KWAME NKRUMAH UNIVERSITY OF SCIENCE AND TECHNOLOGY, KUMASI

DECLARATION

i
 ABSTRACT

With the growth of wireless technology, there has been a huge increase in the demand for

efficient and reliable path loss prediction models in wireless communication networks. Several

path loss prediction techniques have been presented recently to improve network performance.

But the majority of these models don't solve the core problems. Using a single path loss

prediction model that works effectively in all wireless propagation situations is still a challenge.

We provide an ensemble path loss prediction method based on machine learning to solve this

issue. In particular, ensemble approaches have been established to enhance the performance

and accuracy of signal prediction. As basis models, three models with distinct strengths—

Random Forest (RF), Gradient Boosting Regressor (GBR), and Support Vector Regressor

(SVR)—were used. By implementing hyperparameter adjustment, the base models' predictions

were significantly enhanced. The evaluation metrics, Root Mean Square Error, Mean Square

Error, and Mean Absolute Percentage Error, were used to examine the outcomes of the RF,

GBR, SVR, and the ensemble methods effects. The testing revealed that the bagging and

blending ensemble models provided very low MAPE values of 3.09% and 1.94%, respectively.

The blending ensemble approach, which projected path loss closest to observed data and is

suitable for nearly precise path loss predictions, functions as a variance and error reduction

mechanism.

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 TABLE OF CONTENTS

DECLARATION ........................................................................................................................ i

ABSTRACT ...............................................................................................................................ii

TABLE OF CONTENTS ......................................................................................................... iii

LIST OF FIGURES ................................................................................................................... v

LIST OF TABLES .................................................................................................................... vi

LIST OF ABBREVIATIONS ..................................................................................................vii

ACKNOWLEDGEMENT ........................................................................................................ ix

CHAPTER 1 INTRODUCTION ............................................................................................ 1

1.1 Background of Study................................................................................................... 1

1.2 Problem Statement ...................................................................................................... 4

1.3 Research Objectives .................................................................................................... 5

1.3.1 General Objectives ............................................................................................... 5

1.3.2 Specific Objectives .............................................................................................. 5

CHAPTER 2 LITERATURE REVIEW ................................................................................. 6

2.1 Introduction ................................................................................................................. 6

2.2 Path Loss ..................................................................................................................... 6

2.3 Machine Learning Based Path Loss Prediction Models.............................................. 7

2.4 Feature Variables and Feature Selection ..................................................................... 9

2.5 Feature Scaling .......................................................................................................... 10

2.6 Model Selection......................................................................................................... 11

2.7 Hyperparameter Setting and Model Training............................................................ 11

2.8 Model Optimization Techniques ............................................................................... 13

2.9 Model Evaluation and Prediction .............................................................................. 14

2.10 Summary................................................................................................................ 16

CHAPTER 3 METHODOLOGY ......................................................................................... 19

3.1 Signal Propagation through Space ............................................................................ 19

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 3.2 Machine Learning Algorithms .................................................................................. 20

3.2.1 Random Forest Regressor (RFR) ....................................................................... 21

3.2.2 Gradient Boosting Regressor (GBR) ................................................................. 22

3.2.3 Support Vector Regression (SVR) ..................................................................... 24

3.2.4 Artificial Neural Networks (ANNs)................................................................... 26

3.3 The Proposed Path Loss Prediction Modeling Approach ......................................... 27

3.4 Data Collection and Processing Campaign ............................................................... 29

3.5 Comparison of Different Models .............................................................................. 31

CHAPTER 4 RESULTS AND DISCUSSIONS .................................................................. 36

4.1 Development of The Ensemble Path Loss Models ................................................... 36

4.1.1 Bagging ensemble path loss prediction model................................................... 36

4.1.2 Blending ensemble path loss prediction model ................................................. 37

4.2 Experimental Results................................................................................................. 38

4.3 Ensemble Methods Evaluation .................................................................................. 39

CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS ........................................ 44

5.1 Conclusion................................................................................................................. 44

5.2 Recommendations for Future Research .................................................................... 45

5.2.1 Collection of Training Data ............................................................................... 45

5.2.2 Feature Selection Methodology ......................................................................... 45

5.2.3 Hyperparameter Optimization Problem ............................................................. 46

5.2.4 Incremental Learning ......................................................................................... 46

REFERENCES ........................................................................................................................ 48

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 LIST OF FIGURES

Figure 1.1: Propagation Models ................................................................................................. 3

Figure 1.2: Principle of machine learning based path loss prediction [8] ................................. 3

Figure 2.1: Procedure of machine-learning-based path loss analysis [8]. ................................. 9

Figure 3.1: Random Forest Algorithm ..................................................................................... 22

Figure 3.2: Schematic diagram of the gradient boosted regression tree. ................................. 24

Figure 3.3: A schematic diagram of SVR architecture ............................................................ 25

Figure 3.4: The Proposed Path Loss Prediction Model Architecture ...................................... 29

Figure 3.5: Cost-Hata model prediction performance on the test set ...................................... 32

Figure 3.6: Gradient Boosting regressor prediction performance on the test set..................... 33

Figure 3.7: Random Forest Regressor model prediction performance on the test set ............. 33

Figure 3.8: SVR model prediction performance on the test set ............................................... 34

Figure 5.1: Pathloss prediction of the various prediction models on the test data set without

hyperparameter tuning ............................................................................................................. 40

Figure 5.2: Pathloss prediction of the various prediction models on the test data set with

hyperparameter tuning. ............................................................................................................ 41

Figure 5.3: Bagging ensemble method prediction performance on the test dataset. ............... 41

Figure 5.4: Blending ensemble method prediction performance on the test dataset. .............. 42

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 LIST OF TABLES

Table 2.1: Existing Research for Machine Learning Based Path Loss Prediction .................. 14

Table 3.1: Descriptive Statistics .............................................................................................. 31

Table 3.2: Performance evaluation of various models using 30% test samples from the

measured dataset (up to 2.1GHz). ............................................................................................ 35

Table 5.1: Candidate Variable ................................................................................................. 38

Table 5.2: Tuned Hyperparameter Values ............................................................................... 40

Table 5.3: Performance metrics for the developed models on 30% of the dataset (test set) ... 42

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 LIST OF ABBREVIATIONS

EM Electromagnetic Waves

FDTD Finite-Difference Time-Domain

SVR Support Vector Regression

RF Random Forest

ANN Artificial Neural Network

KNN K-Nearest Neighbour

IoT Internet of Things

ML Machine Learning

TX Transmitter

RX Receiver

GPS Ground Positioning System

GBR Gradient Boosting Regressor

MSE Mean Squared Error

AIC Akaike Information Criterion

BIC Bayesian Information Criterion

MaxPE Maximum Prediction Error

MAE Mean Absolute Error

ESD Error Standard Deviation

RMSE Root Mean Square Error

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MAPE Mean Absolute Percentage Error

LTE Long Term Evolution

NN Neural Network

TEMs Transmission Evaluation and Monitoring system

RSRP Reference Signal Received Power

MS Mobile Station

USB Universal Serial Bus

EIRP Effective Isotropic Radiated Power

SVM Support Vector Machine

CSV Comma Separated Values

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ACKNOWLEDGEMENT

ix
 CHAPTER 1

INTRODUCTION

1.1 Background of Study

In order to optimise communication systems' performance, electromagnetic wave (EM)

propagation is a must. As the distance between the transmitting and receiving antennas grows,

the intensity of the EM signal typically decreases. Three separate radio wave propagation

mechanisms—scattering, diffraction, and reflection—have been identified [1]. Pathloss

prediction is a challenging problem due to the complexity of the propagation environment. Path

loss is a term used to explain how radio waves are attenuated as they travel through space [2].

Therefore, a straightforward, accurate, and all-encompassing path loss model is required for

coverage planning, budgeting, base station site selection, and system performance

optimisation. As a result, numerous attempts have been undertaken to locate suitable path loss

models in a variety of applications at various frequencies. The environment has a significant

impact on the numerous propagation mechanisms that wireless signals are subject to, which

causes the signal intensity to decrease. It depends on a variety of elements, including frequency,

antenna height, receive terminal placement in relation to obstructions and reflectors, link

distance, and many more [3].

Historically, empirical or deterministic techniques have been used to construct path loss

prediction models [4]. Empirical models primarily rely on measurements across a specified

frequency range and under a particular set of circumstances. They offer statistical explanations

of the correlation between route loss and other propagation factors, including frequency,

antenna distances, antenna heights, etc. For instance, the route loss exponent, which is derived

empirically, is used in the log-distance model [5] to describe how the receiver power decreases

with the antenna separation distance. The attenuation (measured in decibels) brought on by the

1
fading of the shadow is shown by a Gaussian random variable with zero mean. The Okumura,

Hata, Bullington, Egli, Longley-Rice, and other common empirical models are also included

[6]. Since only a few parameters are needed and the model equations are short, empirical

models are rather straightforward. The parameters of empirical models, however, are inferred

from measured data in a particular situation. When these models are used in more generic

situations, their accuracy might not be adequate [7]. The received power at a certain site cannot

be determined by empirical models, which can only provide statistics of the path loss at a given

distance.

For the purpose of modelling computational electromagnetics, deterministic models, such as

those based on ray tracing and finite-difference time-domain (FDTD), use numerical analysis

methods and radio-wave propagation processes [8]. Generally speaking, they are able to deliver

the path loss value at any particular place with great accuracy. Their drawbacks, however,

include inefficient processing, which results in exorbitant computation times in practical

environments. Additionally, needed are details about the materials' dielectric characteristics

and site-specific shape. Moreover, once the propagation environment has changed, we must

repeat the time-consuming computation process.

In order to build a model that can complete a certain task, a process known as machine learning

is utilised to learn about a set of data [8]. By using algorithms and statistics to learn, machine

learning analyses data to draw conclusions. Regression and classification are the two subtypes

of the supervised learning method. The modelling utilised in path loss prediction belongs to

the class of supervised learning regression. Numeric input and output data types are what define

regression. Regression models include Gradient Boosting Regression, Support Vector

Regression (SVR), Random Forest (RF), Artificial Neural Network (ANN), and K-Nearest

Neighbour (KNN). When contrasted to empirical methods, machine learning has the benefit of

being highly accurate. [9].

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 Figure 1.1: Propagation Models

Due to the large amount of data utilised to train the model, machine learning path loss

prediction models are more accurate than empirical and deterministic models. One of the

biggest drawbacks of empirical and deterministic models is that they are only applicable in the

initial deployment environment. When compared to empirical models, many models that were

established in earlier studies [10] and used different algorithms in different environmental

settings have proven to be very successful predictions. The basic principle of path loss

predictors based on machine learning is shown below.

Figure 1.2: Principle of machine learning based path loss prediction [8]

To meet the needs of applications at new frequencies and in novel propagation settings, an

adaptable modelling framework should be developed. As previously stated, machine-learning-

based approaches can provide an equilibrium between path loss model accuracy and

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complexity. Machine learning, on the other hand, is a data-hungry technology whose

effectiveness is strongly dependent on the amount and quality of training data. The path loss

dataset is always distant from the concept of "big data" that can be easily collected on the web

or Internet of Things (IoT) due to the high cost of making measurements [8]. It is challenging

to acquire enough data for path loss prediction in a short period of time, particularly when new

scenarios or frequencies are used. As a result, data expansion strategies are presented in this

work to cover the research gap.

1.2 Problem Statement

Empirical models provide clarity and simple equations since they are based on statistical

analysis of measured data in particular settings. However, when used in broader situations,

their accuracy might be constrained. The power levels at particular sites cannot be accurately

predicted by these models, but they do statistically describe the relationship between path loss

and propagation parameters. However, deterministic models may provide path loss estimates

at any location with great precision because they are based on numerical analysis methods and

radio wave propagation principles. They call for site-specific geometry information and

material parameters, but they also require a lot of computational work.

In order to overcome the drawbacks of empirical and deterministic models, machine learning

techniques have shown promise as path loss prediction alternatives. Algorithms and statistical

methods are used in machine learning to analyse large data sets and build models that can carry

out specified tasks. Support Vector Regression (SVR), Random Forest (RF), Artificial Neural

Network (ANN), Gradient Boosting Regression (GBR), and K-Nearest Neighbour (KNN) are

examples of supervised learning regression models that have demonstrated potential for

making correct predictions in the area of path loss prediction.

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It is necessary to use machine learning methods to create a path loss prediction model that can

get around the drawbacks of deterministic and empirical models. Based on a variety of input

characteristics, including frequency, antenna height, distance, and environmental conditions,

this model should be able to effectively forecast path loss in wireless communication systems.

The model must be flexible and adaptable to various deployment environments in order to

allow generalisation outside of the initial training setting. The objective is to improve accuracy

in comparison to conventional models and offer insightful data for system optimisation,

coverage planning, and performance assessment by utilising the large data used in machine

learning.

1.3 Research Objectives

1.3.1 General Objectives

To develop an ensemble path loss prediction model for heterogeneous radio network

planning, deployment, and optimization of the network using machine learning

approach.

1.3.2 Specific Objectives

1. To investigate the integration of predictive models for enhanced path loss prediction

in wireless communication networks.

2. To develop and evaluate model optimization strategies for enhanced path loss

prediction in wireless communication networks.

3. To evaluate and validate the performance of the proposed path loss prediction

model against established empirical models.

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 CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

The following review of the literature focuses on the many categories of research fields, feature

variables, and feature selection techniques utilised in the creation of path loss prediction

models. Several academics have created machine learning-based path loss prediction

algorithms for a variety of area conditions. One of them [11] uses an Artificial Neural Network

(ANN) model to examine different indoor building styles. While [12], and [13] look into

diverse area types, such as rural, suburban, and urban areas, [10] also study path loss prediction

with a variety of machine learning models in suburban areas. Other studies that have been

conducted in various locations with a unique measuring field include [14], which examines

route loss prediction in an enclosed space such as an aeroplane cabin. Path loss prediction of

pathloss with the aid of ensemble machine learning methods has only been the subject of a few

studies. This suggests that there is still opportunity for advancement in the study of path loss

prediction with ensemble method approach.

2.2 Path Loss

The planning and optimisation of wireless communication networks must consider path loss

prediction. By taking into account variables including distance, frequency, topography, antenna

height, and environmental characteristics, it includes predicting the attenuation of signal power

as it propagates via the wireless medium. A straightforward, all-encompassing model for trail

loss is needed for link budgeting, system performance optimisation, coverage forecast, and an

associate degree of accuracy.

As a result, researchers and engineers have been hard at work creating algorithms that are

affordable for trail loss prediction in a variety of scenarios and frequencies [4]. In their research

6
paper, [8] described their findings regarding path loss and how to predict it using machine

learning. They stated that path loss is a change in a radio wave's power as it passes through a

building between the transmitter and receiver. Given that receivers need a specific minimum

power to copy data correctly, path loss prediction is important in wireless communication n/w

design and development, including link budget, coverage analysis, and locating base station. A

linear proportion between the distance and the path loss is used in a number of existing route

loss models, and by contrasting the graphical depiction of the data, the problem has been

resolved [15].

In [16] , an explanation for path loss was presented by pointing out that propagation models

account for signal attenuation or path loss as a measure of the power density of an

electromagnetic wave as it travels through space from a transmitter. Path loss can be used to

monitor network planning, coverage, and system performance to provide the best possible

reception. Numerous factors, like as geography, frequency, and the heights of the transmitter

and receiver antennas, can affect how far a signal can travel [17].

2.3 Machine Learning Based Path Loss Prediction Models

In [14], the concept of path loss and how to predict it using machine learning was investigated.

They also investigated the concept of path loss and described the fundamental principle of path

loss predictors based on ML. Once we have the outcome (path loss observation) and the

pertinent input features, such as antenna-separation distance and frequency, we may apply

machine learning techniques to develop an acceptable estimation function for path loss

prediction. This function, which can be either a white box (in decision-tree-based models) or a

black box (in non-decision-tree-based models) (inside SVR-based or ANN-based models),

maps input features to path loss values. The method for machine learning-based path loss

predictors [15].

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The gathered information relates to measurement samples, each of which contains the path loss

value and the associated input parameters. The two categories of input features are system-

dependent parameters and environment-dependent parameters. Carrier frequency, transmitter

and receiver heights and positions, and other system-dependent parameters are examples of

parameters that are not impacted by the propagation environment. The aforementioned

parameters can be used to determine additional system-dependent features, such as the antenna

separation distance and the angle between the line-of-sight path and the horizontal plane [15].

Environmentally dependent parameters are those variables that depend on both the physical

environment and the weather. The geographic environment is influenced by terrain, building

characteristics, and vegetation conditions.

In order to develop the ability to generalise (to generate predictions based on previously

unknown inputs), the models can be trained with sets of provided path loss values and matching

inputs. After knowing the output (path loss observation) and the corresponding input features

such as antenna-separation distance and frequency, we can employ machine learning methods

to find a good estimation function for the path loss prediction. This function is to map input

features to output path loss value, and it can be either a white box (within decision-tree-based

models) or a black box (within SVR-based or ANN-based models). The procedure of machine-

learning-based path loss predictors is shown in figure below and is introduced step by step as

follows.

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 Figure 2.1: Procedure of machine-learning-based path loss analysis [8].

2.4 Feature Variables and Feature Selection

When creating path loss prediction models, a wide range of input feature kinds and quantities

are used. The distance between the transmitter (TX) and receiver (RX) is the only input

information used in the research in [18], [19]. The research of [20] also employs the frequency

feature as an extra input feature in addition to the TX-RX distance feature, and [8] uses two

9
features in addition to the TX-RX distance feature with the addition of onboard GPS sensors.

The TX-RX distance feature is included to the parameters of the input feature in the study by

[21], along with the features of PCC downlink throughput and PDCP downlink throughput. In

the research of [14], which examines the interior space of an aircraft cabin, user position based

on longitude and latitude is used as an input parameter in addition to others. The studies [11]

and [22] also study an outside location using longitude and latitude. Environmental

characteristics are also used as input features in some research in addition to system parameters.

According to the focus of the research field's specific characteristics, some studies employ a

more complex combination of criteria in order to produce results with the highest degree of

accuracy. Six input factors are used in the investigation of [23], [24], including longitude,

latitude, elevation, altitude, clutter height, and TX-RX distance. This demonstrates that the

types and numbers of features can still be developed to correspond with the precise subject of

the research field.

2.5 Feature Scaling

In real life, the machine learning data may have hundreds of features. Poor predictor quality

might result from either keeping irrelevant features or excluding important features. Finding

the best subset with the fewest characteristics that contribute most to learning accuracy is the

aim of feature selection [25].

There are typically three different feature selection methodologies, including filter, wrapper,

and embedding, depending on the link between the feature selection process and the model

architecture. When determining the relevance of a characteristic, the filter technique operates

independently of the suggested model. When calculating the feature scores using the wrapper

approach, the prediction performance is taken into consideration. The embedded approach's

technique incorporates feature selection and prediction accuracy [26]. The halting criteria for

10
various algorithms depend on the search method chosen, the feature evaluation standards, and

the particular application needs.

The size of the input space can affect the performance of some machine-learning-based

algorithms including RF, SVR, and GBR. As a result, the normalisation procedure should be

complete before the training starts. That means, the values of all input characteristics and path

loss should be modified to fall within the range of -1 to 1 or 0 to 1. This work uses the same

normalisation technique as [27], with the same results. It can be stated as

2(𝑥 − 𝑥𝑚𝑖𝑛 )
𝑥𝑁 = −1
𝑥𝑚𝑎𝑥 − 𝑥𝑚𝑖𝑛

where x is the value to be normalized, 𝑥𝑚𝑖𝑛 and 𝑥𝑚𝑎𝑥 are the minimum and maximum values

of the data range, respectively, and 𝑥𝑁 is the value after normalization. By applying anti-

normalization in accordance with the normalization procedure, the expected values can be

produced. By contrast, decision-tree-based approaches do not demand the feature scaling.

2.6 Model Selection

Path loss prediction can be done using a variety of models, and while choosing a model, it's

important to take accuracy and complexity needs into account. In Chapter III, we'll introduce

the Random Forest Regressor, Gradient Boosting, and SVR as examples. The performance of

these algorithms in foretelling path loss values has been found to be good [28].

2.7 Hyperparameter Setting and Model Training

The parameters whose values are predetermined before the learning process starts are referred

to as hyperparameters. A few examples of common hyperparameters are the quantity of hidden

layers and neurons in an ANN, the regularisation coefficients and parameters in the kernel

function of an SVR, the ensemble size and tree depth in decision-tree-based methods, etc. In

order to maximise the efficiency and performance of the path loss prediction, a set of ideal

11
hyperparameters should be carefully selected. Grid search, random search, and Bayesian

optimisation are the major methods for hyperparameter optimisation. In this study, the grid

search approach was used to determine the hyperparameters' final values. It is a thorough search

method that examines all of the potential parameter values before returning the best performing

parameters.

The parameters of a model are those that are discovered by training samples. It is important to

note that various learning methodologies have various model parameters. Model parameters

like weights and biases are automatically learned throughout the model training process.

The research paper [29], discussed how they may train new models for predicting path loss

within buildings or indoors. They argued that training is the most important and crucial role in

the modelling problem. In reality, a well-trained model must be able to extrapolate or

interpolate with high accuracy based on existing knowledge learned during learning from a

new input in order to predict the expected output. The literature has a number of proposed

neural network learning techniques, which can be categorised into supervised and unsupervised

learning [30]. Unsupervised learning is used to cluster data, and this method separates the data

into groups based on certain characteristics. With supervised learning techniques like the

gradient descent approach, the input parameters and output values are known, and the neural

network can offer an inferred function that can be used to map fresh samples. To lower the

mean squared error (MSE) between the input and desired output of the neural model, the bias

and weight of each neuron can be changed [30].

When creating a precise neural network model, the most influential parameters possible must

be taken into account. The multi-wall model is where the inputs for the model that we

developed and presented in this study come from. The components of (L f) are the distance

between the transmitter and receiver (d), the frequency (f), the attenuation of the walls and

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floors (L w), and the frequency. The model has a single hidden layer. This hidden layer's

number of neurons is set to 75% of the input layer's number of neurons [30]. This number may

be altered, and the results of doing so will be discussed in the section that follows. In the output

layer, there is only one output that represents the measured signal route loss.

2.8 Model Optimization Techniques

Techniques for model optimisation are essential for enhancing the effectiveness of predictive

models for predicting path loss. These methods include boosting generalisation skills, choosing

the best configuration, and fine-tuning model parameters. The literature has suggested a

number of methods to improve the ensemble models used for path loss prediction.

A strategy that is frequently used to optimise ensemble models is parameter tuning. It entails

methodically looking for the ideal hyperparameter values, such as the Random Forest's number

of trees, Gradient Boosting's learning rate, and Support Vector Regression's kernel parameters.

The most effective way to efficiently explore the hyperparameter space and find the ideal

configuration is to combine grid search and cross-validation approaches.

Model selection is another optimisation strategy that involves selecting the best ensemble

model from a group of potential models. The choice of a model can be made based on a number

of factors, such as computational effectiveness, forecast accuracy, and model complexity.

Model selection methods include cross-validation and information criteria like the Akaike

information criterion (AIC) and Bayesian Information Criterion (BIC).

A technique called ensemble pruning tries to enhance prediction performance by removing

redundant or unnecessary models from the ensemble. A model's contribution to the ensemble's

predictive power or statistical metrics like feature significance measures in Random Forest can

be used for pruning. Pruning can improve prediction accuracy and decrease computational

complexity by lowering the ensemble size and removing inferior models.

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Predictive model performance is greatly improved by feature engineering. To give more

relevant and educational inputs to the models, it entails altering and developing new

characteristics from the existing dataset. The path loss dataset was subjected to feature

engineering approaches like scaling, categorical variable encoding, and interaction term

creation.

2.9 Model Evaluation and Prediction

Typically, samples from the test dataset—which are absent from the model training process—

are used to gauge how well machine learning-based route loss models perform. The evaluation

criteria include complexity, generalisation ability, and prediction accuracy. Performance

metrics, such as the maximum prediction error (MaxPE), mean absolute error (MAE), error

standard deviation (ESD), root mean square error (RMSE), and mean absolute percentage error

(MAPE), are frequently used to assess accuracy [9].

When the deployment involves additional frequency bands or/and environment types, the

generalisation property is used to define the model's reusability. More data gathered from

various settings, such as various terrains, frequencies, and vegetative cover conditions, may

improve the model's generalisation ability.

Usually, processing speed and memory usage are used to gauge how difficult a computation is.

The primary elements that determine the processing time of machine learning model include,

for illustration, the quantity of iterations and convergence speed during the training phase.

The machine learning algorithm can be chosen, the hyperparameters can be changed, and the

prediction model can be further enhanced based on the evaluated outcomes. Following the

construction of the ideal model, path loss values can be produced using fresh inputs.

Table 2.1: Existing Research for Machine Learning Based Path Loss Prediction

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 Authors Titles Journal Objectives Results Remarks

Akande A. Implementation of EJERS, To develop an The result obtained Hence, the PSO Optimized

Olukunle Particle Swarm European optimized model for from the PSO model could be suitably

et al. Optimization Journal of urban outdoor coverage optimized model deployed for signal

Technique for Engineering in Long Term Evolution demonstrated a attenuation improvement

Enhanced Outdoor Research and (LTE) network at 2300 better performance for LTE network in Port

Network Coverage Science MHz frequency band in which is suitable Harcourt, South-South,

in Long Term Port Harcourt urban for cell coverage Nigeria.

Evolution Network region, Nigeria. planning and

in Port Harcourt, smooth handoff

Nigeria processes.

Joel Delos Neural Network- Conference To propose and Proposed system It's shown to give more

Angeles et Based Path Loss Paper ascertain the viability of improved power accurate results compared

al. Prediction for using an alternative allocation, reduces to more familiar

Digital TV neural network (NN) delay violation propagation models, such

macrocells model to predict path probability. as Free Space and Egli,

loss. while having the

advantage of adaptability

to arbitrary environments.

Erik Macrocell Path- IEEE To investigate the need Non-complex CSBM Rayleigh

Ostlin, et Loss Prediction Transaction for multilayered feed- ANN model distributions. BS and

al. Using Artificial Vehicular forward networks to performs very well Relay antenna array

Neural Networks Technology reduce the training time compared with configuration was not

without introducing any traditional stated.

negative effects on the propagation

path loss prediction models with regard

results. to prediction

accuracy,

complexity, and

prediction time.

Caleb T, A survey of IEEE To provide a thorough The future of Proposed future work in

Phillips, et Wireless Path Loss Communications and up to date survey of wireless path loss this area is likely to focus

al. Prediction and Surveys & path loss prediction prediction methods on refining sampling and

Coverage Mapping Tutorials methods, spanning more will be active learning strategies using

Methods measurement measurement-based

15
 than 60 years of fairly designs that methods, a well as

continuous research. attempt to extract extracting as much

information from information as possible

directed from existing sources

measurements. using data mining.

Yan Air-to-Air Path Wireless To build the prediction The test data have It has been demonstrated

Zhang, et Loss Prediction communications models for path loss in been used to that machine learning

al. [12] Based on Machine and Mobile the air-to-air (AA) evaluate the provides a flexible

Learning Methods Computing scenario based on accuracy modelling approach based

in Urban machine learning. performance of on the training data for

Environments these machine - such complex environment

learning based and Random Forest has

models and two the best prediction

imperial models, performance.

SUI model and Less measurement

COST231-W-I campaigns were carried

model. out in the AA scenario. As

such are measured data are

expected to further

improve the performance

and feasibility of the

machine learning based

path loss predictors.

2.10 Summary

In this study, we looked at the feature selection, hyperparameter tuning and optimization, and

model selection and training available in wireless communication networks. It became clear,

nonetheless, that specialised and improved path loss prediction features are needed due to the

particular difficulties and complexity of heterogeneous smart city environments. Also, a more

robust pathloss prediction model is needed to handle the limited features and make more

accurate prediction.

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The major goal of this study is to provide the best path loss prediction model for the

deployment, planning, and optimisation of heterogeneous radio networks in smart cities. We

defined three particular goals to do this:

1. Examine the incorporation of predictive models for better wireless communication

network path loss prediction: In order to increase the accuracy and reliability of path

loss prediction, this objective focuses on investigating the idea of ensemble methods.

2. Create and assess model optimisation techniques for improved wireless communication

network path loss prediction: To improve the performance of path loss prediction

models, this objective aims to develop and test various model optimisation strategies.

The models will be optimised using cross-validation and parameter adjustment using

grid search.

3. Comparatively analyse various path loss prediction models used in wireless

communication networks: This goal entails comparing a wide range of predictive

models, including Random Forest, Gradient Boosting, and Support Vector Regression.

To find the best strategies for various network circumstances, the study will evaluate

each model's prediction accuracy, robustness, and computing complexity.

We hope to contribute to the effective and efficient deployment of heterogeneous networks in

smart cities by focusing on these particular goals. The suggested path loss prediction model

will take into account elements like various cell types, frequencies, and interference scenarios

in order to be adapted to the dynamic surroundings of smart city environments.

The evaluation measures for the research will include prediction accuracy, generalisation

qualities, and complexity. The research will be directed by a combination of empirical models

and machine learning techniques. For the purpose of gathering information about received

signal strength and path loss in smart city settings, a comprehensive field measurement effort

17
will be carried out. The pre-processed data will be used to develop, test, and validate a variety

of machine learning models.

The development of an improved path loss prediction model, insights into the effectiveness

and applicability of machine learning algorithms in smart city environments, and an extensive

comparative study of path loss prediction models are all anticipated as the outcomes of this

research. We hope to enhance the field of path loss prediction in wireless communication

networks with these contributions, enabling better network design, coverage optimisation, and

resource allocation.

The next chapter will outline the methodology used to accomplish the research's goals,

including the methods for gathering data, developing models, using optimisation techniques,

and performing comparative research.

18
 CHAPTER 3

METHODOLOGY

This chapter goes through the resources and procedures employed. The procedure for gathering

data, the suggested model for predicting pathloss, and a comparison of various models are all

provided. The use of supervised learning techniques such as Random Forest, SVR, and

Gradient Boosting Regressor to predict path loss is introduced, and the performance of these

methods is examined using measured data. Additionally, a theory describing how signals travel

through empty space is offered.

3.1 Signal Propagation through Space

When radio signals are transmitted without considering the effects of a number of different

external obstructions in the propagation paths, a loss can be acquired. The free space path loss

model [31] gives information or a way to quantify this loss. As a result, the received power 𝑃𝑟 ,

the transmit power 𝑃𝑡 , and the antenna gain 𝐺𝑡 are related to the power density 𝑆𝑝 [2,40,50],

obtained over a communication distance r in free space, and the received power is given by (2).

𝑃𝑡 𝐺𝑡
𝑆𝑝 = (1)
4𝜋𝑟 2

𝑃𝑡 𝐺𝑡
𝑃𝑟 = 𝑆𝑝 𝐴𝑒 = 𝐴𝑒 (2)
4𝜋𝑟 2

where 𝐴𝑒 is the antenna aperture area defined below,

𝐺𝑟 𝜆2
𝐴𝑒 = (3)
4𝜋

𝑃𝑟 can be rewritten with respect to 𝐴𝑒 as in (4):

𝑃𝑡 𝐺𝑡 𝜆2
𝑃𝑟 = 𝐴𝑒 = 𝑃𝑡 𝐺𝑡 𝐺𝑟 (4)
4𝜋𝑟 2 (4𝜋𝑟)2

where λ = transmission wavelength in meters.

19
Thus, the path loss, 𝑃𝑙 (𝑑𝐵) over the free space channel can be computed as in (5) using

Equation (4):

4𝜋𝑟 4𝜋𝑓𝑐𝑎 𝑟
𝑃𝑙 (𝑑𝐵) = 20 𝑙𝑜𝑔 ( ) = 20 𝑙𝑜𝑔 ( 𝐶 ) (5)
𝜆 𝑠𝑝𝑒𝑒𝑑

where 𝐶𝑠𝑝𝑒𝑒𝑑 and 𝑓𝑐𝑎 define the speed of light and transmission frequency, respectively. Given

that 𝐶𝑠𝑝𝑒𝑒𝑑 = 3 × 108 m/s, π = 3.142, then Equation (5) can be expressed as (6):

𝑃𝑙 (𝑑𝐵) = 130 + 20 𝑙𝑜𝑔(𝑓) + 20 𝑙𝑜𝑔(𝑟) (6)

The expression in (6) shows that the value of signal loss in free space is reduced by 20 dB. In

other propagation situations, such built-up terrains, a suburban or metropolitan area, this is

unquestionably not the case. Equation (6) can be stated more broadly as Equation (7):

𝑃𝑙 (𝑑𝐵) = 𝑎1 + 𝑎2 𝑙𝑜𝑔(𝑓) + 𝑎3 𝑙𝑜𝑔(𝑟) (7)

Thus, Equation (7) is referred to as the general log-distance path loss model. In literature,

several efforts have been explored to determine the loss coefficients: 𝑎1 , 𝑎2 , and 𝑎3 . These loss

coefficients serve as the identified parameters in this work that need to be tweaked (optimised)

to match the actual terrain on which the signal is propagating. A number of empirical models,

such the Hata [51], SUI [52,53], COST 231 Hata [54–56], and ITU-R M2412-0 [57] models,

have also been developed as a result of this quest. Significant mistakes are produced when

these models are used for path loss estimation in settings other than those in which they were

designed.

3.2 Machine Learning Algorithms

For the purpose of predicting path loss, supervised learning algorithms were used. This section

provides an introduction to the models, SVR, Random Forest, and Gradient Boosting

Regressors, and evaluates prediction accuracy using observed data.

20
 3.2.1 Random Forest Regressor (RFR)

The ensemble learning technique known as the Random forest (RF) [32] consists of several

regression trees. A voting mechanism is used to improve each tree's prediction performance,

helping to compensate for its weak robustness. Breiman and Cutler [33] proposed the unique

non-parametric supervised machine learning technique known as Random Forest.

"Bootstrap aggregation" is the origin of the bagging technique known as RF. The primary

concept behind bagging is to take a dataset, bag a weak learner like a decision tree on it, then

create several bootstrap duplicates of the dataset and develop decision trees on them. To choose

various training samples for each tree, Bootstrap aggregating is used. After training the trees

using these samples, the final result is determined by averaging the performance of each

individual tree.

The RF is still a useful tool for dimensionality reduction or redundancy reduction of datasets.

Despite the fact that datasets with high dimensional input characteristics offer more

information, the redundant and unnecessary components may reduce the prediction accuracy.

In this study, the observed signal dataset was processed using the RF approach to extract the

more pertinent features while removing the unnecessary and unimportant ones. The RF

algorithms have two or more main hyperparameters that must be supplied before using them

for regression analysis or data training [34]. The number of trees is one of these

hyperparameters. The RF input-output function model is explained below in terms of

mathematics.

𝑅𝐹(𝑥𝑛 , 𝑦𝑛 ) = { 𝑓(𝑥𝑛 , 𝜃𝑚 , 𝑦𝑛 )}

where 𝜃𝑚 indicates the tree number. The 𝑥𝑛 , 𝑦𝑛 indicate the input and target output data. In

this case, a collection of trees (200) were used on the target measured signal data sets to

21
complete the work in order to identify the most valuable and informative subset of

characteristics.

Figure 3.1: Random Forest Algorithm

3.2.2 Gradient Boosting Regressor (GBR)

The Gradient Boosting Regressor (GBR) is an ensemble learning technique that belongs to the

family of boosting algorithms [35]. It does this by integrating the benefits of various distinct

regression trees to create a prediction model. GBR, which was first proposed by Jerome

Friedman [36], is intended to handle the constraints of specific weak learners and produce a

reliable and precise regression model.

In GBR, a series of regression trees are trained in an iterative fashion, with each new tree

aiming to fix the mistakes of the preceding ones. The model's ability to anticipate outcomes is

enhanced over time by this iterative process. Instead of using a voting mechanism, GBR

concentrates on optimising the residuals of the previous tree in the series. This is how it differs

from Random Forest. Due to this quality, GBR is very good at identifying complicated links

and optimising forecasts.

22
Giving additional importance to observations that earlier trees failed to accurately anticipate is

the fundamental idea of boosting. As a result, GBR can concentrate on the portions of the

dataset where the model performs poorly. Each new tree is trained to reduce the ensemble's

accumulated residual errors. GBR does exceptionally well at adapting to the subtleties and

patterns found in the data.

GBR's versatility in handling multiple data kinds and issue domains is one of its advantages. It

can deliver excellent predicted accuracy and is ideally suited for datasets with diverse feature

sets. To prevent overfitting, GBR might need more meticulous hyperparameter tuning than

Random Forest. The gradient-based loss function is minimised by the GBR method through a

series of processes, including initialising the target predictions, computing negative gradients,

and creating new regression trees. Combining all of the various trees' projections yields the

ultimate conclusion.

Based on the observed signal dataset, the Gradient Boosting Regressor was used in this work

to forecast path loss. The goal of GBR is to offer precise path loss estimates while managing

the difficulties present in real-world wireless communication settings. This is accomplished by

utilising the benefits of multiple regression trees and iterative error correction.

23
 Figure 3.2: Schematic diagram of the gradient boosted regression tree.

3.2.3 Support Vector Regression (SVR)

A type of machine learning technique built on statistical learning theory is the support vector

machine (SVM). The fundamental principle of SVM is to linearly separate a dataset by

nonlinearly transforming it from a finite-dimensional space to a high-dimensional one. Path

loss prediction is possible with SVR because it is an extension of SVM that is made to handle

regression issues [37]. Finding a hyperplane in the high-dimensional feature space and getting

the sample points to fall on it is the basic goal of SVR. The following linear function can be

used to describe the hyperplane in the feature space.

𝑓(𝒙) = 𝑤 𝑇 𝜑 (𝒙) + 𝑏

where x is an input feature vector, w is the normal vector that controls the orientation of the

hyperplane, φ (·) is the nonlinear mapping function, and b is the displacement item.

The ideal hyperplane is a constrained optimization problem of the form [38]

𝑁
𝑚𝑖𝑛 1 𝑇
∗ 𝒘 𝒘 + 𝐶 ∑(𝜉𝑖 + 𝜉𝑖 ∗ )
𝒘, 𝑏, 𝜉, 𝜉 2
𝑖=1

𝑠. 𝑡. 𝑓(𝑥𝑖 ) − 𝑦𝑖 ≤ 𝜀 + 𝜉𝑖

𝑦𝑖 − 𝑓(𝑥𝑖 ) ≤ 𝜀 + 𝜉𝑖 ∗

𝜉𝑖 , 𝜉𝑖 ∗ ≥ 0, 𝑖 = 1, … , 𝑁

where C is regularization coefficient, ε is insensitive loss which means the predicted value can

be considered accurate if the deviation between the predicted value and the actual value is less

than ε, 𝜉𝑖 , 𝜉𝑖 ∗ are the slack variables which allow the insensitivity range on both sides of the

hyperplane to be slightly different.

24
Then, by introducing Lagrange multipliers and solving its dual problem, the approximate

function can be expressed as

𝑓 (𝑥) = ∑(−𝛼𝑖 + 𝛼𝑖 ∗ )𝐾(𝑥𝑖 , 𝑥) + 𝑏

𝑖=1

where 𝛼𝑖 , 𝛼𝑖 ∗ are Lagrange multipliers, and K (·, ·) is a kernel function, which is used to

perform the nonlinear mapping from the low-dimensional space to the high-dimensional space.

Figure 3.3: A schematic diagram of SVR architecture

The performance of the SVR-based predictor depends on the kernel function that is selected.

Currently, the sigmoid kernel, linear kernel, polynomial kernel, Gaussian radial basis function,

and their combinations are the most frequently used kernel functions. In this work, the kernel

function is a Gaussian kernel with a tuneable parameter, and it is defined by

2
𝐾(𝑥𝑖 , 𝑥𝑗 ) = exp (−γ ||𝑥𝑖 − 𝑥𝑗 || ) , γ > 0

A frequently used kernel function that works well for jobs with limited feature dimensions and

no prior knowledge is the Gaussian kernel [39]. The parameters used in this investigation, such

as the regularisation coefficient, insensitive loss, and kernel function parameter, were looked

up using the same technique in [37].

25
 3.2.4 Artificial Neural Networks (ANNs)

ANN is a well-liked technique for path loss prediction since it can be used to handle nonlinear

regression issues and has low prediction errors when the sample size is big [4]. Neurons connect

to form networks known as ANNs. Based on the neuron model, the feed-forward ANN of

multi-layer perceptron structure typically consists of an input layer, one or more hidden layers,

and an output layer. While there is no connection between neurons in the same layer and no

cross-layer connection, neurons in the next layer are fully connected to those in that layer by

different weights.

The scale of the network, which is based on the number of neurons and hidden layers, greatly

affects the precision and complexity of the model. Unfortunately, there is still a challenge in

determining the best ANN structure for path loss prediction. For a typical rural macrocell radio

network planning scenario, it is demonstrated in [4] that a non-complex ANN, such as a feed-

forward ANN with one hidden layer and only a few neurons, will probably provide adequate

path loss prediction accuracy. When compared to non-complex structures, ANNs with multiple

neurons and hidden layers may have poorer generalisation properties. Overtraining, or when a

model performs exceptionally well on data that is comparable to the training dataset but is not

adaptable enough to do so, is likely the root cause of this issue.

ANNs are typically trained using the low-complexity back propagation approach. A common

name for this kind of network is BPNN. Given a set of training samples as {(x1 , y1 ), (x2 , y2 ),

. . . , (x𝑁 , y𝑁 )}, where 𝑥𝑖 = {x1 𝑖 , x2 𝑖 , . . . , x𝐿 𝑖 } ∈ 𝑹𝐿 is a feature vector and y𝑖 ∈ 𝐑1 is the target

output, measured value of path loss. In the forward propagation phase, the predicted value of

path loss y𝑖 ′ can be expressed as

y𝑖 ′ = f𝑜 (ω𝑜𝑚 (f𝑚 (ω𝑚𝑙 x𝑖 ) + θ𝑚 )) + θ𝑜

26
where ω𝑚𝑙 represents the connection weights between the neurons of the hidden layer and

inputs, ω𝑜𝑚 represents the connection weights between the neurons of the output layer and the

hidden layer, θ𝑚 and θ𝑜 are thresholds of the neurons of hidden layer and the neuron of output

layer, respectively. f𝑚 (·) and f𝑜 (·) are transfer functions for the neurons in hidden layer and the

neuron in output layer, respectively.

3.3 The Proposed Path Loss Prediction Modeling Approach

The proposed model, combines the strengths of the Random Forest (RF), Gradient Boosting

(GB), and Support Vector Regression (SVR) algorithms in accordance with the goals of the

study. The model's creation, application, and evaluation are divided into several phases, as

listed below:

1. Data Collection and Preprocessing: A thorough field measurement campaign is carried

out to collect Received Signal Strength (RSS) values and route loss data from various

metropolitan contexts. The gathered data includes a range of terrain characteristics,

antenna heights, separations, and frequencies, ensuring its representativeness. To

extract pertinent features for path loss prediction, feature engineering is used in the data

pretreatment processes to handle missing values, identify outliers, and handle outliers.

2. Ensemble Model Development: The key idea behind the suggested method is to

combine Random Forest (RF), Gradient Boosting (GB), and Support Vector Regression

(SVR) into a single predictive model. The appropriate hyperparameters and input

features produced from the preprocessed data are used to train and optimize each

particular model.

3. Model Integration and Weighted Averaging: The ensemble integration of the individual

RF, GB, and SVR models is achieved through a weighted averaging mechanism. The

weights are assigned depending on the performance and applicability of each model,

27
 which is combined with the predicted outputs from each model. With the help of this

integration, the predictive accuracy is intended to be improved by utilizing the

complementing capabilities of several algorithms.

4. Cross-Validation and Model Tuning: The model is fine-tuned to optimize its

hyperparameters and undergoes cross-validation to evaluate its generalization

performance. The ensemble model is made stable and calibrated by this repeated

process, enabling it to make precise predictions in a range of scenarios.

5. Performance Evaluation and Comparison: A thorough performance study is carried out

in order to fully assess the suggested model. Utilizing a variety of evaluation criteria,

such as Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and correlation

coefficients, the model's accuracy, robustness, and generalization abilities are

evaluated. Using the same dataset, the model is rigorously contrasted with other path

loss prediction methods, including Cost-Hata.

In order to provide a comprehensive solution for precise and reliable path loss prediction in

heterogeneous radio network design, the Random Forest, Gradient Boosting, and Support

Vector Regression, ensemble path loss prediction model is proposed. The model's effectiveness

and superiority are proved by thorough validation and comparison with existing models,

advancing path loss prediction in wireless communication networks for smart cities.

28
 Figure 3.4: The Proposed Path Loss Prediction Model Architecture

3.4 Data Collection and Processing Campaign

Numerous measurement campaigns were conducted in urban, and rural parts of city, country.

Two city drives were used to gather experimental data. With the aid of a transmission

evaluation and monitoring system (TEM), field measurements were taken. Real-time data

measurement, analysis, and post-processing across the network are all capabilities of TEMs.

The measurement setup consists of a 4G Android phone acting as the mobile station (MS), a

USB connector, GPS, a laptop, serial cables, and TEMs mobile system dongle software. In a

repeated campaign scenario, reference signal received power (RSRP) was measured at 2.4 GHz

for all sites between 23 m and 2.7 km in rural, suburban, and urban regions of city using all of

these linked devices. In order to reduce the Doppler effect, the vehicle moved at a constant

29
speed. At an operational frequency ranging from 1.8 GHz to 2.1 GHz, numerous drive tests

were carried out across networks.

For a transmitter-receiver distance ranging from 23 meters to 2.7 kilometers, the RSRP data

were logged on the computer screen. Mobile antenna heights of 3 m to 30 m were used, and

base station heights of 25 m to 64 m were taken into account for rural, suburban, and urban

locations. The path loss was then calculated for every measured RSRP throughout the drive

route. The first drive route received 2000 measurements, and the second drive route received

2330 measurements, for a total of 4330 measurements over the two drive routes. To achieve

high precision, measurements were made at each spot eight times, with the average being

determined. A reliable data preparation technique was used in the ensemble model building.

Before training the model, sufficient data preparation is required in order to attain accuracy in

path loss predictions. Hundreds of features may be present in the actual data utilized for

machine learning. Inaccurate path loss prediction might occur from both omitting or keeping

unimportant data. The size of the input space has a significant impact on how machine learning

models behave. Therefore, normalizing the data should be done before training the data. The

following steps were taken to preprocess the data for this investigation. The captured data were

imported into Python from an Excel file. The information was then read and checked for

duplicate and missing values. After that, data normalization was done.

Thirty percent of the pre-processed dataset was used for testing, with the remaining 70% going

towards training. The use of uniform random sampling was made. Due to the necessity to

optimize the ensemble model, the hyperparameter values were modified using the training

dataset. By adjusting the hyperparameters, it was possible to use optimized network parameters

in the RF, GBR, and SVR models as well as the ensemble model. The equation below shows

how the path loss was calculated using the measured received power.

30
 𝑃𝑎𝑡ℎ 𝑙𝑜𝑠𝑠 (𝑑𝐵) = 𝐸𝐼𝑅𝑃(𝑑𝐵𝑚) − 𝑅𝑆𝑅𝑃(𝑑𝐵𝑚)

The overall power density delivered from the base station to the propagating medium is known

as the effective isotropic radiated power (EIRP) expressed in dBm.

Table 3.1: Descriptive Statistics

Feature Mean Min Max STD 25% 50% 75%

Distance
594.960 23.740 2677.090 431.213 311.143 479.385 742.555
(m)

Frequency
1930.878 1800.000 2100.000 148.793 1800.000 1800.000 2100.000
(MHz)

Height of
45.229 25.000 63.500 9.816 39.000 43.000 55.000
TX (m)

Height of
14.896 3.998 30.033 5.230 11.087 14.850 18.293
RX (m)

Path loss
119.471 81.000 162.000 17.373 104.000 120.000 134.000
(dB)

3.5 Comparison of Different Models

This part assesses and compares the effectiveness of machine learning models in predicting

path loss to an empirical model (Cost-Hata). Numerous models are used to forecast the path

loss value at each test data point. 4330 samples were collected in total along the routes. Each

sample came with a path loss data and an antenna separation distance that was computed using

GPS data. As the training dataset, we randomly chose 70% of the samples, and the remaining

30% served as the test dataset. In order to predict the path loss values in the test dataset, three

models—GBR, SVR, and RF—were used. Regularization coefficient, insensitive loss, and

kernel function parameter are set to 0.1, 10, and linear, respectively, for the SVR model. The

31
maximum tree depth and ensemble size for the RF and GBR based models, respectively, were

7 and 5, and there were 200 ensemble members. For comparison, the Cost-Hata model was

also taken into account.

The measured data and the results that the various models are shown in Figures 3.5 to 3.8. The

separation between the sending and receiving antennas is shown on the x-axis.

Figure 3.5: Cost-Hata model prediction performance on the test set

32
 Figure 3.6: Gradient Boosting regressor prediction performance on the test set

Figure 3.7: Random Forest Regressor model prediction performance on the test set

33
 Figure 3.8: SVR model prediction performance on the test set

Different models were used to estimate the path loss values at every place in the test dataset.

These values were then compared to the observed data, and the prediction errors were

calculated. The performance measures MAE, MAPE, RMSE, and MaxPE used to assess

prediction performance are as follows:

𝑄
1
𝑀𝐴𝐸 = ∑|𝑃𝐿𝑞 − 𝑃𝐿′ 𝑞 |
𝑄
𝑞=1

𝑄
100 𝑃𝐿𝑞 − 𝑃𝐿′ 𝑞
𝑀𝐴𝑃𝐸 = ∑| |
𝑄 𝑃𝐿𝑞
𝑞=1

𝑄
1 2
𝑅𝑀𝑆𝐸 = √ ∑(𝑃𝐿𝑞 − 𝑃𝐿′ 𝑞 )
𝑄
𝑞=1

𝑄
1 2
𝐸𝑆𝐷 = √ ∑(𝑃𝐿𝑞 − 𝑃𝐿′ 𝑞 )
𝑄−1
𝑞=1

34
 𝑀𝑎𝑥𝑃𝐸 = max(𝑃𝐿𝑞 − 𝑃𝐿′ 𝑞 )

where 𝑞 = 1, …, 𝑄 represents test sample index, Q represents the sum of test samples, and

𝑃𝐿𝑞 and 𝑃𝐿′ 𝑞 are the samples from measurement and path loss, respectively.

The machine learning models' prediction errors are displayed in Table 3.2. It is evident that the

machine learning techniques performed well and outperformed the empirical model (Cost-

Hata). In the measured example, the Gradient Boosting Regressor algorithm outperformed the

SVR, Random Forest Regressor, and Cost-Hata models based on the selected hyperparameters.

Table 3.2: Performance evaluation of various models using 30% test samples from the measured

dataset (up to 2.1GHz).

Metric RF GBR SVR Cost-Hata

MAE (dB) 3.347 2.760 5.704 10.368

MAPE (%) 2.94 2.42 4.94 8.84

RMSE (dB) 4.220 3.574 7.359 12.267

MSE (dB) 17.812 12.772 54.152 150.475

MaxPE (dB) 15.622 16.930 25.047 31.557

35
 CHAPTER 4

RESULTS AND DISCUSSIONS

The research study's findings are presented in this section along with illuminating discussions.

The findings are divided into separate segments, each of which sheds light on a different aspect

of the examination, in order to be consistent with the study's aims. The anticipated values of

path loss are contrasted with the measured values and the values obtained by applying empirical

models in order to assess the viability of the suggested strategies.

4.1 Development of The Ensemble Path Loss Models

Various unique models are integrated in ensemble techniques to produce a more dependable

and accurate prediction model. By using the diversity of numerous models to capture diverse

features of the data, these strategies reduce the biases and mistakes prevalent in single models.

Multiclassification approaches, multistage learning, and the integration of machine learning

algorithms are all names for ensemble methods. The goal of ensemble approaches is to build a

model through combination that is more accurate than a single isolated model. The challenge

determines which ensemble machine learning techniques to use, including bagging, stacking

(blending), and boosting. In this study, path loss is predicted using bagging and blending

models. The ensemble technique uses a labelled dataset to map the input to the appropriate

output, making it a supervised machine learning process. Labelled data were used in each of

the basis models that were used to create the ensemble model.

4.1.1 Bagging ensemble path loss prediction model

A reliable strategy for improving the precision and dependability of prediction models is the

bagging ensemble method, often known as bootstrap aggregating. In order to provide a

coherent final prediction, this technique combines several basic learners. Bagging computes

the mean of predictions from these base models in the context of regression tasks, such as path

36
loss prediction. It's important to remember that each base learner is taught using replacement

learning on a randomly chosen portion of the initial training data.

This study focuses on Random Forest (RF), Gradient Boosting Regressor (GBR), and Support

Vector Machine (SVM), three independent regression models that have proven adept at

detecting complex patterns inside data. The fact that these models can handle non-linear

interactions and incorporate complex dependencies makes them interesting options.

Following training of the foundation models, we use a deterministic averaging strategy to

combine them into an ensemble model. The final forecast for each data point is produced by

combining the predictions from the RF, GBR, and SVM models. The ensemble will benefit

from each base model's unique qualities thanks to this integration.

4.1.2 Blending ensemble path loss prediction model

The predictive capacity of various base models, such as Random Forest (RF), Gradient

Boosting Regressor (GBR), and Support Vector Regressor (SVR), is combined using the

ensemble technique of blending to produce a reliable and accurate path loss prediction model.

This strategy uses a combiner model to carefully combine the predictions of the various models

while leveraging their strengths. A synopsis of the blended ensemble method and how it can

be used to forecast path loss is provided in this study.

A dataset with attributes useful for path loss prediction is used to train each of the three base

models, RF, GBR, and SVR. The fundamental links between input data and path loss are

captured in different ways by these models as they develop. The base models' hyperparameters,

such as the number of trees in RF and the learning rate in GBR, are adjusted to maximize each

model's performance. Each base model is optimized for accuracy through the use of

hyperparameters. A combiner model, a regression model that takes as inputs the predictions

from all three base models, was trained using the validation dataset, and it integrates the

37
predictions from the RF, GBR, and SVR models. The test phase was initiated with the findings

from the trained RF, GBR, SVR, and combiner models. Path loss for the RF, GBR, and SVR

models that were returned from the training phase was estimated for the blended ensemble

model's prediction phase using the input data. The combiner model then used the same sampled

data to forecast path loss using the prediction outcomes from the three models. The combiner

models' prediction results were then sent back.

4.2 Experimental Results

Nine candidate variables altogether, made up of system parameters and environmental

parameters, were included in the preliminary data for this study. The Cost-Hata model, an

empirical model, was used to perform the first step's calculations. In this model, there were

only seven parameter variables used: the distance, the frequency, the height of the TX and the

RX, the angle between the RX and the main beam TX (vertical and horizontal), and the height

of the ambient building. These data were utilized to produce the estimated path loss value and

to calculate the delta value of the difference between the calculated path loss and the measured

path loss. The process of feature selection was then used to analyses which of the nine candidate

variables were chosen as the best variables, as displayed in Table 5.1.

Table 4.1: Candidate Variable

Variable Name Variable Description Level

Distance Distance between transmitter (TX) and receiver (RX) meters

Frequency Frequency used in signal transmission MHz

Height TX Transmitter antenna height + altitude location meters

Height RX Receiver antenna height + altitude location meters

38
 The characteristics of the geographical landscape rural,

Terrain between the transmitter (TX) and receiver (RX) suburban,

urban

Height of Surrounding building height

meters
Building

Distance between Distance between surrounding buildings

meters
Building

The angle difference between the vertical direction of

Vertical angle degree
the antenna and the vertical direction of the receiver

The angle difference between the horizontal azimuth of

Horizontal angle degree
the antenna and the horizontal direction of the receiver

4.3 Ensemble Methods Evaluation

In this research, three machine learning models were used, and where integrated into an

ensemble method to improve path loss prediction. For the training, and test datasets, a

correlation plot of the measured data and the machine learning models are given. The validation

was done using the mean absolute error (MAE), MSE, MAPE, and MaxPE. The samples are

from the dataset, with 70% of the samples as training set and 30% of the samples as test set.

39
 Figure 4.1: Pathloss prediction of the various prediction models on the test data set without

hyperparameter tuning

Hyperparameter adjustment is done in order to improve the functionality of the models in

Figure 5.1. Through a method known as grid search or random search, which investigates

different parameter combinations to find the most efficient configuration for each model, the

values of the hyperparameters are methodically adjusted. Table 5.2 lists the tuning-relevant

hyperparameters.

Table 4.2: Tuned Hyperparameter Values

Hyperparameters RF GBR SVM

n_estimators [100, 200, 300] [100, 200, 300] NA

max_depth [3, 5, 7] [3, 5, 7] NA

learning_rate NA 0.1 NA

kernel NA NA ['linear', 'rbf']

C NA NA [0.1, 1, 10]

epsilon NA NA [0.01, 0.1, 1]

['scale', 'auto'] +
gamma NA NA
list(np.logspace(-3, 3, 7))

40
Optimization Algorithm GridSearchCV GridSearchCV RandomSearchCV

Figure 4.2: Pathloss prediction of the various prediction models on the test data set with

hyperparameter tuning.

Figure 4.3: Bagging ensemble method prediction performance on the test dataset.

41
 Figure 4.4: Blending ensemble method prediction performance on the test dataset.

Table 4.3: Performance metrics for the developed models on 30% of the dataset (test set)

Metrics RFR GBR SVR BAGGING BLENDING

MAE (dB) 3.347 2.760 5.704 3.544 2.792

MAPE (%) 2.94 2.42 4.94 3.09 1.94

RMSE (dB) 4.220 3.574 7.359 4.464 3.160

MSE (dB) 17.812 12.772 54.152 19.923 10.397

MaxPE (dB) 15.622 16.930 25.047 14.689 14.315

It is obvious from the plots in Figures 5.3 and 5.4 and the performance measures in Table 5.3

that the blending ensemble model performed better than the other machine learning models and

is thus appropriate for accurate signal propagation. In machine learning, an ensemble is used

to enhance the performance of the overall model, which was accomplished in this work. For

both the training and test datasets, the mixing algorithm provided the fewest mistakes. The

42
SVR standalone model has the most number of mistakes. As a result, the model's performance,

robustness, and forecast accuracy were all enhanced by the blended ensemble method.

Additionally, the bagging technique outperformed the RF, GBR, and SVR models.

Each machine learning model for the dataset is plotted along with the measured path loss in

Figures 5.2, 5.3 and 5.4. In comparison to the other three models, the mean distance between

the points surrounding the fitted line is smaller for the blending ensemble model. The MSE

value decreases as the mean distance increases. The MSE value for the blending ensemble

model is 10.397 dB, as can be seen in Table 5.3. It demonstrates that the blended ensemble

model predicted route loss properly and fairly closely to the measured data. According to Table

5.3, the blending ensemble model predicted path loss with the most impressive accuracy and

the least amount of error overall.

43
 CHAPTER 5

CONCLUSIONS AND RECOMMENDATIONS

5.1 Conclusion

This work introduces path loss prediction models based on machine learning that were created

using ensemble techniques. To improve the effectiveness and reliability of predictive models,

ensemble approaches were used. By first increasing the number of parameters in each of the

three base models' respective inputs, the performances of the RF, GBR, and SVR models were

first enhanced. The parameters of the basic models were tweaked in accordance with this

because the ensemble methods' performance greatly relied on proper hyperparameter tuning.

The n_estimators and max_depth hyperparameters of the RF and GBR models determine how

many boosting stages or trees will be employed, respectively. The hyperparameters for the

SVR model are the kernel (used to map data into a higher-dimensional space, e.g., "linear,"

"rbf," or "poly,"), C (the regularization parameter, which regulates the trade-off between a

smooth decision boundary and correctly classifying all training points), and epsilon (the

tolerance margin around the predicted value). Next, ensemble path loss prediction models with

bagging and blending were presented. Learners with training and a combiner model make up

the mixing model. Three models—RF, GBR, and SVR—make up the work's base learners. The

base learners' predictions are modelled using linear regression in the combiner model. The

bagging path loss prediction model utilized the identical base learners. The final prediction

algorithm is determined by the mean of the model predictions. Using key performance

indicators for the training, testing, and validation datasets, the five models—RF, GBR and

SVR, blending, and bagging—were then confirmed. For the test datasets, the constructed

blended ensemble path loss prediction model produced the lowest values of errors. The

likelihood of overfitting was reduced by the similar MSE results that were achieved for the

training dataset. Due to the enhanced path loss prediction performance, we therefore draw the

44
conclusion that the blended ensemble method serves as a mechanism for reducing variation

and error. As a result, ensemble approaches outperformed the other standalone machine

learning models in terms of accuracy and can be used to wireless channels for accurate signal

categorization.

5.2 Recommendations for Future Research

5.2.1 Collection of Training Data

For the machine-learning-based model to be accurate and generalizable, it has been emphasized

that gathering sufficient training data is essential. How many samples are necessary for a

certain level of prediction accuracy is a question that must be answered in light of the expense

of running measurement campaigns. Tools and metrics for evaluation must be created for

judgement.

In the meantime, "better data" may be what we require rather than "bigger data." It is important

to take into account the samples' diversity and uniformity. The data ought to be dispersed

equally throughout the measured region in a single instance. Measurement routes need to be

carefully planned in order to collect enough data in various scenarios in order to develop a

model with high generalization properties. Therefore, it is important to carefully analyses the

channel measurement approach. In addition, we have proposed two approaches to exploit the

classical models and measured data. Future research into similar techniques to increase the

training dataset is possible.

5.2.2 Feature Selection Methodology

The path loss predictor's capacity to generalize may suffer from having too few characteristics.

Only system-dependent variables, such as antenna separation distance and frequency, were

chosen as features in the analysis above. These machine-learning-based models have been

demonstrated to have good agreement with measured data. They might only be appropriate for

45
similar urban environments due to their poor generalization properties. Additionally, using

more features may not always translate into greater performance. Too many features lead to

the "curse of dimensionality" and worsen prediction accuracy, as well as increasing the

computing burden. As a result, strategies must be created to direct the feature selection for

machine learning-based path loss predictions.

5.2.3 Hyperparameter Optimization Problem

One of the most challenging machine learning challenges is hyperparameter optimization. For

instance, the final performance of SVR-based prediction models depends on the kernel choice.

The quantity of neurons and hidden layers is also quite important for ANN-based algorithms.

Although strategies like grid search can help solve this issue to some extent, more study is still

required.

5.2.4 Incremental Learning

The majority of machine learning-based methods for path loss prediction up to this point have

been based on batch learning, which relies on the availability of all training data prior to

training. Following learning from these examples, the training procedure is over, and the model

creation is complete. In real-world settings, however, training samples for path loss gradually

grow over time. A significant amount of time and space is required for the relearning process

after the arrival of new samples and all the data.

Algorithms for incremental learning can gradually update, rectify, and enhance prior

knowledge so that the updated one can adapt to new examples without having to learn

everything from scratch again. While much of the previously learned knowledge is kept,

additional knowledge can be learnt from the fresh data to create a path loss predictor that is

more accurate. However, the introduction of incremental learning algorithms, which lack the

46
forgetting mechanism for picking training data, may have a negative impact on the path loss

predictor's accuracy.

47
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