003c/p\u003e \u003cp\u003eMargin: The distance between the nearest points (support vectors) of separate classes to the hyper-plane. The margin is given by 2/(||w||).\u003c/p\u003e \u003cp\u003eThe solution to the optimal hyperplane is a con-strained optimization problem, which can be written as:\u003c/p\u003e \u003cp\u003eMinimize\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$\\:Minimize\\:\\frac{1}{2}{\\left|\\left|W\\right|\\right|}^{2}+C{\\sum\\:}_{i=1}^{n}{\\xi\\:}_{i}subject\\:to\\:{y}_{i}\\left({W}^{T}x+b\\ge\\:1\\right)-\\:{\\xi\\:}_{i}\\:and\\:{\\xi\\:}_{i}\\ge\\:0.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere,ξi are slack variables. C is a regularization parameter controlling the trade-off between maxim-izing the margin and minimizing the error.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Random Forest based path loss prediction\u003c/h2\u003e \u003cp\u003e[36] explored clustering and regres-sion algorithms (random forest, AdaBoost, K-nearest neighbors) for path loss prediction, comparing them against other regression techniques through extensive simulation and tenfold cross-validation. [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e] introduced an environment features-based model (EFBM) using Random Forest for direct path loss prediction, reducing RMSE significantly at 6 and 28 GHz. Random Forest, an ensemble technique, aggregates multiple decision trees to deduce predic-tions. Suitable for classification and regression, it formulates predictions by amalgamating the individ-ual tree outcomes. Each tree in this ensemble learns from distinct data portions, and while determining splits, a random feature subset is chosen. Key strengths of Random Forests include their resilience against data irregularities, competence in high-dimensional datasets, and capability to rank feature significance. The Random Forest algorithm has key hyperparameters to set, including node size, the number of trees, and the number of features sam-pled. Random Forest is composed of decision trees, each built on a bootstrap sample from the training data. It introduces randomness through feature bag-ging to reduce tree correlation. For regression, the trees are averaged. For path loss prediction using decision trees, the predicted value for new samples is obtained by averaging the predictions from all indi-vidual decision trees. Mathematically, the output decision is evaluated as y\u0026thinsp;=\u0026thinsp;1/T \u0026sum;_(t\u0026thinsp;=\u0026thinsp;1)^T▒〖h ̂_t (x)〗. Here, total number of trees used as learning is represented as T and its respective predicted out-come is represented as h ̂_t (x). This method aggre-gates the outcomes of various decision trees to im-prove prediction accuracy.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.4 RNN based path loss prediction\u003c/h2\u003e \u003cp\u003e[40] proposed a RNN-LSTM model for path loss prediction. [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e] also used RNN based path loss model for urban environ-ment model. Recurrent Neural Network (RNN) is also a type of machine learning that learns patterns from temporal data and predict the temporal dependent outcomes. In path loss predictive models RNN pro-vides high data rate with low latency and improved reliability. The path loss data contains informations such as obstacles, terrain types, weather conditions, and other environmental factors that makes the learning process difficult [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e49\u003c/span\u003e]. But the architecture of RNN to utilize the output from the previous state as input to the current state makes it an efficient learner. Therefore, RNN models can be efficiently chosen over traditional ANNs. But conventional RNN face issues while handling long sequences. This lead to development of more efficient RNN models such as Long Short-Term Memory (LSTM) and Gated Re-current Unit (GRU) to address these challenges. Un-like traditional ANN, RNN relies on feed-forward connections, LSTM, or GRU incorporate an internal state or memory that allows them to consider both the current input and information from previous in-puts. This feature makes RNNs particularly suitable for analyzing time-dependent data. The text high-lights the adaptability of RNNs to handle variable-length sequences of inputs thanks to their dynamic behavior and memory capabilities.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Deep Learning based path loss prediction\u003c/h2\u003e \u003cp\u003e[31] compared state-of-the-art sto-chastic and ray-tracing models, finding that satellite images and model-aided techniques can improve path loss predictions by approximately 0.8 dB and 1 dB, respectively. A deep learning (DL) model showed improvements of about 1 dB at 811 MHz and 4.7 dB at 2630 MHz. T. T. [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e44\u003c/span\u003e] presented a model-aided deep learning technique for 7 GHz path loss prediction in urban environments, showing supe-rior performance to empirical models. [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e] proposed a deep learning-based path loss prediction considering obstacles and weather in V2V commune-cation, achieving accurate predictions. Improved modality fusion results through transfer learning and image augmentation, achieving lower mean absolute error (MAE) values. Convolu-tional Neural Networks (CNNs) are a type of deep neural network that was initially used in computer vision tasks. Recently, CNNs have expanded their application to other domains, including human-computer interfaces, due to their ability to detect feature localities. CNNs are distinguished from feed-forward networks by their capability to extract and process features from both 2-dimensional and 3-dimensional data, which is organized into matrices for processing. The more advanced and powerful type of CNN models are transfer learning. Transfer learning leverages a model developed for one task as a foundation for a model on a second task, signifi-cantly benefiting deep learning by utilizing pre-trained models to save on computational resources and time. This approach offers two main ad-vantages: enhanced learning speed and performance due to the transfer of learned features, and a reduced need for large datasets, making it especially valuable when data availability is limited. By employing pre-trained models familiar with complex image features, transfer learning improves accuracy and detection capabilities, which are vital for diagnosing medical conditions with limited specific data. Therefore, this paper have adopted the transfer learning for design-ing a bimodal methodology for path loss.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRecent Research Contribution for path loss prediction using machine learning\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRef\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYear\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eModularity\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFrequency (in MHz)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eEnvironment type\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eTechnique Used\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[31]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBimodal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e811/2630\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eUniversity Campus\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e~\u0026thinsp;4dB\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUnimodal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eUrban/Suburban/Rural\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eANN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e~\u0026thinsp;4-6dB\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e34\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUnimodal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2021.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eUrban\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSVR, RF, ANN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e~\u0026thinsp;4dB\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e35\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUnimodal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3700\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRural\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSVR, RF, k-NN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e~\u0026thinsp;4dB\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[36]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUnimodal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eUrban\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSVR, RF, k-NN, ANN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e~\u0026thinsp;6-6.5dB\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e37\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUnimodal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e189.25/479.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eUrban\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eANN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e~\u0026thinsp;2-21dB\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e38\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUnimodal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eUrban\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSVR, RF, k-NN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e~\u0026thinsp;2-4dB\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBimodal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e900\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eUrban\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e~\u0026thinsp;4dB\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[40]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUnimodal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eUrban\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eWavelet-GA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e~\u0026thinsp;2-4dB\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUnimodal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6000\u0026ndash;28000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eUrban\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eRF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e~\u0026thinsp;0.33\u0026ndash;0.89 dB\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2023\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUnimodal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e60000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eUrban\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e~\u0026thinsp;1-4dB\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[43]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2023\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUnimodal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eUrban\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e~\u0026thinsp;4dB\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e44\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUnimodal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eEnsemble NN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e~\u0026thinsp;2-5dB\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4 Methodology Used","content":"\u003cp\u003eIn this paper, a multi-level and bimodal approach is presented for path loss prediction. The paper introduces a network termed as Dual-Input Integrative Attention Model (DIIAM) for path loss detection based on image and environmental or channel parameters. The model is termed as Dual-input because it is processing image features and environmental features together with attention layer to generate weighted features. DIIAM integrates channel features using machine learning models and visual features from pre-trained CNN architectures like ResNet50. By merging these features and using attention mechanisms, DIIAM can dynamically focus on crucial data points, offering a comprehensive solution for identifying path loss. This model architecture is presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e for path loss prediction involves a multi-layered approach that integrates both environmental or channel features with visual satellite image data. Each layer of the model are described below sub-sections. The algorithm of the proposed methodology is presented below in algorithm 1.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e \u003ccolgroup cols=\"1\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAlgorithm 1: Dual-Input Integrative Attention Model (DIIAM)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInput: Environmental or channel informations \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{EI}_{i}\\:\\)\u003c/span\u003e\u003c/span\u003eand satellite images \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{VI}_{i}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003eOutput: Path loss \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Pl\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003eBegin\u003c/p\u003e \u003cp\u003ePass \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{EI}_{i}\\:and\\:{VI}_{i}\\)\u003c/span\u003e\u003c/span\u003e to DIFEL\u003c/p\u003e \u003cp\u003eExtract Environemental Feature Vector \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{F}_{{EI}_{p}}=\\text{D}\\text{N}\\left[\\text{D}\\text{I}\\left\\{{\\text{E}\\text{I}}_{i}\\right\\}\\right]\\)\u003c/span\u003e\u003c/span\u003e {eq.\u0026nbsp;(\u003cspan refid=\"Equ12\" class=\"InternalRef\"\u003e12\u003c/span\u003e)}\u003c/p\u003e \u003cp\u003eSelect Relevant Features \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{F}_{{EI}_{p}}=\\{{T}_{test}\\left({F}_{{EI}_{p}}\\right)\\oplus\\:{Z}_{test}\\left({F}_{{EI}_{p}}\\right)\\}\\)\u003c/span\u003e\u003c/span\u003e {eq.\u0026nbsp;(\u003cspan refid=\"Equ13\" class=\"InternalRef\"\u003e13\u003c/span\u003e)}\u003c/p\u003e \u003cp\u003eExtract visual Feature Vector \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{F}_{{VI}_{p}}=\\text{R}\\text{e}\\text{s}\\text{N}\\text{e}\\text{t}50\\left[{\\text{V}\\text{I}}_{i}\\right]\\)\u003c/span\u003e\u003c/span\u003e {eq.\u0026nbsp;(14)}\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{F}_{DI}=concat\\{{F}_{{EI}_{p}},{F}_{{VI}_{p}}\\}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:FWAL\\underset{{F}_{DI}}{\\leftarrow\\:}DIFEL\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003eExtract attention weight \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{a}}_{i}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003eEvaluate weighted feature vector \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{F}_{DI}}_{w}\\)\u003c/span\u003e\u003c/span\u003e {eq.\u0026nbsp;(\u003cspan refid=\"Equ17\" class=\"InternalRef\"\u003e18\u003c/span\u003e)}\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:LL\\underset{{{F}_{DI}}_{w}}{\\leftarrow\\:}FWAL\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003eFor \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:m=1\\:to\\:max\\_iter\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Model=build\\_model\\left(x\\right)\\)\u003c/span\u003e\u003c/span\u003e {Where, x can be SVR, RFR, etc.}\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Traine{d}_{model\\underset{\\text{m}\\text{i}\\text{n}\\left(loss\\right)}{\\leftarrow\\:}}Train(x,m,{{F}_{DI}}_{w})\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003eEnd for\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Pl\\leftarrow\\:Predict({Trained}_{model},{{F}_{DI}}_{w})\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003eEnd\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Input Layer\u003c/h2\u003e \u003cp\u003eThis is the first layer dual input are taken, one is environmental or channel informations and other as visual informations. The environmental or channel informations is represented as EI={e_1,e_2,\u0026hellip;.e_n}. The visual information comprises satellite images that provide a visual representation of the terrain and surrounding environment and represented as VI={v_1,v_2,\u0026hellip;.v_n }.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Dual-Input Feature Extraction Layer (DIFEL)\u003c/h2\u003e \u003cp\u003eIt is mentioned that the input is bimodal or dual input in nature as F={EI,VI}. In this step, environmental or channel informations EI as well as visual information VI features are extracted. The EI feature matrix is generated by following steps:\u003c/p\u003e \u003cp\u003eData Imputation (DI): Depending on the context and significance of missing data, data imputation is applied to handle missing data. Imputation is a method used to handle missing values in a dataset by replacing them with substitute values, thereby allowing for more complete analysis without discarding data. For data imputation, K-Nearest Neighbors (KNN) is used. Missing values are imputed using the values of the k most similar instances (neighbors), based on other, non-missing attributes. The similarity between instances is usually measured using a distance metric such as Euclidean distance. The imputed value is the mean (for numerical variables) or mode (for categorical variables) of the k nearest neighbors.\u003c/p\u003e \u003cp\u003eData Normalization (DN): Scaling numerical features to a specific range, typically between 0 and 1, helps with model convergence and interpretation. For this z-score normalization is adopted stated as:\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$$\\:{Data}_{i}=\\frac{{x}_{i}-\\stackrel{-}{x}}{std}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, xi\u0026thinsp;=\u0026thinsp;The data value at instance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\stackrel{-}{x}\\)\u003c/span\u003e\u003c/span\u003e= mean value\u003cdiv id=\"Equ10\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ10\" name=\"EquationSource\"\u003e\n$$\\:\\stackrel{-}{x}=\\frac{1}{n}\\sum\\:_{i=1}^{n}{x}_{i}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003estd\u0026thinsp;=\u003c/em\u003e\u0026thinsp;standard deviation\u003cdiv id=\"Equ11\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ11\" name=\"EquationSource\"\u003e\n$$\\:std=\\sqrt{\\frac{1}{n}\\sum\\:_{i=1}^{n}({x}_{i}-\\stackrel{-}{x}})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThen, relevant features are selected by applying combine T-Test and Z-Test statistical tests. Those features who shows high T-Test and Z-Test values are considered further and others are neglected.\u003c/p\u003e \u003cp\u003eThen final pre-processed feature matrix\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:{F}_{{EI}_{p}}\\)\u003c/span\u003e\u003c/span\u003e is generated as:\u003cdiv id=\"Equ12\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ12\" name=\"EquationSource\"\u003e\n$$\\:{F}_{{EI}_{p}}=DN\\left[DI\\left\\{{EI}_{i}\\right\\}\\right]\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:where\\:\\{i=\\text{1,2},\\dots\\:n\\}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e12\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ13\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ13\" name=\"EquationSource\"\u003e\n$$\\:{F}_{{EI}_{p}}=\\{{T}_{test}\\left({F}_{{EI}_{p}}\\right)\\oplus\\:{Z}_{test}\\left({F}_{{EI}_{p}}\\right)\\}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e13\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eFor, visual feature extraction pre-trained Resnet50 model is used because it captures more distinct and characteristic visual features. For example, a given image \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:I\\)\u003c/span\u003e\u003c/span\u003e, pre-trained learning model are used to derive feature maps from second-to-last pooling layer and reporesented as:\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:{F}_{{VI}_{p}}=ResNet50\\left[{VI}_{i}\\right]\\left(14\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe core component of the ResNet50 is convolution layer and each convolution layer perform convolution operation over \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{V}\\text{I}}_{i}\\:\\)\u003c/span\u003e\u003c/span\u003eas:\u003cdiv id=\"Equ14\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ14\" name=\"EquationSource\"\u003e\n$$\\:{F}_{{VI}_{p}}(i,j)=\\left(g*h\\right)(i,j)\\sum\\:_{p}\\sum\\:_{q}g\\left(p,q\\right)*h(i-p)(j-q)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e15\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{F}_{{VI}_{p}}(\\text{i},\\text{j})\\)\u003c/span\u003e\u003c/span\u003e is the output visual feature map, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:g\\)\u003c/span\u003e\u003c/span\u003e represents the input image or feature map from previous layer of model. The kernal filter is represented as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:h\\)\u003c/span\u003e\u003c/span\u003e with convolution operation \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{*}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Feature Weighted Attention Layer (FWAL)\u003c/h2\u003e \u003cp\u003eTo combine the environmental features \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{F}_{{EI}_{p}}\\:\\)\u003c/span\u003e\u003c/span\u003eand visual features \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{F}_{{VI}_{p}}\\)\u003c/span\u003e\u003c/span\u003e effectively, it is require to combine these features together. Mathematically, dual-input feature \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{F}_{DI}\\)\u003c/span\u003e\u003c/span\u003e is presented as:\u003cdiv id=\"Equ15\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ15\" name=\"EquationSource\"\u003e\n$$\\:{F}_{DI}=\\left(\\begin{array}{cc}{F}_{{EI}_{p}}\u0026amp;\\:{F}_{{VI}_{p}}\\end{array}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e16\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe more detailed visual description for generation of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{F}_{DI}\\)\u003c/span\u003e\u003c/span\u003e to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{F}_{DI}}_{w}\\)\u003c/span\u003e\u003c/span\u003e is represented in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThen \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{F}_{DI}\\)\u003c/span\u003e\u003c/span\u003e is passed to attention layer to generate a weighted feature vector for efficient learning. For this attention mechanism is used. Machine learning are often seen as \u0026ldquo;black boxes\u0026rdquo; because it is difficult to understand their internal workings. The attention mechanism improves its interpretability by allowing the learning process to focus on specific parts of an input, like certain pixels in images or specific feature in input. This method assigns \u0026ldquo;attention weights\u0026rdquo; to elements, indicating their importance for a given task. The attention feature vector is passed through a linear layer to produce a vector \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\widehat{m}\\)\u003c/span\u003e\u003c/span\u003e. This operation is typically a linear transformation represented as: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\widehat{m}={W}_{m}\\bullet\\:{F}_{DI}+{b}_{m}\\)\u003c/span\u003e\u003c/span\u003e. Where, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{W}_{m}\\)\u003c/span\u003e\u003c/span\u003e is the weight matrix of the linear layer, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{b}_{m}\\)\u003c/span\u003e\u003c/span\u003e​ is the bias. The importance of each feature row \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:F{R}_{i}\\)\u003c/span\u003e\u003c/span\u003e​ in the feature matrix \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{F}_{DI}\\)\u003c/span\u003e\u003c/span\u003e is determined by computing the attention weights \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{a}}_{i}\\)\u003c/span\u003e\u003c/span\u003e​. This is done by measuring the similarity between \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\widehat{m}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{F}_{DI}\\)\u003c/span\u003e\u003c/span\u003e​, typically using a dot product, and applying a softmax or a sigmoid function to normalize the weights. The mathematical expression for calculating each attention weight \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{a}}_{i}\\)\u003c/span\u003e\u003c/span\u003e​ is given by:\u003cdiv id=\"Equ16\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ16\" name=\"EquationSource\"\u003e\n$$\\:{\\widehat{a}}_{i}=\\frac{1}{1+exp(F{R}_{i}\\bullet\\:\\widehat{m})}\\:$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e17\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe output \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{F}_{DI}}_{w}\\:\\)\u003c/span\u003e\u003c/span\u003eof the attention layer is a weighted sum of the rows in the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{F}_{DI}\\:\\)\u003c/span\u003e\u003c/span\u003efeature matrix, with the weights being the attention scores \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{a}}_{i}\\)\u003c/span\u003e\u003c/span\u003e​. Mathematically it is represented as:\u003cdiv id=\"Equ17\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ17\" name=\"EquationSource\"\u003e\n$$\\:{{F}_{DI}}_{w}=\\sum\\:({\\widehat{a}}_{i}\\times\\:F{R}_{i})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e18\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{F}_{DI}}_{w}\\)\u003c/span\u003e\u003c/span\u003e is the output weighted feature matrix.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Learning Layer\u003c/h2\u003e \u003cp\u003eFor learning, the weighted feature vector\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{F}_{DI}}_{w}\\)\u003c/span\u003e\u003c/span\u003e is taken as input and passed to six different learning models, i.e., SVR, RFR, BPNN, LSTM, BiLSTM, and GRU. These models are described in detail in previous section.\u003c/p\u003e \u003c/div\u003e"},{"header":"5 Results and Discussion","content":"\u003cp\u003eIn this section, results are presented for implementation of proposed methodology for path loss prediction. The entire model is simulated on python platform over google colab with facility of Tesla P100-PCIE GPU. After the training, the testing performance of the proposed model is evaluated. Subsection \u003cspan refid=\"Sec15\" class=\"InternalRef\"\u003e5.1\u003c/span\u003e presents the description about dataset. Parameters are described in sub-section \u003cspan refid=\"Sec16\" class=\"InternalRef\"\u003e5.2\u003c/span\u003e. The result analysis of the proposed model is presented in subsection \u003cspan refid=\"Sec17\" class=\"InternalRef\"\u003e5.3\u003c/span\u003e and comparative analysis is presented in sub-section \u003cspan refid=\"Sec18\" class=\"InternalRef\"\u003e5.4\u003c/span\u003e.\u003c/p\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e5.1 Datasets Used\u003c/h2\u003e \u003cp\u003eIn this paper the performance is evaluated on four datasets, as described in Table \u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eStatistical Analysis for Dataset D1\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDataset\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModularity\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDescription\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFeatures\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNo. of Samples\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDataset-1 (D1) [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUnimodal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eThis dataset has been generated using NYUSIM 3.0 mm-Wave channel simulator software with environmental factors.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eT-R Separation Distance (m), Time Delay (ns), Received Power (dBm), Phase (rad), Azimuth AoD (degree), Elevation AoD (degree), Azimuth AoA (degree), Elevation, AoA (degree), RMS Delay Spread (ns), Season, Frequency and Path Loss (dB)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2835\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDataset-2 (D2) [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUnimodal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eThis dataset was created for smart campus environment from drive tests along three routes within Covenant University, Nigeria. Environmental details were obtained from a Digital Terrain Map to support the modeling, focusing on an 1800 MHz frequency band.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLongitude, Latitude, Elevation (m), Altitude (m), Clutter height (m), Distance (m), Path Loss (dB)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e937\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDataset-3 (D3) [47]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUnimodal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eThis dataset is composed of geolocation information as well as satellite images for path loss prediction on 2630 MHz frequency band.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLocal coordinates\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e60000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDataset-4 (D4) [47]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBimodal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLocal coordinates, Satellite images\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Parameters Used\u003c/h2\u003e \u003cp\u003eMean Squared Error (MSE): It is evaluated by measuring the averaged square of the error between actual (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{A}_{i}\\)\u003c/span\u003e\u003c/span\u003e) and predicted (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{P}_{i})\\)\u003c/span\u003e\u003c/span\u003e value.\u003cdiv id=\"Equ18\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ18\" name=\"EquationSource\"\u003e\n$$\\:MSE=\\frac{\\sum\\:_{i=1}^{n}{({P}_{i}-{A}_{i})}^{2}}{n}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e19\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eMean Absolute Error (MAE): It is used to represent the error between actual (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{A}_{i}\\)\u003c/span\u003e\u003c/span\u003e) and predicted (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{P}_{i})\\)\u003c/span\u003e\u003c/span\u003e value.\u003cdiv id=\"Equ19\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ19\" name=\"EquationSource\"\u003e\n$$\\:MAE=\\frac{\\sum\\:_{i=1}^{n}|{P}_{i}-{A}_{i}|}{n}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e20\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, n\u0026thinsp;=\u0026thinsp;Number of tested samples.\u003c/p\u003e \u003cp\u003eRoot Mean Square Error (RMSE): It measures the square root of the average squared differences between the predicted path loss and the actual measured path loss.\u003cdiv id=\"Equ20\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ20\" name=\"EquationSource\"\u003e\n$$\\:RMSE\\:=\\:\\sqrt{MSE}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e21\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eMean Absolute Percentage Error (MAPE): It is used to evaluate the average absolute percentage errors between the predicted and actual values.\u003cdiv id=\"Equ21\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ21\" name=\"EquationSource\"\u003e\n$$\\:MAPE=\\frac{100}{n}\\sum\\:_{i=1}^{n}\\frac{|{P}_{i}-{A}_{i}|}{{A}_{i}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e22\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eMaximum Prediction Error (MaxPE): It identifies the maximum absolute difference between the predicted and actual path loss values.\u003cdiv id=\"Equ22\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ22\" name=\"EquationSource\"\u003e\n$$\\:MaxPE={max}|{P}_{i}-{A}_{i}|$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e23\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eError Sum of Squares (ESD): It calculates the sum of the squared differences between the predicted and actual values.\u003cdiv id=\"Equ23\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ23\" name=\"EquationSource\"\u003e\n$$\\:ESD=\\sum\\:_{i=1}^{n}{({A}_{i}-{P}_{i})}^{2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e24\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eR-Squared (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}^{2}\\)\u003c/span\u003e\u003c/span\u003e): It is used to evaluate the variation of dependant variables with independent variables.\u003cdiv id=\"Equ24\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ24\" name=\"EquationSource\"\u003e\n$$\\:{R}^{2}=1-\\frac{{UE}_{variation}}{{T}_{variation}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e25\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{UE}_{variation}\\)\u003c/span\u003e\u003c/span\u003e = Unexplained variation and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{T}_{variation}\\)\u003c/span\u003e\u003c/span\u003e= Total variation.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e5.3 Statistical Analysis of Unimodal System\u003c/h2\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eStatistical Analysis for Dataset D1\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFeatures\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eT-Test\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eZ-Test\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eP-Value\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSimulation Run Number\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.123\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4.343\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.40E-05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT-R Separation Distance (m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20.514\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20.644\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTime Delay (ns)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e19.598\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e19.615\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eReceived Power (dBm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-30.537\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-30.525\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePhase (rad)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-1.898\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-1.898\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.77E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAzimuth AoD (degree)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4.009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.10E-05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eElevation AoD (degree)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-1.185\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-1.184\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.36E-01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAzimuth AoA (degree)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.994\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4.995\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.89E-07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eElevation AoA (degree)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-2.744\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-2.744\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.08E-03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRMS Delay Spread (ns)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5.371\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.373\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7.76E-08\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSeason\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.861\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.848\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.97E-01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFrequency\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20.408\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e22.906\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e presents the result of T-Test, Z-Test and P-Value for each feature of D1 dataset. The T-Test, Z-Test are evaluated as in Eq.\u0026nbsp;(\u003cspan refid=\"Equ25\" class=\"InternalRef\"\u003e26\u003c/span\u003e) and Eq.\u0026nbsp;(\u003cspan refid=\"Equ26\" class=\"InternalRef\"\u003e27\u003c/span\u003e) respectively:\u003cdiv id=\"Equ25\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ25\" name=\"EquationSource\"\u003e\n$$\\:T-Test=\\frac{\\sum\\:{x}_{1}-{x}_{2}}{\\sigma\\:\\sqrt{1/n}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e26\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ26\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ26\" name=\"EquationSource\"\u003e\n$$\\:Z-Test=\\frac{{\\stackrel{-}{x}}_{1}-{\\stackrel{-}{x}}_{2}}{\\sqrt{\\frac{{{\\sigma\\:}_{1}}^{2}}{{n}_{1}}+\\frac{{{\\sigma\\:}_{2}}^{2}}{{n}_{2}}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e27\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\stackrel{-}{x}}_{1}and\\:{\\stackrel{-}{x}}_{2}\\)\u003c/span\u003e\u003c/span\u003e are mean of two features, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\sigma\\:}_{1}and\\:{\\sigma\\:}_{2}\\:\\)\u003c/span\u003e\u003c/span\u003eare represents the standard deviations and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{n}_{1}and\\:{n}_{2}\\)\u003c/span\u003e\u003c/span\u003e are sample size of respective features. The p-value depends on the specific test being conducted (T-test or Z-test). The p-value represents the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed, assuming the null hypothesis is true. These metrics are fundamental in statistical hypothesis testing and are significant for determining the relevance and significance of features for further machine learning analysis. A higher absolute value of T-Test or Z-Test indicates a more significant difference. The P-Value quantifies the probability of observing the given results. A low P-Value (\u0026lt;\u0026thinsp;0.05) suggests rejecting the null hypothesis and that the feature is statistically significant. In D1, features such as Simulation Run Number, T-R Separation Distance (m), Time Delay (ns), Received Power (dBm), Azimuth AoD (degree), Azimuth AoA (degree), RMS Delay Spread (ns), and Frequency have very low P-Values indicating that they are statistically significant with both T-Test and Z-Test. They are highly relevant for further analysis in machine learning models. Phase (rad), Elevation AoD (degree), and Season features show higher P-Values therefore they are not statistically significant. Features with significant T-Test and Z-Test and low P-Values are strong candidates for inclusion in machine learning models. They have shown a significant effect, suggesting a strong relationship with the outcome variable.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eStatistical Analysis for Dataset D2\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFeatures\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eT-Test\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eZ-Test\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eP-Value\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLongitude\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e25.789\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e25.801\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLatitude\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e25.789\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e25.801\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eElevation (m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e19.418\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e21.365\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAltitude (m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e17.589\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e21.029\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eClutter height (m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-10.143\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-7.214\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDistance (m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e25.789\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e25.801\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFor D2 dataset, Table \u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e presents the statistical T-test, Z-Test, and P-value metrices for each feature. These metrics are essential for evaluating the statistical significance of each feature and its potential relevance for machine learning models. Longitude, Latitude, Elevation (m), Altitude (m), and Distance (m) features show very high absolute values for both T-Test and Z-Test indicating extremely strong statistical significance. The high T and Z values suggest these features have a strong effect size. For Clutter Height (m), the T-Test and Z-Test are negative, indicating a negative effect size. But the P-Value is still extremely low that makes this feature statistically significant. The negative values indicate that as the clutter height increases, the dependent variable might decrease (or vice versa), but further domain-specific analysis is needed to interpret this relationship properly. Therefore, Longitude, Latitude, Elevation (m), Altitude (m), and Distance (m) are evidently significant predictors due to their statistical metrics. These features are likely to have a strong relationship with the outcome variable and should be considered for any predictive modelling efforts.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eStatistical Analysis for Dataset D3\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFeatures\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eT-Test\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eZ-Test\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eP-Value\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLongitude\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-66.096\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-66.094\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLatitude\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20.638\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20.639\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpeed (m/s)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e35.2360\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e35.238\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDistance (m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e227.400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e227.400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDistance_x (m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20.638\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20.639\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDistance_y (m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-66.096\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-66.094\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePCI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24.766\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e24.740\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFor the D3 dataset, Table \u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e presents the statistical analysis employing T-test, Z-test, and P-value metrics for each feature. The features Longitude, Latitude, Speed (m/s), Distance (m), Distance_x (m), Distance_y (m), and PCI show very high absolute values for both the T-test and Z-test, indicating an extremely strong statistical significance. The P-value for all features is 0 which means all features are highly significant.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e5.4 Unimodal Performance Evaluation\u003c/h2\u003e \u003cp\u003eThe results presented in Table \u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e for dataset D1 for proposed DIIAM model with six different learning models. Support Vector Regression (SVR) shows moderate performance with a relatively high MSE and RMSE. Random Forest Regressor (RFR) exhibits the best performance across almost all metrics. It has the lowest MSE, MAE, MAPE, MaxPE, and RMSE, alongside the highest R\u0026sup2; value. This indicates that RFR is both accurate and reliable. Backpropagation Neural Network (BPNN) shows good performance with lower errors compared to SVR, LSTM, BILSTM, and GRU but not as low as RFR. Its R\u0026sup2; value is also high. LSTM has higher errors in terms of MSE, MAE, RMSE as compared to RFR and BPNN but its R\u0026sup2; value is good but not more than RFR and BPNN. Bidirectional LSTM (BiLSTM) shows similar performance as LSTM. Gated Recurrent Unit (GRU) shows better performance than both LSTM and BILSTM in terms of errors but not more than RFR. Therefore, it can be concluded that the RFR is most effective model for this dataset.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePerformance Evaluation on Dataset D1\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModels\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMAPE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMaxPE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eESD\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSVR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e58.151\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.319\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.410\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e41.310\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e49486.824\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e7.626\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.746\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRFR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24.763\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3.413\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.108\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e14.515\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e21073.695\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4.976\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.892\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBPNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e44.336\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.155\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.172\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e18.523\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e37729.867\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e6.659\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.807\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e56.784\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.826\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.610\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e21.708\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e48323.270\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e7.536\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.752\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBILSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e57.519\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.788\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.583\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e21.802\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e48948.427\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e7.584\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.749\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGRU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e50.757\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.331\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.297\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e19.483\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e43194.097\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e7.124\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.779\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e presents the performance of propose DIIAM model on dataset D2. SVR shows high values in MSE, MAE, and RMSE. However, its R\u003csup\u003e2\u003c/sup\u003e value of 0.872. RFR present excellent performance across all metrics. This indicates very accurate predictions with minimal error and high reliability in capturing the variance in the data. BPNN has significantly worse performance compared to other models as it shows highest values in MSE, MAE, MAPE, and RMSE, and a negative R\u003csup\u003e2\u003c/sup\u003e value. LSTM networks show good performance with moderate errors and a high R\u003csup\u003e2\u003c/sup\u003e value of 0.970. BILSTM shows the best performance with D2. Gated Recurrent Unit (GRU) also performs well with low error metrics and a high R\u003csup\u003e2\u003c/sup\u003e of 0.991. Therefore, for dataset D2, BILSTM and RFR models outperform the others in terms of predictive accuracy and reliability. The RFR shows better performance in path loss prediction due to its robust ensemble learning method that effectively reduces overfitting and improves prediction accuracy by combining multiple decision trees. The BiLSTM model outperforms others because of its ability to understand and process temporal dependencies in both forward and backward directions. This makes it highly effective for capturing complex patterns in time-series data.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePerformance Evaluation on Dataset D2\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModels\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMAPE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMaxPE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eESD\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSVR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e14.369\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.875\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e24.268\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e4052.038\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e3.791\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.872\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRFR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.436\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.094\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.088\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.875\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e123.014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.660\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e0.996\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBPNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e161.926\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e9.345\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.399\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e23.092\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45663.140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e12.725\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-0.446\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3.397\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.284\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.907\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7.837\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e957.832\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.843\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.970\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBILSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.435\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.497\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.357\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e1.524\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e122.597\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.659\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e0.996\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGRU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.035\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.774\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.555\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.935\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e291.916\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.017\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.991\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e presents the performance of propose DIIAM model on dataset D3. SVR shows a significantly improved performance with a low MSE of 0.828 and a R\u003csup\u003e2\u003c/sup\u003e of approx. 0.993. RFR shows best performance with least MSE, MAE, MAPE, MaxPE, ESD and RMSE and highest R\u003csup\u003e2\u003c/sup\u003e of approx. 1. BPNN, LSTM, BiLSTM and GRU also shows good performance on D3 but not that much RFR. Therefore, from all dataset\u0026rsquo;s results RFR are considered to be the first choice.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePerformance Evaluation on Dataset D3\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModels\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMAPE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMaxPE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eESD\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eR2\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSVR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.828\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.232\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.245\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e13.682\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e14311.801\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.910\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.993\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRFR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.000\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.001\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.001\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.246\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.310\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.004\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e1.000\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBPNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.212\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.317\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.276\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.646\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e3655.888\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.460\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.998\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.044\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.588\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e119.740\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.083\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBILSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.006\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.036\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.034\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.455\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e106.504\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.079\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGRU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.042\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.037\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.960\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e77.813\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.067\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003e5.5 Bimodal Performance Evaluation\u003c/h2\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab9\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 9\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePerformance Evaluation on Dataset D4\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModels\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMAPE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMaxPE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eESD\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eR2\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSVR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.406\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.192\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.193\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8.104\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e366.247\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.638\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.996\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRFR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.000\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.008\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.007\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.119\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.260\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.017\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e1.000\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBPNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6.612\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.943\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.716\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e11.160\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e5957.699\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e2.571\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.940\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.107\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.039\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.948\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7.572\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1898.039\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.451\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.981\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBILSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.986\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.270\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.138\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e9.680\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2690.502\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.728\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.973\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGRU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.029\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.932\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7.846\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1828.523\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.425\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.981\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab9\" class=\"InternalRef\"\u003e9\u003c/span\u003e presents the performance evaluation on dataset D4. DIIAM with different learning models are used for evaluation. Among them SVR shows a significantly improved performance with a low MSE of 0.406 and a R\u003csup\u003e2\u003c/sup\u003e of approx. 0.996. RFR shows best performance with least MSE, MAE, MAPE, MaxPE, ESD and RMSE and highest R\u003csup\u003e2\u003c/sup\u003e of approx. 1. BPNN, LSTM, BiLSTM and GRU also shows good performance on D4 but not that much RFR. Therefore, RFR is considered to be the best regression model for proposed bimodal approach.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003e5.6 Comparative Analysis\u003c/h2\u003e \u003cp\u003eIn this section, performance of Proposed DIIAM Model with all learning models are presented for average result on all datasets i.e., D1, D2, D3 and D4. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e presents the comparative MSE evaluation for various learning models i.e., SVR, RFR, BPNN, LSTM, BiLSTM, and GRU. The graph shows that lowest MSE is achieved by RF learning model in proposed DIIAM model. This is due to the ensemble learning approach of RFR. Whereas second least MSE was achieved by GRU and then by BiLSTM model. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e presents the average MAE evaluation of DIIAM Model. The least MAE was also achieved by RFR and then followed by SVR and GRU. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e presents the average MAPE evaluation of DIIAM Model. The least MAPE was also achieved by RFR and then followed by SVR and GRU. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e presents the average RMSE evaluation on all datasets. In this graph RFR have also achieved the least RMSE and then followed by GRU and BiLSTM. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e presents the average MaxPE evaluation on all dataset. The performance of average MaxPE shows similar pattern as RMSE. Figure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e presents the average ESD evaluation on all dataset. The performance of average ESD shows similar pattern as RMSE. In Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e average R2 is presented and highest R2 was also achieved by RVR and then followed by GRU and BiLSTM. The benefit of integrating the proposed DIIAM model with RFR learning model have shown best performance due to its ensemble learning approach that limit overfitting. Whereas, DIIAM model can be integrated with GRU and BiLSTM as second choice that can efficiently capture dependencies for time-series data with less computational resources than other models.\u003c/p\u003e \u003cp\u003eThe Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e presents the comparative state-of-art in terms of RMSE for different approaches with proposed DIIAM. Lower RMSE presents that model is more predictive robust. Bimodal and unimodal approaches have been applied to different environment types, with techniques ranging from DNN[\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e], CNN[43], ANN [31], RF[\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e35\u003c/span\u003e], Wavelet-GA [40] and Ensemble NN [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e44\u003c/span\u003e]. The performance in terms of RMSE varies from 4-6dB under urban environment. The DIIAM (proposed) which is a bimodal system has a significantly lower RMSE of 1.4. The comparatively lower RMSE for the proposed DIIAM model indicates that it substantially outperforms the existing approaches. The efficacy of the DIIAM model is evident as it provides more accurate predictions across diverse environments which can be particularly challenging due to varying signal interferences and complexities. The bimodal approach of DIIAM, possibly integrating two different types of data or models, seems to enhance the predictive accuracy, making it a potentially more robust and adaptable system in varying environmental conditions compared to the unimodal systems.\u003c/p\u003e \u003c/div\u003e"},{"header":"6. Conclusion","content":"\u003cp\u003eThe proposed methodology for path loss prediction is considered as significant advancement in wireless communication that will make the communication system more accurate and reliable. In this paper, the limitations of conventional approaches for path loss prediction models are removed. From detailed literature review, it can be concluded that most of the path loss prediction models are unimodal in nature that means they are only dependent on different environmental or channel factors. But these unimodal system results in high error during prediction. To mitigate these issues, the paper presented a dual-input (bimodal) system for path loss prediction. In this approach environmental or channel information with satellite images are considered to provide more comprehensive information for learning a model. Therefore, the methodology is multi-layered with dual input based path loss prediction model. To process environmental data, the methodology extracted important and relevant features by applying T-Test and Z-Test approach. And to process the visual data a pre-trained transfer learning model such as ResNet50 is used to reduce computational complexity and that will make the entire system lightweight. Further these features are fused together and then passed to attention layer to generate weighted feature vector for learning models. The key aspect of the proposed model is that it integrated the benefits of machine learning and attention mechanism for robust and accurate prediction model. The multi-layered model architecture, combined with advanced preprocessing and integration techniques, enables the effective utilization of complex data types, leading to superior prediction outcomes. The result analysis was presented on four datasets each for unimodal as well as bimodal systems. The results analysis shows better prediction performance as compared to existing approaches. Future research direction will motivate to design more fine-tuned model to incorporate wider range of environmental and visual data, and applying the methodology to a broader set of scenarios to validate its effectiveness and adaptability to different geographic and urban conditions.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis research recieved no external funding .\u003c/p\u003e \u003cp\u003eData availability: available on request\u003c/p\u003e \u003cp\u003eConflicts of interest : The author declare no conflict of interest.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eMamta Tikaria conceptualized the study, performed the experiments, and wrote the main manuscript text. Dr. Vineeta Saxena (Nigam) supervised the research, contributed to the methodology, and reviewed the manuscript. All authors reviewed and approved the final version of the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThe authors, Mamta Tikaria and Dr. Vineeta Saxena (Nigam), would like to express their gratitude to the Department of Electronics and Communication Engineering, University Institute of Technology, Bhopal, for their continuous support and for providing the necessary facilities for this research. They also thank their colleagues who provided valuable feedback during the development of this work.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eMa, Y., \u0026amp; Zhou, J. (2024). Effects of mixed aerosol on the path loss of NLOS UV communication system. \u003cem\u003eOptoelectronics Letters\u003c/em\u003e, \u003cem\u003e20\u003c/em\u003e(9), 549\u0026ndash;559.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOladimeji, T. T., Kumar, P., \u0026amp; Elmezughi, M. (2024). 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IEEE.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Path loss, 5G, wireless communication, machine learning, bimodal","lastPublishedDoi":"10.21203/rs.3.rs-6732837/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6732837/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePath loss prediction is crucial for optimizing base station placement in cellular networks. Traditional methods rely on extensive field testing, which is time-consuming and resource-intensive. Machine learning (ML)-based approaches offer an alternative, yet most existing models use unimodal systems, limiting predictive accuracy. To address this, we propose a Bimodal Path Loss Prediction System that integrates environmental data with visual information extracted from satellite images. We introduce the Dual-Input Integrative Attention Model (DIIAM), a multi-layered architecture designed for improved path loss prediction. DIIAM consists of three key layers: Dual-Input Feature Extraction Layer (DIFEL), Feature Weighted Attention Layer (FWAL), and Learning Layer (LL). DIFEL extracts environmental features using data imputation, normalization, and statistical feature selection, while visual features are obtained using the ResNet50 transfer learning model. FWAL applies an attention mechanism to enhance feature relevance, and LL employs six different learning models\u0026mdash;SVR, RFR, BPNN, LSTM, BiLSTM, and GRU\u0026mdash;to effectively capture complex feature relationships. Evaluated on four publicly available datasets, DIIAM achieves an average RMSE of approximately 1.5 dB, outperforming state-of-the-art methods. The results demonstrate the effectiveness of integrating environmental and visual data for path loss prediction, offering a more accurate and computationally efficient alternative to traditional and unimodal ML approaches.\u003c/p\u003e","manuscriptTitle":"Dual-Input Multi-Layered Attention Model for Enhanced Path Loss Prediction","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-25 02:27:24","doi":"10.21203/rs.3.rs-6732837/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"e47f3248-7c90-4e4d-99ed-ffc3a3b25054","owner":[],"postedDate":"June 25th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-07-14T06:24:17+00:00","versionOfRecord":[],"versionCreatedAt":"2025-06-25 02:27:24","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6732837","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6732837","identity":"rs-6732837","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}